FR2788104A1 - Lighting system for a microscope assembly, comprises a controlled lighting unit varying light intensity according to application - Google Patents

Abstract

The microscope assembly comprises of a surface capture means (118). A variable lighting unit is locate between the light source and the capture means such that the wavelength of the light intensity can be altered and varied according to the application mode of the microscope.

Description

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Microscope generating a three-dimensional representation of an object and images generated by this microscope.

[Wolf] . Three-diruer7sional.etructure détermination ofsemi-trallsparellt abjects front holographie data, Emil Wolf, Optics communications volume 1 numéro 4 p. 153, octobre 1969. I. Technical field:
The present invention relates to a microscope generating a three-dimensional representation of the observed object, operating on a principle derived from diffracted field inversion imaging, tomography and synthetic aperture systems.
2. Prior technique:
2. 1. References

[Wolf]. Three-diruer7sional.etructure determination ofsemi-trallsparellt abjects front holographie data, Emil Wolf, Optics communications volume 1 number 4 p. 153, October 1969.

[Vishnjako\'J:l11lerferometric computed-microtomography of 3D phase ob7ect.c, Gennadj N. Vishnvakov & Geilnad G Levin, SPIE proceedings vol. 2984 p. 64, 1997 [Ausherman]: Developments in Radar Irrraging, D.A.Ausherman, A.K07lna, J.L.Walkcr, H.M.Jones, E. C.Poggio, IEEE transactions on aerospace and electronic systems vo1.20 no4 p.363, juillet 1984. [Dândliker]: Reconstruction of the three-dimensional refractive index from scattered waves, R. Dândlikcr, K. Wciss, Optics communications volume 1 number 7 p.323, February 1970. percher] Image formation hy inversion of scattered field data 'cxpcriments and computational simulation AFFercher, H. Bartelt, H. Becker, E. Wiltschko, Applied optics vol. 18 no 14 p. 2427. July 1979 [Kawata]: Optical microscope tomography. 1. Support constrainl, S. Kawata, O. Nakamura & S. Minami, Journal of the Optical Society of America A, vol.-1, No.1, p 292, January 1987 [Noda]: Three-dimensional phase-contrast imaging by a conrputed-tonrography microscope, Tomoya Noda, Satoshi Kawata & Shigeo Minami, Applied Optics vol.31 no 5 p.670, February 10, 1992 [Devaney]: The Coherent Optical To / Ko.g / c / <c '<7.s'copc, AJDevaney and A.Schat;: berg. SPIE vol. 1767 p.62, 1992 [Wedberg]: Experimented! simulation Of Il7e quantitative imaging properties () f optical diffraction tomography, Torolf A. Wedberg and Jacob J. Stamnes, Journal of the Optical Society of America A vol.12 no 3 p.493, March 1995.

[Vishnjako \ 'J: l11lerferometric computed-microtomography of 3D phase ob7ect.c, Gennadj N. Vishnvakov & Geilnad G Levin, SPIE proceedings vol. 2984 p. 64, 1997 [Ausherman]: Developments in Radar Irrraging, DAAusherman, A.K07lna, JLWalkcr, HMJones, ECPoggio, IEEE transactions on aerospace and electronic systems vo1.20 no4 p.363, July 1984.

[Goodman]: Synthetic Aperture Optics, Progress in Optics volume VIII, 1970, North Holland Publishing Company.

[Walker]: Range-l7oppler Imaging of Rotating Objects, Jack L. Walker, IEEE transactions on aerospace and electronic s5 stems vol.16 no 1 p.23. January 1980.

[Brown]: Walter modelfor Radar serzsing ofrigid Target Fields, William M. Brown, IEEE transactions on aerospace and electronic S) stems ol. 16 no 1 p. 104, January 1980. [Turpin 1]: US patent 5,384,573

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[Turpin 3]: The Synthetic Aperture Microscope, Expérimental results, P. Woodford, T.Turpin, M. Rubin, J.Lapides, C. Price, SPIE proceedings vol.2751 p.230, 1996 [Lauer 1]: brevet WO 98/13715
2.2. Description de la technique antérieure. [Turpin 21: Theory of the Synthetic Aperture Microscope, Terry Turpin, Leslie Gesell, Jeffrey Lapides, Craig Price, SPIE proceedings vol.2566 p. 230, 1995

[Turpin 3]: The Synthetic Aperture Microscope, Experimental results, P. Woodford, T. Turpin, M. Rubin, J. Lapides, C. Price, SPIE proceedings vol.2751 p.230, 1996 [Lauer 1]: WO patent 98/13715
2.2. Description of the prior art.

A three-dimensional object can be characterized optically by a certain number of local parameters, for example its index and its absorptivity at each point. Mathematically, this can be translated by the data at each point of a complex number which is a function of the local parameters at the point considered. A three-dimensional spatial representation of the object can then be expressed in the form of a three-dimensional array of complex numbers.

By performing the three-dimensional Fourier transformation of this three-dimensional spatial representation, a three-dimensional frequency representation of the object is obtained.

que celle des microscopes classiques. [Dïiidliker] a amélioré le formalisme de [Wolf) et en a donné une interprétation géométrique. A partir de l'onde diffracté par l'objet sous un éclairage donné, on obtient une

partie de la représentation fréquentielle. tridimensionnelle de l'objet. Cette partie est une sphère dans un espace fréquentiel tridimensionnel. En combinant les sphères ainsi obtenues pour diverses ondes d'éclairage, on peut remplir l'espace des fréquences, obtenant la représentation fréquentielle tridimensionnelle de l'objet. Celle-ci peut alors être inversée pour obtenir une représentation spatiale. [Wolf] showed that a three-dimensional representation of a weakly diffracting object can be obtained from the acquisition of the wave diffracted by this object when it is successively illuminated by a series of plane waves of variable direction. [Wolf] also determined the maximum resolution that can be obtained in this way, expressed as a function of the illumination wavelength. This resolution corresponds to a maximum period of # / 2 for the sinusoidal components of the representation of the object, i.e. a sampling period in the Nyquist sense of 4 which is a resolution twice as fine.

than that of conventional microscopes. [Dïiidliker] improved the formalism of [Wolf) and gave it a geometric interpretation. From the wave diffracted by the object under a given lighting, we obtain a

part of the frequency representation. three-dimensional object. This part is a sphere in a three-dimensional frequency space. By combining the spheres thus obtained for various lighting waves, it is possible to fill the frequency space, obtaining the three-dimensional frequency representation of the object. This can then be inverted to obtain a spatial representation.

par [Wolf) et [Dâiidliker]. Dans ce microscope, l'onde diffractée par l'objet est captée sur une surface de réception, sur laquelle elle interfère avec une onde de référence n'ayant pas traversé l'objet et dont la phase peut être modifiée. A partir de plusieurs figures d'interférence différant entre elles par la phase de l'onde de référence, [Percher] obtient, en chaque point de la surface de réception, l'amplitude et la phase de l'onde diffractée par l'objet. [Perchera produced a microscope constituting the first practical application of the principles defined

by [Wolf) and [Dâiidliker]. In this microscope, the wave diffracted by the object is picked up on a receiving surface, on which it interferes with a reference wave that has not passed through the object and whose phase can be modified. From several interference figures differing from each other by the phase of the reference wave, [Percher] obtains, at each point of the reception surface, the amplitude and phase of the wave diffracted by the object. .

[Fercher] does not use several successive lighting waves but several lighting waves generated simultaneously by means of a diffraction grating, which limits the number of possible lighting directions, even though the use of several successive lighting waves do not present any particular technical difficulty. The reason for this choice is not clearly explained However, it

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seems that this technique is adopted to obtain lighting waves all having the same phase at a given point of the image. Indeed, the equation (1) of the document [Wolf] supposes that each lighting wave has a zero phase at the point of origin of the position vectors.

The method defined by [Wolf]. [Dandliker] and [Percher] is generally referred to as diffracted field inversion imaging. Another classic approach to obtaining three-dimensional images is constituted by tomography. Tomography, used for example in X-rays, consists in reconstructing an image from a set of projections of this image in different directions. Each projection depends linearly on a three-dimensional density function characterizing the object, and from a sufficient number of projections we can reconstitute the object, by inverting this linear correspondence.

The tomography was adapted for optical microscopy by [Kawata]. In his tomographic microscope, a flat, non-coherent illuminating wave of variable direction is used. This illuminating wave passes through a sample and then through a microscope objective focused in the plane of the sample. It is received on a receiving surface placed in the plane where the objective forms the image of the sample. Because the illumination is non-coherent, the intensities coming from each point of the object add up and the intensity image produced on the receiving surface therefore depends linearly on the three-dimensional density function characterizing the absorptivity of the object. From a sufficient number of images one can reconstitute the object, by inverting this linear correspondence This microscope differs from the usual tomography systems in that the linear correspondence between the density function of the object and a given image n is not a projection, but is characterized by a three-dimensional optical transfer function.

This microscope is poorly suited to obtaining images taking into account the index of the sample.

[Noda] produced a modified microscope to take this phase into account. The initial idea of [Noda's] microscope is to use phase contrast to obtain an image depending on the index of the sample and to adapt to this configuration the principle of inversion of linear correspondence already established. implemented by [Kawata]. The use of [Noda's] microscope is however limited to the study of non-absorbent objects whose index variations are extremely small.
The text of [Nodal does not refer to holography nor to imaging by inversion of the diffracted field, however its operation can be interpreted in this context. Indeed, the technique adopted by [Noda] amounts to using on the reception surface a reference wave constituted by the lighting wave alone. From the images received for a set of lighting waves of variable direction, a three-dimensional frequency representation is obtained. The complex wave detected on the receiving surface is here replaced by a pure imaginary value obtained by multiplying by j the real value obtained using the single reference wave constituted by the illumination wave shifted in phase by # / 2 . If the reference wave is sufficiently higher, at each point of the reception surface, with a diffracted base, then the quantity thus obtained is the imaginary part of the complex wave actually received on the reception surface, the phase reference being the phase of the lighting wave. The object generating on the reception surface a pure imaginary wave equivalent to that detected by [Noda] is constituted by the

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superposition of the observed real object and of a virtual object whose complex spatial representation is obtained from that of the real object by symmetry with respect to the plane of the object corresponding to the receiving surface, and by inversion of the sign of the real part. By using the imaginary part thus detected in a manner analogous to that in which [Percher] uses the detected complex wave, a function representing the superposition of the real object and of the virtual object is therefore generated in frequency representation. acquisition, the two-dimensional frequency representation obtained by Fourier transformation of the value detected on the reception surface comprises a part corresponding to the real object and a part corresponding to the virtual object, which only intersect at the point corresponding to the lighting frequency. It is therefore possible to select only the part corresponding to the real object, so as to obtain a representation of the latter. [Noda] in fact uses the superposition of the real object with the virtual object that it symmetrizes with respect to the plane of the object corresponding to the receiving surface, thus obtaining a pure imaginary representation representing the imaginary part of the representation which would be obtained by the method of [Wolf].

The theoretical explanations given in the document [Nodal are very different from those presented here and are perfectly valid. The principle of inverting a filter by multiplication in the frequency domain, as applied by [Noda], is found to be equivalent to the explanations given above, although being obtained by a different reasoning. We can consider that Figs 2 and 3 of the document [Nodal illustrate the way in which the frequency, three-dimensional representation of the object is generated from the two-dimensional frequency representations.

essentiellement inspiré de la méthode de [Wolf]. Dans le microscope de [Devaney ] l'onde de référence est confondue avec l'onde d'éclairage. De ce fait, ce microscope ne comporte pas de moyens pour faire varier la phase de l'onde de référence. Comme dans le cas de [Nodal, fonde détectée correspond doncà celle qui serait formée par la superposition d'un objet réel et d'un objet virtuel. [Devancerésout le problème en plaçant la surface de réception hors de l'objet, de manière à ce que l'objet réel et l'objet virtuel ne se recouvrent pas. Lorsque la direction de l'onde d'éclairage varie, seul un des deux objets est reconstitué. [Devaney] proposed a tomographic microscope whose mode of operation is

essentially inspired by the method of [Wolf]. In [Devaney's] microscope the reference wave is confused with the illuminating wave. As a result, this microscope does not include means for varying the phase of the reference wave. As in the case of [Nodal, detected ground therefore corresponds to that which would be formed by the superposition of a real object and a virtual object. [Overcome the problem by placing the receiving surface outside the object, so that the real object and the virtual object do not overlap. When the direction of the illumination wave varies, only one of the two objects is reconstructed.

version du microscope de [Dcvanc\] a été réalisée par [Wcdbcrg. Two versions of the microscope are available: a first version in which the object is fixed and the direction of the illumination wave is variable, and a second version in which the object is rotating around a fixed point, the 'lighting wave then being in a fixed direction with respect to the receiver The first

microscope version of [Dcvanc \] was performed by [Wcdbcrg.

Another approach making it possible to adapt tomography to the production of phase images is that of [Vishnyakov]. [Vishnyakov] introduces a reference wave distinct from the illuminating wave and performs detection of the wave received on a receiving surface according to a method similar to that used by [Percher]. It then generates a profile characteristic of the phase difference between the received wave and the illuminating wave. This phase difference being considered as the projection of the index according to the direction of the illumination wave, it regenerates the distribution of the index in the object according to the tomographic method conventionally used in X-rays. This method can be compared to a ripe method [Wolf]. but in which the portion of sphere acquired in frequency space would be assimilated to a

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des ondes radar et que l'on a envisage très tôt d'appliquer au domaine de l'optique. [Aushcrman] présente un historique de cette technique. L'application de la technique du radar à ouverture synthétique dans le domaine des longueurs d'onde optiques permettrait en principe d'obtenir des images d'un objet observe Toutefois, pour que la technique soit réalisable, il est nécessaire de disposer en permanence des valeurs de position, dans un repère lié à l'objet, de chaque élément de l'ensemble émetteur-récepteur. Ces valeurs doivent être connues à une fraction de longueur d'onde près. Ceci est réalisable dans le domaine des fréquences radar, ou les longueurs d'ondes sont macroscopiques et peuvent être par exemple de quelques dizaines de centimètres. Dans le domaine de l'optique, ou les longueurs d'onde sont sub-micrométriques, ceci est difficilement réalisable. Ce problème est la raison essentielle pour laquelle le système est difficilement adaptable à l'optique, comme indiqué dans [Goodman], pages 36 à 39. shot portion, which is largely unjustified in the case of a large aperture lens like the one used here
The synthetic aperture radar technique is an imaging method used in the field

radar waves and which were considered very early on to apply to the field of optics. [Aushcrman] presents a history of this technique. The application of the synthetic aperture radar technique in the field of optical wavelengths would in principle make it possible to obtain images of an object observed.However, for the technique to be feasible, it is necessary to have permanent position values, in a frame linked to the object, of each element of the transmitter-receiver assembly. These values must be known to a fraction of the wavelength. This can be done in the field of radar frequencies, where the wavelengths are macroscopic and can be for example a few tens of centimeters. In the field of optics, where the wavelengths are sub-micrometric, this is difficult to achieve. This problem is the main reason why the system is difficult to adapt to optics, as indicated in [Goodman], pages 36 to 39.

[Walker] and [Brown] formalized the synthetic aperture radar method in a form similar to that already obtained by [Wolf] for optical systems. This formalism was originally used by [Walker] for a radar imaging method in which the transmitter-receiver assembly is fixed and in which the object is rotated around a fixed point. This makes it possible to overcome the problem of determining the position of the object at each instant.

[devant)]. Du fait que l'axe de rotation, l'émetteur et le récepteur sont fixes, la position de l'ensemble émetteur-récepteur dans un repère lié à l'objet peut être connue avec la précision nécessaire. [Turpin] recently described several microscopes constituting an adaptation in the field of optics of the principles of the synthetic aperture radar.
In the microscope used in [Turpin 3]. the physical configuration employed conforms to the principle used in [Walker] to overcome the problem of determining at any moment the position of the object, that is to say that the emitter and the receiver are fixed and the object is rotating around a fixed axis. This microscope is also analogous to the second version of the microscope of

[in front of)]. Because the axis of rotation, the transmitter and the receiver are fixed, the position of the transmitter-receiver assembly in a frame linked to the object can be known with the necessary precision.

However, an effective resolution supposes not only a mechanical system allowing the knowledge of the movement of the object, but also in the taking into account of this movement in the definition of the algorithms and / or an appropriate adjustment of the system In the absence of particular precautions , the reference ground origin point moves relative to the object on a circle centered on the object's axis of rotation. If this displacement is important, this effect destroys the image. If this displacement is weak, the resolution in the plane of this circle is affected in proportion to the amplitude of the displacement
To solve this problem in the absence of a specific compensation algorithm, the point of origin of the reference wave must be on the axis of rotation of the object. This condition is a priori difficult to achieve. [Turpin] does not mention this problem and does not specify any suitable means of adjustment.

This problem can, however, be solved, for example when using a plane sample, by carrying out an adjustment to verify the following conditions:

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(i) -The image of the reference wave on the CCD array image of Fig. 1 of document [Turpin 3] must be punctual.

(ii) - When the object rotates 180 degrees, the image obtained must be symmetrical with respect to an axis passing through the image point of the reference wave.

The position of the CCD array image must be adjusted to verify (i).

The position of the receiver assembly should be adjusted to verify (ii).

This solution is however rather imperfect, depending essentially on a visual appreciation. It can only reasonably be used for very simple objects.

par [Wotf). The microscope described in [Turpin 3] is a particular case of the generalized system described in [Turpin 1] and [Turpin 2]. The generalized system specifies that the illumination wave and / or the position of the receiver can vary. But the physical configurations proposed do not allow the resolution of the problem consisting in knowing, to a fraction of a wavelength, the position of the emitter and the receiver with respect to the object. This is because the variable direction lighting wave is produced by mechanical devices that cannot be controlled with sub-micrometric precision.
The microscope described in [Lauer 1 allows the generation of the frequency representation of a wave coming from the object and the reconstruction of the object from several of these representations. The method used in [Lauer 1] has no direct relation with that described by [Wolf]. Indeed, in the case where it recombines several frequency representations to obtain the representation of the object: - it uses spatially incoherent lighting and not plane lighting waves - it combines the frequency representations of the waves received by summation in intensity in the spatial domain The image obtained by [Lauer 1] is affected by an effect of residual granularity, does not allow a differentiation of the index and of the absorptivity, and does not allow to reach the indicated theoretical precision

by [Wotf).

Les systèmes dits à formation d'image par inversion du champ diffracté , toinographiques ou à ouverture synthétique apparaissent comme équivalents les uns aux autres, du moins lorsqu'on se limite au domaine de l'optique cohérente. Deux classes de systèmes peuvent être distinguées selon le mode de génération de l'onde de référence: - les microscopes de [Noda] et [Devaney] utilisent une onde de référence confondue avec l'onde d'éclairage. 3.Exposure of the invention 3.1. Problem to be solved by the invention

The so-called image formation by inversion of the diffracted field, toinographic or synthetic aperture systems appear to be equivalent to each other, at least when one is limited to the field of coherent optics. Two classes of systems can be distinguished according to the mode of generation of the reference wave: - the microscopes of [Noda] and [Devaney] use a reference wave confused with the illuminating wave.

- the microscopes of [Fercher]. [Vishnyakov] and [Turpin] use a separate reference wave from the illumination background.

The microscopes of the first category have limitations in terms of observed image size, characteristics imposed on the object, or parameters that can be viewed. These limitations are due to the fact that in the absence of a reference wave distinct from the illuminating wave, it is not possible to acquire under good conditions the complex value of the wave received on the surface of

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reception. It is therefore necessary to have recourse to various devices to eliminate the parasitic images and the various disturbances generated by the imperfection of the acquisition method.

The microscopes of the second group allow this problem to be solved. In principle, the microscopes of the second group should allow the representation of the index and the absorbtivity of the object in three dimensions with a precision of a quarter wavelength, according to the theory developed by [Wolf] and [Dândliker]. Such performance is clearly superior to that of all existing optical microscopes including the confocal microscope, and these microscopes should logically have given rise to industrial applications. However, none of these microscopes has so far made it possible to obtain images of a quality comparable to those produced for example by the [Noda] microscope, and consequently these microscopes have not passed the experimental stage. The reason why these microscopes never made it possible to obtain high quality images, despite their theoretical possibilities, has never been clearly identified.

A first approach to the problem is implicitly contained in equation (1) of the document [Wolf]. all the lighting waves must have the same phase at the point of origin of the representation. However, in an optical system, the only quantities accessible to measurement are the phase differences between a reference wave and a wave to be analyzed. The fact that at a given point the lighting waves all have the same phase at a given point of the object, as implicitly indicated by equation (1) of the document [Wolf]. is therefore not sufficient to ensure the correct operation of the system, it is also necessary for the reference wave to verify appropriate conditions, so that the phase differences accessible to the measurement lead to correct results.

A second approach to the problem is given by [Goodman], pages 36 to 39, in the terms of numerical aperture radars: it is necessary to know with a precision lower than the wavelength the position of the transmitter and the receiver. , and this is impractical in the field of optics.

In the case where the illuminating wave has a variable direction, these two approaches are similar: in effect, an indeterminacy on the position of the emitter results, among other effects, by a phase shift of the wave of lighting at the point of origin of the representation. We will limit ourselves here to these systems, that is to say to the microscopes of [Percher], of [Vishnyakov], and to the versions of the microscope of [Turpin] which comprise an illuminating wave of variable direction.

For example, in [Turpin's] microscopes, the illuminating wave is generated by a mechanical device. This device does not allow the phase of the lighting wave to be controlled. During two successive three-dimensional images, a given lighting wave, characterized by its direction, will not have the same phase difference with the reference wave each time. It follows that the wave detected on the receiving surface will not have the same phase either, and therefore ultimately that two successive three-dimensional images will not lead to the same result, even in the absence of everything. noise This example highlights the essential problem which has hitherto limited the performance of microscopes of the second group: failure to control the phase difference between the illuminating wave and the reference wave results in a failure to reproducibility of the results obtained, and in general results which do not correspond to what is expected given the theoretical approach of [Wolf].

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3. 2. Resolution of the problem according to the invention
The whole of the three-dimensional frequency representation of an object can be multiplied by a complex number Aej [alpha], We will then say that the frequency representation of the object is affected by a phase shift a and a multiplicative coefficient . If an object is characterized by its three-dimensional frequency representation, its spatial representation can be obtained by inverse Fourier transformation of this frequency representation. If the frequency representation of the object is affected by a phase shift a and a multiplicative coefficient A, its spatial representation will be affected by the same phase shift and the same multiplicative coefficient, which corresponds to a modification of the function giving the complex number associated with a point according to the local parameters at this point
It is also possible to multiply each point of the three-dimensional representation by a complex number Aej [alpha] depending on the point. Two different points of the three-dimensional frequency representation can then be affected by a different phase shift and a different multiplicative coefficient. By performing the inverse Fourier transformation of a frequency representation in which the phase shift and / or the multiplicative coefficient depend on the point considered, a modified representation of the object is obtained. in which the complex number associated with a point depends not only on the local parameters at the considered point, but also on the local parameters at a set of other points. This modified representation of the object is a filtered spatial representation, the filter having a frequency representation consisting of the numbers Aej [alpha] defined at each point. Depending on the characteristics of this filter, more or less correct frequency representations will be obtained.

In [Turpin's] microscopes. the lighting wave is generated by a mechanical device At each change in direction of the lighting wave, there is a random phase shift of this wave, and therefore a random phase shift of the corresponding part of the frequency representation , three-dimensional.

[Vishnyakovl devrait être remplacée par I'x, y) = tlx, yy + x sin a + ou rp est la phase de l'onde d'éclairage au point origine de la représentation tridimensionnelle obtenue. Lorsque la direction de fonde

d'éclairage varie, la valeur de (p varie. La non-détermination de la valeur correcte de rp se traduit par l'ajout d'une constante à chaque projection obtenue, cette constante variant aléatoirement entre deux projections Ceci rend donc non-exacte l'assimilation du profil de phase obtenu à la projection de l'indice La méthode de fVishn)ako\] équivaut à peu près à la méthode de [Wolf] dans laquelle on aurait assimilé une portion de sphère de l'espace fréquentiel, obtenueà partir d'une onde d'éclairage donnée, à un plan. La nondétermination de # équivautà un décalage de phase aléatoire de l'ensemble de la partie de la représentation fréquentielle bidimensionnelle générée à partir d'une onde d'éclairage donnée Toutefois, d'autres sources d'erreurs s'ajoutent içi à cet effet, en particulier le fait qu'une reconstruction tomographique classique est utilisée. In the document of [Vishnjakov], and for the same reasons, the background phase of illumination varies randomly with each change in the direction of illumination. Equation (2) on page 67 of the document

[Vishnyakovl should be replaced by I'x, y) = tlx, yy + x sin a + where rp is the phase of the illuminating wave at the point of origin of the three-dimensional representation obtained. When the management founds

of illumination varies, the value of (p varies. Failure to determine the correct value of rp results in the addition of a constant to each projection obtained, this constant varying randomly between two projections This therefore makes it non-exact the assimilation of the phase profile obtained to the projection of the index The method of fVishn) ako \] is roughly equivalent to the method of [Wolf] in which we would have assimilated a portion of a sphere of the frequency space, obtained at from a given lighting wave, to a plane. The nondetermination of # is equivalent to a random phase shift of the whole part of the two-dimensional frequency representation generated from a given lighting wave.However, other sources of error are added here to this effect, in particular the fact that conventional tomographic reconstruction is used.

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In the document of [Percher]. due to the use of a diffraction grating to simultaneously generate the three illumination waves, there is no random phase shift of the illumination waves.

However, a detailed analysis of the system shows that to obtain the same phase shift in the parts of the frequency representation obtained from each illumination wave, it is necessary that the virtual image, in the object. of the focal point of the reference wave, or coincides with a point at which the illuminating waves all have the same phase. This implies a very precise adjustment of the position of the point of origin of the reference wave. Since [Percher's] document does not contain any mention of such an adjustment, it is likely that it has not been carried out. In any case, the solution adopted by [Fercher] greatly limits the number of lighting waves that can be used and the opening under which the wave coming from the object can be acquired.

référence distincte de l'onde d'éclairage, les parties de la représentation fréqiieiitielle qui sont obtenues à partir d'ondes d'éclairage différentes, sont donc affectées par des décalages de phase différents Par conséquence, l'inversion de la représentation fréquentielle globale obtenue génère une représentation filtrée qui est en règle générale d'assez mauvaise qualité et qui est de plus non reproductible, en raison du caractère aléatoire du décalage de phase. In existing microscopes using illuminating waves of varying direction and a wave of

distinct reference of the lighting wave, the parts of the frequency representation which are obtained from different lighting waves, are therefore affected by different phase shifts Consequently, the inversion of the overall frequency representation obtained generates a filtered representation which is generally of rather poor quality and which is furthermore non-reproducible, due to the random nature of the phase shift.

The invention consists in producing a microscope in which the direction of the illumination wave is variable, but comprising means for generating a three-dimensional representation of the object in which the distribution of the phase shift affecting each point, in frequency representation , is concentrated around a constant value. Ideally, this phase shift should be constant, however the existence of disturbances such as Gaussian noise, residual spherical aberration, or low imprecision in controlling the phase difference between the reference wave and the illuminating wave, creates a some spreading of the distribution around the constant value.

In existing existing microscopes using illuminating waves of varying direction and a reference wave distinct from the illuminating wave, and in the case where a large number of distinct illuminating waves are used as in [Turpin] , this phase shift tends to be random and its distribution is therefore roughly homogeneous over the interval [0.2 #]. In the case where a limited number of illumination waves is used, as in [Percher], the distribution of the phase shift has peaks of comparable level centered on several distinct values corresponding to the phase shifts affecting the sub-representations obtained from each. lighting wave.

The fact that the phase shift affecting each point, in frequency representation, is approximately constant, constitutes a new functionality of the microscope which makes it possible, for example, to obtain a better quality spatial representation. However, the generation of a three-dimensional representation of the observed object does not necessarily constitute the final goal sought by the user of the microscope. For example, the microscope can be used for reading three-dimensional optical memories. In this case, the data can be encoded before being stored in the optical memory. The microscope then makes it possible to obtain a three-dimensional representation of this memory

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locaux. Ces paramètres locaux peuvent par exemple être son indice et son absorptiv itc en chaque point, ou encore son absorptivité et un de ses indices dans le cas d'un matériau non isotrope On peut définir en chaque point un nombre complexe qui est fonction de certains de ces paramètres locaux, cette fonction étant en général définie de manière unique dans l'ensemble de la représentation spatiale et ne dépendant donc pas du point considéré Une représentation spatiale tridimensionnelle de l'objet pourra alors être exprimée sous la forme d'un tableau à trois dimensions de nombres complexes. La dépendance entre le nombre complexe et les paramètres locaux peut être définie de diverses manières. Par exemple, ce nombre complexe peut se réduire à un nombre réel caractérisant l'indice, comme dans le microscope de [Nodal. La définition qui sera utilisée le plus souvent sera toutefois du type donné par [Wolf]. mais avec un indice complexe représentant à la fois l'indice et l'absorptivité. Par exemple, la partie réelle du nombre complexe peut être proportionnelle à l'absorptivité et sa partie imaginaire à l'indice On peut aussi utiliser un nombre complexe obtenu par rotation du précédent dans le plan complexe, correspondant à un décalage de phase. Dans tous les cas, la représentation spatiale tridimensionnelle de l'objet est unique à partir du moment ou la correspondance entre le nombre complexe et les paramètres locaux a été définie et ou le point central de la représentation a été défini
En effectuant la transformation de Fourier tridimensionnelle de cette représentation spatiale

tridimensionnelle on obtient une représentation fréquentielle tridimensionnelle de l'objet. optical from which the data can be decoded. The three-dimensional representation of the object is then a computational intermediary ultimately allowing the obtaining of decoded data.
3. 3. Vocabulary and general considerations
A three-dimensional object can be optically characterized by a number of parameters

local. These local parameters can for example be its index and its absorptivity itc at each point, or even its absorptivity and one of its indices in the case of a non-isotropic material. A complex number can be defined at each point which is a function of some of these local parameters, this function being generally defined in a unique way in the whole of the spatial representation and therefore not depending on the point considered A three-dimensional spatial representation of the object can then be expressed in the form of a three-dimensional table dimensions of complex numbers. The dependence between the complex number and the local parameters can be defined in various ways. For example, this complex number can be reduced to a real number characterizing the index, as in the microscope of [Nodal. The definition which will be used most often will however be of the type given by [Wolf]. but with a complex index representing both the index and the absorptivity. For example, the real part of the complex number can be proportional to the absorptivity and its imaginary part to the index. It is also possible to use a complex number obtained by rotating the preceding one in the complex plane, corresponding to a phase shift. In all cases, the three-dimensional spatial representation of the object is unique from the moment the correspondence between the complex number and the local parameters has been defined and the central point of the representation has been defined.
By performing the three-dimensional Fourier transformation of this spatial representation

three-dimensional one obtains a three-dimensional frequency representation of the object.

The phase shift affecting a point of the three-dimensional frequency representation of the object is defined from the moment when the representation of the object has been uniquely defined, that is to say when the complex function of the local parameters and the point of origin, characterizing the spatial representation, have been defined.

When these parameters are not specified, it can be considered that the phase shift is defined with respect to the spatial representation which best coincides with the three-dimensional representation of the object which has been obtained.

d'obtenir la représentation spatiale ou fréquentielle de l'objet par un algorithme connu. The term three-dimensional representation of an object will denote all of the digital data characterizing the spatial or frequency representation of the object, regardless of the way in which these data are combined or stored, for example in a computer memory. example be expressed: - in the spatial domain, in the form of a complex number depending on the spatial coordinates - in the frequency domain, in the form of a complex number depending on the spatial frequency - in any other way from the moment where the three-dimensional representation of the object allows

to obtain the spatial or frequency representation of the object by a known algorithm.

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Part of the three-dimensional frequency representation of the object will be called the frequency under-representation of the object, and the term under-representation will denote the set of corresponding data, regardless of how they are combined or stored.

A wave arriving on a reception surface is entirely characterized by the data of its amplitude and its phase in each direction of polarization and at any point of the reception surface.

ce qu'elle constitue une portion de sphère dans l'espace des fréquences, comme indiqué par [Dàndlikerj. Un intermédiaire de calcul pourra être constitué par une représentation fréquentielle de Fonde, définie par la donnée de la phase et de l'intensité de l'onde sur chaque vecteur d'onde, une représentation scalaire ayant été adoptée. It is also possible to adopt a scalar representation of the wave by limiting itself for example to a single direction of polarization, the wave then being characterized by a single phase and a single intensity at any point on the reception surface. From the wave measured on a receiving surface, it is possible to generate a frequency under-representation of the observed object. This under-representation is two-dimensional in

that it constitutes a portion of a sphere in frequency space, as indicated by [Dàndlikerj. A computation intermediary may be constituted by a frequency representation of the Fund, defined by the data of the phase and the intensity of the wave on each wave vector, a scalar representation having been adopted.

The frequency representation of the wave is two-dimensional and can be projected onto a plane without loss of information. Such a projection gives a plane image which will be called a plane frequency image. In a system like that of [Turpin] or that of [Torcher), such a plane frequency image is obtained directly on the reception surface. In other systems such as the second embodiment of the present invention, such a plane frequency image is obtained by two-dimensional Fourier transformation of the scalar representation obtained directly on the reception surface. A frequency-modified plane image can also be obtained from several frequency plane images differing from one another in the polarization of the illuminating wave and the direction of analysis of the wave received on the receiving surface. The plane frequency image can constitute a calculation intermediary making it possible to obtain the frequency representation of the wave and then a corresponding under-representation of the object.

fréquentielle bidimensionnelle soit une partie bidimensionnelle d'une représentation fréquentiellc tridimensionnelle. En particulier il pourra désigner indifféremment une image plane en fréquence, une représentation fréquentielle d'une onde, ou une sous-représentation bidimensionnelle de l'objet. The term two-dimensional frequency representation will designate either a

two-dimensional frequency is a two-dimensional part of a three-dimensional frequency representation. In particular, it can designate either a flat frequency image, a frequency representation of a wave, or a two-dimensional sub-representation of the object.

The term lens will denote, throughout the text, both simple lenses and compound lenses or achromats, generally sized to limit optical aberration.

In the remainder of the text, five embodiments are described. We will refer to it as embodiments 1,2,3,4 and 5.

3.4. Direct obtaining of the three-dimensional frequency representation
For each direction of the illumination wave, one obtains a frequency sub-representation of the object by directly applying the methods defined in [Perchera and [Turpin. In the systems of [Percher] and [Turpin], the microscope is constructed in such a way that the different sub-representations obtained are affected by different phase shifts. According to one version of the invention, the microscope

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is constructed so that these phase shifts are constant. This version of the invention implies: (i) - that the microscope is constructed so that the phase difference between an illuminating wave and the reference wave with which it interferes is reproducible. This condition implies proper construction of the microscope. It is verified, in the absence of vibrations, in embodiments 3, 4 and 5. Embodiments 1 and 2 are affected by the same problems as the microscope of [Turpin] the phase difference between reference wave and lighting wave varies randomly due to the mechanical design of the assembly. Embodiments 1 and 2 therefore do not allow compliance with this first condition. Embodiments 3 to 5 allow this condition to be met due to a different design of the system for generating the lighting and reference waves.

(ii) - that the microscope be constructed in such a way that, with appropriate adjustment, the phase difference between the illuminating wave and the reference wave can be made constant. Embodiment 3 does not allow this condition to be met because there is no particular point at which all the lighting waves would have the same phase, which would be necessary to verify this condition because the reference wave used is spherical and constant. Embodiment 4, which is moreover quite similar to embodiment 3, allows this condition to be met because, by means of appropriate control of the beam deflection system, it is possible to generate lighting waves, the phase of which at a given point is is constant. Embodiment 5 also allows this condition to be met.

(iii) - that the position of the optical elements be adjusted appropriately so that the phase difference between the illuminating wave and the reference wave is effectively constant. This setting is described in 8.6. for embodiment 4 and in 9. 20. for embodiment 5.

Conditions (ii) and (iii) imply that the phase difference between the illuminating wave and the reference wave is constant. We can define a virtual wave present in the object and such as its image. by the optical device modifying the base coming from the object between the object and the receiving surface, ie reference base. The phase difference between the lighting wave and the reference wave means here the phase difference between the lighting wave and the component of this virtual wave on the wave vector of the lighting wave .

3.5. Phase adjustment method
When the microscope is not constructed so that the phase shift affecting each frequency sub-representation is constant, the differences between the phase shifts affecting each sub-representation must be determined and possibly compensated for.

3. 5.1. General phase adjustment method
We consider a part of the three-dimensional representation of the object: - constituted by a subset A of the three-dimensional representation.

- characterized by a function a (f) defined on.) and conventionally zero outside, 1, where f is the spatial frequency vector and a (f) the value of the representation on this spatial frequency.

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- affectée par un bruit gaussien, t'écart-type du bruit sur une fréquence donnée/ étant # a (f) .

- affected by a Gaussian noise, the standard deviation of the noise on a given frequency / being # a (f).

This under-representation will be designated by the expression under-representation RA. We will say that.) Is the support for RA.

affectée par un bruit gaussien #b(f) , désignée par l'expression sous-représentation RB
Ces deux parties de la représentation sont décalées en phase l'une par rapport à l'autre et sont supposées avoir une intersection non vide. A partir de ces deux parties, on va générer une sous-

représentation /?r définie sur un ensemble C' ~ Au B 'est la réunion de .1 et R) et définie par une fonction c( f ) affectée par un bruit gaussien # c (J) . We consider a second part of the three-dimensional representation of the object, constituted by a subset B of the three-dimensional representation, characterized by a function b (f) defined on B,

affected by Gaussian noise #b (f), denoted by the expression RB sub-representation
These two parts of the representation are phase-shifted with respect to each other and are assumed to have a non-empty intersection. From these two parts, we will generate a sub-

representation /? r defined on a set C '~ Au B' is the union of .1 and R) and defined by a function c (f) affected by a Gaussian noise # c (J).

y/)(7) ~ fEEua 1 + Ub 2 r = J 6p (f ) + b (f ) ou les sommes sont sur un ensemble F de vecteurs fréquences inclus dans feE#;(J)+#l(J) l'intersection des deux ensembles.-! et B, soit E c (..1 Î\ R) , l'ensemble F. étant si nécessaire limité à des points pour lesquels le rapport signal sur bruit est suffisamment élevé. La différence de phase entre les deux représentations est l'argument de r. La différence de phase ainsi calculée est une bonne approximation de la

différence de phase la plus probable connaissant les valcurs des représentations R.l et RI3 sur l'ensemble - la représentation RB peut être recalée en phase par rapport à R.1 en la multipliant par le rapport r:

(/)<-.6(/) ou le signe désigne l'affectation. - la fonction c peut être obtenue par exemple par la formule :

) , + h(f) c(f) = #; 1 (J) ub 2 (f) #; (J) # (J) Les valeurs ainsi affectées à la représentation RC sont les valeurs les plus probables connaissant les représentations RA et RB recalées en phase. We can proceed in two stages: - a complex relationship between the two representations can for example be obtained by the formula:

y /) (7) ~ fEEua 1 + Ub 2 r = J 6p (f) + b (f) where the sums are on a set F of frequency vectors included in feE #; (J) + # l (J) l 'intersection of the two sets.-! and B, or E c (..1 Î \ R), the set F. if necessary being limited to points for which the signal-to-noise ratio is sufficiently high. The phase difference between the two representations is the argument of r. The phase difference thus calculated is a good approximation of the

most probable phase difference knowing the values of the representations Rl and RI3 on the set - the representation RB can be realigned in phase with respect to R.1 by multiplying it by the ratio r:

(/)<-.6(/) where the sign designates the assignment. - the function c can be obtained for example by the formula:

), + h (f) c (f) = #; 1 (J) ub 2 (f) #; (J) # (J) The values thus assigned to the RC representation are the most probable values knowing the RA and RB representations adjusted in phase.

-the function # @ (c) can be obtained for example by the formula-.

2 2 2 # (J) a (f) b (f)
The set of the two preceding operations constitutes the regrouping of RA and RB
More detailed explanations on the calculation of these functions in tabular form are given in paragraph 7.17.1. The formulas indicated above for the phase adjustment simultaneously carry out an intensity normalization, which however is not essential.

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This method helps. from two sub-representations RA and RB whose supports. 1 and B have a nonempty intersection, to obtain an RC sub-representation corresponding to the superposition of RA and RB.

If the three-dimensional frequency representation of the object must be reconstituted from numerous sub-representations whose phases are not known, the above method, applied iteratively. allows to group all these sub-representations. For example, we can start from a given under-representation, group it with a second under-representation. We can then start from the under-representation generated by this grouping, and group it with an additional under-representation. By repeating this grouping operation until all the sub-representations have been integrated into a global representation, we finally obtain the three-dimensional frequency representation of the object. The only conditions that must be verified for this method to succeed are: - that no sub-representation or group of sub-representations has an empty intersection with the set of other sub-representations.

- that the object does not have a too singular frequency representation, which would for example be zero on a set of points separating its three-dimensional frequency representation in two
These conditions are easily satisfied for most biological objects as soon as a high number of representations is acquired.

variable. Dans ce cas, une sous-représentation est constituée par une représentation fréquentielle bidimensionnelle obtenue pour une onde d'éclairage donnée. For example: - an embodiment can be derived from the [Percher] system in which the three simultaneous lighting waves produced by the diffraction grating have been replaced by a single directional lighting wave

variable. In this case, a sub-representation is formed by a two-dimensional frequency representation obtained for a given lighting wave.

- An embodiment can be derived from the microscope implemented in [Turpin 3] in which we have authorized, in addition to the rotation of the object. variations in the direction of the illumination wave. In this case, a sub-representation is formed by the set of two-dimensional frequency representations obtained for a given lighting wave when the object is moved in rotation.

- in the case of embodiment 5. paragraph 9.19., a sub-representation consists of a two-dimensional frequency representation obtained for a given lighting wave. A reduced number of sub-representations are first grouped into a base representation having a non-zero intersection with all the other sub-representations obtained under similar conditions. The set of representations is then readjusted in phase with respect to the base representation, then a global representation is generated.

- in embodiments 3, 4, 5, four intermediate sub-representations are generated each time, as explained in 7.17.1.1. These four representations are combined into one by applying this general method.

According to one version of the invention, the microscope therefore comprises means for:

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- determine. for each sub-representation RB, a coefficient characterizing the phase difference between this under-representation and another under-representation, part of under-representation or group of under-representation RA, this coefficient being calculated from the values of RA and RB on a set included in the intersection of the supports of 101 and RB.

- correct the phase of RB so as to obtain for RB the same phase reference as for RA,
The simplest way to correct the phase of RB is to multiply by the coefficient r as indicated above. However, this correction can also be carried out by physical means, in which case the phase does not have to be corrected during the calculation phase. An example of such an embodiment is described in 7.18.7.

The phase difference affecting each sub-representation can be recalculated at each acquisition. This is necessary in embodiments 1 and 2. for which these deviations are not reproducible. In the case of embodiments 3, 4 and 5, this phase difference is reproducible and can therefore be measured during a phase preparatory to acquisition. An example of such an embodiment is described in 7.18.1
According to one version of the invention, the microscope comprises means for: determining, for a given sub-representation RB, the frequency representation, RC resulting from the grouping of RB with another sub-representations RA, - determining a characteristic coefficient of the bmit affecting RC defined on the whole of the support of RC, obtained from a characteristic coefficient of the bmit affecting RA1 and defined on the support of RA, and from a characteristic coefficient of the bmit affecting RB and defined on the support by RB.

The methods used may differ from the formalism exposed above. For example in embodiment 1 the quantity 1 is assimilated to the number N of representations frequent here reaching them # c @ (f) at a given point.

The calculations can be grouped: after resetting each sub-representation in phase, they can be combined into a global representation, without calculating each intermediate sub-representation.

This is done in all of the embodiments to group two-dimensional sub-representations into full or partial three-dimensional sub-representations.

It is possible to calculate representations of the object without formally going through its three-dimensional frequency representation. For example in 7.17.3.3. a confocal representation of the object is generated using for the final frequency representation a value at each point which is the sum of the values obtained for each representation reaching that point. The representation thus obtained is not strictly speaking a frequency representation of the object but is all the same carrier of information on this object. It is also possible to generate real representations of index or absorptivity. These representations can be generated in a simple way by going through

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the intermediary of the frequency representation of the object, however it is also possible to modify the algorithms so as not to formally use this intermediary.

3. 5.2. Absolute phase alignment
The method explained in 3.5.1. allows a three-dimensional representation of the object to be obtained. However, the overall phase of this three-dimensional representation remains arbitrary.

In the three-dimensional spatial representation of the object. obtained from the three-dimensional frequency representation by inverse Fourier transformation, the complex number associated with each point characterizes the absorptivity and the index of the object at the point considered. If the global phase of the three-dimensional representation is chosen appropriately, the real part of said complex number characterizes the local absorptivity of the object and the imaginary part of said complex number characterizes the local index of the object. The global phase is chosen appropriately when the point of origin of the three-dimensional frequency representation has a real value.

la partie imaginaire des nombres complexes représentent respectivement l'absorptivitc locale et l'indice local. Ceci permet également de normaliser l'ensemble de la représentation. According to one version of the invention, and in the cases where the point of origin of the three-dimensional frequency representation is one of the points which have been acquired, the microscope comprises means for dividing, by its value at the point of origin, the three-dimensional frequency representation obtained by the method detailed in 3.5.1. This makes it possible to obtain a spatial representation in which the real part and

the imaginary part of the complex numbers represent respectively the local absorptivity and the local index. This also makes it possible to standardize the whole representation.

When the point of origin of the three-dimensional frequency representation is not part of the points which have been acquired, this operation is impossible. The operator who visualizes an image then visualizes for example the real part of the complex number, and must intuitively choose the global phase of the representation so as to obtain the most contrasted image possible.
3. 5.3. Phase adjustment with respect to the illumination wave
The general phase-adjustment algorithms defined above have the drawback of being relatively complex to implement. A simplified version can be obtained when the acquisition system allows the acquisition of the non-diffracted part of the illumination wave. This corresponds to the point of origin of the three-dimensional frequency representation of the object. This point is common to all two-dimensional frequency representations.

The phase adjustment described in 3.5. 1. can then be carried out with respect to the part of underrepresentation constituted by this single point. This registration can be grouped with the absolute registration described in 3.5.2. The set of two readjustments then amounts to dividing the whole of the under-representation of the object obtained from a given lighting wave, by its value at the point of origin. When a frequency plane image is generated as a calculation intermediate, this amounts to dividing the entire frequency plane image by its value at the point corresponding to the non-diffracted part of the lighting wave According to a version of invention, the phase-adjustment of the two-dimensional frequency representations is therefore carried out by dividing each sub-representation of the object by its value at the point of origin of the representation

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fréquentielle tridimensionnelle de l'objet. Cette méthode est utilisée par exemple dans les modes de réalisation 1,2,3 et 4.

three-dimensional frequency of the object. This method is used for example in embodiments 1, 2, 3 and 4.

3.5.4. Phase adjustment with respect to pre-recorded phase values
A three-dimensional frequency representation of the object is obtained from a series of two-dimensional frequency representations each corresponding to a different lighting beam.

Each of these two-dimensional frequency representations can be realigned in phase with respect to the under-representation formed by the point of origin alone, as indicated in 3.5.4. However, the high intensity of the corresponding point on each frequency representation, bidimcnsionncllc makes the simultaneous acquisition of the rest of the representation difficult. According to one version of the invention, the acquisition of the frequency plane images is carried out in two stages: a preliminary phase, during which the values obtained at the illumination background image point are recorded, for each illumination wave .

- an acquisition phase proper, during which the direct beam can be obscured and during which the values of the frequency plane images are recorded
A two-dimensional frequency representation can then be obtained for each lighting wave from these two recordings, the value at the image point of the illuminating wave being obtained from the first recording and the value at any other point being obtained from of the second record. The method described in 3.5.4. can then be applied to each two-dimensional frequency representation obtained.

When a series of two-dimensional frequency representations is made, for example to 'film' the movement of cells, the preliminary phase does not have to be repeated. It is enough to do it once before the start of acquisitions.

For this method to be functional, the phase difference between the illumination beam and the reference beam, at the level of the receiving surface, must be reproducible. The systems for generating the lighting beam used in embodiments 3, 4 and 5 satisfy this condition. This phase adjustment method is described for example in 7.18.1. and in 9.18 2.

3.6. Vibration compensation
The method described in 3.5.4. assumes the reproducibility of the lighting beams. The method described in 3.3.3., In the case where several objectives are used, assumes a constant phase shift between the waves received on each of these objectives. However, in embodiments 3, 4 and 5, the vibrations can make these methods inoperative or not very robust. For the results to be reliable, it is necessary to compensate for these vibrations.

To this end, the system can periodically acquire a reference image The reference image consists, for example, of an image obtained on the receiving surface for a fixed illuminating wave, which is not changed when the illuminating wave. lighting used to obtain the flat images in frequency 'useful' varies.

Each acquisition then corresponds to a reference image acquired at a close instant. An image of

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reference acquired at an initial instant is chosen as absolute reference. The term “useful” image is understood to mean an image obtained on the reception surface and from which a two-dimensional frequency representation used to generate the representation of the object will be calculated.

The vector tu traversing the whole of the support of an image, we denote by iii (t,) a 'useful' image obtained on this reception surface and h (v) the corresponding reference image. We denote by ho (v) the reference image chosen as absolute reference, obtained on the same reception surface. v represents the plane projection of the frequency and is therefore a two-dimensional vector varying over the whole of the reception surface. We denote # (v) the standard deviation of the Gaussian noise affecting the function h (v) at each point.

vzw lh( l@)12 u 2(1,) qui représente l'écart de phase le plus probable entre les images de référence /)(<') et 110(1'), L'image 111(\') peut alors être recalée en phase comme suit: 111(1') r,I1{I') ou le signe <- désigne l'affectation. The phase variation of vibratory origin can for example be characterized by the coefficient

vzw lh (l @) 12 u 2 (1,) which represents the most probable phase difference between the reference images /) (<') and 110 (1'), the image 111 (\ ') can then be readjusted in phase as follows: 111 (1 ') r, I1 {I') where the sign <- designates the assignment.

When this preliminary registration has been carried out, the images thus registered in phase can be used in the algorithms defined in 3.5.3. and 3.5.4.

If the system is completely free from vibrations, this preliminary adjustment is not necessary.
If the vibrations are of low frequency, the reference image may only be acquired at a low frequency, however higher than the frequency of the vibrations of the system.
If the \ ibrations are strong, it is possible to acquire a reference image for each useful image.

In the presence of vibrations, - this preliminary adjustment is essential for the application of the algorithm defined in 3.5.4.

- this preliminary adjustment is not essential for the application of the algorithm defined in 3.5.3 in the case where only one objective is used. However, in the case where several objectives are used, it makes it possible to fix the phase difference between the frequency plane images generated from each objective. In this case it is therefore also essential.

This technique is used in Embodiments 3 and 4 and described in 7.17. It is also used in Embodiment 5 when the phase adjustment is performed according to section 9.18.

One version of the invention therefore consists in periodically acquiring reference images corresponding to a fixed illumination direction, and in using these images to compensate for the phase differences of vibratory origin affecting the frequency plane images.

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3. 7. Characterization of the wave vector of the illuminating wave
It is necessary to control the direction of the illumination wave, that is to say its wave vector fe, for example with mechanical means such as for example in [Turpin]. However, these mechanical means must be very precise and are expensive to implement.

Under the conditions defined in 3.5.3., I.e. if the acquisition system allows the acquisition of the non-diffracted part of the illuminating wave, the non-diffracted part of the illuminating wave lighting corresponds to a maximum of the module on the frequency representation of the wave coming from the object. According to one version of the invention, the microscope comprises means for determining the coordinates of this maximum and for calculating from these coordinates, the wave vector fe of the illuminating wave. This method is used for example in embodiments 1 and 2.

However, the presence of the object may slightly distort the value of the wave vector thus obtained According to one version of the invention, the wave vectors fe of each lighting wave are obtained in a preliminary phase or the object is deleted or replaced by a transparent plate. The wave vectors thus obtained are therefore not distorted by the presence of the object. This method assumes that the wave vectors are reproducible from one acquisition to another. On the other hand, it avoids having to calculate these wave vectors as a function of mechanical parameters. This method is used in embodiments 3, 4 and 5.

que [Vishnyakovl utilise une telle configuration sans pouvoir en tirer parti, du fait de l'utilisation de méthodes tomographiques mal adaptées, les algorithmes définis dans la présente invention permettent de tirer le meilleur partie de cette configuration. 3. 8. Receiver characteristics
3. 8.1. using a microscope objective
According to one version of the invention, the receiver comprises a high aperture microscope objective which transforms the rays coming from the object under a large aperture into paraxial rays which can be directed towards a receiving surface. This configuration allows better performance than the configurations defined in [Percher] (missing lens) or [Turpin] (low aperture lens).

that [Vishnyakovl uses such a configuration without being able to take advantage of it, due to the use of poorly adapted tomographic methods, the algorithms defined in the present invention make it possible to take the best part of this configuration.

3. 8.2. Use of a receiving surface in a frequency plane
It is advantageous to acquire the image directly in the frequency domain, as in [Turpin 3]. This can be done for example using the receiver described in [Lauer II, which makes it possible to improve the performance of the receiver of [Turpin 3].

3. 8.3. Use of a receiving surface in a space plan
Apart from the microscope objective itself, the reception system defined in 3. 8 2 has a paraxial part making it possible to modify the optical signal picked up by the objective. to obtain a frequency representation. The signal from the objective first passes through the plane where the objective normally forms the image of the observed sample. This plane will be called the space plane. It is then transformed by a paraxial system so that in the plane where the receiving surface is placed, a plane wave from

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- si la surface de réception est dans un plan de fréquence, l'onde de référence doit être centrée v irtuellcment en un point central de l'objet observé. of the object has a point image. This plane, where the receiving surface is placed, will be called the frequency plane. The paraxial part of the optical system used may include planes of space or of intermediate frequency. The receiving surface can be placed in a space plane, in a frequency plane, or in an intermediate plane. However, to simplify the calculations, it will always be placed either in a space plane or in a frequency plane. In order for the received image to be correct, the following conditions must also be met:

- if the receiving surface is in a frequency plane, the reference wave must be centered v irtuellcment at a central point of the observed object.

- if the receiving surface is in a plane of space, the reference wave must be the image of a virtual wave which is plane when passing through the observed object.

Under these conditions, the signal detected on a reception surface placed in a frequency plane is the optical Fourier transform of the signal which would be detected in a space plane. A version of the invention constituting an alternative receiver defined in 3. 8.2. is therefore to use a reception surface positioned in a plane of space and a reference wave which is the image of a virtual plane wave passing through the observed object. A digital Fourier transform then replaces the optical Fourier transform.

Embodiments number 1, 3, 4 use reception in a frequency plane and embodiments 2 and 5 use reception in a space plane. A frequency plane image can therefore be obtained either directly on a reception surface placed in a frequency plane, or by Fourier transformation of an image received on a reception surface placed in a space plane.

3. 9. Beam attenuation
In the case where the sensor is placed in a space plane, direct illumination base has as representation on the sensor a constant modulus value which is superimposed on the wave diffracted by the object A diffracted wave too weak compared to this constant baseline cannot be detected correctly. On the other hand, this basic level is not very high because the intensity of the reference beam is distributed over the entire sensor, which generally makes it possible to obtain good images. In the case where the sensor is placed in a frequency plane, the illuminating wave is concentrated at a point and as before, a diffracted wave that is too weak compared to this constant base level cannot be detected correctly. wave being concentrated at a point, this base level is high and this limitation is troublesome.

According to an advantageous version of the invention, a device for controlled attenuation of the beam, having one or more attenuation levels, is introduced to solve this problem. The attenuation device makes it possible to successively obtain several recordings differing in the intensity of the illumination background. A less noisy value of the diffracted wave is then obtained by combining these recordings. The final value of the diffracted wave is for example calculated at each point from the recording for which the intensity of the wave received at the point considered is the highest, but for

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in which the sensor remains unsaturated at the point considered and in its immediate neighbors for) 'set of interference figures making it possible to obtain said recording.

Taking into account the use of a beam attenuation device, the version of the invention in which a plane wave has a point image allows the detection of weaker diffracted waves. Indeed these are not superimposed on the sensor to no other wave and very low levels can be detected when the illumination beam intensity is high.

Such a device is used in embodiments 1, 3 and 4.

3.10. Lighting beam generation system
Regardless of the embodiment, it is necessary to design a method for generating the illumination beams. The methods proposed by [Turpin] present the defect of requiring significant mechanical displacements and thus of strongly slowing down the system.

An optical system, for example that described in 8. 1. 1., can transform a parallel beam of given spatial extension and of variable direction into a parallel beam whose spatial extension has been reduced and whose direction variations have been reduced. amplified. In general, small variations in direction applied to a beam of high spatial extent can be amplified by an optical system by reducing the spatial extent of the beam. Since the spatial extent of the illumination beam required for a microscope is small, this principle can be used to optically amplify weak mechanical movements.

A beam of variable direction can be transformed by a lens into a beam of variable position in the image focal plane of this lens. A variation in the direction of the beam in one part of its optical path is therefore equivalent to a variation in position in another part of its optical path and vice versa. In intermediate planes, variation is a joint variation of position and direction.

There is therefore no need to differentiate a system generating variations in the position of the lighting patrol from a system generating variations in direction, these systems being equivalent.

According to one version of the invention, the system for generating the lighting beams comprises - a beam deflector generating variations of a paraxial beam.

an optical element with a large aperture (for example a microscope objective or a condenser) transforming said variations of the incident paraxial beam into significant variations in direction of the outgoing beam.

It can also include a lens system dimensioned so that the beam is parallel at the output of said high aperture optical element.

The beam deflector may for example be a mirror mounted on a positioner making it possible to control its orientation. This solution is implemented in embodiments 1 and 2.

However, this solution has two drawbacks: - the movement of the mirror generates vibrations which disturb the system. After each movement of the mirror, it is necessary to wait for the absorption of the vibrations before proceeding with the acquisition.

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- the phase difference between the reference beam and the illumination beam is not reproducible, which prevents the use of certain algorithms such as those defined in 3.5.4
Each of the beam deflectors described in 3.10.1. , 3.10.2 and 3.10.3. solves both of these problems.

3. 10.1. Beam deflector based on a series of binary deflectors
A system that can return the beam in two directions can be constructed using a birefringent prism which transmits the ordinary beam and the extraordinary beam in two different directions. The laser beam used must then be polarized. A polarization rotator placed in front of the prism makes it possible to orient its polarization in the ordinary direction or the extraordinary direction, which implies a different angle of deflection by the prism. However, ferroelectric polarization rotators available. which have the advantage of being fast, do not allow a rotation of 90 degrees but a rotation of about 80 degrees. This prevents having both a beam polarized exactly in the ordinary direction, for one of the positions of the polarization rotator, and a beam polarized exactly in the extraordinary direction for the other position. It is therefore created, in one of the positions, a parasitic beam deflected in an unwanted direction. In order to eliminate this parasitic beam, it is necessary to use at the output of the birefringent prism a polarizer selecting only the desired radius. So that this polarizer does not eliminate the ray in the other position of the rotator, it is necessary to introduce between this polarizer and the prism a second rotator, used to bring back the electric field vector of the beam in the passing direction of the polarizer, when it is not there directly at the output of the prism.

l'angle de déviation du doublet numéro i soit proportionnel à 2' , on obtient 2 v valeurs de déviation possibles dans chaque direction. Par exemple avec .\=8 on a un total de 256 x 256 directions de déviation du faisceau. A system that can return a beam in many directions can be formed by associating several of these elementary systems in series. By associating two, which produce a deflection of the same amplitude but in two orthogonal directions, we form a doublet. By associating in series N doublets, each doublet being characterized by birefringent prisms with characteristics such as

the angle of deviation of doublet number i is proportional to 2 ', we obtain 2 v possible values of deviation in each direction. For example with. \ = 8 we have a total of 256 x 256 directions of deflection of the beam.

According to one version of the invention, the beam deflection system is therefore constituted by the series association of elementary deflectors, each of these elementary deflectors comprising a birefringent prism deviating differently from the ordinary ray and the extraordinary ray, preceded by a electronically controlled polarization rotator making it possible to orient the electric field vector of the beam along the ordinary axis or the extraordinary axis of said prism, and followed by a second rotator and a polarizer making it possible to eliminate parasitic beams.

Such a device is used in embodiment 3.

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3. 10.2. Beam diverter based on spatial modulators
A spatial modulator is a three-dimensional matrix of pixels making it possible to modulate the phase or the intensity of a wave in a plane. Most space modulators are based on liquid crystals.

Common LCD screens are an example of a spatial intensity modulator.

A space plane, on the path of the illumination beam, will be defined as a plane in which this beam is parallel and is centered on the optical axis. A frequency plane will be defined as a plane in which this beam has a point image.

de la forme exp{ /2:'n/+ /,. } ou (x,y) sont les coordonnées d'un point du plan et ou (fx, fy) sont les coordonnées de la projection du vecteur d'onde dans ce plan. Si un dispositif de modulation de phase est

placé dans ce plan et si un décalage de phase de la forme 0 = 2g-rx+gl,y+c) est appliqué à l'aide de ce dispositif, l'onde a, après traversée dudit dispositif, une représentation complexe eap(2.r(.fx +gz .r+.fy, +gy.)v+c, . Le dispositif de de modulation spatiale a donc modifié la direction de l'onde incidente. Les vecteurs d'onde que peut générer un tel dispositif de modulation spatiale sont compris dans un cône dont ouverture dépend des valeurs maximales de gx et gy permises par le modulateur. Ce cône sera appelé 'cône de déviation'. A parallel beam arriving in a plane of space has in this plane a complex representation

of the form exp {/ 2: 'n / + / ,. } where (x, y) are the coordinates of a point on the plane and or (fx, fy) are the coordinates of the projection of the wave vector in this plane. If a phase modulation device is

placed in this plane and if a phase shift of the form 0 = 2g-rx + gl, y + c) is applied using this device, the wave has, after passing through said device, a complex representation eap ( 2.r (.fx + gz .r + .fy, + gy.) V + c,. The spatial modulation device has therefore modified the direction of the incident wave. The wave vectors that such a device can generate of spatial modulation are included in a cone whose opening depends on the maximum values of gx and gy allowed by the modulator This cone will be called 'deviation cone'.

est possible d'appliquer une fonction d'atténuation du type cosj 2/n gxx + gy y +. en Après traversée du dispositif, l'onde a alors une forme du type eap2( fx +gXx+(fy, +gyy+c)+cxp2r(.fx -gxx+.fy g y)Y - c)} qui correspond à la superposition de deux ondes planes dont les vecteurs d'onde sont symétriques par rapport à un axe orienté suivant le vecteur d'onde de l'onde qui sortirait du dispositif en l'abscence de modulation. Une des deux ondes peut être arrêtée par un diaphragme, moyennant quoi le dispositif constitue un déviateur de faisceau comparable au précédent. If an intensity modulation device is used instead of the phase modulation device, it

It is possible to apply an attenuation function of the type cosj 2 / n gxx + gy y +. in After crossing the device, the wave then has a shape of the type eap2 (fx + gXx + (fy, + gyy + c) + cxp2r (.fx -gxx + .fy gy) Y - c)} which corresponds to the superposition of two plane waves, the wave vectors of which are symmetrical with respect to an axis oriented along the wave vector of the wave which would leave the device in the absence of modulation. One of the two waves can be stopped by a diaphragm, whereby the device constitutes a beam deflector comparable to the previous one.

Intermediate modulation devices, providing joint phase and intensity modulation, can also be used.

One version of the invention therefore consists in using an appropriately controlled spatial modulator as the beam deflector.

B = 2rgt x +gyY . One version of the invention consists in that said modulator is a phase modulator, controlled so as to generate a phase shift of a form as close as possible to

B = 2rgt x + gyY.

Existing modulation devices operate pixel by pixel. This discretization leads to the generation of parasitic frequencies outside the deflection cone. One version of the invention consists of

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remove these parasitic frequencies using a diaphragm placed in a frequency plane on the path of the wave coming from the phase modulator.

Modulation devices allowing rapid modulation are binary, that is to say that to a given pixel only two possible values of phase or intensity correspond. The use of a binary modulation device results in the presence of a parasitic plane wave, symmetrical on the ground, which one seeks to obtain with respect to an axis formed by the direction of a non-deflected beam. In the case of binary modulators, this is true even when it is a phase modulator, while in the case of modulators generating continuous modulation, this problem can be avoided by using a phase modulator. According to one version of the invention, the diaphragm filtering the parasitic frequencies is dimensioned so as to filter not only the frequencies located outside the deflection cone, but also a part of the frequencies located in the deflection cone, so as to stop the wave. parasitic plane.

Binary modulation devices also have the drawback of generating parasitic frequencies included in the deflection cone and constituting frequency 'noise'. According to one version of the invention, these frequencies are stopped by an intensity modulator placed in a frequency plane on the path of the beam coming from the phase modulator, and controlled so as to allow only the desired frequency to pass.

Such a device is used in embodiment 4.

3. 10.3. Beam deflector consisting of a movable mirror whose vibrations are rendered non-disturbing
The beam deflectors described in 3.10.1. and 3. 10.2. are based on the use of liquid crystal devices and polarizers. These devices are not available in the field of ultraviolet radiation. In order to use ultraviolet radiation, therefore, it is necessary to use other means.

In previous devices, the entire system was placed on an optical table.

According to one version of the invention, the beam deflection device consists of a mirror placed outside the optical table, the separation between the illuminating beam and the reference beam being effected by a splitter fixed on the optical table and positioned after said mirror on the path of the beam.

The mirror being placed outside the optical table, it does not generate vibrations of this table. Since the separation of the beams takes place after the mirror, its vibrations do not cause phase shifts between the illumination beam and the reference beam either. This therefore solves the problem of vibrations.

On the other hand, the fact that the separation of the beams takes place after the moving mirror implies that the reference beam varies at the same time as the illumination beam. This variation must be taken into account in the design of the system and compensated for. For example, if the reception surface is placed in a plane of space, the variations in direction of the reference wave result in translations of the plane image in frequency. According to one version of the invention, this effect is compensated by performing a translation in the opposite direction of the plane frequency images obtained.

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This technique is used for example in embodiment 5.

3. 11. Compensation of errors due to polarization
The image generation method described by [Wolf] is based on a scalar diffraction theory and assumes that the wave passing through the object is isotropically diffracted in all directions by every point of the object. It is only with this assumption that the theoretical resolution of # / 4 can be obtained. Scalar diffraction theory is however not valid for high diffraction angles. The intensity diffracted by a point of the object depends on the direction of the diffracted wave, the direction of the illuminating wave, the direction of polarization of the illuminating wave and the direction of polarization of the diffracted wave.

3.11.1. Compensation by multiplication by a real coefficient
The wave diffracted by the object differs from the wave that would be diffracted if the diffraction were isotropic by a real multiplicative factor depending on: - the direction of propagation of the illuminating wave - the polarization of the d wave 'illumination - of the direction of propagation of the diffracted wave - of the polarization of the diffracted wave
According to one version of the invention, the microscope comprises means for determining this multiplying factor and compensating for it by multiplying the waves received by the inverse of said factor. Such a version of the invention is described in 7.18.8.

3. 11.2. Compensation in the case of an anisotropic material
If the observed object consists essentially of an anisotropic material, the effects of diffraction differ from what they are in an isotropic material. The material is then characterized at each point by 6 crystalline parameters plus the absorbency
In the particular case where the object observed is a uniaxial crystal, the diffraction index of the ordinary ray has a constant value. According to one version of the invention, a three-dimensional representation in which the complex numbers obtained characterize the absorptivity and the ordinary index can be calculated. According to this version of the invention, this representation is calculated from plane frequency images obtained for a polarized lighting wave so that it constitutes an ordinary ray.
The direction of ordinary polarization varying with the direction of propagation of the wave, it is necessary to be able to modify the direction of polarization of the illuminating wave However, the phenomena being linear, it is sufficient to record the wave received in any point for two directions of polarization of the lighting wave in order to be able to deduce therefrom the wave diffracted by the object for a lighting wave of any direction. According to one version of the invention, the microscope comprises means for generating two directions of polarization of the illumination wave. According to one version of the invention, the

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microscope also comprises means for analyzing background diffracted in two directions of polarization, which makes it possible to distinguish the ordinary diffracted wave from the extraordinary diffracted wave According to this version of the invention, the frequency plane images are then obtained from four elementary images corresponding to each combination of the two directions of polarization and of the two directions of analysis.

Such a version of the invention is described in 7.18.9. In the version described in 7.18 9. only the direction of anal) corresponding to the ordinary ray is used, however it is also possible to take into account the direction of analysis corresponding to the extraordinary ray. Two frequency plane images are then obtained for each direction of propagation of the illumination wave, one corresponding to the ordinary index and the other to the extraordinary index. The final frequenticlle representation is obtained from this set of images by taking into account the variations of the extraordinary index at each point of the frequency plane images corresponding to the extraordinary index.

3. 11.3. Compensation by combining several polarization and analysis directions
In the case of isotropic material, the method described in 3. II. 1. has the fault of raising the noise level considerably. One method avoiding this problem is to acquire at least four frequency plane images corresponding to each combination of two distinct polarizations of the illumination base and of two distinct directions of polarization of the diffracted wave. An appropriate algorithm then makes it possible, from these four images, to calculate a single image corresponding to the desired scalar quantity. According to one version of the invention, the microscope therefore comprises a means for generating two distinct polarizations of the illuminating wave, and a means for analyzing the diffracted ground according to two distinct polarization directions. According to one version of the invention, the microscope comprises means for calculating, from the frequency plane images corresponding to each combination of the two polarization directions and of the two analysis directions, a single frequency plane image representing a scalar quantity complex verifying the condition of homogeneous diffraction in all directions. This principle is used in embodiments 3, 4, and 5. The principle of calculating said scalar quantity is detailed in 7.12.1.

In the case of visible wavelengths, said means for varying the illumination base polarization may consist of a liquid crystal polarization rotator. Said means for varying the direction of analysis of the diffracted wave may be composed of a polarization rotator associated with a polarizer. In the case of ultraviolet, these devices are not available.

3.11.4. Variation of the direction of polarization of the illumination wave in the UV range
In the UV field, the polarization rotators can be replaced by a quartz wave plate rotating around an axis by mechanical means. However, these mechanical movements significantly slow down the system. This is why we use a system where the only mechanical movements are those of shutters and where the beam to be closed has a spatial extension as small as

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possible, so that the shutter movement is as low as possible. It is then possible to use a fast shutter or a shutter with a crenellated rotating wheel.

According to one version of the invention, such a system comprises: a beam splitter separating the beam into a beam A and a beam B.

- Lenses placed on each beam.-1and B and focusing these beams on focusing points where the shutters are placed.

- a device allowing the beams to be superimposed again.] and B having passed through their respective shutters.

a device placed on the trajectory of one of the beams..1 or B, in the part of the trajectory where the two beams are distinct, and modifying the polarization of this beam.

Such a system can also include additional lenses intended to reform parallel beams after passing through the shutters. It can also include a second device for modifying the polarization. The device for modifying the polarization of the beam may be a wave plate. The beam splitter and beam superposition devices can be semi-transparent mirrors. Such a device is used in embodiment 5.

3. 11.5. Variation of the direction of analysis in the UV domain.

The wave coming from the object can be decomposed into a wave whose electric field vector is parallel to that of the reference wave and a wave whose electric field vector is orthogonal to that of the reference wave. The intensity received on the receiving surface is the sum of the intensity of the electric field wave orthogonal to the reference wave and the intensity produced by the interference of the reference wave and the electric field wave parallel to the reference wave. The first of these intensities does not depend on the reference ground phase and therefore does not modify the complex value of the wave coming from the object measured by combination of interference figures corresponding to different phases of the reference ground. It is therefore only the electric field vector wave parallel to that of the reference wave which is obtained on the receiving surface.

The direction of analysis of a wave can therefore be modified simply by modifying the direction of polarization of the reference background or symmetrically by modifying the direction of polarization of the wave coming from the object.

According to one version of the invention, the direction of analysis is modified by varying the direction of polarization of the reference wave or of the wave coming from the object.

According to one version of the invention, the polarization of the reference wave or of the wave coming from the object is modified by a device comprising: - a beam splitter separating the beam into two beams A and B - a plate d wave LA disposed on the path of the beam: 1 and a wave plate LB disposed on the path of the beam B, the angle between the neutral axes of these two wave plates being 45 degrees.

The direction of polarization of the beam having crossed the Lise wave plate then deduced from the direction of polarization of the beam having crossed the LB wave plate by a rotation of which the angle is

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the angle between the neutral axes of the wave plates LA and LB. If this angle is 45 degrees, the beams coming from the plates L1 and LB will always have orthogonal polarizations, whatever the direction of polarization of the incident beam.

The two beams .1and B can then be joined by a superposition device after having passed through shutters, as in the case of the device described in 3.11.4. This has the disadvantage of requiring the use of shutters at a point on the path of the beam where the direction of the beam is variable and where the beam cannot therefore be focused on a fixed point.

According to one version of the invention, the two beams A and 13 are separately superimposed on the beam coming from the object (if they constitute the reference wave) or on the reference wave (if they are coming from the object). 'object). The interference figures corresponding to each direction of polarization are then formed on two distinct receiving surfaces.

Whether the plane frequency images corresponding to each polarization are obtained on separate reception surfaces or on the same reception surface, a phase shift is then created between these images which must be compensated. According to one version of the invention, the wave plates are positioned so that the reference and illumination beams reaching a receiving surface have different directions of polarization, preferably at 45 degrees from one of the other. Under these conditions, the part of the wave coming from the object which comprises frequencies close to the illuminating wave is detected on the two receiving surfaces and can be used to calculate said phase difference.
3.12. Direct light suppression system
The illuminating wave is generally much more intense than the diffracted wave. It can saturate sensors or dramatically reduce the signal-to-bit ratio of the system, necessitating acquisition at a high level. The elimination of the non-diffracted part of the illumination wave during the acquisition phase or during part of the acquisition phase clearly improves the performance of the system. In a frequency plane, the non-diffracted part of the illuminating wave has a point image and can be suppressed by placing an absorbing element on this point. According to one version of the invention, the system therefore comprises a device for eliminating the non-diffracted part of the illumination background, placed in a frequency plane, and absorbing the beam over a small area around the point corresponding to this wave of lighting.

According to one version of the invention, this device consists of a spatial intensity modulator controlled to pass at any point except over a limited area around the point of impact of the non-diffracted part of the lighting wave. This version is implemented in embodiment 4.

According to another version of the invention, this device consists of a window movable in translation in a frequency plane, an absorbing black point placed on the window having the role of stopping the direct beam, the position of the window being controlled to make this black point coincide with the point of impact of the non-diffracted part of the lighting wave. This version is implemented in Embodiment 5.

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3. 13. Device for using spatial modulators.

The spatial modulators used in 3.10.2. or in 3.12. can in particular be fast binary modulators operating by reflection. They are generally used with the aid of a semi-transparent polarizing mirror, which is a cubic-shaped device returning the incident beams in two different directions depending on their polarization. This device, because of its thickness, generates a slight aberration which widens the point corresponding to a given frequency, which is detrimental to the quality of the images obtained.

To avoid the use of this device, it is possible to use beams reaching the modulator at an oblique angle. The incident and reflected beams are then separated. However, this method distorts the distribution of the generated frequencies. To avoid this deformation, said oblique angle must be small
According to one version of the invention, this problem is solved by using a device consisting of a mirror with two orthogonal reflecting faces and a lens traversed in one direction by the beam directed towards the modulator and in the other direction by the beam reflected by the modulator. The incident beam is reflected by one face of the mirror, passes through the lens, is reflected by the modulator, passes through the lens in the opposite direction and is reflected by the second face of the mirror, returning to its initial direction. The incident and reflected beams may partially overlap on the lens but are separated on the two-sided mirror. In order to achieve this separation on the mirror, while having an oblique angle as low as possible, the two-sided mirror should be roughly positioned in one focal plane of the lens and the modulator should be positioned in the other plane. focal point of the lens.

l'objet. et dans l'autre sens par l'onde diffractée issue de l'objet. Il joue à la fois le rôle d'objectif recon aili l'onde issue de l'objet. et le rôle de système à forte ouverture transformant les variations de direction faibles de l'onde issue du déviateur de faisceau, en variations de direction élevées de l'onde dans l'objet Ceci peut être réalisé par exemple à l'aide d'un miroir semi-transparent placé sur le trajet du faisceau issu de l'objet et superposant le faisceau issu de l'objet et dirigé dans un sens donné au faisceau d'éclairage se dirigeant en sens opposé. Cette version de l'invention est mise en oeuvre dans les modes de réalisation 3,4 et5 qui comportent plusieurs objectifs. Une version n'utilisant qu'un objectif est décrite en 7.18.10. 3.14. Use of objectives crossed in both directions and / or multiple objectives
The object can be illuminated from one side and the wave coming from the object can be picked up from the opposite side by an objective, which makes it possible to reconstitute part of the frequency representation of the object. However, other parts of the frequency representation of the object can only be reconstructed from the wave heading towards the side of the object from which the lighting waves originate. According to one version of the im ention, an objective is associated with an optical system allowing on the one hand the measurement on a sensor of the wave coming from the sample and having passed through the objective, and on the other hand the training of an illuminating wave which, after passing through the objective, becomes in the sample a plane illuminating wave of variable direction. This objective is then crossed in one direction by the lighting wave heading towards

the object. and in the other direction by the diffracted wave coming from the object. It plays at the same time the role of objective recon aili the wave coming from the object. and the role of a system with a large aperture transforming the small variations in direction of the wave coming from the beam deflector, into large variations in direction of the wave in the object This can be achieved for example using a semi-transparent mirror placed on the path of the beam coming from the object and superimposing the beam coming from the object and directed in a given direction to the lighting beam directing in the opposite direction. This version of the invention is implemented in embodiments 3, 4 and 5 which have several objectives. A version using only one lens is described in 7.18.10.

Any limitations relating to the direction of the illumination wave, characterized by its frequency vector, influence the performance of the system. The maximum precision is obtained when

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l'ensemble des éclairages utilisés et génère à partir de ces données la représentation fréqucnticlle tridimensionnelle de l'objet. Chaque couple (direction de l'onde d'éclairage-direction de l'onde issue de

l'objet) correspond à un point de la représentation fréquentielle de l'objet, et la représentation fréquenticllc ainsi générée comprend donc tous les points pouvant être obtenus à partir des ondes d'éclairage et des ondes diffractées respectivement produites et reçues par l'ensemble des objectifs. all possible directions are used. Likewise, it is desirable to record the wave diffracted by the object in all directions. When a single microscope objective is used, its aperture limits the directions in which the wave diffracted by the object can be recorded. According to an advantageous version of the invention, several objectives focused on the sample are used, which make it possible to record the wave coming from the sample following more directions. The objectives then cover almost all of the space around the sample, and the illuminating waves must necessarily pass through these objectives to reach the sample. According to one version of the invention, each objective is associated with an optical system allowing on the one hand the measurement on a sensor of the wave coming from the sample and having passed through the objective, and on the other hand the formation of an illuminating wave which, after passing through the objective, becomes in the sample a plane illuminating wave of variable direction. The illuminating waves can then be generated in all the directions covered by the aperture of the objectives, and likewise the waves emanating from the object can be measured in all these directions. According to one version of the invention, the acquisition and calculation system takes into account all the waves measured on all the sensors for

all the lighting used and generates from these data the three-dimensional frequency representation of the object. Each pair (direction of the lighting wave-direction of the wave resulting from

the object) corresponds to a point of the frequency representation of the object, and the frequenticllc representation thus generated therefore comprises all the points that can be obtained from the lighting waves and the diffracted waves respectively produced and received by the assembly objectives.

It is possible to use a large number of objectives in order to receive all of the waves coming from the sample, or in order to increase the working distance by using objectives with small aperture.

However, most of the samples observed in practice are plane and can conveniently be placed between two coverslips. One version of the invention constituting the best compromise between the difficulty of implementation and the performance is to use two wide-aperture microscope objectives positioned opposite each other, the flat sample being introduced between these two objectives. This solution is used in Embodiments 3, 4, and 5. In Embodiments 1 and 2, of lower performance but easier to realize, only one microscope objective is used.
3. 15. Generation of reverse beams
When two or more microscope objectives are used, a frequency planar image is generated from the wave received by each objective. Each point of a plane frequency image corresponds to a given wave vector of the diffracted wave. In order to be able to calculate the three-dimensional frequency representation of the object, it is necessary to correctly determine these wave vectors, in a frame of reference common to the wave vectors received by each objective.

pour les représentations bidimensionnelles RA ( avant translation de vecteur -/e ) reconstituées à partir de l'image plane en fréquence obtenue à partir d'un objectif donné est différent de celui utilisé pour les représentations RB obtenues à partir de l'objectif en vis-à-vis. Pour établir une correspondance entre ces Knowledge of the K factor and of the optical center, defined in [Lauer 1], allows the determination of the wave vectors corresponding to each point of a frequency image. However the benchmark used

for the two-dimensional representations RA (before vector translation - / e) reconstituted from the plane frequency image obtained from a given objective is different from that used for the RB representations obtained from the screw objective -to-be. To establish a correspondence between these

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two reference points It is necessary to determine the coordinates of certain points both in the reference system used for RA and in the reference system used for RB.

Each point PA of the representation RA is the image of a wave vector fe of the lighting wave which arrives at this point in the absence of an object, and has for coordinates those of this wave vector To this vector corresponds a wave vector -le of opposite direction, the image of which is a point PB of the representation RB. The coordinates of point PB in the frame used for / are the opposite of the coordinates of point PA in this frame.

The correspondence between the two reference marks can therefore be established if the coordinates of the point PB are also determined in the reference mark RB. This can be done by generating by optical means a beam of wave vector opposite to the illumination beam and by determining the coordinates of the image point of this beam in the frame of reference used for RB. If this correspondence is established at a sufficient number of points, the relationship between the marks used for RB and RA can be easily determined and these representations can be modified to use a common mark.

Similarly, a direct correspondence between the marks RB and RA can be obtained by optical means. This requires the adjustment of a number of optical elements. To carry out this adjustment, the correspondence between the coordinates of point PB obtained in each of the reference marks used can be continuously checked, for a certain number of points PB (three points in principle).

In both cases, it is necessary to generate a beam with the same characteristics as the lighting beam, but propagating in the opposite direction. In general, given a beam used in the system, the term reverse indicator beam will designate a beam with the same characteristics but propagating in the opposite direction.

According to one version of the invention, the microscope therefore comprises, during the adjustment phase, means for generating a beam indicating the reverse of the illumination wave. These means can optionally be eliminated after the adjustment phase corresponding to the determination, by calculation means or by optical means, of the correspondences between the marks RB and R.1.

According to one version of the im ention, the microscope also comprises means for generating, during an adjustment phase, an inverse indicator beam of the reference background. This beam will also be used in certain adjustment phases. For example, if the receiving surface is in a frequency plane, the reference wave is virtually centered at a central point of the object. The indicator beam reversing the reference wave allows the position of the objectives to be adjusted so that these objectives are focused on the same point.

According to one version of the feed, when the receiving surface is in a space plane, an additional beam centered on this space plane is also used during an adjustment phase, as well as its reverse indicator beam. This beam facilitates, for example, the position adjustment of the objectives in the absence of a reference wave centered on a point of the object.

In embodiments 3, 4, and 5, each beam used has a reverse indicator beam, and the means for generating these reverse indicators is described as part of the microscope and not

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are not removed after adjustments have been completed: shutters are simply used to stop these beams.

According to one version of the invention, the device generating an inverse indicator beam from an original beam comprises: a semi-transparent mirror separating the original beam into an unmodified beam and a secondary beam.

- a lens focusing the secondary beam in a focusing plane.

a mirror placed at the focal point which returns the inverted beam towards said lens.

The fact that the mirror is placed at the point of focus ensures that the reflected beam has exactly the opposite direction of the incident beam; the reflected beam passes through the lens in the opposite direction. The part of this beam which is then reflected again by the semi-transparent mirror has the same characteristics as the unmodified beam but is directed in the opposite direction.

3. 16. Determination of the differences in position of the objectives.

objectif. Cette translation se traduit par une modulation en fréquence, les points dans l'espace fréquenticl obtenus à partir d'un objectif donné étant donc affectés d'un décalage de phase variable correspondant à cette modulation. Selon une version de l'invention, le microscope comporte des moyens pour compenser compenser cette translation et générer une représentation de l'objet dans laquelle le décalage de phase affectant chaque point de la représentation est constant. Pour pouvoir superposer les représentations obtenues à partir de chaque objectif, et selon une version de l'invention, le microscope comporte des moyens pour déterminer les coordonnées des points caractéristiques de chaque objectif de microscope. dans un repère commun. Il est alors possible de translater de manière appropriée chaque représentation avant de les superposer. Cette translation dans le domaine spatial équivaut à une démodulation dans le domaine fréquentiel, qui peut être effectuée directement sur les images planes en fréquence. From the waves coming from the object and passing through a given objective, it is possible to generate a three-dimensional representation of the observed object. In spatial representation, this representation is relative to a given point of origin, which will be called the characteristic point of the objective. In general, the characteristic points of the objectives used do not coincide. It follows that the part of the frequency representation generated from one objective is translated relative to that obtained from another

goal. This translation results in a frequency modulation, the points in the frequenticl space obtained from a given objective therefore being affected by a variable phase shift corresponding to this modulation. According to one version of the invention, the microscope comprises means for compensating compensating for this translation and generating a representation of the object in which the phase shift affecting each point of the representation is constant. In order to be able to superimpose the representations obtained from each objective, and according to one version of the invention, the microscope comprises means for determining the coordinates of the characteristic points of each microscope objective. in a common reference. It is then possible to appropriately translate each representation before superimposing them. This translation in the spatial domain is equivalent to a demodulation in the frequency domain, which can be carried out directly on the frequency plane images.

3.16.1. determination of the coordinates of the characteristic points of each objective.

According to one version of the invention, this can be obtained by using a beam centered on a central point of the observed object and its inverse indicator beam. This beam is received on one sensor after passing through the objectives, and its inverse indicator is received on another sensor. From the beam received on a sensor, the two-dimensional frequency representation of this beam can be obtained and the coordinates of its focal point can be determined. The focus point of the beam is the same as that of its reverse indicator beam. The difference between the coordinates of the focal point of the beam obtained from one lens and those of its inverse indicator obtained from another lens

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is equal to the difference between the coordinates of the characteristic points of these objectives in a common frame of reference.

This method can be carried out with any number of objectives, provided that the configuration is such that no group of objectives is optically isolated, that is to say that such a group of objectives , if it does not bring together all the objectives used, can always be achieved by a beam coming from an objective outside the group. For example if 6 objectives are used, they should not be grouped two by two: each objective must receive beams coming from two other objectives.

This aspect of the invention is implemented in 7.9. 1. and in 9.12.

* 3.16.2. Determination of the movements of each objective
It is generally necessary to move the objectives in order to introduce the observed object. This operation modifies the coordinates obtained and makes it necessary to repeat the previous operation.

However, the presence of the object disturbs the beam which passes through it and prevents obtaining a precise result. According to one version of the invention, this problem is solved by using parallel beams of variable direction. A parallel beam has a plane image in point frequency and the value obtained at this point is little affected by the local irregularities of the observed sample.

comme quotient de la valeur obtenue en présence de l'objet par la valeur obtenue en l'abscence de l'objet en un point correspondant de l'image plane en fréquence. Cette valeur sera appelée le rapport de phase et d'intensité sur un faisceau parallèle donné. The difference between the phase of such a beam received on a sensor before displacement of the objectives and the phase of the same beam after displacement of the objectives depends on the vector characterizing the displacement of the characteristic point of the objective receiving the beam with respect to the characteristic point of the objective from which the beam comes. From these phase differences established for a sufficient number of beams, it is possible, by an appropriate algorithm, to determine this displacement. According to this version of the invention. the phase of a set of parallel beams reaching a given sensor is therefore measured a first time in the absence of the object and a second time in the presence of the object. From the phase differences and possibly the intensity ratios thus measured, an appropriate algorithm can recalculate the displacement of the characteristic points of each objective. These phase and intensity differences can be characterized, for each parallel beam, by a complex value obtained

as quotient of the value obtained in the presence of the object by the value obtained in the absence of the object at a corresponding point of the plane frequency image. This value will be called the phase and intensity ratio on a given parallel beam.

Knowing the initial coordinates of the point of origin of each representation and its displacements, its current coordinates can be deduced from them and the position deviation can be compensated for This method can be implemented with any number of objectives, at the same provided that in 3. 16.1.

The first measurement in the absence of the object is carried out for example in 7.9.2. and in 9.13. In both cases, the correction related to the position values determined as indicated in 3.16.1. is described in the same paragraph as this measure.

The second measurement in the presence of the object and the calculation of the displacements are for example carried out in 7.11 and in 9.15. In both cases the absolute positions are calculated directly, without going through the

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displacements, the correction linked to the position values having already been carried out as indicated above This determination is coupled with the calculation of the average index of the object, the principle of which is given in the following paragraph.

3.17. Determination of the index and the thickness of the object
3. 17.1. Principle
When two opposing microscope objectives are used and when the observed object forms a layer between two flat coverslips, the average index of the object, if it differs from the nominal index of the objective (index of the optical liquid intended to be used with the objective), creates a spherical aberration which distorts the three-dimensional representations obtained. This spherical aberration results in phase and intensity variations of the beams measured in 3.16.2., These variations depending on the index and the thickness of the object. According to one version of the invention, a program uses the values measured in 3. 16.2. to simultaneously determine the objective displacements, the index and the thickness of the object.

The calculation carried out in 7.11. or in 9.15. is an embodiment of this aspect of the invention.

3. 17.2. Minimization algorithm
For given values of the displacements and the index and the thickness of the object it is possible to calculate the phase and intensity ratios on each parallel beam. According to one version of the invention, the calculation algorithm determines the values of the displacements and of the index and the thickness of the object which minimize the mean square deviation between the theoretical values thus calculated and the values actually measured.

This algorithm must determine an absolute minimum on a set of five parameters of a noisy function, the quadratic deviation function having, even in the absence of noise, local minima other than the absolute maximum. This problem therefore lends itself poorly to conventional minimization methods.

When the values of the parameters are known in an approximate manner, the algorithm can firstly maximize the value at the origin point obtained by compensating for the phase differences due to these parameters. A maximization of a function being equivalent to a minimization of its opposite, we will only use the term maximization to define the algorithm, but we could also speak of minimization.

According to one version of the invention, the algorithm comprises iterative phases during which it determines at each iteration an absolute maximum on a set of parameter values varying in a discrete manner, the function to be maximized having been previously filtered to remove the frequencies which would cause aliasing in a sampling at the step of variation of the parameters. According to this version of the invention, the pitch is reduced at each iteration and the central point of the set on which the parameters vary during an iteration is the maximum determined at the previous iteration.
Such an algorithm generally makes it possible to converge towards the solution despite the local maxima and the high number of parameters.

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Such an algorithm is described in 7.8.2.

3. 18. Determination of the position of the object.

The exact position of the object has no influence on the values measured in 3.16.2. and therefore cannot be obtained from these values. On the other hand, it can modify the three-dimensional representations obtained: the spherical aberration affecting a given three-dimensional representation depends on the position of the object. In the case where the index of the object differs from the nominal index of the objectives, this position must therefore be determined.

The position of the object with respect to the objectives affects the correct superposition of the two-dimensional representations adjusted in phase. If it is not correctly evaluated and taken into account as a correction factor, abnormal phase differences appear between pairs of two-dimensional representations adjusted in phase, on the part of the frequency space which corresponds to the intersection of these representations.

According to one version of the invention, the measurement of the position of the object with respect to the objectives comprises an acquisition phase, during which a series of plane frequency images are acquired, corresponding to a series of beams of variable orientation lighting. Knowing the position parameters, the index and the thickness of the object, previously calculated by the maximization algorithm described in 3.17., And knowing the sought position, a program can determine the two-dimensional representations corresponding to each plane image in frequency. According to this version of the invention, the program for determining the position of the object with respect to the objectives is therefore a minimization program which determines the value of the position parameter which minimizes the abnormal phase differences.

Such a program is detailed in paragraph 17.15.

3.19. Use of lenses with aberrations.

Designing a lens free of aberrations is difficult. As the aberrations increase in proportion to the size of the optical elements used, it is difficult to obtain a long working distance.

It is also difficult to achieve a high numerical aperture.

In the present microscope, the complex value of ground received on a receiving surface is recorded. The frequency representation of a part of the wave coming from the object can be reconstituted as soon as this part of the wave coming from the object reaches the reception surface. The frequency representation of the wave coming from the object is obtained, in all cases, by a linear relation starting from the wave reaching the reception surface. The only essential property of the objective is therefore to capture a significant part of the wave coming from the object, and to transform it into a paraxial beam reaching the reception surface. A lens having this one property can easily be designed and have a high numerical aperture and working distance. According to one version of the invention, an objective affected by aberrations greater than the limit imposed by the diffraction is used, and the calculation program inverts the linear relationship between the wave coming from the object and the wave picked up on the receiving surface so as to compensate for these aberrations.

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According to one version of the invention, the microscope objective is designed so as to verify the following property: (1) - The aberration affecting the image formed in the image plane of the objective must remain less than a fraction of the diameter of the observed part of this image
The constraint (1) makes it possible to ensure that for the major part of the studied object, the whole of the beam coming from a given point reaches the reception surface. Indeed, the spatial extent of the observed sample is limited, depending on the system, by a diaphragm or by the size of the sensor used In the presence of spherical aberration, when the distance between a point and the limit of the zone of observation is less than the characteristic distance of the spherical aberration, then a part of the rays coming from this point does not reach the reception surface and the image of this point cannot therefore be reconstructed with precision. If the area concerned remains small, this drawback is not very troublesome: this is what is guaranteed by compliance with condition (1). If the affected area was too large, the precision would be affected over the entire image.

The constraint (1) is similar to the usual constraint on spherical aberration, but is considerably lightened. Indeed, good quality results can be obtained with a spherical aberration of the order of ten wavelengths, whereas in conventional microscopy the spherical aberration must be of a fraction of a wavelength.

However, a lens that does not have certain additional properties can be difficult to use.

Indeed, the linear relation linking the wave received on the reception surface to the frequency representation of the wave coming from the object can be relatively complex. Algorithmic compensation for aberrations can then require high computational volumes. According to one version of the invention, this problem is solved by using an objective having in addition the following property: (2) - The image, in the image focal plane, of a beam which is parallel in the observed object, must be punctual.

The frequency plane image used in all of the embodiments is equivalent to the image formed directly in the image focal plane. The constraint (2) means that each point of a plane frequency image corresponds to a given frequency of the wave in the object If the constraint (2) was not respected, it would be necessary to use a generalized algorithm consisting in obtaining the value associated with a given point as a linear combination of the values detected on a set of neighboring points. Constraint (2) is relatively easy to comply with. The use of an objective which does not comply with condition (2) would only be of limited interest, but would considerably complicate the calculations necessary to obtain an image. An example of using an objective satisfying constraints (1) and (2) is described in section 7.21.

In the case of an objective meeting only conditions (1) and (2), the image reconstruction algorithm must take into account the relationship between the coordinates of a point on the plane image in frequency and the frequency corresponding wave in the object.

We denote by B ([alpha]) the image point, in the image focal plane, of a parallel beam in the object and forming in the object an angle a with the optical axis.

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(3)- La distance entre le point Braz et le point B(0) doit être proportionnelle à sina . According to one version of the invention, the algorithms are simplified by using an objective verifying in addition the following constraint:

(3) - The distance between point Braz and point B (0) must be proportional to sina.

Compliance with constraint (3) implies that the coordinates of a point on the plane frequency image are directly proportional to the components along two corresponding axes of the wave vector of the wave in the object. which considerably simplifies the calculations. If an objective complies with the constraints (1) (2) (3), the spherical aberration results only in a phase shift of each point of a given frequency representation, a phase shift which can then easily be compensated. an objective satisfying the constraints (1) (2) (3) is described in 7.20 The condition (3) is roughly equivalent to the condition of the sine of Abbot.

In an objective verifying only the constraints (1) (2) (3), the image is disturbed near the diaphragm over a distance equivalent to the characteristic distance of the spherical aberration This disturbance is eliminated by the use of an objective classic devoid of spherical aberration. which therefore allows a priori to obtain the best images. However, using a lens that only satisfies (1) (2) (3) can significantly ease lens design constraints. This allows a higher working distance lens, a cheaper lens, or a higher numerical aperture lens to be obtained.This technical solution may therefore be preferable in certain cases.
The use of such a microscope objective requires the algorithmic compensation of the phase differences affecting the plane frequency image and which are the consequence of the spherical aberration. This implies the determination of the function characterizing the spherical aberration induced by the microscope Due to the fact that the objective presents a symmetry of revolution, the phase shift affecting a point of a plane frequency image depends only on the distance between this point and the optical center. The spherical aberration can therefore be characterized by a one-dimensional function representing the phase shift as a function of this distance.

According to one version of the invention, this function can be obtained by the optical calculation program used for the design of the lens. Indeed, this program makes it possible to perform ray plots and can be easily improved to also allow optical path calculations. The phase shifts being proportional to the optical path differences affecting rays coming from the same point, they can be deduced from this type of geometric considerations.

According to another version of the invention, this function can be measured by optical means According to this version of the invention: - two identical microscope objectives are used facing each other - an illuminating wave centered on a point on the plane or a first objective normally forms the image of the observed sample.

the wave received is detected in the plane where the second objective forms the image of the observed sample.

In the absence of spherical aberration, the phase of the detected wave must be constant. In the presence of spherical aberration, the phase difference due to the aberration is twice the difference due to a single microscope objective. This makes it possible to obtain the desired function.

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3. 20. Compensation for spherical aberration and position deviations.

The spherical aberration due to the index of the object. spherical aberration due to lens properties, and lens positioning errors, all result in applied phase shifts to the frequency plane image. These phase shifts must be corrected to obtain a good quality image.

According to one version of the invention, this correction is carried out by multiplying each plane image in frequency by a correction function taking into account the various parameters determined above. The computation of such a function is exposed in 7.16. and the multiplication operation is performed for example in step 2 of the algorithm described in 7.17. In the case where a lens exhibiting spherical aberration is used, the calculation described in 7.16 should be changed as indicated in 7.20.

3. 21. Regular sampling
When two microscope objectives are used, the sampling step on the frequency plane image generated from one of the receiving surfaces can be taken as the basis of the sampling step of the three-dimensional representation of the object following two corresponding axes If no precaution is taken: - The image points of the lighting waves on this plane frequency image do not correspond to integer values of the coordinates in pixels.

- In the case where two objectives are used, the sampling step and the axes on the plane frequency image generated from a reception surface associated with the opposite objective do not correspond to the step sampling and to the axes of the three-dimensional representation of the object
It follows that the sampling of the three-dimensional representation of the object is not regular According to one version of the invention, this sampling is made regular along two axes corresponding to the axes of the plane frequency representations. The quality of the three-dimensional representation of the object is then significantly improved.
The plane frequency image can in particular be modified, due to imperfections of the optical system, by rotation or by homothety. To obtain regular sampling, it is necessary to cancel or compensate for these imperfections.

On the other hand, in Embodiment 4, there must be point-to-point correspondences between the different SLMs used and the CCDs. The realization of these correspondences requires the same type of adjustments.

According to one version of the intention, the microscope therefore comprises one or more optical devices allowing a rotation adjustment of the images generated in the frequency planes, and / or one or more devices allowing the magnification adjustment of the images generated in the planes of frequency. frequency
3.21.1. Adjustment of the scale of the representation (homothety)
This setting is actually a magnification setting. According to one version of the invention, the magnification of an image is adjusted using an optical system of variable focal length. Such

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The system may for example be composed of two lenses, a variation in the distance between said lenses resulting in a variation in the focal length of the assembly. Such a device is used in embodiments 4 and 5 and is described in 8.1.4.1.

3. 21.2. Rotating an image
According to one version of the invention, this adjustment is carried out using a device consisting of a first group of fixed mirrors and a second group of mirrors, verifying the following conditions: - the first group of mirrors is symmetrical the wave vector of the incident beam with respect to a given axis.

the second group of mirrors symmetrizes the wave vector of the incident beam with respect to a second axis.

- The second group of mirrors is movable in rotation about an axis orthogonal to the plane of these two axes.

The assembly of the two groups of mirrors then has the effect of causing the beam represented in a frequency plane to rotate, the angle of rotation being twice the angle between the two axes of symmetry. Such a device is used in embodiments 4 and 5 and is described in 8.1.4.2.

3. 22. Phase shift system
The phase shift system used can be a piezoelectric mirror, which is the most common solution. However, used at high speed, such a mirror generates \ ibrations. According to an advantageous version of the invention, a birefringent plate is used as a phase shift system inducing a phase shift of 120 degrees between its two neutral axes, preceded by a polarization rotator making it possible to orient the electric field vector of the beam along one or the other of said neutral axes, and followed by a second polarization rotator making it possible to return the direction of polarization of the beam at the outlet of the device to its direction at the inlet of the device. This system only allows an offset of 120 degrees, it is necessary to combine two in series to obtain an offset of -120, 0, or +120 degrees.

3. 23. Data processing method in the case of limited RAM
The three-dimensional frequency representation calculations use large amounts of data. Since these data are normally accessed in random order, they cannot be stored during calculations on a sequential access medium such as a hard disk and can be stored on a random access medium such as internal computer memory (RAM).

According to an advantageous version of the invention, adapted to the case where the system does not have sufficient random access memory to be able to store all the data, the calculation algorithm is modified so as to process the data block by block, a block corresponding to a large quantity of data which can then be stored sequentially on a sequential access medium and loaded into central memory only during the processing time of said block. To this end: - The modified algorithm performs horizontal plane by horizontal plane processing in a three-dimensional space, each horizontal plane being stored on the sequential access medium in a single block

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- In order to also be able to carry out processing along the vertical dimension, the algorithm integrates axis exchange phases which allow the vertical axis to be temporarily brought back to a horizontal plane.

- The axis exchange procedure operates block by block, the blocks generally having equal or similar dimensions according to the two axes to be exchanged and having for size in bytes the maximum size that can be stored in the main memory of the system (RAM memory to random access).

This method is implemented in embodiment 1 and described in paragraph 5.21 3.24. Images generated by the microscope.

The three-dimensional representations generated by this microscope can be stored and transmitted as a three-dimensional array of complex numbers. According to one version of the invention, it is possible to generate from this table sections or two-dimensional projections representing either the index or the absorbency in the object.

In the case of a projection, a projection of the three-dimensional image is generated on a projection plane and in a projection direction orthogonal to the projection plane. Each point of the projection plane is obtained from the set of values of the three-dimensional spatial representation which lie on a straight line passing through this point and directed in the direction of projection.

According to one version of the invention, the value associated with each point of the projection plane is obtained by extracting the maximum value from the real or imaginary part or from the modulus of the points of the three-dimensional spatial representation situated on the corresponding straight line.

According to one version of the invention, the value associated with each point of the projection plane is obtained by integrating the complex value of the points of the three-dimensional spatial representation situated on the corresponding straight line. It is then possible to visualize either the real part or the imaginary part of the projection thus produced. According to this version of the invention, the projection can be obtained more rapidly in the following manner, in two steps: step 1: extraction, in frequency representation, of a plane passing through the origin and orthogonal to the direction of projection. step 2: inverse Fourier transformation of this plane.

The two-dimensional table thus obtained constitutes a projection along the direction which was used to extract the frequency plane.

3. 25. Positioning system of ontic elements.

The embodiments described require the use of numerous positioners of good precision. These positioners are costly elements that are poorly suited to mass production and are liable to become out of adjustment over time.

According to one version of the invention, this problem is solved by using removable positioners during the manufacture of the microscope, each element being positioned and then fixed by a binder, for example an adhesive, and the positioner being removed after final solidification of the binder.

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3. 26. Protection system against shock, vibration and dust.

The microscopes described are made up of a set of elements fixed to an optical table During a possible transport, even slight shocks can cause a disturbance of the system During prolonged use, dust can be deposited on the various elements optics
According to one version of the invention, most of the optical device is included in a hermetically sealed box which is itself included in a larger box, the connection between the two boxes being made by means of dampers arranged on each side of said hermetically sealed box This system protects the microscope from shocks and dust while allowing good suspension of the optical table 4. Brief description of the drawings:
Fig.1 to 24 relate to a first embodiment. FIG. 1 is a general diagram of the optics of the microscope. FIGS. 2 and 3 represent the detail of the angular positioner (1 10) already represented in FIG. 1. Fig.4 is a general diagram of the vertical mechanical support and vibration damper of the microscope. Fig.5 shows the detail of a tensioner from Fig.4. Fig. 6 shows an example of dimensioning of the optical part. Figs. 7 to 9 and 15 and 16 are graphical representations serving as support for the explanation of the operating principle of the microscope. Fig. 10 shows the algorithm of a program for adjusting the drive voltages of the piezoelectric (122). Fig. 11 represents the detailed algorithm of an image taking procedure used in the previous program Fig 12 represents the algorithm of a program allowing to adjust the intensity attenuator consisting of the polarizer (105) and of the polarization rotator (104) and obtain its characteristics. Fig. 13 represents the detailed algorithm of a 'low level' image capture procedure used in the previous program and in the 2D or 3D image acquisition programs. Fig. 14 shows the algorithm of a focusing program for obtaining a 2D image and focusing the microscope objective (113).

Fig. 17 serves as a support for the explanations concerning the adjustment of the condenser Fig. 18 represents the algorithm of the three-dimensional image acquisition program Fig. 19 represents the algorithm of a calculation program generating from the results of the 'acquisition of a three-dimensional representation of the object. Fig. 20 schematically represents an operation performed by the first part of this program. Fig. 21 represents the detail of the algorithm of this first part. Fig. 22 schematically represents an operation performed by the second part of this program. Fig. 23 represents the algorithm of a third part of this program. Fig. 24 represents the algorithm of a last part of this program.

Figs. 25 and 26 relate to a second embodiment. Fig. 25 is a general diagram of the optical part of the microscope. Fig. 26 shows the algorithm of the 'low level' image acquisition procedure used.

Fig. 71 illustrates a specific apparatus used in the adjustment operations for embodiments 3 to 5.

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Figs. 27 to 59 relate to a third embodiment. Figs. 27 and 28 are a general diagram of the optical part of the microscope. Fig. 29 schematically shows the optical path of the rays between the objective and the sensor. Fig. 30 shows the beam attenuation device used. Fig. 31 is a block diagram illustrating its operation in the event that there is indeed attenuation. Fig. 32 is a block diagram illustrating its operation in the case where there is no attenuation. Fig. 33 shows the phase shift device used. Fig. 34 is a block diagram illustrating its operation. Fig. 35 repeats FIG. 34 indicating the phase shifts of the various vectors. Fig. 36 repeats Fig. 34 indicating the modulus of the different vectors. Fig. 37 shows a basic unit of the beam deflection device used. Fig. 38 represents the beam deflection and switching device, formed by association of these elementary units. Figs. 39 and 40 are block diagrams for understanding the operation of an elementary unit. Fig. 39 corresponds to one direction of deviation and Fig. 40 to the other possible direction of deviation. Fig. 41 illustrates the calculation of the beam deflection by a prism. Figs. 42 to 44 illustrate steps in a phase rotator labeling procedure. Fig. 42 illustrates the first step and Figs. 43 and 44 illustrate a second step, in two different cases. Fig. 45 illustrates the calculation of the path difference produced on a parallel beam by an object of given index and thickness. Fig. 46 illustrates the calculation of the path difference produced on a parallel beam by a displacement of the point of origin of the reference wave, with respect to which the optical path is calculated. Figs. 47 to 50 and Fig. 60 illustrate an algorithm for calculating the index and thickness values of the sample as well as the displacement of the point of origin of the reference wave. Fig. 47 corresponds to the highest level of this algorithm and FIG. 50 at the lowest level. Fig. 51 represents in a three-dimensional space various vectors used to evaluate the effect on the diffracted wave of the polarization of the illumination beam. Fig. 52 represents in the plane of a sensor vectors deduced from the previous ones. Fig. 53 represents an algorithm for obtaining control indices of the beam deflector from the coordinates of the direct point of impact sought for the illumination beam. Fig. 54 illustrates the calculation of the path difference of a wave coming from a point of the object with respect to a reference wave. Fig. 55 illustrates the calculation of the path difference between a wave coming from a point of the object and the reference waves used on the two sensors of the system. Fig. 56 illustrates the trajectory, on one of the sensors, of the point of direct impact of the illumination wave, during an image taking procedure. Fig. 57 represents an algorithm determining the position of the object with respect to the objectives. Fig. 58 illustrates how the three-dimensional frequency representation of the object is obtained by superimposing two-dimensional representations. Fig. 59 represents in section the three-dimensional frequency representation of the object.

Figs. 61 to 70 and 72 relate to a fourth embodiment of the invention, constituting the preferred embodiment. Figs. 61,62,63 constitute an overall diagram of the optical part of the microscope. Figs. 64 and 65 illustrate the operation of the beam diverter used in this embodiment. Fig. 66 illustrates the operation of a direct illumination background suppression system.

Figs. 67 and 68 illustrate the principle used to control the path of the beam. Figs. 69 and 70

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illustrate a system used to effect a controlled rotation of a beam. FIG. 72 illustrates the image to be obtained in one of the adjustment operations
Figs. 73 to 82 relate to a fifth embodiment. Figs. 73 and 74 constitute an overall diagram of the optical part of the system. Figs. 75 and 76 illustrate images obtained during an intermediate calculation step. Fig. 77 illustrates an algorithm used to determine the driving sequence of a beam deflecting mirror and to determine the driving sequence of a stopping the direct illuminating wave. Figs. 78 and 79 represent images obtained during an adjustment step. FIG. 80 illustrates the principle used to vary the polarization of the illumination background and the direction of analysis. Fig. 81 shows the points corresponding to various illumination waves used in a phase adjustment algorithm Fig. 82 shows a diaphragm used in this embodiment
Figs. 83 to 85 relate to a device for positioning and permanently fixing optical elements. Fig. 83 and Fig. 84 show parts of this device and Fig 85 shows the whole of this device.

Figs. 86 to 88 relate to a device for protecting the microscope from impact and dust. Fig. 86 represents a block diagram of the device. Figs. 87 and 88 show a specific configuration adapted to the case of embodiment 4.

5.Dcscrii)tion d'un premier mode de réalisation:
Ce mode de réalisation est le plus simple et il est peu coûteux. Figs. 89, 90 and 91 relate to the use of non-stigmatic lenses. Fig. 89 shows an example of the realization of such a goal. Fig. 90 serves as a support for the statement of the constraints to be verified by this objective. Fig. 91 shows a frequency plane image obtained using this objective

5.Dcscrii) tion of a first embodiment:
This embodiment is the simplest and it is inexpensive.

la société Displaytech Inc., 2602 Clover Basin Dr., Longmont, CO 80503, Etats-Unis. Il traverse ensuite un polariseur (105). Le faisceau traverse ensuite un achromat (106) puis un diaphragme (107) et un achromat (108). Il est réfléchi par un miroir (109) fixé sur un positionneur angulaire (110) commandé par deux moteurs pas à pas. Il traverse ensuite un achromat (124) puis un condenseur (111) et atteint l'objet (112). Le condenseur est par exemple un condenseur aplanétique/achromatique Nikon d'ouverture 1.4. prévu pour une source de lumière située à l'infini. L'objet (112) est un échantillon placé entre lame et lamelle, dont l'absorptivité et les variations d'indice sont relativement faibles, et dont onveut obtenir une image tridimensionnelle. L'achromat (124) est placé aussi près que possible de la lentille la plus basse du condenseur (111), éventuellement dans le corps du condenseur. Le point focal objet de l'achromat (124) est 5.1. Material characteristics:
A laser beam of wavelength 633 nm polarized in the direction orthogonal to the figure is emitted by the helium-neon laser (100) and passes through the filter (101) consisting of zero, one or more stacked filters, in Schott tinted glass It is then separated into an illumination beam Fe and a reference beam Fr by the semi-transparent mirror (102). The illumination beam then passes through a filter (103) of the same type as (101), then a polarization rotator (104) based on ferroelectric liquid crystals and marketed by

Displaytech Inc., 2602 Clover Basin Dr., Longmont, CO 80503, USA. It then passes through a polarizer (105). The beam then passes through an achromat (106) then a diaphragm (107) and an achromat (108). It is reflected by a mirror (109) fixed on an angular positioner (110) controlled by two stepper motors. It then passes through an achromat (124) then a condenser (111) and reaches the object (112). The condenser is for example a Nikon aplanatic / achromatic condenser of aperture 1.4. intended for a light source located at infinity. The object (112) is a sample placed between a slide and a coverslip, the absorptivity and index variations of which are relatively small, and of which a three-dimensional image is to be obtained. The achromat (124) is placed as close as possible to the lowest condenser lens (111), possibly in the condenser body. The object focal point of the achromat (124) is

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coincident with the center of rotation of the mirror (109). The lenses (106) and (108) must be such that the laser beam focuses in the object focal plane of the assembly consisting of the condenser (111) and the achromat (124). and has a sufficient opening when it arrives in this focal plane. The beam is therefore again parallel when it reaches the object (I 12). The plane of the object should be horizontal so that the optical oil needed to use the objective and the immersion condenser does not leak. The optical axis is therefore vertical and the elements of Fig.1 are fixed on a vertical plate (300) shown in Fig.4.

The angular positioner (110) is detailed in Figs. 2 and 3. Fig 2 shows a plate on which the mirror (109) is glued, seen from below. Fig. 3 represents the entire device seen from the side The plate (200) is placed on movable contact pads (205) and (212) whose points of contact with the plate are at (203) and (204), and on a fixed contact pad whose point of contact is at (201), the plate (200) being slightly hollowed out at this point. It is held by a spring (210) fixed to the plate at (202) and to a fixed stud (211). The movable contact pad (205) moves vertically in translation and is integrated into an actuator with a conventional axis: it is locked in rotation by a flexible (207) and is driven in translation by the rotation of the rod (206) leaving the stepping motor (208) which is for example a stepping motor 400 steps / revolution. The drive is done for example by means of a screw thread. The contact pad (212) is likewise driven by the rotation of the motor (213). The fixed point of contact (201) must be in the optical axis of the objective (113) and the center of the mirror must be on this point of contact. The motors (208) and (213) are fixed on a plate (209) which is itself fixed on the support plate (300). The center of rotation of the mirror, which must be positioned on the optical axis, is a point on the reflecting surface of the mirror, located on a line orthogonal to the plane of the mirror and passing through the center of (201).

The wave from the object (112) passes through the microscope objective (113). This objective is a plane objective (which gives a plane image of a plane), with a large aperture (for example 1.25), with immersion, and forming an enlarged image of the object at a finite distance.

In the plane where the objective normally forms the image of the object to be observed, a diaphragm (114) is interposed allowing spatial filtering of the image Behind this plane, an achromat (115) is positioned whose focal plane object must be confused with the image focal plane of the objective (113). A second achromat (117) whose image focal plane is in the plane of a CCD sensor (118) forms in the plane of this CCD the image of the image focal plane of the objective (113). The CCD (118) is integrated with a camera (119) outputting an analog video signal and a pixel clock.

The reference beam first passes through a filter (120) of the same type as (101) and then is reflected by a mirror (121) mounted on the mobile end of a piezoelectric translator (122). It then passes through a lens (123) which focuses the beam at a point. The divergent beam coming from this point is partially reflected by the semi-reflecting mirror (116), which superimposes it on the beam coming from the object and makes it possible to record their interference on the CCD (118). The focal point of the beam coming from the lens (123) must have its virtual image after reflection on the semi-transparent mirror (116) at the center of the image of the diaphragm (114) by achromat (115). The piezoelectric translator (122) makes it possible to modulate the phase of the reference beam.

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The manual positioners used in the system are not shown in the figure. The microscope objective (113) is mounted on a focusing device. The laser (100) is mounted on a two-axis positioner for adjusting the direction. The fixed part of the piezoelectric battery (122) is mounted on a two-axis positioner allowing rotation with respect to an axis orthogonal to the plane of the figure and passing through the center of the mirror (121), and with respect to a second axis located in the plane of the mirror (121), orthogonal to the first axis and passing through the center of the mirror (121). The condenser is mounted on a three-axis positioner in translation. The camera (119) is mounted on a three-axis positioner in translation. The angular position of the semi-transparent mirrors (102) and (116) can be adjusted manually. The lens (106) can be translated along its axis. The object (112) is attached to a two-dimensional positioner allowing it to be moved in a horizontal plane. The diaphragm (114) can be moved in a horizontal plane.

The assembly is fixed on the support plate (300), on the side of the plate opposite to the point of view of Fig.4. This plate is fixed to two triangular plates (301) and (302) themselves fixed to a square base (303). The plate (300) is also attached directly to the square base (303). The plates (300) (301) (302) (303) are made of rigid AU4G aluminum alloy, for example 20 mm thick.The fixing of the plates can be done by screws and tapped holes, and must be made in a sufficient number of points to ensure perfect rigidity of the assembly. This keeps the system vertical while ensuring sufficient rigidity. The assembly is placed on an anti-vibration support consisting of a 30 mm thick granite plate (304) placed on a low pressure inflated van air chamber (305) which dampens vibrations and which is itself placed on a rigid wooden table (306). A rigid wooden frame (311) is fixed in height via uprights (307) (308) (309) (310) to the table (306). The whole wooden construction is reinforced so as to be perfectly rigid. The top of the plate (300) is connected by tensioners (3 12) (3 13) (3 14) (3 15) to the corners of the rigid frame. Each tensioner, detailed in Fig. 5, consists of a set of elastic bracelets (316) stretched between two rings (318) (317), these rings themselves being fixed to the plate (300) and to the frame ( 311) by cords (320) (319), the whole being put under tension. The air chamber (305) makes it possible to have, for the assembly suspended in AU4G, low resonance frequencies for the translational movements, of the order of 2 Hz. The tensioners (312) to (315) make it possible to limit the sway of the whole. The sway frequency can be estimated simply by imparting a slight pendulum motion to the assembly and measuring the time it takes to have it. for example, ten swings. The swing frequency is adjusted by modifying the number of elastic bands used for each tensioner. The higher it is, the more the swing frequency increases. It must be adjusted so that the swing frequency is of the same order as the resonant frequency for translational movements, ie around 2Hz.

The mounting of the various elements on the plate (300), and in particular of the mirrors and semi-transparent mirrors, must be carried out in such a way as to ensure maximum rigidity of the assembly. All usual precautions must be taken to limit vibrations.

The following details relate to a particular example of practical sizing of the device. The distances quoted are shown in Fig. 6. Dimensions given are approximate

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and some of them must be corrected in an adjustment phase. The lens (106) is an achromat with a focal length of 10 mm. The lens (108) is an achromat with a diameter of 24 mm and a focal length of 120 mm. The distance D7 between (106) and (108) is 250 mm. The distance D6 between the lens (108) and the center of the mirror (109) is about 100 mm. The distance D5 between the center of rotation of the mirror (109) and the achromat (124) is 120 mm. The achromat (124) is placed approximately 5mm from the lowest condenser lens in the condenser body. The condenser is an achromatic / aplanatic brightfield 1.4 aperture immersion condenser, for example the Nikon model. The microscope objective is a planachromatic objective x 100 of aperture 1.25, at finite distance, forming the image 160 mm from the neck of the objective, focal length approximately 1.8 mm. for example the Zeiss model. The distance D4 between the neck of the objective and the diaphragm (114) is 160 mm. The distance D3 between the diaphragm (114) and the achromat (115) is 20 mm. The achromat (115) has a focal length of 200mm and a diameter of 30mm and its most domed face is oriented towards the semi-transparent mirror (116). The achromat (117) has the same characteristics and its more convex face is also oriented towards the mirror (116). The distance D2 between the two achromats is 85 mm. allowing the insertion of a semi-transparent mirror (116) of sufficient dimensions. The distance between the achromat (117) and the CCD (118) is 200 mm. The lens (123) has a diameter of 4mm and a focal length of 6mm. The distance D9 between this lens and the optical axis is approximately 70 mm. The distance D8 between the achromat (115) and the center of the semi-transparent mirror (116), located on the optical axis, is approximately 45 mm. The laser (100) is a helium-neon laser with a wavelength in vacuum 1 = 633 nm polarized in the direction orthogonal to the figure, with a power of approximately 0.5 mW, with a beam diameter of 0.5 mm. The CCD sensor is a square pixel sensor, the area of the pixel being approximately 8.5 x 8.5 micrometers, and the effective area in pixels being of a dimension at least equal to 512 x 512 pixels. The camera outputs a CCIR video signal and a pixel clock, and its exposure time is half the length of a field, or 1 / 50th of a second for a non-interlaced CCIR camera whose fields are 1 / 25th of a second. This allows a delay between the end of a field and the start of the next exposure period, which can be used to modify the lighting conditions without the transition influencing the image. The piezoelectric positioner (122) is a pre-stressed cylinder-shaped piezoelectric 'stack' with a fixed body and an end that moves 15 microns at an applied voltage of 100 volts.

réel, échantillonne le signal sur 8 bits et acquiert des images de taille Jrpix x va- ou hpix et l'pix sont supérieurs à 512 et multiples de 4 Les pixels sont échantillonnés suivant l'horloge pixel, donc correspondent exactement aux pixels du CCD. Le positionneur piézoélectrique est piloté directement par une carte de conversion digitale/analogique sortant un signal compris par exemple entre zéro et Uma@, avec

par exemple f rmax = 10 volts. Une résistance est interposée entre la sortie de la carte de conversion et les bornes de l'actionneur piézoélectrique de manière à limiter le courant. Sa valeur est réglée de sorte que le temps de montée de la tension aux bornes de l'actionneur (122) soit d'environ 1 ms. Le rotateur de The calculation system is for example a 'PC' type computer, equipped with appropriate acquisition and control cards and possibly additional calculation means, operating for example under the Windows 95 operating system. video signal, running in time

real, samples the signal on 8 bits and acquires images of size Jrpix x va- or hpix and the pixel are greater than 512 and multiples of 4 The pixels are sampled according to the pixel clock, therefore correspond exactly to the pixels of the CCD. The piezoelectric positioner is controlled directly by a digital / analog conversion card outputting a signal ranging for example between zero and Uma @, with

for example f rmax = 10 volts. A resistor is interposed between the output of the conversion board and the terminals of the piezoelectric actuator so as to limit the current. Its value is set so that the voltage rise time across the actuator (122) is approximately 1 ms. The rotator

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polarization (104) is equivalent to a half-wave plate whose axis can rotate and has two equilibrium positions separated by an angle of 45 degrees. If it is positioned so that the polarized beam is parallel to this axis in one of the equilibrium positions, it will rotate the beam 90 degrees in the other position. The polarization rotator is controlled by application of a bipolar voltage, -5V corresponding to a position of equilibrium and +5 Vat 'other. Each terminal of the bias rotator is connected to a 0 / 5V output of a digital output board, and its two positions are controlled by applying in one case OV to one output and 5V to the other, and inverting for the other position. Stepper motors (208) and (212) are also driven from the computer, via a control board and appropriate electronics. The computer has sufficient internal memory (at least 32 MB) and a sufficiently large hard disk (at least 4 GB).

5.2 Miscellaneous agreements
The following conventions will be used in the remainder of this description, including in the other embodiments: The letter / sometimes represents an index, sometimes the pure imaginary complex number of modulus 1.

In the case where there may be ambiguity, the complex number / will be denoted by J '- the sign = symbolizes the assignment operation or the equality depending on the case - the expression a + = h signifies a = a @ b -a multiplied by b is written ab, ab or a * b -the modulus of a complex number z is denoted # z # and its conjugate is denoted z.

!-première permutation: E[i]=E[(i+fdiml2)%fdrnr] 2- transformation de Fourier usuelle du tableau E 3- permutation inverse: E[r]=E[(i+fdrml2)%jdinr] ou le signe % désigne le modulo -La transformée de Fourier bidimensionnelle d'un tableau de lignes et colonnes est obtenue en effectuant la transformation de Fourier monodimensionnelle définie ci-dessus sur chaque ligne du tableau, ce qui génère un tableau intermédiaire, puis en effectuant cette transformation sur chaque colonne du tableau intermédiaire pour obtenir le tableau transformé. - the expression a% b will mean a modulus b - if a is a Boolean integer, a is its complement, that is to say 0 = 1 and I = 0 0 - The discrete Fourier transform, in its most usual form, transforms a Dirac located at the origin to a constant and transforms a constant into a point located at the origin. The discrete Fourier transform used throughout this patent transforms a constant into a Dirac located in the middle of the transformed array and transforms a Dirac located at this point into a constant This means that the * zero 'in frequency or in position is placed in the middle of the table and not at the origin of the table. This modified transform is obtained from the usual form by performing a permutation of indices before and after the transformation. An array E of dimension hunger is transformed as follows

! -first permutation: E [i] = E [(i + fdiml2)% fdrnr] 2- usual Fourier transformation of table E 3- inverse permutation: E [r] = E [(i + fdrml2)% jdinr] or the sign% designates the modulo -The two-dimensional Fourier transform of an array of rows and columns is obtained by performing the one-dimensional Fourier transformation defined above on each row of the array, which generates an intermediate array, then by performing this transformation on each column of the intermediate table to obtain the transformed table.

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-Likewise, the three-dimensional Fourier transform consists in carrying out successively along each axis one-dimensional transforms extended to the whole of the table.

5.3.Operating principles
The value of the light wave coming from the object under a given lighting at a point of the CCD sensor is obtained from the recording of three interference figures received on the sensor, the phase of the reference wave being shifted 120 degrees between each of these figures.

trois enregistrement successifs sont: So = s + r, sI = s + re 3 , S2 = S + re .Les intensités enregistrées successivement sont donc: 1soi = 12 + 11'12 + (sr + sr) 2,r 2 1Sil I2 = 1 + II'IZ + SY2 3 2ffJ ISII 11'1 sre sre ISZ IZ = IS'I2 ( 2ff 2ffJ 1s2 1 2 + ri + sre sre On peut inverser ces formules et on obtient: s Irl = ~II 1 (2Jsl-lsJ z - Ls212 ) + j 2Ij.l ( s 2 - .s '
La valeur ci-dessus est la vibration lumineuse provenant de l'objet seul, la référence de phase étant conventionnellement égale à zéro pour une vibration en phase avec l'onde de référence. Ce calcul permet donc de reconstituer la valeur complexe de l'onde à partir des enregistrements d'intensité. If s is the light vibration coming from the object and r is the light vibration constituting the reference wave during the first recording, the total light vibrations reaching the sensor during the 2 # 2 #

three successive recordings are: So = s + r, sI = s + re 3, S2 = S + re The intensities recorded successively are therefore: 1soi = 12 + 11'12 + (sr + sr) 2, r 2 1Sil I2 = 1 + II'IZ + SY2 3 2ffJ ISII 11'1 sre sre ISZ IZ = IS'I2 (2ff 2ffJ 1s2 1 2 + ri + sre sre We can invert these formulas and we obtain: s Irl = ~ II 1 (2Jsl -lsJ z - Ls212) + j 2Ij.l (s 2 - .s'
The above value is the light vibration from the object alone, the phase reference conventionally being zero for vibration in phase with the reference wave. This calculation therefore makes it possible to reconstitute the complex value of the wave from the intensity recordings.

note('x,('y. ses coordonnées en pixels. L'objectif vérifiant la condition des sinus, la déviation en sortie d'objectif d'un rayon originaire d'un point central de l'objet est proportionnelle au sinus de son angle d entrée dans l'objectif, qui vaut sin = . .r 2 + fy 2 + z , ou ,fx, jy., f ) sont les coordonnées du vecteur fréquence spatiale du faisceau en entrée de l'objectif, de norme - 1 ou ;. est la longueur d'onde dans # le milieu observé, et de direction la direction du faisceau. Le reste du système optique étant paraxial, la déviation du point d'arrivée du rayon sur le capteur par rapport au centre optique du capteur est également

proportionnelle à cette grandeur, et donc les coordonnées i C\j - r.. de ce point par rapport au centre By construction, each point of the CCD sensor corresponds to a pure frequency fc of the wave coming from the sample. We call the optical center of the sensor the point of the sensor illuminated by a ray entering the objective with a direction strictly parallel to the axis of symmetry of the latter and we

note ('x, (' y. its coordinates in pixels. The objective verifying the condition of the sines, the deviation at the objective output of a ray originating from a central point of the object is proportional to the sine of its entry angle into the objective, which is sin =. .r 2 + fy 2 + z, or, fx, jy., f) are the coordinates of the spatial frequency vector of the beam entering the objective, with norm - 1 or;. Is the wavelength in # the observed medium, and direction the direction of the beam. The rest of the optical system being paraxial, the deviation of the point of arrival of the ray on the sensor with respect to the optical center of the sensor is also

proportional to this magnitude, and therefore the coordinates i C \ j - r .. of this point with respect to the center

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optique sont proportionnelles à ( fx, fy,) . Dans le cas ou le capteur a des pixels carrés, le vecteur fréquence en entrée de l'objectif du rayon qui illumine le point du capteur de coordonnées (I.j) vaut donc: .ic'v= K7 (r x, j-('y, 2 -(i-C'x)Z -(J--y.12 ou K est une constante à déterminer. On appellera 'fréquence caractéristique' du point ce vecteur fréquence.

optics are proportional to (fx, fy,). In the case where the sensor has square pixels, the frequency vector at the input of the objective of the ray which illuminates the point of the coordinate sensor (Ij) is therefore worth: .ic'v = K7 (rx, j - ('y , 2 - (i-C'x) Z - (J - y.12 where K is a constant to be determined. We will call 'characteristic frequency' of the point this frequency vector.

Knowing the characteristic frequency of each point of the sensor and the light vibration coming from the object and received at this point, we therefore obtain, for a given illumination of the sample, the frequency representation of the wave coming from this sample.

lumineuse AeJ2'f 'r ou fe est le vecteur fréquence spatiale du faisceau d'éclairage et r le rayon-vecteur au point considéré de l'objet, l'origine étant prise au point d'origine virtuel de l'onde de référence. When a sample that is thin enough, not very absorbent and has small variations in index is crossed by a parallel laser beam, each point of the sample is subjected to a vibration

AeJ2'f 'r where fe is the spatial frequency vector of the lighting beam and r the ray-vector at the point considered of the object, the origin being taken at the virtual point of origin of the reference wave.

qui se superpose à l'onde d'éclairage. Un petit volume (/l'créc une onde secondaire AeJ27ife rll(r)dT' ou u(r) est un coefficient complexe dont la partie réelle est liéeà l'absorptivité locale de l'échantillon et la partie imaginaire à son indice. L'image tridimensionnelle de l'échantillon que ce microscope génère est l'ensemble des valeurs u(r) en chaque point de l'échantillon. The absorbency and index variations of the sample result in the appearance of a secondary wave

which is superimposed on the lighting wave. A small volume (/ the créc a secondary wave AeJ27ife rll (r) dT 'or u (r) is a complex coefficient whose real part is related to the local absorptivity of the sample and the imaginary part to its index. L The three-dimensional image of the sample that this microscope generates is the set of u (r) values at each point of the sample.

.s(r)e J2ifc,r . Un petit volume dl'de l'objet, de rayon-vecteur l', éclairé par une onde plane de fréquence fe , crée donc au point du capteur de fréquence caractéristique fc une vibration Ac 2f' fc'ru(r)u'I' qui se superpose à la vibration principale. Intégrée sur l'ensemble de l'objet, la vibration reçue en un point du capteur \aut donc s(P) = f f f Aej2tr(fe-lc ).ru(r)dV . Cette vibration est donc un élément de la transformée de Fourier de la fonction u(r) , correspondant à la fréquence de Fourier ft = fc - fc Le principe de ce microscope est d'enregistrer cette vibration pour un ensemble de fréquences fe et fc, puis de reconstituer la représentation fréquentielle de u(r) et finalement u(r) en inversant la transformée de Fourier. When a point of the sample, of radius-vector r, locally emits a light vibration s (r), the light vibration received on the sensor at a point of characteristic frequency fc is then equal to

.s (r) e J2ifc, r. A small volume dl 'of the object, of ray-vector l', illuminated by a plane wave of frequency fe, therefore creates at the point of the characteristic frequency sensor fc a vibration Ac 2f 'fc'ru (r) u'I 'which is superimposed on the main vibration. Integrated on the whole of the object, the vibration received at a point of the sensor \ aut therefore s (P) = fff Aej2tr (fe-lc) .ru (r) dV. This vibration is therefore an element of the Fourier transform of the function u (r), corresponding to the Fourier frequency ft = fc - fc The principle of this microscope is to record this vibration for a set of frequencies fe and fc, then to reconstitute the frequency representation of u (r) and finally u (r) by inverting the Fourier transform.

The samples studied are not very absorbent and have small variations in the refractive index.

A = -7T Cirnrrx-C'x, jmax-C'y, kz -inrax-C'x)Z -( j mz-('1.1Z Consequently, the lighting wave remains very intense and illuminates a point of the CCD, which will be called the point of impact of the lighting wave, and which is the point of the CCD where the light vibration received is the most high If this point has for coordinates (imax, jmax) then the frequency of the lighting wave is:

A = -7T Cirnrrx-C'x, jmax-C'y, kz -inrax-C'x) Z - (j mz - ('1.1Z

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représentation fréqtientielle tridimensionnelle (et non plus bidimensionnelle comme dans le cas ou un seul enregistrement est utilisé). A partir de cette représentation tridimensionnelle dans l'espace des fréquences, on peut générer la fonction u(r) par transformation de Fourier inverse. FIG. 7 shows the set (500) of the characteristic frequencies corresponding to the points of the sensor. It is about a portion of sphere of radius limited by the opening of the objective; centered on the optical # axis (501) of the system. An example of a lighting frequency vector (502) is superimposed on this set. Finally, the set (503) of the corresponding frequencies ft = fc-fe is deduced therefrom. When the lighting frequencies (502) are sorted according to an arc of a circle (504) as indicated in FIG. 8, each position of the lighting frequency vector corresponds to a set of frequencies f @ forming a portion of sphere FIG. 9 shows in section a set of such arcs of a sphere (505) (506) and others, generated when the illumination frequency vector moves on the arc of a circle (504). When the displacement of the illumination frequency vector on the circular arc (504) becomes continuous, a volume is generated, the sectional view of which is shown in FIG. 15. In top view, the arc of a circle (504) is represented by the segment (1102) of FIG. 16. When the end of the lighting frequency vector travels through several arcs of a circle so as to generate a path shown in top view in FIG. 16, the volume generated is approximately that which would be generated by rotation of the surface (I 100) around the vertical axis (1101) We thus obtain a

three-dimensional frequency representation (and no longer two-dimensional as in the case where a single recording is used). From this three-dimensional representation in frequency space, we can generate the function u (r) by inverse Fourier transformation.

fréquentielles bidimensionnelles atteignant ce point. To obtain the frequency representation of u (r) from the set of two-dimensional frequenticlles representations, we will calculate at each point the mean value of the representations

two-dimensional frequencies reaching this point.

The calculation of the frequency representation of u (r) then finally of u (r) can for example be carried out in 6 steps: step 1: for each lighting wave, the two-dimensional frequency representation of the received wave is determined, which is a portion of a sphere of a three-dimensional space.

issue de l'objet, ce point ayant la fréquence /e ('- v) = )1 (i - C'x , j - Cl , l 2 - i - C.x~ z - ( / -A 2 et ayant comme valeur complexe la valeur complexe obtenue au point considéré du capteur CCD par la / 2 2 2\ ,2 2\ formule .s II = 61,.1 (2Ls 12 ~ IS. 12 -IS2 12) + .121'.I (Ls I - .s2 I formule S-II = ~II -isii -ls21 +J ISII -ls21 61jl 2v31rJ étape 2 : pour chaque onde d'éclairage, on détermine la fréquence fe de Fonde d'éclairage en déterminant

les coordonnées (inrax jmax) du point d'intensité maximale sur le capteur CCD et en appliquant la formule: f* " ~F7 Cinrnx-l'x, jnrax-C'y, Kz -irrrax-C'X -(jnrax-C',)2 étape 3: pour chaque onde d'éclairage, on translate la représentation obtenue à l'issue de l'étape 1, d'un vecteur - fe ou est la fréquence de l'onde d'éclairage, obtenue à l'issue de l'étape 2. From a point of the CCD sensor of coordinates (i, j) we obtain a point of the representation of the wave

resulting from the object, this point having the frequency / e ('- v) =) 1 (i - C'x, j - Cl, l 2 - i - Cx ~ z - (/ -A 2 and having as value complex the complex value obtained at the considered point of the CCD sensor by the / 2 2 2 \, 2 2 \ formula .s II = 61, .1 (2Ls 12 ~ IS. 12 -IS2 12) + .121'.I (Ls I - .s2 I formula S-II = ~ II -isii -ls21 + J ISII -ls21 61jl 2v31rJ step 2: for each lighting wave, the frequency fe of the lighting background is determined by determining

coordinates (inrax jmax) of the point of maximum intensity on the CCD sensor and applying the formula: f * "~ F7 Cinrnx-l'x, jnrax-C'y, Kz -irrrax-C'X - (jnrax- C ',) 2 step 3: for each illumination wave, the representation obtained at the end of step 1 is translated by a vector - fe where is the frequency of the illumination wave, obtained at the outcome of step 2.

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step 4: for each illumination wave, the two-dimensional frequency representation obtained at the end of step 3 is divided by its value at the point of coordinates (0,0). This step constitutes the phase adjustment operation described in 3.5.3. and is essential for the two-dimensional frequency representations to overlap in a coherent way. step 5: the set of two-dimensional frequency representations obtained at the end of step 4 is superimposed, obtaining the frequency representation of u (r). The value assigned to a point not reached is 0 and the value assigned to a point reached is the average of the values at this point of each two-dimensional frequency representation reaching this point. step 6: an inverse three-dimensional Fourier transformation of the frequency representation is performed, finally obtaining the function u (r) in spatial representation.

/-l ,2\ . 1 /. In practice, the steps will be carried out in a different order and in a modified form, in order to optimize the calculation time and limit the memory space required. The method actually used comprises two phases, equivalent to the 6 preceding steps: acquisition phase: for each lighting wave, determine the frequency plane image obtained on the CCD sensor by applying the formula to each point

/ -l, 2 \. 1 /.

(imax,jmax), et à partir de chaque point de coordonnées (i,j) du capteur, on obtient un point de la représentation fréquentielle tridimensionnelle de fréquence .it Ct Cx',l C'' k2 t Cx2-(J-,y2 - Cinrax-C'x, jmax-C'y, h2 -immc-C'x2 -(JlIlax-ry)2) Lorsqu'un point n'est pas atteint on y affecte la valeur nulle Lorsqu'il est atteint plusieurs fois on ) affecte la moyenne des valeurs obtenuesà chaque fois. Lorsque cette opération a été effectuée pour toutes les ondes d'éclairage et tous les points du capteur, la transformation de Fourier tridimensionnelle inverse peut être effectuée. S-- - = - (21s. (Ls12 ~ sl) li-J 6li- 1 -sy2 -Szlz) +. 2 rlr.l (SIz -IS2 We also determine the coordinates (il1lax,} l1lax) of the point of maximum intensity on the CCD sensor and we divide the whole of the plane frequency image obtained on the CCD sensor by its value at the coordinate point (il1lax, jl1lax), three-dimensional calculation phase: From each lighting wave characterized by the values

(imax, jmax), and from each point of coordinates (i, j) of the sensor, we obtain a point of the three-dimensional frequency representation of frequency .it Ct Cx ', l C''k2 t Cx2- (J- , y2 - Cinrax-C'x, jmax-C'y, h2 -immc-C'x2 - (JlIlax-ry) 2) When a point is not reached, it is set to zero When it is reached several times on) assigns the average of the values obtained each time. When this operation has been carried out for all the illumination waves and all the points of the sensor, the inverse three-dimensional Fourier transformation can be carried out.

This method poses a practical problem, which is that the point illuminated directly by the beam passing through the sample is illuminated much more intensely than the points corresponding to the diffracted wave. The three-dimensional representation generated during an image capture essentially contains frequencies close to that of the lighting beam, the other frequencies being drowned in the noise. For

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To remedy this drawback, a device for controlled attenuation of the beam is used. The part of the frequency representation corresponding to the frequencies on which the intensity is high is obtained with a strong attenuation and that corresponding to the other frequencies is obtained with a low attenuation. The values obtained under high attenuation are then multiplied by a complex coefficient characteristic of the phase shift and of the amplitude ratio of the illuminating wave between the two positions of the controlled attenuation device. This controlled attenuation device consists of the polarization rotator (104) and the polarizer (105).

The three-dimensional representation obtained from hpix x vpix size images corresponds to large file sizes. In order to limit the size of the files and the calculation time, the size of the images will be halved by averaging during the procedure for acquiring the three-dimensional representation. This is equivalent to grouping the pixels 4 by 4, a group of 4 pixels on the original image being equivalent to an effective pixel used for the calculation. The size of the observable object is of course reduced accordingly. The values of Cx, Cy and K are divided by 2 to account for the new coordinate system. This limitation of the observed image size is of course optional.
The use of the microscope itself includes: - a phase of focusing on the sample described in paragraph 5.17.

- a position adjustment of the condenser, which is described in paragraph 5. 18.

- a filter adjustment described in paragraph 5.19.

- the phase of acquisition of the normalized two-dimensional frequency representations described above and detailed in paragraph 5.20.

- the three-dimensional calculation phase described above and detailed in paragraph 5.21.

- a display phase described in paragraph 5.22.

Before this microscope can be used, various settings must be made: - The settings of the manual positioners, described in paragraphs 5.6, 5.7, 5.8, 5.9. make it possible to correctly adjust the trajectory of the beam, to ensure that the image of a plane wave on the camera is indeed point, and that the condenser does indeed form a parallel beam at its exit. In particular, the adjustment described in paragraph 5.8. allows a first adjustment of the position of the condenser.

- The adjustment described in paragraph 5.10. makes it possible to obtain the number of steps per pixel, useful for controlling the beam deflection mirror (109).

- The level of the reference wave is adjusted as indicated in paragraph 5.11.

- The adjustment described in paragraph 5.12. allows obtaining appropriate control voltages of the piezoelectric actuator.

- The adjustment described in paragraph 5.13. allows the adjustment of the beam attenuator and obtaining the attenuation and phase shift constants characterizing it.

- The adjustment described in paragraph 5.14. allows to obtain the constant K.

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- The aperture of the diaphragms and the position of the semi-transparent mirror (I 16) must be adjusted so as to obtain a centered image without spectrum aliasing. This adjustment is described in part in paragraph 5.14 and is completed in paragraph 5.15.

- The reference wave must be recorded, which is described in paragraph 5.16.

5.4. Handling filters
The adjustment operations require permanent manipulation of the filters to adjust the intensity received on the sensor. These manipulations are not systematically recalled in the remainder of the text.
The filter at (120) determines the intensity of the reference wave. Its value is determined in a particular step of the adjustment. Subsequently, when a reference wave is required, the filter thus determined is inserted. When the reference wave is to be removed, an opaque element is inserted at (120).

The filter at (103) determines the intensity of the illuminating wave. Its value depends on the current adjustment operations. For most operations, the filter is adjusted so that the current received on the sensor (118) is high, without reaching saturation. For some operations the sensor is saturated. For others the lighting wave must be suppressed, which is done by inserting an opaque element.

The filter at (101) is used only for adjustment operations requiring visual monitoring of the beam, identified by its diffusion spot on a piece of white paper. The filter is then adjusted so that the diffusion stain is visible without being dangerous for the eye.

In cases where only the illuminating wave is present, the relative intensity of the image received on the CCD sensor will be called the ratio of the intensity received on the sensor to the intensity at the output of the filter (103).

In an operation where one seeks to maximize the relative intensity received on the sensor, it is necessary to change the filter regularly in order to maintain the intensity at a level measurable by the sensor.

5.5 Commonly used programs
Certain simple programs are used frequently during adjustment, without this being recalled: - movement of the mirror (109): this mirror being motorized, a program is necessary to modify its position. This program asks the user for a number of steps and an axis number corresponding to either the motor (213) or the motor (208), then causes this motor to perform the number of steps requested.

-Visualization of the image received on the sensor: a program allows the direct display on the computer screen of the image received on the sensor (118).

-Visualization of the image and maximum characteristics: this program performs the direct display on the computer screen of the image received on the sensor (118). It also displays the maximum value detected by the sensor, the coordinates of the corresponding point, and the ratio between the intensity of this point and the sum of the intensities of its 8 neighbors. This program is used to check the appearance of an image.

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to check the sensor for non-saturation (maximum value less than 255). to know the coordinates and the value of the maximum, to appreciate the punctual nature of this maximum by direct observation of the image and by use of the displayed values: the (relative) intensity of the maximum must be as high as possible, as well as the ratio of its intensity to that of its neighbors.

5.6. adjustment of the position of the laser (100) and mirror (121)
Firstly, the illuminating wave is suppressed and the position of the laser (100) is adjusted so as to effectively target the center of the mirror (121), which is verified by following the path of the beam using d 'a piece of paper to visualize it. The position of the mirror (121) is then adjusted so that the reference beam actually passes through the lens (123) and reaches the camera. The reference beam should be centered on the sensor (118).

l'objectif de microscope. A cet effet, les éléments (IOG)(108)(111)(105)(10-1) sont provisoirement enlevés, l'onde de référence est supprimée, l'objectif de microscope est positionné en position à peu près focalisée sur l'objet. L'objet (112) utilisé est une lame transparente et de l'huile optique est interposée entre (112) et (113). La position angulaire de (102) est alors ajustée pour que le faisceau parvienne directement au centre du miroir (109). La position du miroir (109) est réglée de sorte que le faisceau parallèle entre directement dans l'objectif (113) et est affinée de manière à maximiser l'intensité relative du signal reçu sur le capteur CCD. La position du capteur CCD est alors réglée en translation dans la direction de l'axe optique de manière à ce que l'image produite soit parfaitement ponctuelle, puis est réglée en translation dans les directions orthogonales à l'axe optique de sorte que ce point soit au centre de la zone utile du capteur Il est enfin réajusté en translation dans le sens de l'axe optique. 5.7. translational adjustment of the camera position and mirror adjustment (102)
The position of the camera is adjusted in translation by directly sending a parallel beam on

the microscope objective. For this purpose, the elements (IOG) (108) (111) (105) (10-1) are temporarily removed, the reference wave is suppressed, the microscope objective is positioned in a position approximately focused on the 'object. The object (112) used is a transparent slide and optical oil is interposed between (112) and (113). The angular position of (102) is then adjusted so that the beam arrives directly at the center of the mirror (109). The position of the mirror (109) is adjusted so that the parallel beam enters directly into the objective (113) and is fine-tuned to maximize the relative strength of the signal received on the CCD sensor. The position of the CCD sensor is then adjusted in translation in the direction of the optical axis so that the image produced is perfectly point-like, then is adjusted in translation in the directions orthogonal to the optical axis so that this point or in the center of the useful zone of the sensor It is finally readjusted in translation in the direction of the optical axis.

5.8. adjusting the position of the condenser (111) and obtaining the position of the optical center
The elements (106) (108) (111) are put back in place. Microscope oil is interposed between (111) and (112) and between (112) and (113). A piece of white cardboard is placed on the mirror (109) to diffuse the light. The diaphragm (107) is fully open and the opening of the diaphragm (114) is approximately 6mm. The microscope objective is put in a roughly focused position. The position of the condenser (111) is then adjusted so as to obtain on the CCD a clear, slightly grainy disc of as large a radius as possible and of almost constant intensity over the entire disc. In Fig. 17, the useful area of the CCD (1200) is shown, and the light disc (1201) stands out against this black background. A specific program is then used to determine the coordinates Cx, Cy of the optical center and the radius R of the disc. This program determines: - the lines (1206) and (1205) constituting the right and left limits of the disc (1201).

- the line (1207) defined as the midpoint of the lines (1206) and (1205).

- the straight lines (1202) and (1203) constituting the lower and upper limits of the disc (1201).

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- the line (1204) defined as the midpoint of the lines (1202) and (1203).

- the optical center, intersection of the lines (1204) and (1207) - the radius R of the disc, equal to half the distance between the lines (1205) and (1206).

5. 9.adjusting the position of the lens (106)
The piece of white cardboard placed on the mirror (109) is deleted. The position of the mirror is modified so as to bring the illuminated point on the edge of the previously obtained disc. The position of the lens (106) is then adjusted along its axis so as to have the most punctual image possible on the CCD sensor.

5.10 Determination of the number of steps per pixel.

nombre de pas A cr ' 1 l pas~par~pixel = nombre de pas . On effectue de même sur l'autre axe et on retient le plus petit rapport nombre de pixels obtenu
5. 11. réglage du niveau de l'onde de référence
Si on considère une onde de référence et une onde d'éclairage ayant même intensité maximale à leur arrivée sur le capteur, s'additionnant en amplitude lorsqu'elles sont en phase, la condition de nonsaturation du capteur est que l'amplitude commune des deux ondes soit la moitié de l'amplitude saturant le capteur, ou de manière équivalente que l'intensité commune des deux ondes soit le quart de l'intensité saturant le capteur. Pour régler le niveau de l'onde de référence à cette valeur, l'onde d 'éclairage est supprimée et la valeur du filtre (120) est ajustée pour obtenir une image dont le niveau maximal est d'environ le quart du niveau maximal autorisé par la carte d'acquisition, soit dans le cas d'un échantillonnage sur 8 bits du signal vidéo, un niveau d'environ 64. Avant la prise d'images, le niveau maximal de l'onde d'éclairage devra être réglé de la même façon. The piece of paper obscuring the mirror is then removed. The motor is moved along an axis of a known number of steps. The position in pixels of the point of maximum intensity is noted before and after the displacement, and the number of pixels traversed is deduced from it.We then calculate the ratio

number of steps A cr '1 l step ~ per ~ pixel = number of steps. The same is done on the other axis and the smallest number of pixels ratio obtained is retained.
5.1.11 adjustment of the reference wave level
If we consider a reference wave and a lighting wave having the same maximum intensity when they arrive on the sensor, adding in amplitude when they are in phase, the condition of non-saturation of the sensor is that the common amplitude of the two waves is half the amplitude saturating the sensor, or in an equivalent manner that the common intensity of the two waves is a quarter of the intensity saturating the sensor. To set the level of the reference wave to this value, the illuminating wave is suppressed and the value of the filter (120) is adjusted to obtain an image whose maximum level is about a quarter of the maximum allowed level. by the acquisition card, that is to say in the case of an 8-bit sampling of the video signal, a level of approximately 64. Before taking images, the maximum level of the illumination wave should be set to the same way.

5.12. adjustment of the control voltages of the piezoelectric actuator,
This calibration of the piezoelectric actuator can be done outside the system by a known interferometric method. Three positions of the actuator are used. The displacement of the mirror between each position must be # / 3 # 2 The control voltages corresponding to each position 3 # 2 must be determined, the actuator having a regular cycle to avoid hysteresis effects.

However, it is also possible to carry out this adjustment while the actuator is in place. This makes it possible to compensate for the imprecision on the orientation of the mirror and to have a simple calibration procedure not using specific equipment.

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This is done using a program which varies the control voltages and which is described by the algorithm of figure 10. Before running the program, the position of the mirror (109) must be adjusted so that the point produced on the CCD sensor using as an object a completely transparent slide either in the center of the sensor. To use this program, the object used must be highly diffusing. One could for example use a piece of white paper soaked in gelatin and then placed between slide and coverslip. The paper should be thick enough to stop the direct beam and thin enough to pass a scattered beam. The diaphragm (107) is fully open and the diaphragm (114) is set for an aperture of approximately 0.8mm. The reference wave then interferes on the CCD sensor with the clear disc produced by the wave coming from the object. The intensity of the lighting wave must be adjusted so that the sensor is at the saturation limit.

de phase de ,0, 3 seront respectivement l'max 2-diff bas, l'max 2, l'max 2 t diff haut, ou drff haut et diff~bas sont choisis pour produire les décalages de phase indiqués. Afin d'éviter tout effet d'hystérésis, à chaque acquisition la tension est initialisée à 0, les différentes images sont acquises dans l'ordre croissant des tensions appliquées à l'actuateur et une tension finale Umax est finalement appliquée, de sorte que le même cycle est toujours utilisé. Ce cycle devra également être utilisé en phase normale de fonctionnement. If the maximum voltage applied to the actuator is Umax, the voltages corresponding to the offsets

The phase values of, 0, 3 will respectively be the max 2-diff low, the max 2, the max 2 t diff high, or drff high and diff ~ low are chosen to produce the indicated phase shifts. In order to avoid any hysteresis effect, at each acquisition the voltage is initialized to 0, the different images are acquired in increasing order of the voltages applied to the actuator and a final voltage Umax is finally applied, so that the same cycle is always used. This cycle should also be used in the normal phase of operation.

.S'P = C6 C21P'0 ICP' 23, ICP' 3 JJ + 2 CI CP z3 ICP 3 / dans laquelle l'onde de référence a été remplacée par une constante et l'expression 1(P,[alpha]) désigne l'intensité enregistrée au point P pour un décalage de phase a.

Le réglage des tensions de commande de t'actuateur consiste à évaluer (liff haut et (liff bas. Le principe est d'obtenir deux représentations fréquentielles décalées entre elles de #/3. La deuxième image # peut être recalée en phase en la multipliant par e3 et l'écart moyen entre la première image et cette

image recalée peut être calculé. Cet écart est minimal lorsque les tensions diff haut et (liff bas sont correctement réglées. Les décalages de phase permettant l'acquisition de la 2cme image élémentaire en In ir r 21r ff fréquence sont donc -#+#, #,#+# et correspondent respectivement, en première approximation, 3 3 3 aux tensions l'max 2-diffas # diffbas'2, [TmaX'2(difLbas diff~hautF2, ['maxI2T (liff haut Fdiff haut 2. Le programme de réglage calcule l'écart moyen pour des séries de valeurs de (liff haut et diff~bas et choisit celles qui correspondent à un écart moyen minimal. Son algorithme est détaillé sur la figure 10. The images taken with the phase shifts indicated above make it possible to calculate a frequency representation by applying to each pixel P the formula

.S'P = C6 C21P'0 ICP '23, ICP' 3 JJ + 2 CI CP z3 ICP 3 / in which the reference wave has been replaced by a constant and the expression 1 (P, [alpha]) denotes the intensity recorded at point P for a phase shift a.

The adjustment of the actuator control voltages consists in evaluating (high liff and (low liff. The principle is to obtain two frequency representations shifted between them by # / 3. The second image # can be realigned in phase by multiplying it) by e3 and the average difference between the first image and this

registered image can be calculated. This difference is minimal when the voltages diff high and (liff low are correctly adjusted. The phase shifts allowing the acquisition of the 2nd elementary image in In ir r 21r ff frequency are therefore - # + #, #, # + # and correspond respectively, in a first approximation, 3 3 3 to the voltages l'max 2-diffas # diffbas'2, [TmaX'2 (difLbas diff ~ hautF2, ['maxI2T (high liff Fdiff high 2. The adjustment program calculates the mean deviation for series of values of (liff high and diff ~ low and choose those which correspond to a minimum mean deviation. Its algorithm is detailed in figure 10.

The essential steps of this algorithm are:

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effectue toujours le même ejele commençant par la tension 0 et finissant par la tension 1 "itiax. Le temps d'attente après l'application d'une tension nulle au piézoélectrique permet à celui-ci de se stabiliser. Le temps d'attente avant le lancement de l'acquisition évite d'acquérir une trame qui aurait été exposée avant l'application des conditions d'exposition voulues. La fin de l'exposition d'une image est signalée sur les cartes d'acquisition par le début du transfert de l'image correspondante. L'utilisation d'un temps d'exposition inférieur au temps de transfert de l'image permet à l'image de ne pas être affectée par les états transitoires. La mise du processus en priorité maximale évite la perturbation de l'acquisition par d'autres tâches système sous un système d'exploitation multitâches. Les 6 images sont acquises successivement et en temps réel (pas d'image perdue) par la carte d'acquisition afin de minimiser le temps pendant lequel des vibrations peuvent affecter le résultat. Chaque image a pour dimension horizontale hpix et pour dimension verticale vpix. Pendant l'acquisition, les images sont transférées automatiquement par la carte d'acquisition dans le tableau qui leur est réservé en mémoire centrale de l'ordinateur. A l'issue de la procédure d'acquisition, on dispose d'un tableau I[a,b,i,j], l'indice a correspondant à la différence de phase, l'indice b correspondant à l'image (décalée ou non décalée en phase), les indices i et étant les coordonnées en pixels et variant respectivement de 0 à hpix-1et de 0 à vpix-1. (600): image acquisition. The acquisition procedure is specified in FIG. 11. By @ the images' we mean here 6 interference figures received consecutively by the CCD sensor This procedure

always performs the same ejele starting with voltage 0 and ending with voltage 1 "itiax. The waiting time after applying zero voltage to the piezoelectric allows it to stabilize. The waiting time before the launch of the acquisition avoids acquiring a frame which would have been exposed before the application of the desired exposure conditions. The end of the exposure of an image is indicated on the acquisition cards by the start of the transfer of the corresponding image. Using an exposure time less than the image transfer time allows the image to be unaffected by transient states. Setting the process to maximum priority avoids disturbance acquisition by other system tasks under a multitasking operating system. The 6 images are acquired successively and in real time (no image lost) by the acquisition card in order to minimize the time during which vibrations may affect the result. Each image has the horizontal dimension hpix and the vertical dimension vpix. During the acquisition, the images are transferred automatically by the acquisition card to the table reserved for them in the central memory of the computer. At the end of the acquisition procedure, we have a table I [a, b, i, j], the index a corresponding to the phase difference, the index b corresponding to the image (shifted or not phase-shifted), the indices i and being the coordinates in pixels and varying respectively from 0 to hpix-1 and from 0 to vpix-1.

complexes .SO[i,j] et SI [r,J], en appliquant les formules: Sty.j] = 6 21O.O,i, j - II,O,i, j -1 2.O,i, j) + j 2 II,O,i, J - 72,O,i, J) Sl[I,}] = 621O,l,i,j-Il.l,i,j-12,1,i,j+j 2Il,I,r,J-I2,l,r,Jy (602) Le programme modifie le tableau SI en multipliant chacun de ses éléments par e 3

(603): le programme calcule la valeur maximale mod maux= max 1.\'q/,.I]1 du module sur 0<i<hpix-\ OS,jS,\pix-1 SO, (604): Le programme calcule l'écart moyen entre les deux tableaux de la manière suhante: Le programme initialise ecart et nombre~valeurs à 0 et parcourt l'ensemble des points i,j en

testant la condition (605): l0[i, j]l 0,5 mod max . Chaque fois que cette condition est réalisé, il effectue les opérations suivantes (606): ecart+ = ISO[I,}] - Sl[I,}]1 nombre valeurs4 =I Lorsque le programme a terminé de parcourir les indices (i,j) il divise ecart par nombre ~valeurs (607), ce qui lui donne l'écart moyen. Cet écart n'intègre donc que des valeurs pour lesquelles l'onde d'éclairage est suffisamment forte, afin d'éviter un résultat trop bruité Il est stocké dans un tableau (601) calculation of the two frequency representations These are stored in arrays of

complexes .SO [i, j] and SI [r, J], by applying the formulas: Sty.j] = 6 21O.O, i, j - II, O, i, j -1 2.O, i, j) + j 2 II, O, i, J - 72, O, i, J) Sl [I,}] = 621O, l, i, j-Il.l, i, j-12,1, i, j + j 2 Il, I, r, J-I2, l, r, Jy (602) The program modifies the SI array by multiplying each of its elements by e 3

(603): the program calculates the maximum value mod mal = max 1. \ 'Q / ,. I] 1 of the module on 0 <i <hpix- \ OS, jS, \ pix-1 SO, (604): The program calculates the average difference between the two arrays as follows: The program initializes deviation and number ~ values to 0 and iterates all the points i, j in

testing condition (605): l0 [i, j] l 0.5 mod max. Each time this condition is met, it performs the following operations (606): deviation + = ISO [I,}] - Sl [I,}] 1 number values4 = I When the program has finished iterating the indices (i, j ) it divides deviation by number ~ values (607), which gives it the average deviation. This difference therefore only integrates values for which the lighting wave is sufficiently strong, in order to avoid a result that is too noisy It is stored in a table

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(608): le programme passe à la valeur suivante du couple (diffhaut.diffbas) et réitère les opérations jusqu'à ce que la série d'écarts ait été calculée.

(608): the program goes to the next torque value (diffhigh.difflow) and repeats the operations until the series of deviations has been calculated.

vibrations du système. Le filtre passe-bas utilisé est représenté dans le domaine fréquenticl par une 'marche d'escalier' passant d'une valeur de 1 en basse fréquences à une valeur de 0 en hautes fréquences, et sa bande passante est déterminée empiriquement pour avoir une bonne limitation du bruit sans trop déformer la courbe. (609): the program applies a low-pass filter to the table obtained to limit the bit due to

system vibrations. The low-pass filter used is represented in the frequenticl domain by a 'staircase' going from a value of 1 at low frequencies to a value of 0 at high frequencies, and its passband is determined empirically to have a good noise limitation without distorting the curve too much.

(611): la valeur du couple (dlfLbas,diff~haut) correspondant au minima est affichée. (610): the table is represented graphically to check its appearance

(611): the value of the torque (dlfLbas, diff ~ high) corresponding to the minimum is displayed.

(J;/MM,<7</~/'a.s') ) que le programme filtre pour éliminer le bruit (609) et qu'il représente graphiquement (610). La valeur d'indice du tableau correspondant à l'écart minimal correspond alors à la valeur correcte du couple (diff~bas,diff~hauf) et ce couple est affiché (611). The series of torque values (difLbas, difLhaut) are determined as follows: First, the program varies the values of drff haut and clrfj 6a.c, leaving them the iiiia - r ['max equal to each other. For example, they can vary between 0 and in steps of if 12 conversion bits are used. This results in an array of 1024 elements (the deviations calculated for each value of

(J; / MM, <7 </~/'a.s')) that the program filters to eliminate noise (609) and that it graphs (610). The index value of the table corresponding to the minimum difference then corresponds to the correct value of the torque (diff ~ low, diff ~ high) and this torque is displayed (611).

une valeur plus précise de clifj haut. Secondly, the program is restarted by setting drff has to the value previously obtained and by varying only cliff high. A new minimum is thus obtained, which corresponds to

a more precise value of high clifj.

Thirdly, the program is restarted by setting tliff high to the value previously obtained and by varying only diffas, obtaining a more precise value of <7 </ <7.y.

The operator can repeat these steps by varying separately and alternately <7 <///) fM and drff high, but the maximum precision on these values is obtained fairly quickly.

5.13. adjustment of polarization (105) and polarization rotator (104)
The next step is to adjust the position of the polarization rotator (104) and the polarizer (105). This device is intended to achieve a controlled attenuation of the lighting beam by controlling the phase rotator, and the assembly will be called the 'optical switch' It has a closed position corresponding to a low intensity passing through it and an open position corresponding to an intensity. higher.

The object used is the same as in the previous step, the adjustment of the mirror (109) and the diaphragms is also the same, the reference wave is removed first. First, the polarizer is placed and adjusted to maximize the intensity passing through it and received on the sensor (118).

Secondly, the polarization rotator is put in place. A voltage corresponding to a state arbitrarily defined as closed is applied to it and it is rotated to minimize the current passing through the entire switch. In a third step, the reference wave is re-established and a program is used which calculates the ratio of the intensities and the phase difference between the two.

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positions of the polarization rotator, ratio which will be necessary during the image acquisition phases to combine the waves corresponding to the open and closed states of the switch. The algorithm of this program is in Fig. 12. The steps are as follows - (800): The program first acquires the images using the acquire images procedure described in Fig.13. By “the images” is meant here 6 interference figures received consecutively by the CCD sensor. This procedure always performs the same cycle starting with voltage 0 and ending with voltage UMax. The waiting time after the application of a zero voltage to the piezoelectric allows it to stabilize The waiting time before launching the acquisition avoids acquiring a frame that would have been exposed before the application of the conditions desired exposure. The end of the exposure of an image is indicated on the acquisition cards by the start of the transfer of the corresponding image.The use of an exposure time less than the image transfer time allows the image not to be affected by transient states. Setting the process to the highest priority prevents disruption of acquisition by other system tasks under a multitasking operating system. The 6 images are acquired successively and in real time (no image lost) by the acquisition card in order to minimize the time during which vibrations can affect the result. Each image has the horizontal dimension hpix and the vertical dimension vpix. During the acquisition, the images are transferred automatically by the acquisition card to the table reserved for them in the central memory of the computer.

(801) the program calculates the two frequenticlles representations SO and SI which differ by the state of the switch..S'0 corresponds to the open switch and SI to the closed switch.

6 6 (2IO.O, i, j-Il.O, i, j-12, O, i, J + j 2 (II, O, i, J-12, O, r, Jy SI [!.}] = 62I (ll, rj-ll.l, i, j-I2.l, i.J + j 2I1, lr, J-I2.I, r, Jy (802): The program calculates the maximum value mod- max = . max 1. "'; 0 [1, ill reached by the 0 <~ i <-hprx-1 0 <- j <-t pix-1 modulates the elements of the SO array.

(804): LSOr. JI >~ 0,5 mod tax Lorsque la condition est vérifiée, il effectue (805) : S0 [i,j] rapport+ = @
S1 [i,j] nombre valeurs-' 1 Lorsque l'ensemble des indices i,j a été parcouru, le programme divise rapport par nombre~valeurs (806) ce qui donne le rapport recherché.

(803): the program calculates the average ratio between the two frequency representations It initializes ratio and number ~ values to 0 then it runs through all the indices (i, j) by testing the condition

(804): LSOr. JI> ~ 0.5 mod tax When the condition is verified, it performs (805): S0 [i, j] report + = @
S1 [i, j] number of values- '1 When all the indices i, j have been scanned, the program divides ratio by number ~ values (806) which gives the sought ratio.

(807) the program calculates the mean ratio ave of the ratio values obtained since its launch.

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rapport moy. (808): the program displays the real and imaginary parts as well as the report module and

avg ratio

(809) The program continuously repeats this procedure to allow continuous adjustment. The program ends on operator instruction.

la valeur moyenne complexe rapport moy est notée et servira de base dans la suite des opérations. The angular position of the polarization rotator must be adjusted so that the ratio modulus is approximately equal to 30. The program is then stopped and restarted, and after a sufficient number of iterations.

the complex mean value avg ratio is noted and will be used as a basis in the following operations.

5.14. obtaining the constant K and adjusting the diaphragm (114) and the mirror (116)
K is the maximum value in pixels corresponding to the maximum spatial frequency of the wave or # v is the wavelength in the observed medium, assumed to have an index equal to) the nominal index nv of the objective. The nominal index of the lens is the index for which it was designed and for which it does not create spherical aberration. It is also the index of the optical oil to be used with the lens.

Fourier, .V valeurs de fréquences sont prises en comptes, allant de - V à # '- Y # 2K#v 2K#v
Après transformation on obtient .V valeurs de position avec un pas en position égal à la moitié de l'inverse de la fréquence maximale avant transformation. There are K pixels between the frequencies 0 and #. The frequency step along an axis is therefore 1 The frequencies vary in total from - 1 to 1 in steps of 1 #v #v K # v
If .V is the total number of pixels along each axis taken into account for the transform of

Fourier, .V frequency values are taken into account, ranging from - V to # '- Y # 2K # v 2K # v
After transformation we obtain .V position values with a step in position equal to half of the inverse of the maximum frequency before transformation.

The step in position is therefore 1 / N = K # v / N.

D,,, . on a donc: Dreel # - Dpa d'ou K = N Dree, La longueur d'onde à considérer ici est la N #v Dpix longueur d'onde dans le matériau, supposé être d'indice égal à l'indice nominal nv de l'objectif soit: #v = #. On a finalement: nv K = nv/# n/Dpix Dreel. 2 2K # v
If we consider two points between which the distance in pixels is Dpix and the real distance is

D ,,,. we therefore have: Dreel # - Dpa where K = N Dree, The wavelength to be considered here is the N #v Dpix wavelength in the material, assumed to be of index equal to the nominal index nv of the objective is: #v = #. We finally have: nv K = nv / # n / Dpix Dreel.

To obtain the constant K, we take the image of an objective micrometer for which the real distances are known, then we apply the above formula.

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This is achieved by using a focusing program which will be reused later whenever focusing on a sample is required prior to taking the three dimensional image.

(1000): Le programme acquiert une image par la procédure acquiert images de la Fig. 1 On obtient donc un tableau d'entiers (type unsigned char pour 8 bits) I[p, C,I,}] ou l'indice p variant de 0 à 2 correspond à l'état de phase, l'indice c variant de 0 à 1 correspond l'état du commutateur (0=ou ert, 1 = fermé) et les indices i et j variant de 0 à hpix-I et de 0 à vpix-1 correspondent aux coordonnées du pixel. The algorithm of this program is in figure 14. Its main steps are:

(1000): The program acquires an image by the acquire images procedure of FIG. 1 We therefore obtain an array of integers (type unsigned char for 8 bits) I [p, C, I,}] where the index p varying from 0 to 2 corresponds to the phase state, the index c varying from 0 to 1 corresponds the state of the switch (0 = or ert, 1 = closed) and the indices i and j varying from 0 to hpix-I and from 0 to vpix-1 correspond to the coordinates of the pixel.

(1001). An array of boolccns H [i, j is generated: it is initialized to 0. then for each pixel, the maximum value reached by I [p.0, i, j on the three images corresponding to the open position of the switch is calculated . If this value is equal to 255 (the highest value of the digitizer), the images corresponding to the closed position of the switch must be used in the calculation of the frequency associated with the pixel and its 8 immediate neighbors, and the table [Il.] ] is set to 1 for these 9 pixels.

,li, il 621O,H[r, j,i>j-I1>Ili, j,i>J-12,Hi>.1,1>.1 +j 2'I I>HLr>J>t>J-[2>H[r>J>i>jJl +r'l'Por'1~mo3, ~ lj[i,J Si H[i,j] vaut 1, la valeur complexe ainsi obtenue est donc multipliée par le nombre complexe rapport~moy obtenu lors de l'opération de calibration du commutateur pour donner la valeur finale de l'élément de tableau S[i,j], afin de tenir compte du décalage de phase et de l'absorption induits par le commutateur. (1002): the frequency representation S [i, j] of complex numbers is generated: for each pixel, the value is generated according to the following equations:

, li, il 621O, H [r, j, i>j-I1> Ili, j, i> J-12, Hi>.1,1> .1 + j 2'II>HLr>J>t> J - [2> H [r>J>i> jJl + r'l'Por'1 ~ mo3, ~ lj [i, J If H [i, j] is equal to 1, the complex value thus obtained is therefore multiplied by the complex number ratio ~ avg obtained during the switch calibration operation to give the final value of the array element S [i, j], in order to take into account the phase shift and absorption induced by the switch .

.S''r, J ~ SPI ,2} +.S'[2r + t,2j + l;[21,2j + Il + .S'[2; + 1,2 j + 1 . .Ce moyennage, couplé à une réduction de l'ouverture du diaphragme (114), permet de diminuer le diamètre de la zone observée et de réduire le temps de calcul. Il est équivalent à un filtrage passe-bas suivi d'un sous-échantillonnage. (1003): The program limits array S to dimensions of 512x512. The program then optionally performs one or the other, or neither, of the following two operations: - an averaging over a width of 2, which returns the array S to an array S 'of dimensions 256x256 with

.S''r, J ~ SPI, 2} + .S '[2r + t, 2j + l; [21,2j + Il + .S'[2; + 1.2 d + 1. This averaging, coupled with a reduction in the aperture of the diaphragm (114), makes it possible to reduce the diameter of the observed zone and to reduce the calculation time. It is equivalent to low pass filtering followed by downsampling.

.S'r. J ~ .S[128+i,128+ j] . Ceci permet de diminuer le temps de calcul au prix d'une réduction de la résolution. - a limitation of all the frequencies observed in a square of 256x256 pixels with

.S'r. J ~ .S [128 + i, 128 + j]. This makes it possible to reduce the computation time at the cost of a reduction in the resolution.

However in this case the program does not perform either of these two operations.

(1004): The program then performs the inverse Fourier transform of the table thus obtained (1005): It displays the result on the screen, by extracting the module, the real part or the imaginary part. In this case it will display the module. Whatever variable is displayed, the corresponding real number table is first normalized, either with respect to the mean value, or with respect to the

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maximum value. The program also writes the corresponding real file to disk. When the real part or the imaginary part is represented, it is essential that the point of impact of the direct beam is indeed at (256,256) on the image of size 512 x 512, otherwise a modulation becomes visible.

When the modulus is shown, the exact point of impact of the direct beam does not significantly influence the result.

(1006): The program then starts acquiring a new image again, thus operating continuously. It stops on the instruction of the operator.

To obtain the image of the micrometer, the objective is first put in a somewhat focused position, the micrometer having been introduced as an object. First, the reference wave is removed, the diaphragms are opened to the maximum, and the program for direct real-time display of the image received on the sensor is started, the filters at (103) and the polarization rotator. being adjusted to allow sufficient intensity to pass through to saturate the sensor sufficiently largely at the point of direct impact of the beam The object is then moved in the horizontal plane using the corresponding positioner until the image consisting of many intense aligned points, characteristic of the micrometer, appear. The micrometer is then correctly positioned under the objective.

The diaphragms at (107) and (114) are then set for an opening of about 8 mm. The filters in (103) are then set so that the maximum intensity on the CCD is at a level of about a quarter of the maximum value of the digitizer, i.e. 256/4 = 64. The reference wave is reintroduced. The focusing program is then launched. The diaphragm (114) should be adjusted so that it is clearly visible in the displayed image, while being as open as possible.If the image is not well centered, the centering can be improved either by changing the orientation of the mirror (116), in which case it may be necessary to readjust the orientation of the mirror (121), either by changing the position of the diaphragm (114), The diaphragm at (107) must be adjusted so that the observed area appears uniformly illuminated . The focusing program is then stopped, the reference wave is removed and the intensity of the beam is readjusted as before. The reference wave is then reintroduced and the focusing program restarted.

(1 =0,633 micromètres) et si le nombre de points de la transformée de Fourier est .V (.,nu512) alors on a ny N K = # Dp* reel, ou bien entendu u reel et A sont dans la même unité. The microscope objective is then moved by the focusing device so as to obtain a good image of the micrometer. To facilitate focusing, it is advantageous to visualize a part of the micrometer where lines of different lengths are present. This limits 'false focusing' due to interference phenomena in front of the micrometer. Between two movements, it is necessary to let go of the manual focusing device to obtain an image undisturbed by vibrations. When a good image has been obtained, the program is stopped and the image obtained is used to obtain the distance in number of pixels between two lines, the metric distance between these lines being known. If the distance between two graduations separated by Dreel micrometers is on the image thus obtained of Dpix pixels, if the nominal index of the objective is nv (in general, nv = 1.5) and if the wavelength of the laser in vacuum is

(1 = 0.633 micrometers) and if the number of points of the Fourier transform is .V (., Nu512) then we have ny NK = # Dp * real, or of course u real and A are in the same unit.

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5.15. remained diaphragms
The three-dimensional image that will be calculated has a side of size 256 pixels, which makes it possible to limit the file sizes and the calculation times. Adjusting the iris consists of reusing the focus program, this time with the intermediate averaging option, and adjusting the iris (114) so that its image is clearly visible while being as large as possible. The diaphragm (107) is then adjusted so that it is slightly more open than the minimum allowing even illumination of the observed part of the sample.

enregistre l'image résultante dans un tableau Iref [,] ou i varie de 0 à hpix-I et j varie de 0 à vpix-l
5. 17. Focalisation sur l'objet étudié
Cette étape doit être réitérée pour chaque échantillon dont on souhaite obtenir une image. L'onde d'éclairage est rétablie. L'échantillon à étudier est mis en place. Le miroir (109) est réglé pour que le point d'impact direct du faisceau d'éclairage soit au centre du capteur. Les filtres en (103) sont réglés pour qu'en l'abscence d'onde de référence l'intensité maximale reçue sur le capteur CCD soit d'environ 64. L'onde de référence est alors rétablie. Le programme de focalisation est lancé avec l'option de moyen nage intermédiaire, et la position de l'objectif est ajustée à l'aide du dispositif de focalisation pour obtenir une image nette de la zone d'intérêt de l'échantillon. 5.16. Recording the reference wave
Knowledge of the reference wave is essential for the precise calculation of the complex values of the wave reaching the sensor. This must therefore be recorded independently of the constant value of mean noise which characterizes each pixel. For this purpose a specific program is used. First, the illumination and reference waves are removed and the program records the resulting 'optical black' image on the CCD sensor. It averages the intensity obtained over 100 images to have a denoised optical black. Secondly, the reference wave is reestablished and the lighting wave remains suppressed. The program saves the resulting image, averaged over 100 images to denoise.Then the program calculates the difference between the image of the reference wave alone and the image of optical black, and

save the resulting image in an array Iref [,] where i ranges from 0 to hpix-I and j ranges from 0 to vpix-l
5. 17. Focus on the studied object
This step must be repeated for each sample for which it is desired to obtain an image. The illumination wave is restored. The sample to be studied is set up. The mirror (109) is adjusted so that the point of direct impact of the illumination beam is at the center of the sensor. The filters at (103) are set so that in the absence of a reference wave the maximum intensity received on the CCD sensor is about 64. The reference wave is then reestablished. The focusing program is started with the intermediate averaging option, and the objective position is adjusted using the focusing device to obtain a sharp image of the sample area of interest.

5. 18. Adjusting the position of the condenser and adjusting the diaphragm (107)
After the focusing phase, the position of the condenser must be adjusted so that the image, in the sample, of the illuminated part of the mirror, coincides with the observed part of the sample.

The reference wave is removed, the illumination beam attenuator is put in the open position, the filters in the path of the illumination beam are removed, and a piece of wet white paper is plastered over the mirror surface (109) so as to constitute a thin diffusing surface which can be considered to coincide with the mirror surface. A specific program for viewing the image received on the CCD is used. This program averages the image, for example over 8 successive acquisitions, and represents on the screen the root of the value obtained at each point, so as to make the image more visible even in the absence of a strong brightness. The

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diaphragm (107) is first wide open, and the position of the condenser is adjusted to obtain a homogeneous clear disc of high radius. It is then gradually closed up to the limit of visibility of the image, the position of the condenser itself being readjusted as and when. The final opening of the diaphragm (107) must be significantly smaller than that determined in 5.15.

The filters are then reintroduced, the reference wave is also reintroduced, and the focusing program is started. We should see the image of the diaphragm (114) with a central light spot corresponding to the defocused (therefore blurred) image of the diaphragm (107). The position of the condenser can then be adjusted in a plane orthogonal to the optical axis so that the central light spot is centered.

The diaphragm (107) is then adjusted so as to be slightly more open than the minimum allowing regular illumination of the observed area.

5. 19. Filter setting
The filters at (103) are adjusted so that in the absence of a reference wave and in the open position of the beam attenuator the maximum intensity measured on the CCD sensor is about 64. It can also be useful. , just before the acquisition, to re-adjust the position of the polarization rotator (104) and of the polarizer (101). This adjustment can be carried out using the same program as in 5.13, but leaving the observed sample in place and without modifying the adjustment of the diaphragms and filters. This adjustment makes it possible to compensate for the time drift of the characteristics of the polarization rotator.

Cette étape permet d'acquérir les représentations fréquenticllcs bidimcnsionnclles à partir desquelles sera calculée la représentation tridimensionnelle. Le point d'impact direct du faisceau d'éclairage est déplacé suivant une série de rayons partant du centre optique et de longueur Rh légèrement inférieur à R, par exemple Rb = R - 6, le centre optique et le rayon R ayant été déterminés dans l'étape 5.8. On note

nbangles le nombre total de rayons qui seront parcourus, par exemple nhmgle.9. rahrm est le nombre de représentations fréquentielles bidimensionnelles à acquérir et a pour valeur nhnn = -iibaiigles. A chaque étape, le programme calcule et enregistre dans un fichier//c/7 acquis une représentation fréquentielle qui sera utilisée dans la phase de calcul tridimensionnel. La taille de l'image acquise depuis la caméra est hpix x vpix, mais cette taille est divisée par deux pour obtenir des représentations fréquentielles de dimension hel x vel, selon le principe de moyennage intermédiaire déjà utilisé dans le programme de focalisation. 5. 20. acquisition step

This step makes it possible to acquire the frequent two-dimensional representations from which the three-dimensional representation will be calculated. The point of direct impact of the illumination beam is moved along a series of rays starting from the optical center and of length Rh slightly less than R, for example Rb = R - 6, the optical center and the radius R having been determined in step 5.8. We notice

nbangles the total number of rays that will be traversed, for example nhmgle. 9. rahrm is the number of two-dimensional frequency representations to acquire and has the value nhnn = -iibaiigles. At each step, the program calculates and records in an acquired // c / 7 file a frequency representation which will be used in the three-dimensional calculation phase. The size of the image acquired from the camera is hpix x vpix, but this size is halved to obtain frequency representations of hel x vel dimension, according to the principle of intermediate averaging already used in the focusing program.

(1300): Les données de base de l'acquisition sont enregistrées dans le fichier fich-acui.c: nbim: nombre de représentations fréquentielles bidimensionnelles helhpix @2 : nombre final de points dans le sens horizontal

vel=vpixl2: nombre final de points dans le sens vertical The acquisition program is detailed by the algorithm of Fig. 18, the steps of which are as follows:

(1300): The basic data of the acquisition are recorded in the file Fich-acui.c: nbim: number of two-dimensional frequency representations helhpix @ 2: final number of points in the horizontal direction

vel = vpixl2: final number of points in the vertical direction

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(1302). Le programme acquiert les images par la procédure cM/-< //n(7gc. de la Fig 13. On obtient donc un tableau d'entiers (type unsigned char pour 8 bits) I[p,e,i,j] ou l'indice/? variant de 0 à 2 correspond à l'état de phase, l'indice c variant de 0 à 1 correspond à l'état du commutateur (0=ouvert,

1=fermé) et les indices / et/variant respectivement de 0 à hpix-1 et de 0 à lpix-1 correspondent aux coordonnées du pixel. (1301): waiting time allowing the absorption of vibrations created by the movement of the positioner (110). A waiting time of about 2s may be suitable

(1302). The program acquires the images by the procedure cM / - <// n (7gc. Of Fig 13. We thus obtain an array of integers (type unsigned char for 8 bits) I [p, e, i, j] or the index /? varying from 0 to 2 corresponds to the phase state, the index c varying from 0 to 1 corresponds to the state of the switch (0 = open,

1 = closed) and the indices / and / varying respectively from 0 to hpix-1 and from 0 to lpix-1 correspond to the coordinates of the pixel.

(1303): An array of Booleans H [i, j] is generated: it is initialized to 0. then for each pixel, the maximum value reached on the three images corresponding to the open position of the switch is calculated. If this value is equal to 255 (the highest value of the digitizer), the images corresponding to the closed position of the switch must be used in the calculation of the frequency associated with the pixel and its 8 immediate neighbors, and the array H is set to 1 for these 9 pixels.

Vmax = maat 1 , (21O,O,i,j-II,O,i,j-12>0>r>J)+j (],0,', /1 - 42,0,; (i,j)eE 6 Iref[r>J] 2 3lrof[i>J 'I] ou EI est l'ensemble des couples (/,/) vérifiant H11, il 0 Le programme calcule ensuite: rapport-may = C 1 6210>0>i>J-!t>0,i>J-12ç),i,j+.J ll>0>r>J-lz>0>r>J 2i,1)EE'2 6210>1>i>jyll>1>i>J-12.I,i,j)+ j'(ll.l.r,j-12,1>r,J) E2 est l'ensemble des couples (i,j) vérifiant H11. Ji = 0 et 1 (21[O,O,i,)] -1[1,0,1.}] -I[2,0,I,}]) + } 1 (I[I.O,i,)] -I[2,0,i,}]) ? coef -f'max 6Iref [i, j (21[0,0, I[1,0,i. 1[2,0,1, jl) 2JIreJ[I..I] (1[1O z1] I[2,0,i,.I]) cocu - T'ilia--c avec par exemple coef-0,5. Le coefficient coefpeut être ajusté pour que E2 contienne suffisamment de points. N2 est le nombre d'éléments de E2. (1304) - calculation of ratio ntoy. The ratio nro. Calculation, already carried out during the switch calibration operation, must be repeated for each image in order to compensate for the time drifts.The program first determines:

Vmax = maat 1, (21O, O, i, j-II, O, i, j-12>0>r> J) + j (], 0, ', / 1 - 42,0 ,; (i, j) eE 6 Iref [r> J] 2 3lrof [i> J 'I] where EI is the set of pairs (/, /) verifying H11, il 0 The program then calculates: rapport-may = C 1 6210>0>i> J-! T> 0, i> J-12ç), i, j +. J ll>0>r>J-lz>0>r> J 2i, 1) EE'2 6210>1> i >jyll>1>i> J-12.I, i, j) + j '(ll.lr, j-12,1> r, J) E2 is the set of pairs (i, j) satisfying H11. Ji = 0 and 1 (21 [O, O, i,)] -1 [1,0,1.}] -I [2,0, I,}]) +} 1 (I [IO, i,) ] -I [2,0, i,}])? coef -f'max 6Iref [i, j (21 [0,0, I [1,0, i. 1 [2,0,1, jl) 2JIreJ [I..I] (1 [1O z1] I [ 2,0, i, .I]) cuckold - T'ilia - c with for example coef-0.5. The coefficient coef can be adjusted so that E2 contains enough points. N2 is the number of elements of E2.

= o / 1 210,Hr,J,r J II,Hr, r l2,llr ,r +J 2 îlre (/[)7l.'j]-2[<,])()+(r~-l)//[,]) Si H[i,j] vaut 1, la valeur complexe ainsi obtenue est donc multipliée par le nombre complexe

rapport moy obtenu lors de l'opération de calibration du commutateur pour donner la valeur finale de (1305): the frequency representation S [i, j] of complex numbers is generated: for each pixel, the value is generated according to the following equations:

= o / 1 210, Hr, J, r J II, Hr, r l2, llr, r + J 2 îlre (/ouvern)7l.'j marge-2→<,,3)()+(r~-l ) // [,]) If H [i, j] is equal to 1, the complex value thus obtained is therefore multiplied by the complex number

avg ratio obtained during the switch calibration operation to give the final value of

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l'élément de tableau .S[r], afin de tenir compte du décalage de phase et de l'absorption induites par le commutateur

( 1306)-Le point de module maximal du tableau -S'est déterminé. Ses coordonnées (i w<7-T. LlIlax) sont enregistrées.

the array element .S [r], in order to take into account the phase shift and the absorption induced by the switch

(1306) -The maximum modulus point of the table -It has been determined. Its coordinates (i w <7-T. LlIlax) are recorded.

i-ob7 = Gx +Ck%CRbll .cosCEC 2k 2r 1 2 2 Rb nbangles C CRbll -f C2k 2 'll j-ob 1\ Rb nbangles ou i-obj etLobj sont les coordonnées de la position objectif en pixels, et ou le signe % désigne le modulo, et ou E(x) désigne la partie entière de x. * (1307) The position 'objectifest calculated, the angle being k.pas:

i-ob7 = Gx + Ck% CRbll .cosCEC 2k 2r 1 2 2 Rb nbangles C CRbll -f C2k 2 'll j-ob 1 \ Rb nbangles where i-obj andLobj are the coordinates of the objective position in pixels, and or the sign% denotes the modulo, and where E (x) denotes the integer part of x.

/?a.y =(/~-/~/Mo;r)./M.'.~pa'<:)/ pas-(j o6 j max).pas-parixe! ou pas~par pixel est le nombre de pas des moteurs par pixel de déplacement, déterminé expérimentalement pendant les réglages. The displacement of the motors is calculated:

/? ay = (/ ~ - / ~ / Mo; r) ./ M. '. ~ pa'<:) / pas- (j o6 j max). not-parix! or steps ~ per pixel is the number of motor steps per displacement pixel, determined experimentally during the adjustments.

la position du point d'impact direct du faisceau d'éclairage (pour pas i<O, il doit effectuer un nombre de pas -pas i dans la direction opposée). L'autre moteur permet de déplacer le point d'impact direct du

faisceau dans la direction de Paxey. De même, il doit effectuer un nombre de paspasj. (1309) - Un tableau de fréquences moyennées est généré:

Chaque dimension du tableau initial .s est divisée par deux pour donner un tableau .11,t avec ii,fk Il. 1] .S-[2<+2y+<7] 0#p#1 0#q#1

(1310)-Le point de module maximal du tableau A est déterminé, ses coordonnées imaxJ... ' jmax et la valeur en ce point max - moy = AI tH#../H< 1 sont enregistrées (1311) -Les éléments du tableau Alk sont normalisés en les divisant par w<7y wo) [,..]= ,\1 ,dl. ) max~moy (1312) - imaxk , jmaxk et la représentation fréquentielle @fk sont enregistrés dans le fichier

frch acquis. (1308) - One of the motors makes it possible to move the point of direct impact of the beam in the direction of the axis i. He must take a number of steps ~ 1 in the direction corresponding to an increasing index i for

the position of the point of direct impact of the lighting beam (for step i <O, it must perform a number of steps -pas i in the opposite direction). The other motor moves the point of direct impact of the

beam in the direction of Paxey. Likewise, he must perform a number of paspasj. (1309) - A table of averaged frequencies is generated:

Each dimension of the initial array .s is divided by two to give an array .11, t with ii, fk Il. 1] .S- [2 <+ 2y + <7] 0 # p # 1 0 # q # 1

(1310) -The maximum modulus point of table A is determined, its coordinates imaxJ ... 'jmax and the value at this point max - avg = AI tH # .. / H <1 are recorded (1311) -The elements of the Alk table are normalized by dividing them by w <7y wo) [, ..] =, \ 1, dl. ) max ~ avg (1312) - imaxk, jmaxk and the @fk frequency representation are saved in the file

frch acquired.

(1313) - The algorithm ends when the angle is 2r. The motor then returns to its initial position and the acquired acqtiisitionfich ~ file is closed.

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chaque représentation. Dans la k -ième représentation fréquentielle tridimensionnelle la relation entre les coordonnées et la fréquence caractéristique est: K)fc =Ci-C'x,J-'3. JK2 -(1 - C 7), ~(j ~ C J,)2 La relation entre les coordonnées et la fréquence d'éclairage est K, =Cinrcrxk -C'x, Jmczxk -C., K2 -(inlczrk -C' Z -(Jmaxk -('y ) z La relation entre les coordonnées et la fréquence totale est donc: kifr=Ci-inraxk,j-jmcrx, KZ-i-Cx2-(j-C'y)z 2 K -(mlaxk -CJ2 -(}l1laxk - C )2 ) La procédure de calcul tridimensionnel consiste en principe à générer dans un premier temps une représentation tridimensionnelle sous forme d'un tableau F de dimensionsfil1m \fdim xfilil1l avec fdim=5\2, puis à en effectuer la transformée de Fourier pour obtenir un tableau F de mêmes dimensions correspondant à la représentation u(r), et dans lequel les indices correspondent donc au rayon-vecteur. La

représentation F cst un tableau dont les indices représentent les coordonnées de Raz,. le zéro étant ramené par translation au point de coordonnées (fdim/2/dim/2/dim/2). On obtient donc, à partir de chaque point de coordonnées i,j d'une représentation bidimensionnelle Mk. un point de la représentation tridimensionnelle par :

Frri,rj,nk ~ .11.r.J avec: fdun ni = t - ;W#rt. + fdrnr fdim n} =} - }maxk + fdl 2 rrl nk= h2-r-Czz-(j-C)2 J"2 (, 2 - (jiiiaxk - fi/un = - I-Cx - }-C.y Ullaxk -Cx - l'naxk -() 2
Lorsque un point du tableau F, de coordonnées (ni,nj,nk), est obtenu successivement à partir de plusieurs représentations bidimensionnelles distinctes, la valeur de F retenue en ce point est la moyenne des valeurs obtenues à partir de chacune de ces représentations bidimensionnelles. Lorsque ce point n'est jamais obtenu, on affecte une valeur nulle. 5. 21. three-dimensional calculation
The acquisition procedure generated two-dimensional frequency representations Mk. Where the index k represents the sequence number of each representation. These representations having been averaged over a width of 2, the values of Cx, Cy and K must be divided by 2 to correspond to the new coordinate system. It is these divided values which are used in the following. The set of two-dimensional representations can be considered a three-dimensional representation (i, j, k) in which the index k represents the image index and the indices / and represent the Cartesian coordinates of

each performance. In the k-th three-dimensional frequency representation the relation between the coordinates and the characteristic frequency is: K) fc = Ci-C'x, J-'3. JK2 - (1 - C 7), ~ (j ~ CJ,) 2 The relation between the coordinates and the illumination frequency is K, = Cinrcrxk -C'x, Jmczxk -C., K2 - (inlczrk -C ' Z - (Jmaxk - ('y) z The relation between the coordinates and the total frequency is therefore: kifr = Ci-inraxk, j-jmcrx, KZ-i-Cx2- (j-C'y) z 2 K - ( mlaxk -CJ2 - (} l1laxk - C) 2) The three-dimensional calculation procedure consists in principle in first generating a three-dimensional representation in the form of an array F of dimensionsfil1m \ fdim xfilil1l with fdim = 5 \ 2, then to perform the Fourier transform to obtain an array F of the same dimensions corresponding to the representation u (r), and in which the indices therefore correspond to the radius-vector.

representation F is an array whose indices represent the coordinates of Raz ,. the zero being brought back by translation to the coordinate point (fdim / 2 / dim / 2 / dim / 2). We therefore obtain, from each point of coordinates i, j of a two-dimensional representation Mk. A point of the three-dimensional representation by:

Frri, rj, nk ~ .11.rJ with: fdun ni = t -; W # rt. + fdrnr fdim n} =} -} maxk + fdl 2 rrl nk = h2-r-Czz- (jC) 2 J "2 (, 2 - (jiiiaxk - fi / un = - I-Cx -} -Cy Ullaxk - Cx - l'naxk - () 2
When a point of the table F, of coordinates (ni, nj, nk), is obtained successively from several distinct two-dimensional representations, the value of F retained at this point is the average of the values obtained from each of these two-dimensional representations . When this point is never obtained, a null value is assigned.

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When table F has been generated, table U can be obtained by inverse three-dimensional Fouricr transform.

This method can be applied directly if the program has sufficient RAM. The program, the algorithm of which is described in FIG. 19, however, makes it possible to perform the calculations on a system with limited RAM, the files being stored on a sequential access medium (hard disk).

For practical reasons, part of the Fourier transformation will be carried out as the table F is generated, which will therefore never be truly generated.

nr= i-inrcrx-fdrml2,nj=j jmnx-fdr t12, les dimensions suivant ni et iii du tableau ainsi généré étant defil1m v fdim. L'algorithme de cette partie est représenté figure 21. Les étapes sont les suivantes: (1600): les valeurs de hel,vel,nbim sont lues dans le fichicry/c//~tfr<7w/.Y. The program operates in five stages. Each step uses an input file stored on the hard drive of the computer and generates an output file also stored on the hard drive, the name of which is in italics in the figure. The program could theoretically perform more directly the operations necessary for the generation of the three-dimensional image, but the size of the files involved is too large for them to be entirely contained in the memory of a computer. manage their disk storage. Since the reading / writing of file items to disk is faster if the items are stored together, the program should be designed to read and write to the disk only blocks of sufficient size. This is what the algorithm described allows, whereas a direct method would require reads / writes at non-contiguous addresses and would not be practicable because of the time lost in disk access. The steps of the algorithm are as follows (! 400) - centering of the two-dimensional frequency representations:
This procedure consists in translating the two-dimensional representations to pass from a representation in the coordinate system (i, j, k) to a representation in the system (ni, nj, k) with

nr = i-inrcrx-fdrml2, nj = j jmnx-fdr t12, the following dimensions ni and iii of the array thus generated being defil1m v fdim. The algorithm of this part is represented in figure 21. The steps are as follows: (1600): the values of hel, vel, nbim are read in the file / c // ~ tfr <7w / .Y.

. Tk [ni, n = .11 Ini - fdint l 2 + inrrzx , rtj - fdtm 12 + jl1laxd lorsque 0 < ni - fdim 12+ imaxk < hel -1 1 et 0 < nj - fdrm l 2 + jnrrrxt. < tel - 1 . (1601): the frequency representation Mk corresponding to the index k is transferred to the main memory with the corresponding values imaxk and jmaxk '(1602). A translated frequency representation Tk of dimensions, /? ///// xfdun is generated with

. Tk [ni, n = .11 Ini - fdint l 2 + inrrzx, rtj - fdtm 12 + jl1laxd when 0 <ni - fdim 12+ imaxk <hel -1 1 and 0 <nj - fdrm l 2 + jnrrrxt. <tel - 1.

. Tk [ni, ni] = 0 in the other cases FIG. (20) shows an original image with its coordinate point (illlaxk jnrax) and an arbitrary drawing around this point, and the new translated image.

(1603): The values of Imaxk jmax, t, and the representation Tk are saved in the file-centered file in the following order: imaxk jnrmc,. Tk [0,0], Tk 1.0, ...... Tdfdl / J / - 1,0], imaxk 'J'7'axk, - T [0, Il- Tk 1.1, ...... T,, fdrnr -1, l.

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imaxk > jmaxk . 7k 0, fdrm I [l,fdim], ...... Th ~ fdinr -1, fdnar -1 Notons que imaxk et jmaxk sont répétés à chaque ligne de Tk, dans le fichier fich centré Ceci

permet que ces données, indispensables au changement d'indice A- -># rab- , restent disponible après l'opération d'échange des axes.

imaxk> jmaxk. 7k 0, fdrm I [l, fdim], ...... Th ~ fdinr -1, fdnar -1 Note that imaxk and jmaxk are repeated on each line of Tk, in the file centered file This

allows these data, essential for changing the index A- -># rab-, to remain available after the axis exchange operation.

(1604): the process is restarted as long as k is less than nbim.

(1401) -Exchange of the 'plane' and 'line' axes The change of indices i # ni and j # nj having been carried out, it remains to make the change of index k # nk. To perform this change of index in a reasonable time, it is necessary to be able to load a plane (nt, k) into the main memory quickly. For this operation to be possible, the k and nj axes must first be exchanged. This is what this algorithm does.

The previously created centered file file is reread, the data order is changed and an ech file file is written in which the data is in the following order: w! # <- o. y / no. TO [O.0], 7o [1.0] ....... 7o [w! - 1.0], / M, # <- t, 7, [00]. 7, [1.0] ...... Ta fdmr -1,0, im # cnbim ~ x, jj) rnhrrn-1 Tnbrm-1 0,0], Tnbiiei-1 1.0] ....... Tnbrm -1 .fcllW - 1,0], Imaxo, jmaxp.7p0, l, Tol, l ....... Tpfdinr-1,1, at .yw # f ,. Tl [0, I], Tl [1, in Il [flint -1,1], i, 71axnbitn-1 jmaxnbi, e-1 'mt [0-1] - T ,, b, pn-1 [1.1] , ....., TnlJ / m- [fdull-l, 1], irarcrxo, jnaaxp.7r0, fdtm-1,11, fdrnt-1, ...... hfdrnr-I, 1, fdiiei - 11 , w7, #f), Tx \ 0, fdim - \\ Tt l, jdtnt - 1, ... ~. Tl fdrm -1, fdnat -1 imct-rnbrrn-1, Jnlnhrm-1 Tnbll / II [0, fdiill - Il Tnbrrn-I 1> .fdr7lt - 1], ...... Tnhrm-1 [fdim - 1 , fd1l1 / - 1, That is to say that the axes nj andk are exchanged. This axis exchange operation is carried out block by block. Fig. (22) symbolically represents (1700) the content of a three-dimensional file corresponding to indices i, j, k, stored in memory horizontal plane by horizontal plane and each plane being arranged line by line, a line being in the direction of the depth on the drawing. The axes i, j, k and the origin O of the coordinate system are specified on the drawing. The content of the file obtained by inverting the} and k axes is represented in (1702). The transfer of data from one file to another is done block by block, the block (1701) being copied into main memory then transferred to (1703). Reading and writing of the blocks is done horizontal plane by horizontal plane, a horizontal plane in the read file does not correspond to a horizontal plane in the file

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written. The block size is the maximum size that can fit in the available internal memory of the computer. The operation is repeated for all the blocks, the blocks located 'at the edge' generally not having the same size as the others. This way of operating makes it possible to exchange the axes with a computer whose internal memory is smaller than the size of the files used.

void echange~axes(FILE* read~file,FILE* -N rite~f-ile,iiit ktot,inl jtot,int itot,int memorLlimit ) { int knumjnum,bknum,bjnuni,keffjeffkj,bk,bj-, char* buff; knum= (int )sq rt( ((double )memOlL limi t)1 (( doub le)i tot : jnum=knum; buf(char*)malloc(itot*knum*jnum); bknum=ktot/knum; if (knum*bknum!=ktot) bknum+= 1 ; bjnum=jtot/jnum ; if (jnum*bjnum!=jtot) bjnum+= 1;

for (bk=O;bk≤bknum-1 ;bk++) for (bj=O;bj≤bjnum-l;bj++)

if (bk==(bknum-1)) keff ktot-knum*(bknum-1); else keff--knum; if (bj==(bjnum-I)) jei=jtot jnum*(bjnum-1); else jefT=jnum; for (k=O;k≤kef l;k++) for =0,j≤jcff- 1 -,j++) { fseek(read file.(bk*knum+k)*jtot*itot+(bj*jnum+j)*itot,SEEK~SET); fread(buff+k*jeff*itot+j*itot, 1, itot, read~file); }

for(j=0.j≤jeff-t:j++) for (k=O;k≤keff l;k++) fseek(w-rite file,(bj*jnum+j)*ktot*itot+(bk*knum+k)*itot,SEEK SET); fwrite(buff+k*jeff*itot+j*itot, 1, itot, writç file); } The procedure in C language (Microsoft C / C ++ under Windows 95) which allows this operation is the following

void echange ~ axes (FILE * read ~ file, FILE * -N rite ~ f-ile, iiit ktot, inl jtot, int itot, int memorLlimit) {int knumjnum, bknum, bjnuni, keffjeffkj, bk, bj-, char * buff; knum = (int) sq rt (((double) memOlL limi t) 1 ((double) i tot: jnum = knum; buf (char *) malloc (itot * knum * jnum); bknum = ktot / knum; if (knum * bknum! = ktot) bknum + = 1; bjnum = jtot / jnum; if (jnum * bjnum! = jtot) bjnum + = 1;

for (bk = O; bk≤bknum-1; bk ++) for (bj = O; bj≤bjnum-l; bj ++)

if (bk == (bknum-1)) keff ktot-knum * (bknum-1); else keff - knum; if (bj == (bjnum-I)) jei = jtot jnum * (bjnum-1); else jefT = jnum; for (k = O; k≤kef l; k ++) for = 0, j≤jcff- 1 -, j ++) {fseek (read file. (bk * knum + k) * jtot * itot + (bj * jnum + j) * itot, SEEK ~ SET); fread (buff + k * jeff * itot + j * itot, 1, itot, read ~ file); }

for (j = 0.j≤jeff-t: j ++) for (k = O; k≤keff l; k ++) fseek (w-rite file, (bj * jnum + j) * ktot * itot + (bk * knum + k) * itot, SEEK SET); fwrite (buff + k * jeff * itot + j * itot, 1, itot, writç file); }

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read file: pointeur sur le fichier fich centré write~file: pointeur sur le fichier fichechl ktot: nombre total d'images nbim jtot: nombre total de lignes dans une représentation fréquentielle: fllim itot: taille en octets d'une ligne:./î//m*sizeof(complexe)+2*sizeof(int), ou si7eof(compleae) désigne la taille en octets d'un nombre complexe (Tk [i,j] par exemple) et sizeof(int) la taille en octets d'un nombre entier (imaxk par exemple).

memor3,~Iiiiiii: taille maximale en octets de la mémoire à accès aléatoire (RAM) dont dispose la procédure pour stocker les blocs. } free (buff); } The parameters to pass when calling the procedure are:

read file: pointer to the centered file write ~ file: pointer to the file ecl file ktot: total number of images nbim jtot: total number of lines in a frequency representation: fllim itot: size in bytes of a line: ./ î // m * sizeof (complex) + 2 * sizeof (int), or si7eof (compleae) designates the size in bytes of a complex number (Tk [i, j] for example) and sizeof (int) the size in bytes of an integer (imaxk for example).

memor3, ~ Iiiiiii: maximum size in bytes of random access memory (RAM) available to the procedure for storing blocks.

The files must be opened in 'commited' mode, that is to say that read / write operations are carried out directly from or to the hard disk, without intermediate buffering in main memory.

(1402) - calculation phase.

nk = fdfi)1 + h - 2 i - Cx - 2 ( j - Cy., 2 I: - Z i uzr. - '.. z - Jrmrk - ('y, ou i,j sont les coordonnées dans le repère d'origine (avant centrage). Dans le repère centré on a donc nk = ;;2 [ni - fdinr,'2+imaxk -C'z)2 -( j- film/2+ jiiia-vk. - ('J,)2 '2 (' )2 (. )2 + ' 2 1/1laxk -Cx - j11laxk -( +2 Lorsque les mêmes indices (i,j,k) sont obtenus plusieurs fois par remplacement de l'indice image, la valeur retenue pour l'élément correspondant de la représentation fréquentielle tridimensionnelle est la moyenne des valeurs pour lesquelles les indices (ij,k) sont obtenus. The purpose of this calculation phase is to replace the 'image' index k by the index nk given by the formula:

nk = fdfi) 1 + h - 2 i - Cx - 2 (j - Cy., 2 I: - Z i uzr. - '.. z - Jrmrk - (' y, or i, j are the coordinates in the reference of origin (before centering). In the centered frame we therefore have nk = ;; 2 [ni - fdinr, '2 + imaxk -C'z) 2 - (j- film / 2 + jiiia-vk. - (' J,) 2 '2 (') 2 (.) 2 + '2 1 / 1laxk -Cx - j11laxk - (+2 When the same indices (i, j, k) are obtained several times by replacing the image index , the value retained for the corresponding element of the three-dimensional frequency representation is the average of the values for which the indices (ij, k) are obtained.

(1800) les éléments suivants sont lus dans le fichierfich echl et transférés en mémoire interne imaxo, ,j11laxo To [0. nj], To[1.nj]....... Ta fdrnr -1, 1, nj], il1wx , jmaxl ' Tl [0, iijl, Tl [1, lij ]....... TI [fdi11l - 1, ni], A point of the three-dimensional frequency representation, of coordinates (ni, nj, nk), can only be obtained by this change of coordinates from a given plane (ni, k) corresponding to its index nj. The planes (ni, k) can therefore be processed independently of each other. When the index k has been replaced in a plane (ni, k) by the index nk, it is therefore possible to directly perform the inverse two-dimensional Fourier transform of this plane before going to the next plane. This is what this part of the program does, the algorithm of which is detailed in Fig. 23. Its main stages are:

(1800) the following elements are read from the echl file and transferred to internal memory imaxo,, j11laxo To [0. nj], To [1.nj] ....... Ta fdrnr -1, 1, nj], il1wx, jmaxl 'Tl [0, iijl, Tl [1, lij] ....... TI [fdi11l - 1, ni],

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mlaxnbl/11-1 JnW nbrrn-1 Tnb1/11-1 [0, nj]. Tnbnn-1 [1, J...... Tnbll11-1 .fr7lr - I, i7j] (1801) les tableaux Dnj et Poids, de dimensionsfdi/1/ xflhm, sont initialisés à 0.

mlaxnbl / 11-1 JnW nbrrn-1 Tnb1 / 11-1 [0, nj]. Tnbnn-1 [1, J ...... Tnbll11-1 .fr7lr - I, i7j] (1801) the Dnj and Weight tables, of dimensions fdi / 1 / xflhm, are initialized to 0.

nk = K2 -(ni- fdml 2+11naxk -Cx)2 -(nj- fllim /2+ jmaxk -ry)2 K2 - -(unaxk -rx)2 -(jmaxk -c}Y + fdim/2 (1804) La valeur correspondante de fréquence est additionnée au tableau Dnj.L'élément correspondant du tableaux des poids, qui sera utilisé pour calculer la valeur moyenne, est incrémenté

Dnj [I1I,nk]+ = Tk [11I,n)] POlds(ni,nk]+ = 1 (1805)Lorsque l'ensemble des indices ni,nk a ainsi été parcouru, le programme parcourt l'ensemble des indices ni et nk en testant la condition POld,1ni ,nk] f= 0 et à chaque fois que cette condition est réalisée il effectue: [iii,nkl Dn, ;.nkl Dnl [nr, MA-] = ###-###ni [11I,nk] = Po 1 d,\ .r [111 , nk (1806)le programme effectue une transformée de Fourier bidimensionnelle inverse du tableau Dnj.

(1802) The following condition is tested: [ni - fdml 2 + imaxk -Cx) 2 + (nj - fdi / 1 / 2+ jmaxk ~ ('y) 2 <[k'# I where o is the opening of the microscope, and n the index of the optical oil and the coverslip used, i.e. approximately: 0 = 1.25 If the condition is true, the point corresponds to a frequency vector not exceeding n 1.51 l 'aperture of the objective and is therefore in the observable zone (1803) The value nk is calculated by the formula

nk = K2 - (ni- fdml 2 + 11naxk -Cx) 2 - (nj- fllim / 2 + jmaxk -ry) 2 K2 - - (unaxk -rx) 2 - (jmaxk -c} Y + fdim / 2 (1804 ) The corresponding frequency value is added to the table Dnj The corresponding element of the weight table, which will be used to calculate the average value, is incremented

Dnj [I1I, nk] + = Tk [11I, n)] POlds (ni, nk] + = 1 (1805) When the set of indices ni, nk has thus been scanned, the program scans the set of indices ni and nk by testing the condition POld, 1ni, nk] f = 0 and each time this condition is fulfilled it performs: [iii, nkl Dn,; .nkl Dnl [nr, MA-] = ### - ## #ni [11I, nk] = Po 1 d, \ .r [111, nk (1806) the program performs an inverse two-dimensional Fourier transform of the array Dnj.

(1807) it stores the transformed array in the output file calc file in the following order Dn [0.0]. Dnr [1.0] ...... D'Y [fdim - 1.0], Z) M; [0.l], [l, l] Dnl jdrn r -1,1, D'Y 0, fdtm - 1 ], Dnr [1, fdim - l] Dnj fdrnt -1, fdinr -1 (1403) -2nd exchange of the axes: It remains at this level to perform an inverse Fourier transform in one dimension along the axis nj In order to be able to to perform this transformation in a reasonable time, it is necessary to exchange the axes nj and nk beforehand. The program will then be able to load complete plans (ni, nj) into central memory in order to process them.

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Dp [0,0]. Dp [1,0]...... D p [ fdim -1,0]. In the file file the data are arranged in the following order

Dp [0.0]. Dp [1.0] ...... D p [fdim -1.0].

Do [<U], Do [1.1], ..... Dp [fdrm - I, 1], Do [0, fdii? J - 1]. Do [1, jdrnr -1] ...... Do [fdim -1, farm -1], Dl [0.0], Dl [1.0], ..... Dl [fdiiii - 1.01, Dl [0.1]. Dl [1.1], ..... D, [fdim - 1.1], D, [0, fdm -1], D, [1. fdint -1], ..... D, [fdim -1, fdu) -1], D fdrrn-1 [0.0]. D fdrm-1 [1.0] ...... D fd, m-, [, fdu) r -1,0], Dfdrrn-1 [0.1]. 1) fdllli-i [1,1] ...... D fdrrn-1 [.Îdi1)) - 1,1], D jdzm-l [0, .fdrnr -1]. f) fdlllz- [1. jdrnr -1] ...... Dfd ,,, - l [frlrm -1, fdinr - 1] This file is re-read, and a file chisel is generated, in which the data is rewritten in the following order: Do [0,0]. IJo [1.0] ... '"Do [fdl1ll - 1.0].

D, [0.0]. D, [1.0] ..... D, [fditii - 1.0].

D fdrm-1 [0.0]. Dfdnn-1 [1.0], D fdzm-l [Idrn1- I, 0], Dp [0.1], Dp [1,1], ..... Do [fdim - 1,1], Dl [0.1], Dl [1,1] ..Dl [fdiiii-1, I], Dfdrm-1 [, 1]. I) fdrm-I [1,1], ..... D3drm-1 [.fdint- 1, 11, Do [0, fdim -1], Do [1. 1, fdin) - 1] ...... Dp [, fdrnr -1, fdull- I].

D, [0, fthm - 1), D, [/ ri1 // - 1], ..... D, [, fdi)) t -1, fau) r - 1], Dfdmr-i [0, .idrm -1]. D fdlln-l [1, .iaim -1], ..... D fdzm-t [fdim - l, fdl1ll- 1] This exchange of axes nj and nk is carried out in blocks like the previous exchange of axes. The same procedure is used, the parameters to be passed being:

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read-file: pointeur sur le fichier fich calc writefile: pointeur sur le fichier fwh~ech2 ktot: fdim jtot : fdim

itot: taille en octets d'une ligne. fdim*sizeof(complexe) ou sizcof(complexe) désigne la taille en octets d'un nombre complexe.

memory-limit: comme précédemment, la taille en octets de la mémoire disponible.

read-file: pointer to the calc file writefile: pointer to the fwh ~ ech2 ktot: fdim jtot: fdim file

itot: size in bytes of a line. fdim * sizeof (complex) or sizcof (complex) is the size in bytes of a complex number.

memory-limit: as before, the size in bytes of the available memory.

D0[0, ma-]. I701. nk, ..... Do[fdi11l - 1, nk]. (1404) -Last Fourier transformation This procedure consists of performing the inverse Fourier transformation along the nj axis. This is an iterative processing on the nk index. The algorithm for this part of the program can be found in Fig. 24. Its essential steps are as follows: (1900): the program loads the values into internal memory:

D0 [0, ma-]. I701. nk, ..... Do [fdi11l - 1, nk].

Enk.O . Enk,l 0, .... Enk, fdim-1 , Enk.O [1]. Enk,1 f1] EFnk, fdrm-1 [1]. Dl 0, nk D) 1, nk, ..... Ten [dim - 1, nk D fdim-I U, 1 k. D fdl / nI [1. nk] ...... D fdun-1 Idrm -1, 1, nk] (1901): The program generates the one-dimensional array Enk, n: Enk, m [nj] = DnJ [11l, nkJ It performs the inverse Fourier transform of this array, generating the array # nk, n @ (1902): it saves the results in the file Fich ~ dir, in the following order:

Enk.O. Enk, l 0, .... Enk, fdim-1, Enk.O [1]. Enk, 1 f1] EFnk, fdrm-1 [1].

Enk, O [Jdull-1]. Enk.! Idinr -1], .... Enk, fdrrn-1 [Jdim - 1] The file thus generated then contains the three-dimensional representation of the object in the format [l11l, nj, nk] or the complex element 1 Ini, nj , ilkl is stored in the file dir file at the address (nk * fdull * filim -'- nj * fd / 1ll: ni) counted from the start of the file, the addressing being done by elements of type 'complex number '
5.22. visualization
The table having been generated, we can view its content.

tableau l'(ni, n}] = Re(f '[ni, nj, nk~fy ou nk a une valeur fixée, et ou Re(.v) désigne la partie réelle de x. Il The simplest visualization consists in extracting a section from it, one of the indices being fixed at a constant value. On this section, we can visualize the real part, the imaginary part or the module For example to extract a partly imaginary section at constant nk, the program first generates the

array l '(ni, n}] = Re (f' [ni, nj, nk ~ fy or nk has a fixed value, and where Re (.v) denotes the real part of x.

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détermine ensuite les valeurs minimales et maximales du tableau I'soit V min = min!'y7i,n , nI.ll} Y m,n = min,(1 '[ni, 11))) . Il génère alors un tableau de pixels à afficher sur l'écran (bitmap), le niveau de gris ni ,n} t'fn/,//1-r d'un pixel donné de coordonnées ni,nj étant: valni,nj ~ 1 mav ! mm max min
Un autre mode de visualisation consiste à en extraire des projections. L'image visualisée dépend fortement du type de projection utilisée.

then determine the minimum and maximum values of the table I. Let V min = min! 'y7i, n, nI.ll} Y m, n = min, (1' [ni, 11))). It then generates an array of pixels to be displayed on the screen (bitmap), the gray level ni, n} t'fn /, // 1-r of a given pixel with coordinates ni, nj being: valni, nj ~ 1 mav! mm max min
Another visualization mode consists of extracting projections from them. The image viewed strongly depends on the type of projection used.

I [w. /] = Re [ni, /, nA-1). ou Re(x) désigne la partie réelle de x, la somme sur nk étant prise entre k deux plans 'limite' selon ce que l'on veut représenter, et le tableau V étant représenté comme précédemment
Pour une projection de la partie réelle selon )' axe nk. par extraction du maximum envaleur absolue, on représentera le tableau T'avec:

1'[ni,nil = maxf!Re 'i, ', /?A 1))) nk Dans ces deux cas on peut représenter le tableau Vàl'écran selon la méthode déjà utilisée pour la

t'fM/,n/1-t' représentation d'une coupe, soit l'al[ni,nj] = # #r #r ou Fmin et 1 ma sont respectivement les
Vmax-Vmin valeurs minimales et maximales de V. For example for a projection of the real part according to) 'axis nk, by integration, we will represent the table V with

I [w. /] = Re [ni, /, nA-1). or Re (x) denotes the real part of x, the sum over nk being taken between k two 'limit' planes depending on what one wants to represent, and the table V being represented as previously
For a projection of the real part along) 'axis nk. by extraction of the maximum absolute value, we will represent the table T'with:

1 '[ni, nil = maxf! Re' i, ', /? A 1))) nk In these two cases we can represent the table V on the screen according to the method already used for the

t'fM /, n / 1-t 'representation of a cut, that is al [ni, nj] = # #r #r or Fmin and 1 ma are respectively the
Vmax-Vmin minimum and maximum values of V.

Although the example taken was cuts with fixed nk and projections along nk, these cuts and projections can be carried out in any direction, including oblique directions.

projection par rapport à la verticale: la direction de projection doit faire avec la \ verticale un angle suffisamment inférieur à Arc sin(ouv/nv). Dans le cas de la projection par extraction du maximum, des (nv) défauts seront présents quelque soit l'angle d'observation. Par contre, la projection par extraction du maximum est moins sensible au bruit gaussien que la projection par intégration. Since a large part of the frequency representation is not acquired, certain defects ensue in the images obtained in spatial representation, which depend on the type of image represented. In general, the defects will be less important for a top view. In the particular case of integration projection, the image produced will remain of good quality up to a limit angle of the direction of

projection with respect to the vertical: the direction of projection must make with the \ vertical an angle sufficiently smaller than Arc sin (open / nv). In the case of projection by extraction of the maximum, (nv) defects will be present whatever the angle of observation. On the other hand, the projection by extraction of the maximum is less sensitive to Gaussian noise than the projection by integration.

projection. Cette méthode nécessite le stockage en mémoire de la représentation fréqueiiiielle de l'objet Celle-ci peut par exemple avoir été obtenue comme indiqué en 5. 21 mais en n'effectuant pas les transformations de Fourier prévues en (1806) et en (1901). La méthode rapide comporte deux étapes: étape 1: extraction, en représentation fréquentielle, d'un plan passant par l'origine et orthogonal à la direction de projection. In the case of the projection by integration, a fast method can be obtained to carry out the

projection. This method requires the storage in memory of the frequency representation of the object This one can for example have been obtained as indicated in 5.21 but by not carrying out the Fourier transformations envisaged in (1806) and in (1901) . The rapid method comprises two stages: stage 1: extraction, in frequency representation, of a plane passing through the origin and orthogonal to the direction of projection.

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step 2: inverse Fourier transformation of this plane.

The two-dimensional table thus obtained constitutes a projection along the direction which was used to extract the frequency plane.

It is possible to generate a stereoscopic view by extracting two projections following appropriate directions and using for example the anaglyph method to visualize them. In this case, the use of the fast method makes it possible, if the computer has sufficient memory for storing the three-dimensional representation, to modify in real time the observation angle of a precomputed image in the form of a frequency representation.

6. Description of a second embodiment.

This embodiment is a simple variant of the first and is shown in Fig. 25.

6. 1. Principle
In the first embodiment, the sensor (118) is in the image focal plane of the optical assembly consisting of the objective (113) and the lenses (115) and (117). The plane illuminating wave therefore has a point image in this plane, and a spherical reference wave virtually centered on the object must be used to obtain homogeneous illumination on the sensor (118). In this second embodiment, the sensor (2018) is placed directly in the image plane of the objective. A plane illumination wave therefore no longer has a point image. The reference wave should be the objective image of a virtual plane wave passing through the object.

. /, Siri = ~111 (21su12 -ls,12 -ls212) + j (IX -iS,i2) l' 61' 2 311'1
La transformée de Fourier bidimensionnelle de cette image donne une image en nombres complexes équivalente à celle qui, dans le premier mode de réalisation, était obtenue directement dans le plan du capteur CCD. Cette image remplace donc l'image directement obtenue sur le capteur dans le premier mode de réalisation. Pour le reste, ce mode de réalisation utilise les mêmes principes que le premier. An image in complex numbers is obtained on the CCD (2018) from three images differing by the phase of the reference wave, using as in the first embodiment the formula

. /, Siri = ~ 111 (21su12 -ls, 12 -ls212) + j (IX -iS, i2) l '61' 2 311'1
The two-dimensional Fourier transform of this image gives an image in complex numbers equivalent to that which, in the first embodiment, was obtained directly in the plane of the CCD sensor. This image therefore replaces the image obtained directly on the sensor in the first embodiment. For the rest, this embodiment uses the same principles as the first.

6. 2. Physical description.

The system is shown in Fig. 25. The elements of this figure, identical to that of FIG. I, are numbered by replacing the first digit 1 of the elements of FIG. 1 by the number 20 For example (116) becomes (2016). This system is similar to that used in the first embodiment, except that the controlled attenuation device of the beam, consisting of the elements (104) and (105) is omitted.

-the CCD (2018) is placed in the plane where the diaphragm (114) was previously. Consequently, elements (114) (117) (115) are deleted.

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voisins) doit être inférieure jazz , ou ouv désigne l'ouverture numérique de l'objectif, la longueur 2 ouv d'onde dans le vide du laser utilisé, g le grandissement Par exemple, pour un objectif x 100 d'ouverture 1,25 on trouve 25 micromètres. On peut utiliser un objectif modifié pour avoir un grandissement x50, de manière à obtenir 12 micromètres, ce qui permet d'utiliser une caméra courante de pas 10 micromètres de manière plus optimale qu'avec un objectif x100. - The virtual image, after reflection on the semi-transparent mirror (2016), of the focal point of the beam coming from the lens (2023), must be located on the optical axis and in the image focal plane of the objective (2013). The elements (2023) (2022) (2021) (2016) are therefore moved so as to satisfy this condition -On the CCD sensor (2018), the base cell size (distance between the central points of two pixels

neighbors) must be less than jazz, or open denotes the numerical aperture of the objective, the wavelength 2 open in the vacuum of the laser used, g the magnification For example, for an objective x 100 of aperture 1.25 25 micrometers are found. We can use an objective modified to have a magnification x50, so as to obtain 12 micrometers, which makes it possible to use a current camera of 10 micrometers in a more optimal manner than with a x100 objective.

-The lens (2023) is mounted on a positioner allowing translation along the axis of the beam entering this lens.

6. 3.settings: overview
In the previous embodiment, the image received on the sensor was in the frequency domain. An image in the spatial domain could if necessary be obtained from it by inverse two-dimensional Fourier transform, which was achieved by the focusing program described in Fig. 14. In this second embodiment, the image received on the sensor is in the spatial domain and an image in the frequency domain can be obtained by Fourier transform.

Whenever the two-dimensional frequency image received directly on the CCD sensor (118) was used, it is now necessary to use the two-dimensional Fourier transform of the image received on the CCD sensor (2018), which constitutes a frequency image which can for example have a dimension of 256x256 square pixels. At the same time, the focusing program must be replaced by a program for direct viewing of the image received on the CCD sensor.

With the beam attenuation device removed, only one image should be used instead of two in the stages where this device was used.

The camera (2019) is fixed. The position adjustment of this camera along the optical axis is replaced by a position adjustment of the lens (2023) along the axis of the beam entering this lens The position adjustment of the camera in the plane orthogonal to the axis optics is replaced by an angular adjustment of the mirror (2016).

mode de réalisation, qui permettait d'observer une image dans le domaine fréquentiel. Pour utiliser ce programme, une onde de référence doit être utilisée, alors que dans le programme de visualisation directe For the rest, the operating mode is similar to the previous system. The adjustment steps and the programs used are detailed below: 6.4. Common use program:
In addition to the programs described in 5. 5. a frequency image display program is used. This program generally replaces the direct view program used in the first

embodiment, which made it possible to observe an image in the frequency domain. To use this program, a reference wave must be used, while in the direct view program

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used in the first embodiment, it was not necessary. When this program is used, vibrations must be avoided and therefore at least temporarily let go of the focusing device if it is used, or wait for the absorption of vibrations before each image when stepping motors are used.

This program is similar to the focusing program described in 5.1-1 and whose algorithm is in Fig. 14. It is amended as follows:
The image acquisition step (1000), detailed in FIG. 13, is modified as shown in Fig. 26, in order to take into account the absence of the beam attenuation device.

Step (1001) is deleted.

s[..7] = C6 (2lO,i, j-II,r,J-12>i,j +j 2 (II,t,J-I2,,jJ
Lors de l'étape (1002) le programme limite le tableau S à des dimensions de hpix x hpix mais n'effectue pas de moyennage
L'étape (1004) est remplacée par une transformée de Fourier directe
Lors de l'étape (1005), le programme affiche l'intensité, correspondant au carré du module des éléments du tableau S transformé, ainsi que la valeur maximale de cette intensité, les coordonnées du point correspondant et le rapport entre l'intensité de ce point et la somme des intensités de ses huit voisins
Ce programme permet d'apprécier la ponctualité et l'aspect général d'une image en fréquence Par contre, pour apprécier la non-saturation (qui doit être vérifiée dans presque toutes les étapes, ce qui ne sera plus rappelé) on continue d'utiliser les programmes décrits en 5 5., la non-saturation devant être vérifiée directement sur le capteur CCD (2018). Step (1002) is modified to take account of the absence of the table H For each pixel, the value is generated according to the following equations:

s [.. 7] = C6 (2lO, i, j-II, r, J-12> i, j + j 2 (II, t, J-I2,, jJ
In step (1002) the program limits array S to dimensions of hpix x hpix but does not perform averaging
Step (1004) is replaced by a direct Fourier transform
During step (1005), the program displays the intensity, corresponding to the square of the modulus of the elements of the transformed array S, as well as the maximum value of this intensity, the coordinates of the corresponding point and the ratio between the intensity of this point and the sum of the intensities of its eight neighbors
This program allows to appreciate the punctuality and the general aspect of a frequency image On the other hand, to appreciate the non-saturation (which must be checked in almost all the stages, which will not be recalled any more) one continues to use the programs described in 5 5., the non-saturation having to be checked directly on the CCD sensor (2018).

6.Adjustment of the position of the laser (2000) and mirror (2021)
This step is similar to the step described in 5.6.

6. 6.adjustment of the control voltages of the piezoelectric actuator,
The process is identical to that described in 5.12. , except that there is no adjustment of the diaphragm (114) removed and that the position of (2009) is adjusted so as to maximize the intensity received on the sensor. The fact that the image received directly by the sensor is in the spatial domain does not affect the result.

6.7. adjustment of the reference wave level.

This step is identical to that described in 5.11, the level of the reference wave being measured on the direct image.

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6. 8. Position adjustment of (2023) (2002) (2016):
This setting is similar to that described in 5. 7. The direct display program is replaced by the frequency image display program described in 6.4., For which the presence of the reference wave is necessary. The position adjustment of the camera along the optical axis is replaced by a position adjustment of the lens (2023) along the axis of the beam entering this lens. The camera position adjustment in the plane orthogonal to the optical axis is replaced by an angular adjustment of the mirror (2016).

6. 9. adjustment of the condenser position (2011).

This setting is similar to that described in 5.8. but it is the frequency image which must be observed in the presence of the reference wave, and not the direct image in the absence of the reference wave 6.10. lens position adjustment (2006).

It is similar to that described in 5.9, but it is the frequency image that allows us to appreciate punctuality.

6.11. determination of the number of steps per pixel.

This step is similar to that described in 5.10, but the pixel of maximum intensity is observed on the frequency image.

6. 12. obtaining the constant K.

This step is carried out on the same principle as that described in 5.14 but it is modified to take account of the inversion between direct image and frequency image.

To obtain the image of the micrometer, the objective is first put in a roughly focused position, the micrometer having been introduced as the object. The program for direct viewing of the image received on the CCD is launched, in the absence of a reference wave. The diaphragm in (2007) must be adjusted so that the observed area appears uniformly illuminated. The micrometer is moved under the objective until an image is obtained of it.

The microscope objective is then moved by the focusing device so as to obtain a correctly focused image. To facilitate focusing, it is advantageous to visualize a part of the micrometer where lines of different lengths are present. This limits 'false focusing' due to interference phenomena in front of the micrometer.

When a good image has been obtained, the program is stopped and the image obtained is used to obtain the distance in number of pixels between two lines, in the same way as in 5.14. If the distance between two graduations separated by Dreel micrometers is on the image thus obtained of Dpix pixels, if the nominal index of the objectives is nv (in general, nv is close to 1.5) and if the wavelength of the laser in vacuum is 2 (# = 0.633 micrometers) and if the number of points of the Fourier transform which

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sera utilisée pour l'acquisition d'image est X (=25G) alors on a: .: = rr-'' i 17 y, Dreel . ou Dreel et a sont # Dpix dans la même unité.

will be used for image acquisition is X (= 25G) then we have:.: = rr- '' i 17 y, Dreel. where Dreel and a are # Dpix in the same unit.

6.13. diaphragm adjustment:
This step is similar to that described in 5.15. but the focusing program is replaced by a direct display of the image received on the sensor in the absence of a reference wave.

6.14. recording of the reference wave:
This step is similar to that described in 5.16. The reference wave alone is recorded on the live image.

6. 15. focus on ('studied object.

This step is simplified, the specific focusing program being replaced by a program for direct viewing of the image received on the CCD sensor in the absence of a reference wave.
6.16. Adjustment of the position of the condenser and adjustment of the diaphragms
This step is similar to that described in 5.18 but: - the frequency image is now obtained in the presence of a reference round by Fourier transformation of the image received directly on the CCD sensor, and not directly as in 5.18.

- on the contrary, the image of the object in the spatial domain is now obtained directly and not by Fourier transformation of the image received on the CCD sensor.

6.17. filter adjustment.

The filters are set so that the image formed on the CCD by the illumination wave alone has a maximum intensity of 64.

6. 18. image acquisition.

This step is similar to that described in 5. 20 but the following modifications must be taken into account: -step (1302): is replaced by the image acquisition described in Fig. 26 -step (1303) deleted.

Sr,J= t 2lO,i,j-ll,r,j-lZ,r,J)+j I (II,t>J-f1>IJ fil 2 3rraf(r.l puis en effectuant la transformée de Fourier du tableau S. -step (1304) modified: the representation S [i, j] of complex numbers is generated by assigning to each point the following value

Sr, J = t 2lO, i, j-ll, r, j-lZ, r, J) + j I (II, t>J-f1> IJ fil 2 3rraf (rl then by performing the Fourier transform of the table S.

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6.19. calculation etane:
This step is identical to that described in 5.21.

6. 20. visualization: this step is identical to that described in 5.22
7. Description of a third embodiment.

This embodiment is more complex and more expensive than the previous ones, but it allows superior performance in terms of definition and speed.

7. 1. Principle.

This acquisition mode improves the performance of mode 1 as follows: - increase in the image acquisition speed:
In the first embodiment, this speed is limited by the mechanical movement of the stepping motors and the need to wait until absorption of the vibrations induced after each movement. The present embodiment makes it possible to accelerate this taking of images by replacing this mechanical system by an optical system for deflection of the beam, based on liquid crystals and not inducing mechanical displacements in the system.

- improved precision:
In the first embodiment, the precision is limited by the impossibility of adopting all the possible directions for the illumination beam and by not taking the reflected background into account. The present embodiment uses a two-lens system. The illumination is then effected by means of an objective, which allows the frequency vector of the illumination wave to vary over all of the two portions of the sphere limited by the opening of each objective. In addition, the reflected wave crosses the lighting objective and can be taken into account.

In the first embodiment, the variations in intensity of the diffracted wave as a function of the direction of polarization of the illuminating wave are not taken into account, which leads to errors in the measurement of high frequencies. In the present embodiment, polarization rotators make it possible to vary the direction of polarization of the illuminating wave and the direction of analysis of the diffracted wave. An algorithm takes into account all the measurements thus obtained in order to obtain frequency representations in which the dependence of the diffracted wave with respect to the polarization of the illuminating wave has been eliminated.

-compensation for spherical aberration:
In the preceding embodiments the average index in the observed sample must be close to the nominal index of the objective. Otherwise, the difference between the mean index of the sample and the nominal index of the objective results in a spherical aberration which strongly limits the thickness of the observable sample. In this new embodiment, the hardware configuration and

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the algorithms used make it possible to compensate for the phase differences induced by the mean index of the sample and to cancel this spherical aberration.

Paragraph 7.2. physically describes the microscope used.

This microscope is the subject of a set of preliminary adjustments carried out in the absence of the observed sample and which do not normally have to be repeated when the observed sample is modified: - The position adjustment of the various elements of the system is carried out as described in paragraph 7.4.

- The modulus of the reference wave is determined as described in paragraph 7.4.

- The Kp parameters. equivalent to the parameter K used in the first embodiment, are determined as described in paragraph 7.6.

- The characteristics of the lighting beams used are determined as described in paragraph 7.9.

- The order index tables are determined as described in paragraph 7.13.

After introduction of the sample, the microscope is subjected to a second set of adjustments: - The position of the objectives is adjusted as described in paragraph 7. 10.

objectif, ainsi que l'indice moyen 110 de l'échantillon et son épaisseur L, sont déterminés comme décrit au paragraphe 7.11. Cette détermination suppose l'utilisation d'un algorithme spécifique décrit au paragraphe 7.8., utilisant des équations établies au paragraphe 7. 7. Une version simplifiée de cet algorithme est également utilisée au paragraphe 7.9. - The relative x, y, z coordinates of the points of origin of the reference beams associated with each

objective, as well as the average index 110 of the sample and its thickness L, are determined as described in paragraph 7.11. This determination assumes the use of a specific algorithm described in section 7.8., Using equations established in section 7. 7. A simplified version of this algorithm is also used in section 7.9.

- The value w0 characterizing the position of the sample is calculated as described in paragraph 7.15. The determination of this value calls for an image acquisition procedure described in paragraph 7.12. and to the equations established in paragraph 7. 14. Simultaneously, a first adjustment of the position of the sample is carried out as indicated in paragraph 7.15.3.

- The aberration compensation function, in the form of Dp tables, is obtained as described in paragraph 7.16.

When these preliminary adjustments have been made, the procedure for obtaining three-dimensional representations can be started. This procedure is described in 7.17. It uses the image acquisition procedure described in 7.12. and uses the Dp table determined in 7.16. By repeating this procedure indefinitely, it is possible to obtain a succession of three-dimensional representations characterizing the temporal evolution of the observed sample. It is necessary to adjust the position of the sample so that the representation obtained is that of a zone of interest of the sample. This adjustment is carried out as indicated in 7.17.3. and may involve repeating the preliminary steps for calculating w0 and Dp described in 7.15.2, respectively. and in 7.16.

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Various variations of the algorithms and the settings made are described in 7.18. Many settings can be omitted if conditions are favorable, for example if the sample index and thickness are known in advance.

A method of designing microscope objectives, specifically adapted to this microscope, is described in paragraph 7.19.

7.2. physical description.

7.2.1. overview
Figs. 27 and 28 provide an overview of the system. Most of the system, shown in Fig. 27, lies in a horizontal plane and is supported by an optical table.

However, the two microscope objectives used must be positioned on a vertical axis (2263) in order to use a sample (2218) positioned horizontally. The axis (2263) is at the intersection of two vertical planes further defined by their horizontal axes (2261) and (2262). These horizontal axes can form an angle of 0 degrees, 90 degrees or 180 degrees between them. FIG. 28 shows partly a section along the vertical plane defined by (2261) and partly a section along the vertical plane defined by (2262).

The beam from a laser (2200) polarized in the vertical direction will be derived into four beams feeding the right and left optical chains associated with the two objectives of the microscope. These four beams are designated in the diagram and in the text by the following acronyms: - FRD right reference beam.

- FRG: left reference.

- FED: right light beam.

- FEG: left lighting.

Each of these beams will subsequently be divided into a main beam. which will be noted as the original beam, and a reverse indicator beam. The reverse indicator beams will be denoted FRDI, FRGI, FEDI, FEGI.

The beam comes from the laser (2200) and has its electric field vector directed along an axis orthogonal to the plane of the figure. It passes through a beam expander (2201) and is then separated into an illumination beam and a reference beam by a semi-transparent mirror (2202). The illumination beam passes through a diaphragm (2248), a filter (2203) then a beam attenuation device (2204), a phase shift device (2205), a beam deflection device (2206) which makes it possible to vary the direction of this parallel beam. It is then deflected by a semi-transparent mirror (2207) which separates a right illuminating beam and a left illuminating beam, intended to illuminate the sample in two opposite directions. The straight FED illumination beam is deflected by a mirror (2208), passes through a beam deflection and switching device (2209), a phase rotator (2210), and is separated by a semi-transparent mirror (2211) into a main lighting beam and a reverse indicator beam. The main light beam then passes through an achromat (2212). a diaphragm (2213), is reflected on a mirror

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(2214) returning it upwards, then on mirrors (2215) and (2216), and crosses the objective (2217) to go to illuminate the sample (2218). After passing through the sample, it passes through the objective (2219), is reflected by the mirrors (2220) (2221) (2222), then passes through the diaphragm (2223), the achromat (2224). the semitransparent mirror (2225), the phase rotator (2226), the achromat (2227), the semitransparent mirror (2228) and the polarizer (2253) and is received by the CCD sensor (2229).

Both objectives (2217) and (2219) must have their optical axis (2263) vertical so that the optical oil necessary to use them does not leak. The mirrors (2214) (2215) (2216) (2220) (2221) (2222) serve to deflect the beam so that it can pass through the objectives in a vertical direction. Fig. 28 represents a section along the axes (2262) and (2263), articulated around the optical axis (2263).

Fig. 29 is a representation of the optical path of light rays between the objective (2219) designated as 'OM' and the CCD sensor (2229) designated as 'CCD'. The mirrors, semi-transparent mirrors and phase rotator have been omitted in the figure but influence the position of the various elements. The rays propagate along an optical axis represented 'straight', which in reality ceases to be rectilinear between the planes P2 and P1, an area where it is deflected by mirrors (2220) (2221) (2222) to approach the lens in a vertical plane. The left part of the figure represents the optical path of rays which are parallel in the studied sample, and the opposite right part the optical path of rays coming from a point in the observed zone. The achromat (2224) is designated by 'L1', the diaphragm (2223) by 'D', the achromat (2227) by 'L2'. f1 is the focal length of LI, f2 is the focal length of L2. PI is the plane in which focus rays entering parallel to the objective (image focal plane). This plane must coincide with the object focal plane of the achromat (LI) so that a parallel ray entering the objective is also parallel between the achromats L1 and L2. P2 is the plane in which the image of the observed sample is formed. It is in this plane that the diaphragm (D) must be positioned. P3 is the virtual image of plane P2 by achromat LI. P3 must coincide with the object focal plane of L2 so that a ray coming from a central point of the observed object, forming a point image in P2, reaches the CCD in the form of a parallel ray. P6 is the image focal plane of L2. It is in this plane that the CCD must be placed, so that a parallel ray entering the objective forms a point image on the CCD
The optical path of the rays between the objective (2217) and the sensor (2239) is symmetrical to the previous one.

The reference beam separated by the mirror (2202) is reflected by (2233), passes through a filter (2234), and a semi-transparent mirror (2235) transforming it into a left part and a right part. The left part is reflected by the mirrors (2254) (2236), passes through the complementary filter (2255), the phase shift device (2251) and the diaphragm (2250) then reaches the semi-transparent mirror (2228) which it splits into a main beam and a reverse indicator beam The main beam is directed to the CCD (2229).

Both the illumination beam and the reference beam have reverse indicator beams having the same characteristics as the main beam but pointing in the opposite direction. The indicator FRGI reverses the reference beam FRG, coming from the semi-transparent mirror (2228). passes through the achromat (2281) and is focused on a mirror (2282) which reflects it. It then crosses again the achromat (2281) which makes it parallel again, then it is again reflected by the semi-transparent mirror (2228). He then has the same

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direction (but in the opposite direction) than the reference beam directed towards the CCD sensor (2229). Likewise, the reverse indicator FRDI of the lighting beam FRD, coming from the semi-transparent mirror (2211), is focused by the achromat (2231) on the mirror (2232). This reflects it, and after a new reflection on the semi-transparent mirror (2211) it has the direction opposite to that of the main illumination beam directed towards the objective (2217).

The entire device is optically symmetrical with respect to the observed object. There is therefore a left lighting beam having a role symmetrical with respect to the right lighting beam, and a right reference beam having a role symmetrical with that of the left reference beam.

The left lighting beam FEG, coming from the semi-transparent mirror (2207), is reflected on the mirrors (2280) and (2283) then passes through the deflection and switching device (2240) equivalent to (2209). It then passes through the polarization rotator (2241) and is then separated by the semi-transparent mirror (2225) into a main beam which goes towards the microscope objective (2219), and a reverse FEGI indicator beam which passes through the achromat (2242). is focused on the mirror (2243) and finally reflected again on (2225).

The right reference beam FRD, coming from the semi-transparent mirror (2235). is reflected by the mirror (2244) and passes through the complementary filter (2256). The semi-transparent mirror (2245) separates it into a main beam which passes through the polarizer (2252) and reaches the CCD (2239), and a reverse FRDI indicator beam which passes through the achromat (2246) and is focused on the mirror ( 2247), then returns to the semi-transparent mirror (2245) which reflects it towards the objective (2217).

The polarizers (2252) and (2253) are thin plates made of a dichroic sheet held between two panes of glass.

The zones (2274) (2275) (2276) (2277), delimited by dotted lines in the drawing, correspond to parts of the system entirely immersed in optical oil. Such a zone therefore constitutes a sealed container containing the optical elements visible in the drawing. The entry and exit of the beam in this receptacle is through windows treated with anti-reflective coating on their external face. This makes it possible to limit the defects linked to the size of the glasses used in the various devices included therein.

The CCDs (2239) and (2229) are integrated into cameras (2284) and (2230) themselves attached to three-axis positioners making it possible to adjust their position along the axis (2264) and along the two orthogonal axes at (2264), as well as in rotation around the axis (2264). Achromats (2227) (2224) (2212) (2237) (2246) (2231) (2242) (2281) are fixed to positioners one axis allowing fine adjustment of the position in the direction of the axis (2264) . The mirrors (2282) (2243) (2232) (2247) are attached to positioners allowing adjustment of their orientation. The diaphragms (2213) and (2223) are adjustable and attached to two-axis positioners allowing their position to be adjusted in the plane orthogonal to (2264). The semi-transparent mirrors (2225) (2228) (2211) (2245) are attached to positioners to adjust their orientation. The mirrors (2214) and (2222) are attached to positioners making it possible to adjust their orientation. The microscope objective (2219) is attached to a 2-axis positioner allowing it to be moved in a plane orthogonal to the axis (2263). The objective (2217) is attached to a focusing device allowing

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to move it along the axis (2263). The entire system is manufactured with the greatest possible precision in the positioning of the various elements.

The mirrors (2247) (2232) (2243) (2282) are equipped with manual shutters (2257) (2258) (2259) (2260) making it possible to suppress the beams reflected by these mirrors. FRD and FRG beams can be suppressed using completely opaque filters.

The sample (2218) consists of two strips of standard thickness (150 m) between which the substance to be observed is in a thin layer (50 to 100 m) This sample is fixed to a thicker slide so that this does not prevent the access of the sample by the objectives. The assembly is attached to a 3-axis positioner in translation.

The objectives used can for example be planapochromatic objectives of numerical opening OR \ = 1, -1 and of magnification g = 100 forming the image at 160mm from the neck of the objective. It is also possible to use other types of lenses, described in paragraphs 7.19 to 7.21.

Achromats (2212) (2237) (2224) (2227) (2246) (2231) (2242) (2281) can have for example the same focal length f = f1 = f2 = 200mm.

pour longueur D = 2/2 oui' le nombre de pixels étant X pix x N pix avec par exemple N'plv =256
Les dispositifs de contrôle du faisceau (2204) (2205) (2206) (2209) (2240) (2251) (2210) (2241) (2226) (2238) sont tous pilotés par des rotateurs de phase commandés par des tensions bipolaires La commande de ces dispositifs doit être synchronisée avec l'acquisition des images par la caméra La caméra peut être une caméra rapide de type analyseur de mouvement, dotée d'une mémoire suffisante, disponible par exemple chez Kodak. Le système de calcul est un ordinateur doté d'une mémoire suffisante pour stocker les tableaux tridimensionnels nécessaires. Des machines ayant par exemple 8Go de mémoire sont disponibles chez Digital Equipment. The CCD sensors used must have square pixels and a square useful area whose side has

for length D = 2/2 yes' the number of pixels being X pix x N pix with for example N'plv = 256
The beam control devices (2204) (2205) (2206) (2209) (2240) (2251) (2210) (2241) (2226) (2238) are all driven by phase rotators controlled by bipolar voltages. The control of these devices must be synchronized with the acquisition of the images by the camera. The camera can be a fast camera of the motion analyzer type, with sufficient memory, available for example from Kodak. The computing system is a computer with sufficient memory to store the necessary three-dimensional tables. Machines with 8 GB of memory, for example, are available from Digital Equipment.

The filters in (2203) (2234) (2255) (2256) make it possible to adjust the intensity of the different beams As in the first embodiment, their values must be frequently adjusted during the various settings and during the use of the microscope. These adjustments are made similarly to what was done in the first embodiment and will not be recalled. Their role is also to limit the intensity of the beams which are directed in the direction opposite to the normal and tend to return towards the laser (2200), during certain adjustment operations.

7.2.2.Beam attenuation device:
The attenuation device is shown in Fig. 30. It consists of a phase rotator (2501) designated 'RI' in the figure, a Glan-Thomson polarizer (2502) designated 'POLl', a second rotator (2503) designated 'R2', and d 'a second polarizer (2504) designated' POL2 '. The beam entering the device is vertically polarized. The angle of the neutral axis of (2501) with the vertical is 0 for a bipolar voltage applied to the terminals of the device of -5V and is rotated by an angle a by application of a voltage of + 5V, with a = About 22 degrees. The neutral axis of the rotator (2503) is characterized by the same

<Desc / Clms Page number 87>

angles, but relative to the horizontal and not to the vertical. The polarizer (2502) selects the horizontal polarization direction. The polarizer (2504) selects the vertical polarization direction.

Fig.3 illustrates the operation of the part of the device consisting of (2501) and (2502) for an applied voltage of -5V. It represents in bold lines the electric field vector (2505) of the beam at the input of the device, in a frame consisting of the vertical axis of polarization (2506) and of) the horizontal axis of polarization (2507). The passage through the rotator RI (2501) rotates this vector by an angle 20 ci it is therefore transformed into (2508). The passage through the POLI polarizer (2502) constitutes a projection on the horizontal axis. At the output of this polarizer, the electric field vector (2509) of the beam is therefore horizontal and its amplitude has been multiplied by a factor sin (20).

par siv{l0 + 2a) . Le facteur d'atténuation entre les positions 'ouverte' (+5V) et 'fermée' (-5V) est donc de si 20)

si2a + 20) expression qui s'inverse en: 1 Arc tan si2a) 0 = -Arctan - # " # '- # -cos2a a1 Par exemple pour a1 = 1 et a = 22 on trouve 0 = 1,30
16 La seconde partie du dispositif, constituée de (2503) et (2504). fonctionne exactement comme la première, à ceci près qu'elle prend en entrée un faisceau polarisé horizontalement et délivre en sortie un faisceau polarisé verticalement. Le facteur d'atténuation a2 de cette seconde partie est donc donné par la même formule que a, et on règlera les deux parties du dispositif de façon à avoir dans chaque partie la même atténuation (ou à peu près). Du fait de disparités de réglage entre les deux parties du dispositif, a2 et a1 ne sont cependant pas rigoureusement égaux en pratique. Figure 32 illustrates the operation of the part of the device consisting of (2501) and (2502) for an applied voltage of + 5V. The neutral axis of RI before been rotated by an angle a, the electric field vector is rotated by a total angle 2 (a + #) and the amplitude of the electric field at the output is multiplied

by siv {l0 + 2a). The attenuation factor between the 'open' (+ 5V) and 'closed' (-5V) positions is therefore si 20)

si2a + 20) expression which is reversed in: 1 Arc tan si2a) 0 = -Arctan - # "# '- # -cos2a a1 For example for a1 = 1 and a = 22 we find 0 = 1.30
16 The second part of the device, consisting of (2503) and (2504). works exactly like the first, except that it takes a horizontally polarized beam as input and outputs a vertically polarized beam. The attenuation factor a2 of this second part is therefore given by the same formula as a, and the two parts of the device will be adjusted so as to have in each part the same attenuation (or approximately). Due to disparities in adjustment between the two parts of the device, a2 and a1 are not however strictly equal in practice.

The attenuation control is made according to the table below, where V1 denotes the bipolar voltage applied to (250 1) and ['2 that applied to (2503).

<tb>
<tb>

VI <SEP> V2 <SEP> attenuation
<tb>

-5V -5V a a2

-5V -5V a a2

<tb>
<tb> -5V <SEP> + 5V <SEP> a1
<tb> + 5V <SEP> -5V <SEP> a2
<tb>

<Desc / Clms Page number 88>

1 +5V 1 +5V 1
7.2.3.Dispositif de décalage de phase:
Ce dispositif est constitué de deux unités identiques placées l'une à la suite de l'autre Une unité est constituée comme indiquée Fig.33.

1 + 5V 1 + 5V 1
7.2.3.Phase shift device:
This device is made up of two identical units placed one after the other. One unit is made up as shown in Fig. 33.

The vertically polarized beam at the input of the device first passes through a phase rotator (2601) designated by 'RI' then a uniaxial birefringent plate (2602) designated by 'LP', then a second phase rotator (2603) designated by ' R2 'and a polarizer (2604) designated by' POL 'The two positions of the neutral axis of each rotator are arranged symmetrically with respect to a vertical axis The positions of the two rotators corresponding to the same control voltage are the same side of the vertical axis: for a voltage of -5V they are shown in dotted lines, for a voltage of + 5V they are shown in solid lines. Likewise, the two axes of the birefringent plate are arranged symmetrically with respect to this vertical axis (the third axis being in the direction of propagation of the beam). Fig. 34 shows the state of the electric field vector of the beam at each stage of the crossing of the device. for a voltage of -5V applied to each rotator.

Fig. 35 repeats FIG. 34 by specifying the values of the angles between the various ectcurs and the phase shifts between these vectors and the vector at the input of the device. Fig. 36 repeats Fig. 34 by specifying the values of the angles between the different vectors and the attenuation on each vector.

affectée d'un décalage de phase # et est réduite en amplitude d'un facteur cosC - j La composante (2608) est affectée d'un décalage de phase - # et est réduite en amplitude d'un facteur sinC -a) . Après traversée du rotateur (2603) l'ensemble est symétrisé par rapport l'axe neutre (2612) de ce rotateur (2608) est transformé en (2611), (2609) est transformé en (2610) Après traversée du polariseur (2604), ces deux composantes sont projetées sur un axe vertical. La composante (2610) est multipliée par un facteur

COS( 4 - a) et a donc été affectée globalement par un facteur COS2 (4 - ai . La composante (2611) est multipliée par un facteur sin( 4 - a) et a donc été affectée globalement par un facteur sin2 1 # - au . Les deux sont ensuite ajoutées pour donner une composante unique (2615) de valeur: v = cosl <y/-# COS2 cas + cos cot + # sin la ou # est la pulsation de l'onde, t est le temps. On vérifie : The electric field vector (2605) at the input of the device is vertical After crossing the rotator RI (2601) it is symmetrized with respect to the neutral axis (2606) of this rotator, which gives the vector (2607) After crossing the birefringent plate, the vector (2607). shown in dotted lines, is broken down into two components (2608) and (2609) corresponding to each neutral axis of the blade. The component (2609) is

affected by a phase shift # and is reduced in amplitude by a factor cosC - j The component (2608) is affected by a phase shift - # and is reduced in amplitude by a factor sinC -a). After passing through the rotator (2603) the assembly is symmetrized with respect to the neutral axis (2612) of this rotator (2608) is transformed into (2611), (2609) is transformed into (2610) After passing through the polarizer (2604) , these two components are projected onto a vertical axis. The component (2610) is multiplied by a factor

COS (4 - a) and was therefore affected globally by a factor COS2 (4 - ai. The component (2611) is multiplied by a factor sin (4 - a) and was therefore affected globally by a factor sin2 1 # - The two are then added to give a single component (2615) of value: v = cosl <y / - # COS2 case + cos cot + # sin la where # is the pulse of the wave, t is the time. We check:

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v = cos(m7J cos +sin( wt) sin z sin(2a) soit en représentation complexe: c = cos + j sin sin2a
2 2 Si 0 est l'argument de c alors on a: cos# cos# = 2

sin' (2a + cos2 (1- sin' 2a) sin6'=-, sin q, 2 sin(2a) 1+sin C-1+sin'2a) Ces formules s'inversent en :

sin V - sin6' 2 sin2 0+cos2 Bsin2a lu cossin(2a) cos#= .

v = cos (m7J cos + sin (wt) sin z sin (2a) either in complex representation: c = cos + j sin sin2a
2 2 If 0 is the argument of c then we have: cos # cos # = 2

sin '(2a + cos2 (1- sin' 2a) sin6 '= -, sin q, 2 sin (2a) 1 + sin C-1 + sin'2a) These formulas are reversed by:

sin V - sin6 '2 sin2 0 + cos2 Bsin2a lu cossin (2a) cos # =.

Avec 0 = 60 et a = -10 degrés on obtient: rp=120,7566 degrés. Il faut donc utiliser une lame uniaxe créant pour la longueur d'onde considérée une différence de phase de 120,75 degrés entre ses deux axes. 2 sin2 () + cos2 () sin2 (2a) We want to create a phase shift of 0 = 60 in a position of the rotators el 0 = -60 in the symmetrical position, which corresponds to a total phase shift of 120 degrees The above equation is used to determine the value of the total phase shift # created by the blade between its two neutral axes

With 0 = 60 and a = -10 degrees we get: rp = 120.7566 degrees. It is therefore necessary to use a uniaxial plate creating for the wavelength considered a phase difference of 120.75 degrees between its two axes.

que Dp -4rpz -+120degrés. La lame uniaxe doit être orientée de manière à ce que le rotateur (2601) fasse tourner la polarisation du rayon incident vers l'axe 2 quant il est soumis à une tension bipolaire de - 5 V. The two axes of the blade do not have a symmetrical role. If ## 1 is the phase shift at the crossing of the blade for a ray polarized along the axis i, there is only one choice of axes 1 and 2 such

than Dp -4rpz - + 120degrés. The uniaxial blade must be oriented so that the rotator (2601) rotates the polarization of the incident ray towards axis 2 when subjected to a bipolar voltage of - 5 V.

U'i F12 V2X riz décalage -V -V -SV -SV 0 SV 5V -5V -SV +120 The phase shift device consisting of two units of this type, ie V @ the voltage applied to the i-th rotator of the y-th device (i and / varying from 1 to 2). The phase shift S) steme is controlled according to the following table:

U'i F12 V2X rice offset -V -V -SV -SV 0 SV 5V -5V -SV +120

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<tb>
<tb> -5V <SEP> -5V <SEP> 5V <SEP> 5V <SEP> +120
<tb> 5V <SEP> 5V <SEP> 5V <SEP> 5V <SEP> -120
<tb>
the other combinations being unusual.

7.2.4. Beam diverter
The beam diverter is shown in Figs. 37 and 38. Its basic unit is an elementary variation block made up of elements (2801) to (2804).

An elementary variation block consists of a first rotator (2801) noted 'R1' followed by a birefringent prism (2802) noted 'PD' (deflection prism) then a second rotator (2803) noted 'R2' and a Glan-Thomson polarizer (2804) denoted 'POL'. The rotator (2801) has its neutral axis in the vertical direction for an applied voltage of -5V. For the same applied voltage, the rotator (2803) has its neutral axis in the horizontal direction. The prism (2802) is made of a birefringent material, calcite or quartz.

The direction of polarization of the extraordinary ray (first neutral axis) is for example in the vertical direction, and the direction of polarization of the ordinary ray (second neutral axis) is in the horizontal direction.

An incident ray on this prism is therefore divided into an ordinary ray polarized in the vertical direction and an extraordinary ray polarized in the horizontal direction. The ordinary ray and the extraordinary ray have a different inclination at the exit of the prism (angle of their direction of propagation with that of the incoming beam).

Figs. 39 and 40 illustrate the operation of this basic variation block. Fig. 39 corresponds to a deviation in one direction and Fig. 40 to a deviation in the other direction. The arrows in bold represent the electric field vectors of the beams considered
In the case of FIG. 39, the voltages applied to the two rotators are respectively -5V for (2801) and + 5V for (2803). The electric field vector of the incoming beam is vertical (2901). After crossing the first rotator whose neutral axis (2902) is vertical, it remains vertical (2903). After passing through the deflection prism, it is made up of the single extraordinary ray (2904). After passing through the second rotator, it is symmetrized with respect to the axis (2906) of this rotator, which itself makes an angle of 40 degrees with the horizontal (we have assumed for the drawing that a = 40 but the result does not not depend on the correctness of this value). It is therefore transformed into a vector (2905) forming an angle of 10 degrees with the horizontal.

The polarizer projects this vector onto the horizontal to obtain the vector (2907), the deviation of which corresponds to the single extraordinary radius.

In the case of FIG. 40, the voltages applied to the two rotators are respectively + 5V for (2801) and -5V for (2803). The field vector of the incoming beam is vertical (2911). After passing through the first rotator, it is symmetrized with respect to the axis (2912) of this rotator. which itself makes an angle of 40 with the vertical. It is therefore transformed into a vector (2913) forming an angle of 10 degrees with the horizontal. After passing through the deflection prism, the beam is decomposed into an extraordinary beam of field vector (2914) and an ordinary beam of field vector (2915) After passing through the second rotator, of horizontal axis, the field vector of the extraordinary beam is symmetrized compared to

<Desc / Clms Page number 91>

horizontal and becomes (2916). The polarizer then selects the only horizontal component and the outgoing vector (2917) therefore corresponds to the only ordinary ray.

A complete elementary block is represented by the rectangle (2805), the direction of the field of the incoming beam being represented by the arrow (2806). The block (2807) is identical but rotated 90 degrees with respect to a horizontal axis so that the direction of the field of the incoming beam is horizontal (2808). The set of two blocks forms an elementary doublet (2809) allowing elementary deflection of the beam in the horizontal and vertical directions. As indicated in Fig. 38, the entire deflector consists of eight successive elementary doublets. However, in order to have an efficient switching system, the last doublet (numbered 0) is placed on the part of the beam where the left and right lighting beams have already been separated Two identical doublets (DO) and (DOb) are therefore used, one on each branch of the bundle. When a voltage of -5V is applied to its two rotators, an elementary block acts as a closed switch. The last doublet can therefore effectively switch the beam, a voltage of -5V having to be applied to all its rotators to have a closed switch.

The block (2209) in Fig. 27 therefore represents the doublet DOb. Block (2240) represents the DO doublet. The block (2206) represents the doublets D1 to D7.

The type of crystal in which the prism is made and the angle between its two faces determine the angle of variation of the inclination of the beam between the two positions of an elementary doublet.

:1 : ouverture du faisceau en entrée du dispositif de déviation, à peu près égale à sa \ saleur au niveau du diaphragme ou se forme l'image..9 est défini comme le sinus du demi-angle au sommet du cône formé par les rayons provenant de l'objectif. g : grandissement de l'objectif. d : distance entre les plans P2 et P4 de la Fig.29. f@: distance focale de la lentille L1 sur la Fig.29. The following notations are adopted: n @: index of the immersion liquid used for the beam deflection device. o: lens aperture

: 1: opening of the beam at the input of the deflection device, roughly equal to its \ salt at the diaphragm where the image is formed. 9 is defined as the sine of the half-angle at the top of the cone formed by the rays coming from the lens. g: magnification of the objective. d: distance between the planes P2 and P4 in Fig. 29. f @: focal length of lens L1 in Fig. 29.

A =(1-) ig\ /:)
La Fig.41 montre le principe du calcul de la déviation par le prisme des rayons ordinaires. Le rayon (2922) pénètre dans le prisme (2921) et en ressort en (2923). Abbe's relation and the resolution of the optical equations gives:

A = (1-) ig \ / :)
Fig. 41 shows the principle of calculating the prism deviation of ordinary rays. The ray (2922) enters the prism (2921) and leaves it at (2923).

#d is the angle at the top of the deflection prism.

#e is the angle of the outgoing extraordinary beam with the outer face of the prism.

#o is the angle of the outgoing ordinary beam with the outer face of the prism. ne is the extraordinary index of the deflection prism. no is the ordinary index of the deflection prism.

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On a: sin6' = # sin0rf et de même pour le rayon extraordinaire sinOe = sis 0 d'ou: n, 111 sin()e -sin()o = e 0 sin()d nl soit au premier ordre en (#e-#0) :

( () e - () 0 ) cos () d = ne - no ' sm 0 Le i-ième doublet doit créer une variation de l'inclinaison d'amplitude:

0, -0, = ' 21 4 Le demi-angle au sommet du i-ième prisme vaut donc :

()d = ArctaJ 4- ni (2@ ne-no) soit avec la valeur de.-1 précédemment obtenue:

9d = ArctanC 1 t 1 C1- d JJ 2 ô ne -no fI Dans cette équation il faut prendre en compte les valeurs suivantes : quartz: ne-no = 0,009 calcite: ne - no =-0,172 Pour chaque prisme: -inverser les axes ordinaire et extraordinaire permet d'inverser le sens dans lequel sont déviés les rayons lorsque on passe d'un couple de tensions (-5V,5V) à un couple de tension (5V.-5V) appliqué aux rotateurs du bloc élémentaire concerné Ce sens étant inversé entre le quart/: et la calcite pour un même choix des axes ordinaire et extraordinaire, ces axes doivent être inversés dans un prisme en calcite par rapport à leur position dans un prisme en quartz.

We have: sin6 '= # sin0rf and in the same way for the extraordinary radius sinOe = sis 0 from where: n, 111 sin () e -sin () o = e 0 sin () d nl is in the first order in (# e- # 0):

(() e - () 0) cos () d = ne - no 'sm 0 The i-th doublet must create a variation of the inclination of amplitude:

0, -0, = '21 4 The half-angle at the top of the i-th prism is therefore:

() d = ArctaJ 4- ni (2 @ ne-no) or with the value of.-1 previously obtained:

9d = ArctanC 1 t 1 C1- d JJ 2 ô ne -no fI In this equation the following values must be taken into account: quartz: ne-no = 0.009 calcite: ne - no = -0.172 For each prism: -invert the ordinary and extraordinary axes make it possible to reverse the direction in which the spokes are deflected when passing from a voltage couple (-5V, 5V) to a voltage couple (5V.-5V) applied to the rotators of the elementary block concerned direction being reversed between the quarter /: and calcite for the same choice of ordinary and extraordinary axes, these axes must be reversed in a calcite prism in relation to their position in a quartz prism.

-Inverting the orientation of the prism (top facing downwards instead of the top) also makes it possible to reverse the direction in which the rays are deflected when going from a couple of voltages (-5V, 5V) to a couple of voltage (5V, -5V) applied to the rotators of the elementary block concerned But at the same time this operation reverses the direction of deflection of the spokes when a fixed voltage couple is applied In order to have a minimum 'fixed' deviation of the spokes the prism at greater deviation of each series, calcite or quarter /, must be reversed in relation to the others. In order to maintain the deflection in the desired direction, its ordinary and extraordinary axes must be reversed.

nrnin1r{' ft i-vfr-anrclin5iirp nnnr niip lae ramnnc cnipnt fnl1innTC tiqnc In InA",,, c,-nc lnrcnm'nn nnec For each prism we choose the material, quartz or calcite, which most easily allows this angle at the top to be obtained. The orientation of the prism is then chosen so that, at a fixed voltage applied to the rotators, the variations in direction induced are best compensated between the prisms. We choose the position of the axes

nrnin1r {'ft i-vfr-anrclin5iirp nnnr niip lae ramnnc cnipnt fnl1innTC tiqnc In InA ",,, c, -nc lnrcnm'nn nnec

<Desc / Clms Page number 93>

from a voltage pair (-5V, 5V) to a voltage pair (5V, -5V) applied to the rotators of the elementary block concerned. For each doublet, it is necessary to specify for the two prisms included in the doublet. which have the same characteristics: the angle at the apex, the orientation of the apex (normal or inverted with respect to Fig. 37 on which it is oriented upwards), the position of the ordinary or extraordinary axes (normal or inverted by compared to figure 37 on which the extraordinary axis is vertical). For example for an objective o = l, 25 g = 100 and with f1 = 200 mm, d = 20 mm we obtain the following table where the angles are in degrees:

<tb>
<tb> index <SEP> of <SEP>#d<SEP> (calcite) <SEP>#d<SEP> (quartz) <SEP> choice <SEP> orientation <SEP> of <SEP> position <SEP> of <SEP> axes
<tb> prism <SEP> vertex <SEP> ordinary <SEP> and
extraordinary <tb>
<tb> 0 <SEP> 3.742 <SEP> 51.340 <SEP> calcite <SEP> inverted <SEP> normal
<tb> 1 <SEP> 1.873 <SEP> 32.005 <SEP> calcite <SEP> normal <SEP> inverted
<tb> 2 <SEP> 0.937 <SEP> 17.354 <SEP> calcite <SEP> normal <SEP> inverted
<tb> 3 <SEP> 0.468 <SEP> 8.881 <SEP> quartz <SEP> inverted <SEP> inverted
<tb> 4 <SEP> 0.234 <SEP> 4.467 <SEP> quartz <SEP> normal <SEP> normal
<tb> 5 <SEP> 0.117 <SEP> 2. <SEP> 237 <SEP> quartz <SEP> normal <SEP> normal
<tb> 6 <SEP> 0.058 <SEP> 1.119 <SEP> quartz <SEP> normal <SEP> normal
<tb> 7 <SEP> 0.029 <SEP> 0.559 <SEP> quartz <SEP> normal <SEP> normal
<tb>
A deflection of the beam is a variation of its direction. But at a great distance from the doublet creating the deflection, it also results in a spatial shift of the illuminated area So that this phenomenon is not penalizing, the distances between the elements of the deflector must be reduced to a minimum and these elements must have a sufficient section so that. Regardless of the orientation chosen, the beam 'completely fills' the area delimited by the diaphragm. For example, this section can be 12 mm, the Glan-Thomson polarizers then being of dimension 12 × 30 mm. All parts of the deflector which do not directly transmit the beam should be as absorbent as possible in order to limit noise.

Pour la calcite: ni = 1.658 2 1.86 = 1.572 . In order to eliminate the constant deviations by the deviation prisms, the index of the optical liquid in which a prism is immersed must be equal to the average value of the ordinary and extraordinary indices of the prism either:

For calcite: ni = 1.658 2 1.86 = 1.572.

For quartz: n, = 1.5 - I 2 + 1.553 = 1.5.185
The part of the beam deflector whose prisms are made of calcite must therefore be immersed in a liquid of index 1.572, and the part of which the prisms are made of quartz must therefore be immersed in a liquid of index 1.5485. The tank containing the deflector and the optical liquid must therefore be separated into two parts,

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a glass window allowing the passage of the beam between these two parts which contain optical liquids of different indices.

The device is controlled by controlling the 36 rotators. In each doublet the phase rotators are numbered 0 to 3, the number 0 being the most 'left' rotator in Fig. 28 If i is the index of the doublet, varying from 0 to 7 and is the index of the rotator in a doublet, varying from 0 to 3, then we assign to the rotator the global index k = i + 1 + j * 9 , except for the doublet numbered Ob for which we have ak = j * 9. A 36-bit control word is used in which the number bit k corresponds to the rotator of global index k. For each bit, a value of 0 corresponds to an applied voltage of -5V and a value of 1 corresponds to a voltage of + 5V.

capteur coor- mot de commande rOA1Jp, i,j] données (2239). (t,J) Oi,ig,0i,i,Oi,JgOiJs p=O (2229): 0J) ((i%2),O,y/2,i%2,O,(i72,(y%2),O,jI2),J%2i,01,(J72))

A lighting is characterized by the sensor on which the direct lighting beam arrives and by symbolic coordinates on this sensor. The sensor will be indexed by annuitant /? and the symbolic coordinates will be i, j or i and vary between 0 and 255. The symbolic coordinates do not necessarily correspond to pixel coordinates on the sensor. When one wishes to obtain a lighting characterized by the indices p, i, j, the command word is given by the table above:

sensor coor- command word rOA1Jp, i, j] data (2239). (t, J) Oi, ig, 0i, i, Oi, JgOiJs p = O (2229): 0J) ((i% 2), O, y / 2, i% 2, O, (i72, (y% 2), O, jI2), J% 2i, 01, (J72))

<tb>
<tb> p = 1
<tb>
In this table: a% b means a modulo ba / 2 represents the product of the integer division of a by 2, i.e. a shifted to the right (a, b, c ..) represents a concatenated with b then with c etc ... a, represents a expressed on 1 bits.

Sia is an integer, its expression in binary is a sequence of 0 and 1 By transforming 0 into 1 and vice versa we get its complement which we denote by a. This rating will be maintained thereafter
When you want to suppress the two light beams, the command word to use is 0.

7.3.Rcglagc of the set.

7.3.1.First installation of the system
The system, with the exception of the elements (2204) (2205) (2206) (2209) (2240) (2210) (2241) (2238) (2226), is geometrically set up with maximum precision. The path of the beam is controlled by using a piece of diffusing paper interposed in its path. The position of mirrors, semi-transparent mirrors, as well as (2200) and (2201) is adjusted thereby controlling the path of the beam.

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7.3.2.Implementation of beam control systems.

For the installation of the beam monitoring systems it is necessary to have a photometer of sufficient precision, which will be used to measure attenuations or to detect beam extinctions. These systems are composed of optical elements (prisms, rotators, polarizers, birefringent plates) which must be positioned with precision in relation to the optical axis and be mounted on positioners allowing fine adjustment in rotation about this axis.

7.3.2. l.Rotator marking
The entire lighting beam modification system is based on the use of phase rotators. It is essential that the axis of each rotator turn in the direction intended for the application of a tension opposite to that used during its installation. The position of the rotator must be defined when it is put in place and the adjustment is only made over a few degrees. To specify the position of the axes of the rotator before installation, a test between crossed polarizers is carried out in two stages.

Step 1, described by Fig. 42. the rotator (3001) is set between the polarization direction input polarizer (3002) and the polarization direction output polarizer (3003). A voltage of + 5V is applied. The rotator is rotated so as to cancel the outgoing ray. The corresponding position, corresponding to the input polarizer, is marked with a red dot (3004).

Step 2: a -5V voltage is applied. The output polarizer is adjusted to cancel the ray. A green point is marked corresponding to the middle of the two polarizer positions, on the side where the angle is the smallest. Figs. 43 and 44 describe this step in the two possible cases defined by the new position of the output polarizer, respectively (3005) and (3006). In the case of Fig. 43 the green point is marked at (3007) and in the case of Fig. 44 it is marked at (3008).

The red point then marks the position of the axis for a voltage of + 5V and the green point marks its position for a voltage of -5V. These points then allow the elements to be correctly pre-positioned during the adjustment procedure.

7. 3.2.2.Installation of the beam attenuator
The polarizer (2502) is first put in place and a fine adjustment in rotation is carried out so as to have the outgoing beam extinguished. The rotator (2501) is then put in place and a fine adjustment of its rotational position is carried out so as to have the desired attenuation when passing from the open position (voltage of + 5V applied to (2501)) to the position closed (applied voltage of -5V).

Then (2501) is switched to the open position (voltage of + 5V) and the polarizer (2504) is put in place, which is adjusted in rotation so as to have extinction of the outgoing beam. The rotator (2503) is then put in place and a fine adjustment of its rotational position is carried out so as to have the desired attenuation a22 when passing from the open position (voltage of + 5V applied to (2503)) to the closed position

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16 mesurables par le photomètre: a12= a21
256

On mesure alors les valeurs exactes obtenues des coefficients a, et a2 . Les coefficients al et a2 ainsi obtenus seront utilisés par la suite. (applied voltage of -5V). For example we can use a1 = a2 = -which gives as attenuations

16 measurable by the photometer: a12 = a21
256

The exact values obtained of the coefficients a, and a2 are then measured. The coefficients a1 and a2 thus obtained will be used subsequently.

7. 3.2.3. Installation of phase shift devices
These devices (2205) and (2251) are put in place with the best possible precision given the markings made previously.

7.3.2.4. Installation of the beam deflection and switching device.

Each elementary block is placed successively, starting from the block closest to the phase shift device. The beam attenuator must be in the open position An elementary block is put in place in the following order: -Installation of the POL polarizer (2804). Fine adjustment in rotation to cancel the outgoing beam.

-implementation of the R2 rotator (2803). Fine adjustment in rotation to keep the outgoing spoke at a zero value, a voltage of -5V being applied to R2.

-implementation of the RI rotator (2801). Fine adjustment in rotation to keep the outgoing spoke at a zero value, a voltage of -5V being applied to R2 and RI.

-implementation of the PD deflection prism (2802). Fine adjustment in rotation to keep the outgoing spoke at a zero value, a voltage of -5V being applied to RI and R2.

The DO and DOb blocks are set up in the same way as the others.

7.3.2.5.Installation of phase rotators (2210) (2241) (2238) (222fui).

These rotators must have their vertical neutral axis for an applied voltage of -5V (green dot facing up). The axis of (2210) must turn to the right in Fig. 27 when a voltage of + 5V is applied (red dot on the right). The shaft of (2241) should turn to the left in Fig. 27 when a voltage of + 5V is applied (red dot on the left). The axis of (2238) and (2226) must turn upward in Fig. 27 when a voltage of + 5V is applied (red dot at the top).

7. 3.2.6. Positioning of the polarizers: The polarizers (2252) and (2253) are put in place with their passing axis oriented vertically.

7. 3.3. Geometry adjustment
Secondly, a geometry adjustment is carried out aimed at correctly positioning the cameras, the achromatic lenses and certain mirrors. Some of these settings use an auxiliary CCD sensor, whose pitch (distance between the centers of two neighboring pixels) should be as small as possible.

From the image received either on one of the sensors of the system, or on the auxiliary sensor, a

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algorithm allowing the assessment of the punctuality of the image and the localization of the maximum. The image received on a sensor is obtained by causing a reference wave to interfere with this sensor and the wave whose punctuality must be evaluated.

apprécier le caractère ponctuel et le centrage de telles images, dans le domaine spatial ou fréquentiez Ces images seront soit reçue sur un des capteurs CCD du dispositif, soit reçues sur un capteur auxilliaire. Les décalages de phase seront réalisés soit à l'aide de (2205) soit à l'aide de (2251). Dans certains cas, l'onde d'éclairage jouera le rôle d'onde de référence et vice-versa. Dans tous les cas, le système réalise donc trois images successives avec des décalages successifs, indicés par l'entier d, de +120 (d=O), 0 (d=1), -120 (d=2) degrés. Ceci donne un tableau de pixels I[d,i,j] ou l'indice d variant de 0 à 2 indice le déphasage. L'image en nombre complexes en est déduite par:

S[/,1'] = C6 2IO,i, jJ- ll,i>jJ- I 2>t>JJ +j 2 l 1>r>.7J - I 2>r> 7JJ Si on cherche à évaluer la ponctualité dans le domaine spatial, une transformation de Fourier inverse est appliquée à cette image
Dans les deux cas (qu'il y ait eu ou non transformation de Fourier), à partir de cette image de

dimensions N puc x N PIX correspondant au nombre de pixels utiles du capteur concerné (par exemple 256), on évalue la ponctualité par un programme comportant les étapes suivantes:

Etape 1: le programme calcule le maximum max du module de ,""'[1, j] et détermine ses coordonnées (intaxl jnraxl). 7.3.3. 1. Obtaining a three-dimensional image and assessing punctuality:
We have seen in the first embodiment how a two-dimensional image in complex numbers can be generated from three images differing from one another by the phase difference between the illuminating wave and the reference wave. This image in the frequency domain can be transposed into the spatial domain by Fourier transform. In the adjustment phases that follow, we will have to

assess the punctual nature and the centering of such images, in the spatial domain or frequented These images will either be received on one of the CCD sensors of the device, or received on an auxiliary sensor. The phase shifts will be carried out either using (2205) or using (2251). In some cases, the illuminating wave will act as the reference wave and vice versa. In all cases, the system therefore produces three successive images with successive shifts, indexed by the integer d, of +120 (d = O), 0 (d = 1), -120 (d = 2) degrees. This gives an array of pixels I [d, i, j] or the index d varying from 0 to 2 index the phase shift. The complex number image is deduced from it by:

S [/, 1 '] = C6 2IO, i, jJ- ll, i> jJ- I 2>t> JJ + j 2 l 1>r> .7J - I 2>r> 7JJ If we try to evaluate the punctuality in the spatial domain, an inverse Fourier transformation is applied to this image
In both cases (whether or not there has been a Fourier transformation), from this image of

dimensions N puc x N PIX corresponding to the number of useful pixels of the sensor concerned (for example 256), the punctuality is evaluated by a program comprising the following steps:

Step 1: the program calculates the maximum maximum of the modulus of, ""'[1, j] and determines its coordinates (intaxl jnraxl).

Etape 4. le tableau Sa est complété par des zéros et on obtient un tableau si de dimensions .'b x -N'b, Sbr, ~ ,SaCr - 2b + 2 j - l Zb + 2p 5,b J =Sa 2 2-2 2 quand Vo-1>i-.b +r- >0 et .Np-1>~ j--b ±- >-0 2 2 2 2 et Sb[i,j] =0 sinon. Step 2: the part of the array S [i, il located around (/ mfur /, yw <7-T /) is extracted We thus create an array Sa [l, j] of dimensions ll 'a X Va with for example .Va = 16: .ali, JI = 4 i - 2 + iiiiax I, j -'Va 2 + jniax 1 Step 3: a direct Fourier transform is performed on the table Sa

Step 4.the array Sa is completed by zeros and we obtain an array si of dimensions .'bx -N'b, Sbr, ~, SaCr - 2b + 2 j - l Zb + 2p 5, b J = Sa 2 2 -2 2 when Vo-1> i-.b + r-> 0 and .Np-1> ~ j - b ± -> -0 2 2 2 2 and Sb [i, j] = 0 otherwise.

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Etape 6: imax,jmax,max sont calculés par les formules: 'LISb[I,}]121 imax2 = -###### iniax2 'LISb[I,}]12 @

lbli@ J,12 jnlax2 = l,) 0 'LISb[I,} ]1I,j max = 1'%[lnWx2,j1llax2]1 l777QX' = /M#r7 + #- CII17QX2- 12b N--b jnl( ix - jniaxl + #- jniax2 - Nb ) Nb (2)

Les valeurs réelles maximaxjniax ainsi obtenues caractérisent respectivement la valeur et la position du maximum. La ponctualité est d'autant meilleure que la valeur max est plus élevée. Le programme visualise en outre le module du tableau .S'et le module du tableau Sb pour avoir une appréciation visuelle de la ponctualité. Step 5: the inverse Fourier transformation of table Sb is performed. We thus obtain an oversampled version of the part of the initial table S located around the point of maximum modulus.

Step 6: imax, jmax, max are calculated by the formulas: 'LISb [I,}] 121 imax2 = - ###### iniax2' LISb [I,}] 12 @

lbli @ J, 12 jnlax2 = l,) 0 'LISb [I,}] 1I, j max = 1'% [lnWx2, j1llax2] 1 l777QX '= / M # r7 + # - CII17QX2- 12b N - b jnl (ix - jniaxl + # - jniax2 - Nb) Nb (2)

The real maximaxjniax values thus obtained characterize respectively the value and the position of the maximum. Punctuality is all the better as the max value is higher. The program also displays the panel module .S 'and the panel module Sb to have a visual appreciation of punctuality.

7. 3.3.2. devices used
A diffuser is used, for example a piece of paper that can visually follow the path of the beam.

An auxiliary CCD is used for more precise beam tracking than with the diffuser. His step should be as small as possible.

A frequency meter is also used. This term will denote the apparatus described by Fig. 71, which is intended for measuring the spatial frequencies of a paraxial beam It consists of a mirror (5000) which reflects an incoming parallel beam towards a lens (5001), which focuses this beam to a CCD (5002) mounted on a camera (5003). An optional polarizer (500-1) can be inserted between the mirror and the lens. The use of the mirror (5000) allows the frequency meter to have minimal space requirement in the horizontal plane which is that of FIGS. 61 and 62. The optical axis of the lens and of the CCD is always vertical during the measurement operations.

Taking into account the sizing choices made, the maximum angle) at which the beams enter the frequency meter is o If the total width of the CCD (5002) is @, then the focal length of g (5001) is calculated so that the rays arriving at angles between -o and o can be taken gg

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into account. It is therefore worth: / = g / o 1/2. A slightly lower value can be adopted to keep a safety margin.
Before using the frequency meter, the distance between the lens (5001) and the CCD (5002) must be adjusted so that the image of a parallel beam is as point as possible, which is done simply by sending a beam to the frequency meter. the parallelism of which has been previously verified by an interferometric method and by adjusting the distance between the lens and the CCD accordingly.

The punctuality of the image obtained on the CCD (5002) makes it possible to check the parallelism of an incoming beam. The relative position of several points on this CCD characterizes the angle between the corresponding beams.

In the absence of other precision in the description of an adjustment, the polarizer (5004) is not used.

7. 3.3.3. Adjustment cycle Adjustments are designed to ensure that: (1) the beams follow the intended path. This can generally be checked using a simple diffuser. These beam path checks are not described but must be carried out before other adjustments are made. For example the orientation of the mirror (2247) must be adjusted so that the reflected beam is actually superimposed on the incident beam, occupying the same area of space as the latter at the level of the semi-transparent mirror (2245).

(2) the illumination beams and their inverse indicators have a point image on the CCD sensors (3) the reference beams have a point image in the plane of the diaphragms (2213) and (2223).

(4) a beam entering parallel to the objective (2217) and directed along the optical axis has a point image and centered on the sensor (2239).

(5) when a command word COM [1, i, j] is used, the coordinates of the point illuminated by the beam FED are deduced from those of the point illuminated by FEDI by a homothety of ratio close to 1.

The adjustments to be made result from these conditions. The description of the adjustment steps is given for information only and constitutes an example of the ordering of the adjustment steps.

déviateur de faisceau est COUr 1,128,128] . CO,f[O, 128,1281 ou 0 selon que l'on génère le faisceau d'éclairage droit FED, le faisceau d'éclairage gauche FEG ou aucun des deux. Les obturateurs (2257) (2258) (2259) (2260) et des obturateurs non représentés sur la trajectoire des faisceaux FRG et FRD permettent de choisir les faisceaux utilisés. During the entire setting except step 14, the control word used for the

beam diverter is COUr 1,128,128]. CO, f [O, 128,1281 or 0 depending on whether the right light beam FED, the left light beam FEG or neither of the two are generated. The shutters (2257) (2258) (2259) (2260) and shutters not shown on the path of the FRG and FRD beams make it possible to choose the beams used.

During certain adjustment phases, a given beam is measured on a sensor using a second beam serving as a reference. The program described in 7.3.3.1. is then used to assess the punctuality of the measured beam. The phase variations between the beam serving as reference and the beam at

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Une image ponctuelle est considérée comme centrée sur un capteur de taille N"px x .1'p,.i si ses coordonnées sont ##,## l 2 2 étape 1: réglage en translation de la lentille (2231) Le fréquencemètre est positionné entre le miroir semi-transparent (2211) et le rotateur de polarisation (2238) . La lentille (2231) est réglée pour que l'image du faisceau FEDT sur le CCD du fréquencemètre soit ponctuelle. étape 2 : en translation de la lentille (2246) Le fréquencemètre est positionné entre le miroir semi-transparent (2245) et la lentille (2237). La lentille (2246) est réglée pour que l'image du faisceau FRDI sur le CCD du fréquencemètre soit ponctuelle. étape 3: réglage en translation de la lentille (2242) Le fréquencemètre est positionné entre le miroir semi-transparent (2225) et le rotateur de polarisation (2226) . La lentille (2242) est réglée pour que l'image du faisceau FEGI sur le CCD du fréquencemètre soit ponctuelle. étape 4: réglage en translation de la lentille (2281) Le fréquencemètre est positionné entre le miroir semi-transparent (2228) et la lentille (2227) . La lentille (2281) est réglée pour que l'image du faisceau FRGI sur le CCD du fréquencemètre soit ponctuelle. étape 5: réglage en translation de la lentille (2212)
Un faisceau d'éclairage provisoire FEP est introduit. Celui-ci est dérivé directement de la sortie de l'élargisseur de faisceau (2201) à l'aide d'un miroir semi-transparent et est redirigé par un jeu de miroirs vers l'objectif (2217) dans lequel il pénètre par le coté ou se trouve normalement l'échantillon, et en étant dirigé selon l'axe optique de l'objectif. L'objectif (2217) doit être à peu près en position focalisée, c'est-àdire dans la position ou il sera lors de l'utilisation normale du microscope. L'objectif (2219) doit être provisoirement supprimé pour pouvoir introduire FEP. to measure are obtained using (2205) or (2251). When no beam is used as a reference, for example if the CCD is that of the frequency meter, the image used is that directly received on the CCD.

A point image is considered to be centered on a sensor of size N "px x .1'p, .i if its coordinates are ##, ## l 2 2 step 1: translation adjustment of the lens (2231) The frequency meter is positioned between the semi-transparent mirror (2211) and the polarization rotator (2238). The lens (2231) is adjusted so that the image of the FEDT beam on the CCD of the frequency meter is punctual. step 2: in translation of the lens (2246) The frequency meter is positioned between the semi-transparent mirror (2245) and the lens (2237). The lens (2246) is adjusted so that the image of the FRDI beam on the CCD of the frequency meter is punctual. Step 3: adjustment in translation of the lens (2242) The frequency meter is positioned between the semi-transparent mirror (2225) and the polarization rotator (2226). The lens (2242) is adjusted so that the image of the FEGI beam on the CCD of the frequency meter is punctual. step 4: adjustment in translation of the lens (2281) The frequency It is positioned between the semi-transparent mirror (2228) and the lens (2227). The lens (2281) is adjusted so that the image of the FRGI beam on the CCD of the frequency meter is point. step 5: translational adjustment of the lens (2212)
A temporary FEP lighting beam is introduced. This is derived directly from the output of the beam expander (2201) using a semi-transparent mirror and is redirected by a set of mirrors to the objective (2217) into which it enters through the side where the sample is normally located, and being directed along the optical axis of the objective. The objective (2217) should be approximately in the focused position, that is, in the position where it will be during normal use of the microscope. The objective (2219) must be temporarily deleted in order to be able to introduce FEP.

The frequency meter is positioned between the lens (2212) and the semi-transparent mirror (221 1) The lens (2212) is adjusted so that the image of the FEP beam on the CCD of the frequency meter is point. step 6: translational adjustment of the lens (2237) and adjustment of the orientation of the semi-transparent mirror (2245):

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An auxiliary CCD is placed at the location of the diaphragm (2213). The lens (2237) is adjusted so that the image of the FRDI beam on this auxiliary CCD is point. The semi-transparent mirror (2245) is adjusted so that the image of the FRDI beam on this auxiliary CCD is centered. step 7: CCD (2239) in translation.

The position of the CCD (2239) is adjusted so that the image of the FEP beam obtained by the procedure described in 7.3.3.1. from the CCD (2239) is punctual and centered. step 8: semi-transparent mirror (2211)
The position of this mirror is adjusted so that the image of the FEDI beam obtained by the procedure described in 7.3.3. from the CCD (2239) is punctual and centered. step 9: adjusting the position of the objectives.

The FEP beam is removed and the objective (2219) is replaced. An auxiliary CCD is placed at the location of the diaphragm (2223). The sample is for example a transparent slide, optical oil being used on each side of the slide. The position of the objectives is adjusted so that the image of the FRDI beam on this auxiliary CCD is punctual and centered. step 10: translational adjustment of the lens (2224)
The frequency meter is positioned between the lens (2224) and the semi-transparent mirror (2225) The lens (2224) is adjusted so that the image of the beam FED on the CCD of the frequency meter is point. step 11 translational adjustment of the lens (2227) and adjustment of the orientation of the semi-transparent mirror (2228):
An auxiliary CCD is placed at the location of (2223). The lens (2227) is adjusted so that the image of the FRGI beam on this auxiliary CCD is point. The semi-transparent mirror (2228) is adjusted so that the image of the FRGI beam on this auxiliary CCD is centered. step 12: adjustment of the CCD (2229) in translation.

The position of the CCD (2229) is adjusted so that the image of the FED beam obtained by the procedure described in 7.3.3.1. from the CCD (2229) is punctual and centered. step 13: adjustment of the semi-transparent mirror (2225)
The position of this mirror is adjusted so that the image of the FEGI beam obtained by the procedure described in 7.3.3.1. from the CCD (2229) is punctual and centered. step 14: adjustment of the CCDs (2229) and (2239) in rotation and translation

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d'axes soient confondus. A cette fin, les mots de commande COM[1.128,128] . COM[1,250,128] , COM[1.l28,2501 sont utilisés alternativement. Les deux capteurs sont réglés en translation dans un plan orthogonal à l'axe (2264) et en rotation autour de ce même axe Sur chaque capteur on définit un système de coordonnées (i j) ou les indices pixels i et j vont de 0 à .'P,X -1 avec .V =256, et qui repère la zone utile du capteur qui sera utilisée par la suite. Le point origine du système de coordonnées, de coordonnées (0.0). peut être un quelconque des quatre coins de la zone utile du capteur. En même temps qu'on effectue le réglage, on choisit le point origine du système de coordonnées. Les critères de réglage et de choix du point origine sont les mêmes pour les deux capteurs et sont les suivants:

- quand COM[l,128,128] est utilisé, le point d'impact du faisceau d'éclairage, c'est-à-dire du faisceau d'éclairage direct sur (2229) ou de son indicateur inverse sur (2239). doit être au point de coordonnées (128,128). This step consists in adjusting in rotation the position of (2229) and (2239) so that their systems

of axes are merged. To this end, the command words COM [1,128,128]. COM [1,250,128], COM [1,128,2501 are used alternatively. The two sensors are adjusted in translation in a plane orthogonal to the axis (2264) and in rotation around this same axis. On each sensor, a coordinate system (ij) is defined where the pixel indices i and j range from 0 to. 'P, X -1 with .V = 256, and which identifies the useful zone of the sensor which will be used subsequently. The point of origin of the coordinate system, of coordinates (0.0). can be any of the four corners of the useful area of the sensor. At the same time that the adjustment is carried out, the origin point of the coordinate system is chosen. The criteria for setting and choosing the origin point are the same for the two sensors and are as follows:

- when COM [l, 128,128] is used, the point of impact of the lighting beam, that is to say of the direct lighting beam on (2229) or of its inverse indicator on (2239). must be at the point of coordinates (128,128).

-when COM [1,250,128] is used, the point of impact of the illumination beam must be at a point with coordinates (x, 128) where x is positive.

* -when COM [1,128,6] is used, the point of impact of the illumination beam must be at a point with coordinates (128, x) where x is positive.

vecteurs de base unitaires 1 7 , -: c'est-à-dire par les repères Op, 17 ou p est l'indice du capteur (p=0 pour (2239) et p=1pour (2229)). The coordinate systems thus determined are defined by their point of origin Op and their

basic unit vectors 1 7, -: that is to say by the references Op, 17 where p is the index of the sensor (p = 0 for (2239) and p = 1 for (2229)).

These coordinate systems will be systematically used subsequently.

7.4. Determination of the modulus of the reference wave.

As in the first embodiment, the filters (2255) and (2256) are set so that the level of the reference wave is about a quarter of the maximum level allowed by the digitizer, i.e. a level of 256/4 = 64 in the case of an 8-bit sampling of the video signal, and this on both sensors.

fait que deux capteurs sont présents on obtient un tableau Irerr p,i, j] ou i,j sont les indices pixels comme dans le premier mode de réalisation, et ou p est l'indice capteur soit p=(1 pour (2239) et p=1 pour (2229). This reference wave is then determined as in the first embodiment, but from

fact that two sensors are present we obtain an Irerr array p, i, j] or i, j are the pixel indices as in the first embodiment, and where p is the sensor index or p = (1 for (2239) and p = 1 for (2229).

Iref [O, i, j] is the intensity received on the sensor (2239) when only the FRD beam is present and Ircf [l, r,] is the intensity received on the sensor (2229) when only the FRG beam is present.

7. 5. Simple two-dimensional image capture.

on sera amené à générer ce type de représentation fréquentielle, Pour générer une telle représentation, le système réalise trois images successives avec des décalages successifs de We have seen in the first embodiment how a two-dimensional frequency representation in complex numbers can be generated from three images differing from one another by the phase difference between the illuminating wave and the reference wave. In the following adjustment phases

we will have to generate this type of frequency representation, To generate such a representation, the system produces three successive images with successive shifts of

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référence. Ceci donne un tableau de pixels Id, p,i, j ou l'indice d variant de 0 à 2 indice le déphasage et ou l'indice/? désigne le capteur. La représentation fréquentielle en est déduite parS[p,,j] C6 6' - - '-'- +j 2 3lref 1 [P,i, j II,P,i,j-I,P,i,jJ On obtient, à chaque acquisition, une image pour chaque capteur, et le tableau ,5' p.r, J comporte donc un sous-tableau pour chaque capteur, l'indice p désignant le capteur. Toutefois dans la phase de réglage on n'utilisera en général qu'une seule de ces deux images. + 120.0, -120 degrees applied to the illumination wave. The order of the phase shifts is the reverse with respect to that used in the first embodiment because they are applied to the lighting wave and not to the lighting wave.

reference. This gives an array of pixels Id, p, i, j or the index d varying from 0 to 2 index the phase shift and or the index /? designates the sensor. The frequency representation is deduced from it by S [p ,, j] C6 6 '- -'-'- + j 2 3lref 1 [P, i, j II, P, i, jI, P, i, jJ We obtain, at each acquisition, an image for each sensor, and the table, 5 ′ pr, J therefore comprises a sub-table for each sensor, the index p designating the sensor. However, in the adjustment phase, generally only one of these two images will be used.

7.6 Obtaining the Kp parameters and adjusting the diaphragms.

These parameters correspond to the parameter K of the first embodiment, but due to the asymmetries of the embodiment, the parameter is not necessarily the same for each sensor. Two parameters K and K are therefore defined, corresponding to the two sensors. These parameters are obtained as in the first embodiment. by simple image capture using an objective micrometer. The objective micrometer used must however be designed for this purpose the marks must be made on a thin coverslip, a thick slide cannot be used with this microscope.

First of all, the objectives must be properly focused. To this end, the parallel beams FED and FEG are suppressed. Only the FRD and FRG reference waves are present. The mirrors (2282) and (2247) are used to obtain centered waves with two directions of propagation. The mirrors (2243) and (2232) are closed. The phase shifter (2251) is used to modify the phase of the waves. The micrometer is moved so that the marks are outside the scope of the objectives. The wave measured on one side of the objectives is the equivalent of the reference wave used on the other side. The program described in 7.3.3.1. with Fourier transformation allowing to pass from the frequency domain to the spatial domain, is used to evaluate the punctuality of the image. The position of the objectives is adjusted to obtain a point centered in the middle of the image.

de faisceau CO.II[0,128,128]. La position de l'échantillon dans le plan horizontal est modifiée jusqu'à ce que l'on obtienne une modification caractéristique de l'onde reçue sur les capteurs en l'abscence d'onde de référence, comme dans le premier mode de réalisation. Secondly, the sample must be correctly positioned. The mirrors (2282) (2247) (2243) (2232) are closed. Only the FEG bundle is used, with a diverter control word

beam CO.II [0,128,128]. The position of the sample in the horizontal plane is modified until a characteristic modification is obtained of the wave received on the sensors in the absence of a reference wave, as in the first embodiment.

The FRD reference wave is then reintroduced and a focusing program similar to that used in the first embodiment, and using the image obtained on the sensor (2239), is started. This program differs, however, from that used in the first embodiment in that the phase and amplitude modifications of the illuminating wave are now controlled by the devices.

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commande du déviateur de faisceau CO.11[ 1, 128,128]. Le faisceau de référence FRG est également introduit On relance le programme de focalisation, qui cette fois utilise l'image reçue sur le capteur (2229). La position du diaphragme (2223) est alors ajustée dans un plan perpendiculaire à (2264) de manière à ce que son image soit correctement centrée. Son ouverture est ajustée de manière à être aussi élevée que possible, le diaphragme devant toutefois rester entièrement visible sur l'image obtenue Sur l'image obtenue, on mesure la distance (Dpix)1 entre les mêmes graduations que précédemment.

(2204) and (2205) and in that the average ratio value characteristic of the attenuation is real and is that which was measured in 7.3.2.2. between two positions of the beam attenuator which are the only ones used here
The position of the diaphragm (2213) is then adjusted in a plane perpendicular to (2264) so that its image is correctly centered. Its aperture is adjusted so as to be as high as possible, the diaphragm must however remain entirely visible in the image obtained. The position of the micrometer is then adjusted in the vertical direction so as to obtain a clear image. On this image, we then measure the distance (Dpix) between two graduations separated by a real distance
Dreel -
The FEG and FRD beams are then deleted. The FED bundle is introduced with the word of

CO.11 beam diverter control [1, 128,128]. The reference beam FRG is also introduced. The focusing program is restarted, which this time uses the image received on the sensor (2229). The position of the diaphragm (2223) is then adjusted in a plane perpendicular to (2264) so that its image is correctly centered. Its aperture is adjusted so as to be as high as possible, the diaphragm having to remain entirely visible on the image obtained. On the image obtained, the distance (Dpix) 1 between the same graduations as previously is measured.

(D PIX) est la distance en pixels mesurée sur l'image issue du capteur indicé p, avec p=0 pour (2239) et p= 1 pour (2229)
Dreel est la même pour chaque mesure. We then have K = -? -, # # D reel or: # (Dpix) p reel

(D PIX) is the distance in pixels measured on the image from the sensor indexed p, with p = 0 for (2239) and p = 1 for (2229)
Dreel is the same for each measurement.

programme de focalisation soit par eaemple . P,=2i6. Npix is the number of pixels of the useful sensor area and of the Fourier transform used in the

focusing program either for example. P, = 2i6.

The diaphragm openings obtained at the end of this procedure will be maintained thereafter.
7.7. Induced rate difference on a parallel beam.

The observed sample does not necessarily have the nominal index of objectives as its average index.

This difference in index can lead to significant spherical abberration. In order to correct this abberration, it is necessary to take into account the average index no in the sample and the thickness L of the sample lying between two coverslips at the nominal index.

The subsequent reconstruction of a three-dimensional image also requires knowledge of the relative position of the virtual points of origin of the reference beams used on each side of the system. This relative position is defined by x, y, z which are the coordinates of the point of origin of the reference beam used in the left part with respect to the point of origin of the beam used in the right part.

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vecteur fréquence dans l'objet a pour coordonnées, dans un repère orthonormé àp, b p, c ou c est parallèle à (2263) et ou 5p,bp se déduisent simplement des vecteurs i p ,jp définis en 7.3.3.3.: ..-.#'p'-' i2 ~j2) et il fait avec l'axe (2263) un angle de:

sina = ±i2 + /
Kp Si le faisceau issu de l'objectif n'était pas dévié par les miroirs (2214) (2215) (2216) ou (2222) (2221)

(2220) les vecteurs âp,bp seraient égaux aux vecteurs r p .j . Bien que ce ne soit pas réellement le cas, les vecteurs de base â p , b p , c seront notés dans la suite de l'exposé i p , 1 je k p , sans différencier les vecteurs â p , b des vecteurs correspondants î p , j p définis en 7.3.3.3. sur les capteurs. The parameters x, y, z, L, no lead to phase shifts of a parallel wave passing through the sample.The calculation of these phase shifts is explained below: -correspondence between the direction of a parallel beam in the object and the coordinates of the corresponding point on the sensor: i and are the coordinates of a pixel with respect to the optical center, expressed in pixels, on the sensor /?, in the frame defined in step 14 of the adjustment cycle described in 7.3. 3.2. A unit vector parallel to

frequency vector in the object has for coordinates, in a coordinate system orthonormal to p, bp, c or c is parallel to (2263) and or 5p, bp can be deduced simply from the vectors ip, jp defined in 7.3.3.3 .: ..- . # 'p'-' i2 ~ j2) and it makes with the axis (2263) an angle of:

sina = ± i2 + /
Kp If the beam coming from the objective was not deflected by the mirrors (2214) (2215) (2216) or (2222) (2221)

(2220) the vectors âp, bp would be equal to the vectors rp .j. Although this is not really the case, the base vectors â p, bp, c will be denoted in the remainder of the discussion ip, 1 i kp, without differentiating the vectors â p, b from the corresponding vectors î p, jp defined in 7.3.3.3. on the sensors.

A =lona -l"n" ou n" désigne l'indice nominal des objectifs, c'est-à-dire l'indice pour lequel ils ont été conçus et qui doit être celui de l'huile optique employée.

- rate difference induced by the presence of the object: Fig. 45 shows the principle of calculating this rate difference. We have:

A = lona -l "n" or n "designates the nominal index of the objectives, that is to say the index for which they were designed and which must be that of the optical oil used.

A = Lno cos J3- Ln "cosa 0 = L 1-C-" sinaJ lz -n, 1-sinZ a [11 n. either: 4 = L no 1-Cn - '' J n l2 r 2 + J z 2 -nv 1-t 2 k + z Kp2 K p2 -Procedure difference induced by a displacement of the illuminated point: The quantity accessible to the measurement is the path difference between the inverted beam coming from FRG and the reference beam FRD. If these two beams are merged and if the medium separating the objectives has the nominal index of the objectives as an index, the path difference is zero. However, if the point of origin

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U. 1, i j 1 2 2 2 4=u.v=C -1- - 2 ,2 ,2) ( p Kp Y, Z) p p 4 = x k +1.' +Z i %1Y2 -l2 - J2 L'l=X-+1!-+z- K K différence de marche totale: c'est la somme de la différence de marche dûe à la présence de l'objet et de celle due à la non-coincidence des points source.

virtual reference beam FRD has for coordinates (x, y, z) with respect to the virtual point of origin of the reference beam FRG, materialized by the focal point of its inverted beam, then this path difference is calculated as follows :
We use the vector v- (x, y, z) and the vector u defined above. Fig. 46 shows the geometric principle of calculation. The induced rate difference is:

U. 1, ij 1 2 2 2 4 = uv = C -1- - 2, 2, 2) (p Kp Y, Z) pp 4 = xk +1. ' + Z i% 1Y2 -l2 - J2 L'l = X- + 1! - + z- KK total operating difference: it is the sum of the operating difference due to the presence of the object and that due to the non-coincidence of the source points.

j2g- - 2,,- LI - 21< [( 1 j 1 - 2 2 +L no I Cno,Z 1 2 + j 2 1 2 + j 2 À=ex i- - +Y~L+z - Kr 2~j2) +Ln --II 1-- JIRI Kp Kp K no K,,2 7. 8. Programme de maximisation. (j 1 -2, 2, 2) [(nv) 22 + / i2 + /] L'l = n x- + y- + z- tn 1- - 1 I- In the absence of diaphragm, the wave measured on the wave measured at the point of the coordinate sensor (i, j) is therefore

j2g- - 2 ,, - LI - 21 <[(1 j 1 - 2 2 + L no I Cno, Z 1 2 + j 2 1 2 + j 2 À = ex i- - + Y ~ L + z - Kr 2 ~ j2) + Ln --II 1-- JIRI Kp Kp K no K ,, 2 7. 8. Maximization program.

7. 8.1. Principle.

utiliser une méthode simple pour déterminer les valeurs de x,y,z,L, n . Pour ce réglage les faisceaux d'éclairage FED et FEG sont supprimés et les faisceaux de référence FRD et FRG sont introduits en utilisant les miroirs (2282) et (2247) pour renvoyer des faisceaux symétriques vers les objectifs. Le faisceau FRG réfléchi par (2282) et se dirigeant vers l'objectif (2219) est centré sur un point central du diaphragme (2224). Il est focalisé par l'objectif (2219) en un point de l'objet (2218). Il traverse ensuite l'objectif (2217) et parvient au CCD (2239) sur lequel il se superpose au faisceau de référence FRD réfléchi par le miroir semi-transparent (2245) en direction du CCD (2239) Le décaleur de phase (2251) est utilisé pour générer un décalage de phase entre les deux faisceaux, ce qui permet de mesurer en valeur complexe le faisceau issu de FRG et reçu sur (2239), en utilisant la procédure de prise d'image simple décrite en 7.5. L'onde ainsi

reçue est stockée dans un tableau Frec de dimensions .4r p;x x pix - In the 'ideal' case where the sample is simply a slide of thickness L and index no, we can

use a simple method to determine the values of x, y, z, L, n. For this adjustment the illumination beams FED and FEG are removed and the reference beams FRD and FRG are introduced using the mirrors (2282) and (2247) to return symmetrical beams to the objectives. The FRG beam reflected from (2282) and directed towards the objective (2219) is centered on a central point of the diaphragm (2224). It is focused by the objective (2219) at a point on the object (2218). It then passes through the objective (2217) and reaches the CCD (2239) on which it is superimposed on the FRD reference beam reflected by the semi-transparent mirror (2245) in the direction of the CCD (2239) The phase shifter (2251) is used to generate a phase shift between the two beams, which makes it possible to measure in complex value the beam coming from FRG and received on (2239), using the simple image capture procedure described in 7.5. The wave as well

received is stored in a Frec array of dimensions .4r p; xx pix -

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l'acquisition d'un tableau F,ec de dimensions IV plX x . p,z. équivalent à celui qui serait obtenu dans le cas idéal. In practice, the acquisition method will often differ from the ideal case but will always allow

the acquisition of an array F, ec of dimensions IV plX x. p, z. equivalent to that which would be obtained in the ideal case.

I abscence de diaphragme, et dans un repère centré sur le centre optique, est donnée par la formule établie en 7.7.: 2g- Â -+y-+z 0 ryl 12 +j2 ho2 j-2-'" { 2 ,,J.#++z 1-##- ( )2.2+.2 .2+ '2]]} 1\.0 110 1\.0 La présence du diaphragme a en outre un effet de filtrage qui peut également être simule

Le programme utilisé a pour objectif de calculer x,y,z, l., no en minimisant la différence entre l'onde ainsi simulée et l'onde réellement reçue. Due to the phase shifts induced by the sample, the value of the wave at a point in

The absence of diaphragm, and in a frame centered on the optical center, is given by the formula established in 7.7 .: 2g- Â - + y- + z 0 ryl 12 + j2 ho2 j-2- '"{2 ,, J. # ++ z 1 - ## - () 2.2 + .2 .2+ '2]]} 1 \ .0 110 1 \ .0 The presence of the diaphragm also has a filtering effect which can also be simulated

The objective of the program used is to calculate x, y, z, l., No by minimizing the difference between the wave thus simulated and the wave actually received.

x,y>z,L,no: étape 1-la représentation fréquentielle suivante, de dimensions.\' x No avec par exemple.\' =4096, est calculée :

rc2 + cz n z rcz + c2 +1 Fr,=eap \-:- 27r [ ( Ic jC R,2 2 + i,C2 1 2 je2 Yt'rJ'Yi'd n, 1- R/ avec R ~ . K. et ou ic et jc sont les indices centrés soit: ic = i - # . yc = y - #-
Npix 2 2 étape 2-la transformée de Fourier inverse de Fc est calculée. étape 3- Fc étant maintenant en représentation spatiale, la présence du diaphragme constitue une simple

limitation dans ce domaine. Le programme calcule donc le tableau F. de dimensions . pr, x .V,,, en l'initialisant à 0 puis en effectuant: Fa i, j - F Ci - ep + Nc > j - Np + Nc c[ 2 2 2 2 pour tous les couples (i,j) tels que

(' ,v P1X) (. N P1X) 2 N PIX) i-@pix/2 J (j-Npt/2 J # (Npix/2 étape 4- le programme effectue une transformation de Fourier du tableau Fd This difference can be characterized by the standard deviation U (x, .v, z, L, nu) between the simulated wave and the received wave. The received wave being recorded in a Free array of dimensions A'p, y x. \ 'P1X' this standard deviation can be calculated as follows, in 6 steps, for a given value of the quintuple)

x, y> z, L, no: step 1-the following frequency representation, of dimensions. \ 'x No with for example. \' = 4096, is calculated:

rc2 + cz nz rcz + c2 +1 Fr, = eap \ -: - 27r [(Ic jC R, 2 2 + i, C2 1 2 i2 Yt'rJ'Yi'd n, 1- R / with R ~. K. and where ic and jc are the centered indices either: ic = i - #. Yc = y - # -
Npix 2 2 step 2-the inverse Fourier transform of Fc is calculated. step 3- Fc now being in spatial representation, the presence of the diaphragm constitutes a simple

limitation in this area. The program therefore calculates the array F. of dimensions. pr, x .V ,,, by initializing it to 0 then by performing: Fa i, j - F Ci - ep + Nc> j - Np + Nc c [2 2 2 2 for all pairs (i, j) such as

(', v P1X) (. N P1X) 2 N PIX) i- @ pix / 2 J (j-Npt / 2 J # (Npix / 2 step 4- the program performs a Fourier transformation of the array Fd

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L Frec[!.} )1'd[I,}] étape 5- Le programme calcule la valeur rapport (i,j)#E ou E est un ensemble défini de

(1, jFE manière à éviter les valeurs trop atténuées, qui permet de recaler en phase et en intensité le tableau Fd avant de le comparer à Frec.

étape 6- Le programme calcule alors l'écart-type 6z (x. v, z, l., n ~ <-t,['-7]' ['- /J i, j Le programme de calcul de x,y,z,L, no détermine la valeur de x,y,z,L, no qui permet de minimiser

l'écart-type ainsi calculé. Tout programme de minimisation de la grandeur 0'2 (x, y, z, Lyno) peut être utilisé de manière équivalente. L'algorithme décrit en 7.8.2. constitue un exemple d'un tel programme mais peut être remplacé par tout programme de minimisation équivalent.

Pour simplifier les calculs et faciliter la convergence, la minimisation de 0'2 (x, y, z, !-, nu) est remplacée dans l'algorithme décrit en 7.8.2. par la maximisation d'une grandeur caractéristique qui varie selon une variable mode qui augmente au fur et à mesure que l'algorithme converge vers la solution. 3 valeurs de mode sont utilisées: -#2##/@

mode=l: l'image réellement reçue est corrigée en phase par multiplication par e a . Une transformée de Fourier inverse permet d'obtenir une représentation spatiale. La grandeur choisie est le maximum du module sur l'ensemble de la représentation spatiale. mode=2. identique au cas mode= 1, mais la partie centrale de la représentation spatiale est suréchantillonnée et la grandeur choisie est la valeur du module au barycentre des points de la représentation spatiale. mode=3: l'onde devant être reçue sur le capteur pour lesvaleurs considérées de x,y,z,l., no est calculée en

tenant compte du filtrage par le diaphragme. La grandeur choisie est l'opposé de l'écart-lype entre )'onde ainsi simulée et l'onde réellement reçue soit -0'2 (x,y,z, !-,110)
7. 8.2. Algorithme.

L Frec [!.}) 1'd [I,}] step 5- The program calculates the ratio value (i, j) #E where E is a defined set of

(1, jFE so as to avoid excessively attenuated values, which makes it possible to readjust in phase and in intensity the table Fd before comparing it with Frec.

step 6- The program then calculates the standard deviation 6z (x. v, z, l., n ~ <-t, ['- 7]'['- / J i, j The program for calculating x, y, z, L, no determines the value of x, y, z, L, no which allows to minimize

the standard deviation thus calculated. Any minimization program for the quantity 0'2 (x, y, z, Lyno) can be used in an equivalent manner. The algorithm described in 7.8.2. is an example of such a program but can be replaced by any equivalent minimization program.

To simplify the calculations and facilitate convergence, the minimization of 0'2 (x, y, z,! -, nu) is replaced in the algorithm described in 7.8.2. by the maximization of a characteristic quantity which varies according to a mode variable which increases as the algorithm converges towards the solution. 3 mode values are used: - # 2 ## / @

mode = 1: the image actually received is phase corrected by multiplication by ea. An inverse Fourier transform makes it possible to obtain a spatial representation. The quantity chosen is the maximum of the modulus over the whole of the spatial representation. mode = 2. identical to the case mode = 1, but the central part of the spatial representation is oversampled and the selected quantity is the value of the modulus at the barycenter of the points of the spatial representation. mode = 3: the wave to be received on the sensor for the considered values of x, y, z, l., no is calculated in

taking into account the filtering by the diaphragm. The magnitude chosen is the opposite of the standard deviation between) 'wave thus simulated and the wave actually received, i.e. -0'2 (x, y, z,! -, 110)
7. 8.2. Algorithm.

la grandeur caractéristique pour l'indice no , entre nomin et nomax. Ceci correspond à la boucle interne (3201). Le programme détermine la nouvelle valeur de nocentre. qui doit correspondre à la valeur maximale de maxb. Il commence alors une nouvelle itération du type (3201) ou les valeurs de no sont

centrées autour de la nouvelle valeur de nocentre et ou la largeur nolarg-l1omax-nomin de l'intervalle de recherche a été divisée par 2. Ceci constitue la boucle externe (3202) qui est réitérée jusqu'à ce que la The algorithm of this program is described in Figs. 47 to 50 and FIG. 60
Fig. 47 depicts the highest level of the program. This level consists of a double loop of variation of the index no.The program calculates nopixels values of maxb, greatest value reached by

the characteristic quantity for the index no, between nomin and nomax. This corresponds to the internal loop (3201). The program determines the new nocentre value. which must correspond to the maximum value of maxb. It then begins a new iteration of type (3201) where the values of no are

centered around the new nocentre value and where the nolarg-l1omax-nomin width of the search interval has been divided by 2. This constitutes the outer loop (3202) which is repeated until the

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width of the search interval corresponds to the precision sought on index no. This method avoids having to test too many values of no to arrive at a result with a given precision.

nomin ini, nontax i i (indice no ), Lmin, Lmax (largeur L), zmin,zmax (profondeur ). Le programme n'a pas besoin d'une valeur maximale et minimale des coordonnées x et y. The program must have the following values as input: - minimum and maximum values of each value sought, taking into account the information available.

nomin ini, nontax ii (index no), Lmin, Lmax (width L), zmin, zmax (depth). The program does not need a maximum and minimum value of the x and y coordinates.

complexes Frec [1, } de dimensions N plX x N plX '
Les étapes principales du programme sont: - (3203): la valeur courante de no est calculée. - operating parameters. for example nopixels - 5 and pixels = 50 - image obtained for example as described in 7.8.1., in the form of an array of numbers

complexes Frec [1,} of dimensions N plX x N plX '
The main steps of the program are: - (3203): the current value of no is calculated.

- (3204): this procedure calculates the maximum value maxb reached by the characteristic quantity for the current index no, as well as the corresponding values of x, y, z, L. It is detailed in Fig. 48 - (3205): When the maxb value corresponding to the current iteration is greater than max ~ no, the current values of x, y, z, L, (calculated by procedure (3204)), and no are stored and constitute the current approximation of the sought result.

peut par exemple avoir lim = 0.05 inopixels - (3207): Le programme se termine. Les valeurs x f' }'f' Z f' L f' nocentre correspondent à la meilleure approximation des valeurs réelles de x,y,z,L, no. Elles sont affichées et enregistrées pour être réutilisées ultérieurement. - (3206): The width is compared to a certain limit to determine the convergence condition. We

may for example have lim = 0.05 inopixels - (3207): The program ends. The values xf '}' f 'Z f' L f 'nocentre correspond to the best approximation of the real values of x, y, z, L, no. They are displayed and saved for later reuse.

c = --1 n. ou nv est l'indice nominal des objectifs. For each index no, the procedure (3204) calculates a maximum value of the characteristic quantity and the associated values of x, y, z, L. However, a change of variables is made and the variables actually used in the procedure are x, y, u, v with: u = cL + v = L-cz

c = --1 n. where nv is the nominal index of the objectives.

The procedure consists in varying u and v and for each pair (u, v) to calculate x, y, and the max value of the characteristic quantity.

The couple (u, v) varies initially on a discrete set of points of size upixels x pixels, u and v varying respectively on intervals of width ularg and vlarg centered around the points ucentre ini and vcentre ini. The program determines the new value of (ucentre, vcentre) which corresponds

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au couple (u,v) pour lequel la valeur max est la plus élevée. Il détermine également des valeurs xhar et J'har qui correspondent à l'écart entre les valeurs de x,y utilisées pour le calcul et la valeur de x,y affinée à l'issue du calcul. Ces opérations constitue la procédure (3305) détaillée Fig. 49
Lorsque une nouvelle valeur de (ucentre,vcentre) a été obtenue, le programme diminue la largeur

ularg et vlarg des intervalles de recherche, ainsi que leurs centres ucentre ini, vcentre ~ini et les valeurs de x et y, puis calcule la valeur \dit. Si la valeur obtenue est inférieure à une limite fixée comme critère de convergence, le programme calculez et L par inversion du changement de variables, ce qui termine la procédure (3204). Sinon, il modifie éventuellement le choix de grandeur caractéristique (modification de mode), puis répète la procédure (3305). Ceci constitue la boucle (3301). L'ensemble de ces opérations constitue la procédure (3204) décrite Fig. 48
La Fig.48 décrit la procédure (3204). Ses étapes essentielles sont : - (3302): les intervalles de variation de u et v sont déterminés.

to the torque (u, v) for which the max value is the highest. It also determines values xhar and J'har which correspond to the difference between the values of x, y used for the calculation and the value of x, y refined at the end of the calculation. These operations constitute the procedure (3305) detailed in FIG. 49
When a new value of (ucentre, vcentre) has been obtained, the program decreases the width

ularg and vlarg search intervals, along with their centers ucentre ini, vcentre ~ ini, and the values of x and y, then calculate the value \ dit. If the value obtained is less than a limit set as the convergence criterion, the program calculate and L by inverting the change of variables, which ends the procedure (3204). If not, it possibly modifies the choice of characteristic quantity (modification of mode), then repeats the procedure (3305). This constitutes the loop (3301). All of these operations constitute the procedure (3204) described in FIG. 48
Fig. 48 depicts the procedure (3204). Its essential steps are: - (3302): the variation intervals of u and v are determined.

- (3303): The purpose of this procedure is to determine upixels and vpixels in an optimal way. Its algorithm is described in Fig. 60.

d'impact à un faisceau de direction parallèle à z est: dif 1 110 - n,,) L +On considère que l'algorithme a convergé quant cette grandeur est connue avec une précision suffisante. L'incertitude sur cette grandeur vaut:

Adif = I I ~ [(noc-n"c+n"u+(-no +nv +n,c)Ai,l # 1+c2

ou ularg ularg et vlarg ou Au = # ct Av = # upixels vpixels

Le programme modifie mode et détermine la fin de convergence en fonction la v alcur obtenue de ldrf . On peut par exemple avoir liml=2, lini2=0.25,lini3=0.0 - (3305) cette procédure calcule la grandeur caractéristique pour un ensemble de couples (u,v) et détermine le couple ucentre, vcentre correspondant à la plus grande valeur caractéristique, la valeur maxb de cette grandeur caractéristique, et les valeurs xbar,ybar qui représentent l'écart entre la nouvelle approximation de x,y et les valeurs courantes de x,y. Elle est détaillée Fig. 49.

- (3304). The deviation of (phase / 27t) caused by the crossing of the blade and the next displacement / of the point

of impact to a beam of direction parallel to z is: dif 1 110 - n ,,) L + We consider that the algorithm has converged when this quantity is known with sufficient precision. The uncertainty on this quantity is worth:

Adif = II ~ [(noc-n "c + n" u + (- no + nv + n, c) Ai, l # 1 + c2

or ularg ularg and vlarg or Au = # ct Av = # upixels vpixels

The program modifies mode and determines the end of convergence according to the value obtained from ldrf. We can for example have liml = 2, lini2 = 0.25, lini3 = 0.0 - (3305) this procedure calculates the characteristic quantity for a set of pairs (u, v) and determines the torque ucentre, vcentre corresponding to the largest characteristic value , the value maxb of this characteristic quantity, and the values xbar, ybar which represent the difference between the new approximation of x, y and the current values of x, y. It is detailed in Fig. 49.

y y tj/'<7 si upixels < 4 alors ucentre ini, ularg ne sont pas modifiés. si upixels >- 5 alors: ucentre-ini-ticentre et ularg = 4 ularg upixels si pixels < 4 alors vcentre ini, vlarg ne sont pas modifiés. - (3306): modification of; r ,, u / g ./ 'g, MC6, vcen ~; the program makes the following modifications: x = x -xbar

yy tj / '<7 if upixels <4 then ucentre ini, ularg are not modified. if upixels> - 5 then: ucentre-ini-ticentre and ularg = 4 ularg upixels if pixels <4 then vcentre ini, vlarg are not modified.

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si vpixels > 5 alors: vcentre ini=vcentre et vlarg = 4 vlarg vpixels La Fig.49 décrit la procédure (3305). Ses étapes essentielles sont :

- (3401): cette procédure calcule la grandeur caractéristique l1lax pour les valeurs courantes de u,v, n0 En mode 1 et 2 elle calcule également xbar et ybar qui représentent l'écart entre la nouvelle approximation de x,y et la valeur en entrée de la procédure.

- (3402): dans le cas du mode 3, la procédure (3401) n'a pas calculé xhar et yhar. Elle est relancée en mode 2 pour effectuer ce calcul.

if vpixels> 5 then: vcentre ini = vcentre and vlarg = 4 vlarg vpixels Fig. 49 describes the procedure (3305). Its essential steps are:

- (3401): this procedure calculates the characteristic quantity l1lax for the current values of u, v, n0 In mode 1 and 2 it also calculates xbar and ybar which represent the difference between the new approximation of x, y and the value in entry of proceedings.

- (3402): in the case of mode 3, the procedure (3401) did not calculate xhar and yhar. It is restarted in mode 2 to carry out this calculation.

a[t, 1{ c 1 -Cnvl2 J iCZ + jCZ - 1 + 1-C n" 1 ~ lCZ + jC2 - r [l + c2 [\ n^ Ka 1+.2 [\ K02 br. .]- 1 1 (nv)2 ie2 + jc2 2 1+c ic2 + jc2 b,} -- -no 1- - --nI' À. 1 + c2 n K 2 1 + e2 K 2 ou ic et jc sont les indices centrés soit: ic = i - 2 # , ic = i - #-
2 On vérifie alors, à une constante près indépendante de ; 1 et}:

nv( yc , à =z.1- ( ic jc +a[i,jlu+b Il, - = # - 0 +o ;./lM+6k/! Le programme génère la représentation fréquentielle corrigée de la manière suivante: F = ['.j J = [''/] ['j]) /(['.7]') exp -2 ' x 1 - .' 0 2 ptr +y y 0 2 yr.t ] + + i Ju H[" 1] ularg vlag ou /(j) = 0 quand \x\ > # et y(x) = 1 quand \x\ < # , et Au = # , Av = ## - 2 upixels vpixels a[i,j] et b[i,j] représentent respectivement les fréquences suivant u et v de la fonction corrigée obtenue. On vérifie que ces fréquences ont toutes deux un signe constant. La multiplication par les fonctions 7 permet d'annuler les éléments pour lesquels ces fréquences sont trop élevées et d'éviter ainsi les repliements de spectre qui empêcheraient la convergence de l'algorithme. Fig. 50 describes the procedure (3401). Its essential steps are: - (3501): calculation of the corrected frequency representation. From the Frec [i, j] array the program calculates a corrected representation using:

a [t, 1 {c 1 -Cnvl2 J iCZ + jCZ - 1 + 1-C n "1 ~ lCZ + jC2 - r [l + c2 [\ n ^ Ka 1 + .2 [\ K02 br.] - 1 1 (nv) 2 ie2 + jc2 2 1 + c ic2 + jc2 b,} - -no 1- - --nI 'À. 1 + c2 n K 2 1 + e2 K 2 where ic and jc are the indices centered either: ic = i - 2 #, ic = i - # -
2 We then check, up to a constant independent of; 1 and}:

nv (yc, à = z.1- (ic jc + a [i, jlu + b Il, - = # - 0 + o; ./ lM + 6k /! The program generates the frequency representation corrected as follows: F = ['.j J = [''/][' j]) /(().7] ') exp -2' x 1 -. '0 2 ptr + yy 0 2 yr.t] + + i Ju H ["1] ularg vlag or / (j) = 0 when \ x \># and y (x) = 1 when \ x \ <#, and Au = #, Av = ## - 2 upixels vpixels a [ i, j] and b [i, j] represent respectively the frequencies following u and v of the corrected function obtained. We check that these frequencies both have a constant sign. Multiplication by the functions 7 makes it possible to cancel the elements for which these frequencies are too high and thus avoid the aliasing of spectrum which would prevent the convergence of the algorithm.

- (3502): an inverse Fourier transformation of the table Fcor is performed.

- (3503): max is the maximum value of the modulus on the array Fcor [i, j] We denote by imax etjmax the coordinates of the pixel in which the maximum is reached. We then have:

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xba,r Ko -pix 00 ###-## ;WOX' - N PIX) nvNpix( 2

ybar = ##-## jiliax - - 2 ybar i7v.'prx (3 504): la partie centrale du tableau Feor [l, jl est extraite. On crée ainsi un tableau Fa [l, i] de dimensions %Ta 'p avec par exemple .'' =16: - [' ,Va /1[ P , lVa lV PIX] - (3505)' une transformée de Fourier directe est effectuée sur le tableau Fa - (3506): le tableau Fa est complété par des zéros et on obtient un tableau Fb de dimensions .'4'b .'1 avec par exemple .V=512.

xba, r Ko -pix 00 ### - ##; WOX '- N PIX) nvNpix (2

ybar = ## - ## jiliax - - 2 ybar i7v.'prx (3 504): the central part of the array Feor [l, jl is extracted. We thus create an array Fa [l, i] of dimensions% Ta 'p with for example.''= 16: - [', Va / 1 [P, lVa lV PIX] - (3505) 'a direct Fourier transform is carried out on the array Fa - (3506): the array Fa is completed with zeros and we obtain an array Fb of dimensions .'4'b .'1 with for example .V = 512.

et lb 11, J] 0 sinon. - (3507): la transformation de Fourier inverse du tableau Fb est effectuée

- (3508): xbar,ybar,max sont calculés par les formules: IlFb[l,j]l 2 iniax = r.J !MOy = ########### Y lFb [t. j Il2 i, j ##Fb [i,j]#2j

}max = r IFnw12 >J l,j 7Max = IFb hwoy, jmax]1 'ooy = #### ## foy - ## xbar = nv>\' plX ,\ ,a b max -----É... 2 =~~r,~ ybar = n v.v 0 plX .v b a i - (3509):la représentation fréquentielle suivante, de dimensions Ne x Ye avec par exemple ,V c =-1096, est calculée: Fr.r=ea 2z n" C x-+ R y R lc2 jc2 +L n" ( 'Iv )2 IC + jC 2 IC2 JC2 Fc [i,j] = exp[{#@@/## nv@x@/Rc + y@/Rc + z#1-@@@/Rc2@ + L#no#1-(nv/no) @@@/Rc2 - nv#1-@@@/Rc2##} Fbr.J = FaCi- 2a +2, l- 2b r + 2a l,} 2-2 2 2 when l'v'a -12i-- ± 20 and Na -12j-- ± 20 2 2 2 2

and lb 11, J] 0 otherwise. - (3507): the inverse Fourier transformation of table Fb is performed

- (3508): xbar, ybar, max are calculated by the formulas: IlFb [l, j] l 2 iniax = rJ! MOy = ########### Y lFb [t. j Il2 i, j ## Fb [i, j] # 2j

} max = r IFnw12> J l, j 7Max = IFb hwoy, jmax] 1 'ooy = #### ## foy - ## xbar = nv>\' plX, \, ab max ----- US. .. 2 = ~~ r, ~ ybar = n vv 0 plX .vbai - (3509): the following frequency representation, of dimensions Ne x Ye with for example, V c = -1096, is calculated: Fr.r = ea 2z n "C x- + R y R lc2 jc2 + L n"('Iv) 2 IC + jC 2 IC2 JC2 Fc [i, j] = exp [{# @@ / ## nv @ x @ / Rc + y @ / Rc + z # 1 - @@@ / Rc2 @ + L # no # 1- (nv / no) @@@ / Rc2 - nv # 1 - @@@ / Rc2 ##}

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avec Re = ##- "'0 et ou ic et jc sont les indices centrés soit: ic = i - #- . ic = y-#
Npix 2 2 - (3510) la transformée de Fourier inverse de Fc est calculée.

with Re = ## - "'0 and or ic and jc are the centered indices either: ic = i - # -. ic = y- #
Npix 2 2 - (3510) the inverse Fourier transform of Fc is calculated.

limitation dans ce domaine. Le programme calcule donc le tableau 1,-,, de dimensions .Y. x X pn en l'initialisant à 0 puis en effectuant: r]=L+,y.+ cIl- 2 2 2 Fd J 2 2 2 J2 pour tous les couples (i,j) tels que 'NI pix2 Vplx 'YPIX (. N PIX) 2 (. N PIX) 2 ( N plX ) 222 - (3512): le programme effectue une transformation de Fourier du tableau Fd #Frec [i,j]Fd[i,j] (i,j)#E - (3513): Le programme calcule la valeur rapport = ##Fd [i,j]#2 (i,j)#E

ouFest!'ensemb!edescouptes(/.y)vérifiant: Free[l, J ]/<; [1.}]:2: Coef . max IFm [a, h ]1' [a, h ]1. 0#a#N -il pix

OSb <~.''P-1 avec par exemple Coef = 0,5 . La justification de cette formule peut être trouvée en 7.17.1.2. - (351-1): Le programme calcule alors la grandeur caractéristique max:

max = - I Frec l . J - rapport. F, t , J 11 I,j La Fig. 60 décrit la procédure (3303). Cette procédure vise à déterminer lIpixels et l'pixels suivant les principes explicités ci-après : On peut exprimer la grandeur #/# calculée en 7.7. , à une constante près, sous la forme :

L'1 I1v -=#hr##+ +a(+ avec :

. 1+cz CnI 1+cz l+c2 I+C2 6(sol- l - (n-" Sz -1 - 1 + c n,, s2 - 1+cz Cl 1+cz - (3511): Fc being now in spatial representation, the presence of the diaphragm constitutes a simple

limitation in this area. The program therefore calculates the table 1, - ,, of dimensions .Y. x X pn by initializing it to 0 then by performing: r] = L +, y. + cIl- 2 2 2 Fd J 2 2 2 J2 for all the pairs (i, j) such that 'NI pix2 Vplx' YPIX ( . N PIX) 2 (. N PIX) 2 (N plX) 222 - (3512): the program performs a Fourier transformation of the array Fd #Frec [i, j] Fd [i, j] (i, j) # E - (3513): The program calculates the report value = ## Fd [i, j] # 2 (i, j) #E

orFest! 'setcouptes (/. y) verifying: Free [l, J] / <; [1.}]: 2: Coef. max IFm [a, h] 1 '[a, h] 1. 0 # a # N -il pix

OSb <~. '' P-1 with for example Coef = 0.5. The justification for this formula can be found in 7.17.1.2. - (351-1): The program then calculates the maximum characteristic quantity:

max = - I Frec l. J - report. F, t, J 11 I, j Fig. 60 describes the procedure (3303). This procedure aims to determine the pixels and the pixels according to the principles explained below: We can express the quantity # / # calculated in 7.7. , except for a constant, in the form:

L'1 I1v - = # hr ## + + a (+ with:

. 1 + cz CnI 1 + cz l + c2 I + C2 6 (sol- l - (n- "Sz -1 - 1 + cn ,, s2 - 1 + cz Cl 1 + cz

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s = i2 + 2 , 2 i et étant des indices centrés. 2 2

s = i2 + 2, 2 i and being centered indices.

-j2* - j2tr somme d'éléments de la forme e . Cette grandeur caractéristique peut être considérée comme une fonctionfonc(u, v) de u et v. Si on fixe la valeur de v, elle devient simplement fonction de u Si on limite la représentation Frec à un disque de rayon (en pixels) Koso cette fonction de u a comme fréquence maximale a(s,) . a(.\,o) est donc la fréquence maximale de fonc suivant u De même, />(.vo) est la fréquence maximale defonc suivant v. upixels et vpixels doivent être déterminés de manière à ce que pour une valeur donnée de s0 aussi élevée que possible, les pas d'échantillonnage suivant u etsoient suffisamment précis pour é\iter le repliement de spectre. Cette condition s'écrit:

1 a 5.0 1 ularg - -Ib(' '\0 )1 vlarg 2 1 upixels ' l'pixels 2 Par ailleurs le nombre total de pixels est limité à une valeur pixels, ce qui s'écrit: upixels vpirels = pixels En combinant ces équations on obtient l'équation El:

1 ( ( )1 pixels a so)b So 4.ularg.vlarg Deux cas se présentent alors: premier cas: (OUI') (ouv)1 pIxels premier cas: a - nv n,, -1. ularg. vlarg L'équation Et a une solution s0 que le programme peut déterminer par dichotomie. Les valeurs de upixels et vpixels sont alors déterminées par: upixels = 2#a(so )!ularg

vpixels = 21b( So I vlarg Deuxième cas: a ouv b oun pixels Deuxième 1 (ouv)b(ouv)1 < pixels 7 nv -1. ularg. vlarg L'équation El n'a pas de solution. Les valeurs de upixels et vpixels sont alors déterminées pour être

proportionnelles à celles obtenues pour la valeur s0 = ## soit: nv @ K02 The method of generating the characteristic quantity, in the cases mode = 1 or mode = 2, consists in -j2 ## / @ multiplying the frequency representation Frec by the phase correction factor e # then performing a Fourier transform . The representation thus obtained is in the spatial domain. The characteristic quantity is approximately the value of this representation at the point of origin. It is therefore obtained as

-j2 * - j2tr sum of elements of the form e. This characteristic quantity can be considered as a long function (u, v) of u and v. If we fix the value of v, it simply becomes a function of u If we limit the representation Frec to a disk of radius (in pixels) Koso this function of ua as maximum frequency a (s,). a (. \, o) is therefore the maximum frequency of func following u Similarly, />(.vo) is the maximum frequency of func following v. upixels and vpixels must be determined such that for a given value of s0 as high as possible, the following sampling steps u are sufficiently precise to eliminate aliasing. This condition is written:

1 a 5.0 1 ularg - -Ib ('' \ 0) 1 vlarg 2 1 upixels'l'pixels 2 In addition, the total number of pixels is limited to a pixel value, which is written: upixels vpirels = pixels By combining these equations one obtains the equation El:

1 (() 1 pixels a so) b So 4.ularg.vlarg Two cases then arise: first case: (YES ') (open) 1 pIxels first case: a - nv n ,, -1. ularg. vlarg The equation Et has a solution s0 that the program can dichotomously determine. The values of upixels and vpixels are then determined by: upixels = 2 # a (so)! Ularg

vpixels = 21b (So I vlarg Second case: a open b oun pixels Second 1 (open) b (open) 1 <pixels 7 nv -1. ularg. vlarg The equation El has no solution. The values of upixels and vpixels are then determined to be

proportional to those obtained for the value s0 = ## i.e.: nv

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upixels # ou ularg upixels = QT (7 ### M/-g nv . , .[OM] , %,pixels = ar( ul l ivlarg nv Par ailleurs la condition upixels vpixels = pixels doit toujours être vérifiée. La résolution de ces équations donne : 2 z ~ pixels

a =1 (OUI') (ouv)1 vlarg nv nv ularg. vlag et on obtient donc finalement:

<! ### M/org upixeLc n v pixeLs M/'/.S' ###### #### t; /7;X'C/.S' upixels (OU\') pixels A # vlarg n Jv ,( ouv\ 1 (ouv)1 pixels n v pixel.s l'pixels b -;;:: pixels i,pixel,ç (ou\') lularg -pixel. nv Dans les deux cas, les valeurs ainsi déterminées sont des nombres réels qui peuvent être inférieurs à 1 ou

supérieurs à pixels. Une dernière étape consiste donc à les traduire en nombres entiers dans l'inten alle [ 1,pixels]. L'algorithme résultant, qui permet de déterminer upixels et \'Pixels, est représenté sur la Fig.60. Les étapes suivantes doivent être détaillées:

(4201): sa est la solution de l'équation la( .'10 )b( so)1 = pixels. . Le programme résout cette équation 4. ularg. t,,Iarg par dichotomie entre 0 et ouv nv (4202):Ie programme prend pour upixels et vpixels le nombre entier le plus proche de la valeur réelle obtenue, puis il limite ces valeurs de la manière suivante:

- si upixels< le programme effectue upixel.c=1 - si vpixels<1 1 le programme effectue vpixels=1 - si upixel.s>pixels le programme effectue upixels=pixels -si vpixels>pixels le programme effectue ipixels- pixels

upixels # or ularg upixels = QT (7 ### M / -g nv.,. [OM],%, pixels = ar (ul l ivlarg nv In addition, the condition upixels vpixels = pixels must always be checked. The resolution of these equations give: 2 z ~ pixels

a = 1 (YES ') (open) 1 vlarg nv nv ularg. vlag and we finally get:

<! ### M / org upixeLc nv pixeLs M / '/. S'##########t;/7;X'C/.S'upixels (OR \') pixels A # vlarg n Jv, (open \ 1 (open) 1 pixels nv pixel.s l pixels b - ;; :: pixels i, pixel, ç (or \ ') lularg -pixel. nv In both cases, the values thus determined are real numbers which may be less than 1 or

greater than pixels. A last step therefore consists in translating them into integers in the inten alle [1, pixels]. The resulting algorithm, which makes it possible to determine upixels and \ 'pixels, is shown in Fig. 60. The following steps should be detailed:

(4201): sa is the solution of the equation la (.'10) b (so) 1 = pixels. . The program solves this equation 4. ularg. t ,, Iarg by dichotomy between 0 and open nv (4202): the program takes for upixels and vpixels the whole number closest to the real value obtained, then it limits these values as follows:

- if upixels <the program performs upixel.c = 1 - if vpixels <1 1 the program performs vpixels = 1 - if upixel.s> pixels the program performs upixels = pixels -if vpixels> pixels the program performs ipixels- pixels

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7. 9. Obtaining the characteristics of parallel beams.

Each parallel beam generated by the illumination beam control system has an independent phase. The purpose of this procedure is to determine the phases and coordinates of these parallel beams. It breaks down into two parts:
7.9.1. Adjusting the objectives and obtaining the rotating position of the focal points.

The objective of this step is to determine the relative position of the points of origin of the reference beams FRD and FRG. This objective can be achieved by adjusting the position of the objectives so that the image produced by the FRGI beam on the sensor (2239) is perfectly punctual.

For this purpose, only the FRGI and FRD beams are used. The mirror (2282) is used to obtain a centered wave with two directions of propagation. The mirrors (2243) (2232) (2247) are closed. The phase shifter (2251) is used to change the phase of this wave. The space between the two objectives is occupied by optical oil at the nominal index of the objectives. The wave measured on the right side of the objectives on the sensor (2239) indexed by /? = 0 is the equivalent of the reference wave used on the other side. Its punctuality is evaluated by the procedure described in 7.3.3.1. , with the use of a Fourier transform in said procedure. The position of the objectives is adjusted to obtain a point centered in the middle of the image.

If this adjustment of the position of the objectives is carried out with the greatest care and with sufficiently precise positioners, of sub-micrometric precision. for example, microscope focusing devices of sufficient quality, or positioners with piezoelectric control, then the points of origin of the images obtained from each side of the microscope are the same.

avec soin, les points d'origine des représentations fréquentiellcs finalement obtenues sont confondus. Leurs coordonnées relatives sont donc (x,y,z)=(0,0,0). Il est alors préférable de ne pas modifier les positions obtenues pour les objectifs. However, this requires extremely precise positioning of the objectives. The adjustment procedure described in 7.3.3.2. However, it is possible to obtain this quality of adjustment by using positioners of medium precision for the objectives. In fact, the fine adjustments are made, in this procedure, by moving the cameras and not the lenses. If the adjustment procedure described in 7.3.3.2. is done

with care, the points of origin of the frequency representations finally obtained are merged. Their relative coordinates are therefore (x, y, z) = (0,0,0). It is then preferable not to modify the positions obtained for the objectives.

des objectifs sont en général imparfaits. Il est possible d'utiliser (x,y,z)=(0,0,0) mais une meilleure superposition des images provenant de chaque capteur sera obtenue si un algorithme adapté est utilisé pour calculer une valeur plus précise de ces paramètres. However, the settings obtained by procedure 7.3.3.2. or by a new position adjustment

objectives are generally imperfect. It is possible to use (x, y, z) = (0,0,0) but a better superposition of the images coming from each sensor will be obtained if a suitable algorithm is used to calculate a more precise value of these parameters.

alors enregistrée en un tableau Frec[I,}], Les coordonnées x,y,z du point d'origine de l'onde de référence issue de FRD par rapport au point d'origine de l'onde de référence issue de FRG sont alors déterminées à partir de Frec[i,j] en utilisant le programme décrit en 7.8. Toutefois, afin de tenir compte de l'abscence d'échantillon, la procédure (3303) est remplacée par les deux affectations suivantes :

upixels-pixels vpixels= 1 The wave measured on the sensor (2239), obtained according to the procedure described in 7.5. with /? = 0, is

then recorded in an array Frec [I,}], The coordinates x, y, z of the point of origin of the reference wave coming from FRD with respect to the point of origin of the reference wave coming from FRG are then determined from Frec [i, j] using the program described in 7.8. However, in order to account for the missing sample, procedure (3303) is replaced by the following two assignments:

upixels-pixels vpixels = 1

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nomax ini= nomin ini=nv . nv étant l'indice nominal des objectifs. In addition, the variables used are:

nomax ini = nomin ini = nv. nv being the nominal index of the objectives.

znrin = -2<M et max = 20À (par exemple) 7. 9.2. Obtention des valeurs complexes et des coordonnées des faisceaux d'éclairage. Lmirz-Lnrax = 0 nopixels = 1 1 pixels = 20

znrin = -2 <M and max = 20À (for example) 7. 9.2. Obtaining complex values and coordinates of lighting beams.

p,i,j du mot de commande C'0,1f[p,r,] du déviateur de faisceau - les coordonnées du point d'impact direct du faisceau d'éclairage sur le capteur/). Ces coordonnées seront stockées dans les tableaux In(p,0,i] ..Ta[p,0,i,j]. The objective of this procedure is to determine, for each parallel beam defined by the indices

p, i, j of the control word C'0,1f [p, r,] of the beam deflector - the coordinates of the point of direct impact of the lighting beam on the sensor /). These coordinates will be stored in the arrays In (p, 0, i] ..Ta [p, 0, i, j].

- the coordinates of the point of direct impact of the lighting beam on the sensor / 7 These coordinates will be stored in the tables Ia [p, 1, ijl, Ja [p, 1, ij].

stockée dans un tableau Ra[p,I,J]. Comme la mesure directe des faisceaux donne des coordonnées relatives au point d'origine de l'onde de référence utilisée sur le capteur/?, cette valeur doit être corrigée en fonction des valeurs de position déterminées en 7.9. 1. - the complex value of the corresponding illumination beam, its phase being measured at the point of origin of the reference wave used on the p sensor. This phase measurement convention in fact ensures that the complex value thus obtained is independent of the position of the objectives, except for an overall phase factor affecting all the beams characterized by the same index p. This complex value will be

stored in an array Ra [p, I, J]. As the direct measurement of the beams gives coordinates relative to the point of origin of the reference wave used on the /? Sensor, this value must be corrected according to the position values determined in 7.9. 1.

d'éclairage défini par un mot de commande variable CO,1[p, ijl du déviateur de faisceau. Les miroirs (2243) et (2232) sont utilisés pour créer un faisceau indicateur inverse du faisceau d'éclairage qui va frapper le capteur opposé au capteur normalement éclairé par ce faisceau. Les miroirs (2247) et (2282) sont obturés. During this procedure, the FRD and FRG reference beams are used, as well as a

lighting defined by a variable control word CO, 1 [p, ijl of the beam diverter. The mirrors (2243) and (2232) are used to create a reverse indicator beam of the illumination beam which will strike the sensor opposite to the sensor normally illuminated by this beam. The mirrors (2247) and (2282) are closed.

The procedure described in 7.5. is used to obtain two-dimensional images in complex numbers on each sensor. Phase shifts are performed using element (2205).

A program makes it possible to obtain these parameters in the form of tables Ia [p, q, ijl. Ja [p, q, i,], Ra [p, i, jl. By an oversampling method it determines Ia [p.q, I, J] Ja [p, q, i j] with a precision lower than one pixel. These arrays are therefore arrays of real numbers.

réglage 7.3.3.2., défini par les vecteurs directeurs (1p - 7o ) Cette convention de repérage sera maintenue par la suite. The coordinate system used on the sensor /) is the one determined in step 14 of the

setting 7.3.3.2., defined by the direction vectors (1p - 7o) This registration convention will be maintained subsequently.

The program is made up of three loops successively run Loop 1: it is a loop on the index /), which successively takes the values 0 and 1

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Pour chacun de ces indices le programme utilise le mot de commande ro.\ p, 2' 2 . Il détermine alors les coordonnées entières /w0p,yw0 du maximum de l'image résultante sur le capteur p.

For each of these indices the program uses the command word ro. \ P, 2 '2. It then determines the integer coordinates / w0p, yw0 of the maximum of the resulting image on the sensor p.

Loop 2. This is a loop on the set of triples p, i, jo. For each of these triples, the program generates the values /'?o../o] ['o''o-7 (]] Ra [p ,,, io i () 1. At each iteration, corresponding to a given triplet po, io, jo the program performs the following 8 steps: Step the command word COA / o, # -, ## 1 is used and the resulting images on each sensor are saved in two tables of complex numbers .'lf0y y, J or q = 0 for the image obtained on the sensor Po and q = 1 for the image obtained on the opposite sensor.

Step 2: the command word C0.lfpo, io, j, is used and the resulting images are saved in the tables. \ F 1 q [l,} Step 3: The program determines the coordinates iiiiax jmaxq of the maximum modulus point of the array. \ fl [;. y] for each value of q.

Step -1: The program extracts an image of size 1'p x .V. with for example 'Q = 1G, around the point of coordinates imaxy jmax9: ~ 112 r, J ~ .lll9 Ci - a + irnax9, j - + jmax9. \ f2q [lj] jmaxq when F -1> - i - # s- + intax9> - t "1> '# s- + jnrrrYH> - quaiiid- plx - 2 + iniaxq: Vptx - 1 i - 2 + jieiax and. \ f2q Ly] = 0 otherwise.

Step 5. the program performs a direct Fourier transform of the. \ 12q arrays, Step 6: the program completes the .1f2 arrays with zeros, generating the .lf3y arrays of dimensions Yb x lVb with for example ~ b = 512. The .If3q array is initialized to zero then the program performs for all the indices <j each ranging from 0 to .Vu -1 and for the two indices q- .lf3qCt- + b, j- 2 + 2bJ = .lTqy.J Step 7: the program performs the inverse Fourier transform of table A / 3.

l:lf3qi, j z J1nax3q f,j 2 iniax3q LIM3q[i,}]1 i, j Step 8: the program calculates the coordinates and the complex value at the barycenter of the array, 113.

l: lf3qi, jz J1nax3q f, j 2 iniax3q LIM3q [i,}] 1 i, j

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113 y. jl j yway3 =# # jntax3 Ial39r, J12 [o. ?' 'o .70 nraxg + #'- Cimax3q - 26 JaPo..lo.jo=jnrax9+ -b I jmax3g- 2b1 RaPo a . Jo ~ il3omrax3o. jnrax3o A/Oo ;0, jnraxOpol j###################\'\ ~-2 o.Oo.7o] ,JaPo0ro,Jo+z {)A'o-7o]' +[n.0.'o.7o]' j '' Â K ou x,y,z sont les coordonnées calculées en 7.9. 1.

113 y. jl j yway3 = # # jntax3 Ial39r, J12 [o. ? ''o .70 nraxg + #' - Cimax3q - 26 JaPo..lo.jo = jnrax9 + -b I jmax3g- 2b1 RaPo a. Jo ~ il3omrax3o. jnrax3o A / Oo; 0, jnraxOpol j #################### \ '\ ~ -2 o.Oo.7o], JaPo0ro, Jo + z {) A'o -7o] '+ [n.0.'o.7o]' j '' Â K where x, y, z are the coordinates calculated in 7.9. 1.

programme parcourt à nouveau les indices po,io, jo, en testant à chaque fois la condition Ra[po 1 io io 1- z 1 . Lorsque cette condition est satisfaite, le programme effectue: [o,127,127] 8 Ra[po . 10, JO 1 = Iapp,0,io. jo=-1000 Japo,0,io, jo=-1000
7. 10. Réglage de position des objectifs. Loop 3: The program performs a final operation consisting of canceling the values of Ra and assigning high values to Ja and la each time the point of direct impact of the beam is outside the zone limited by the aperture of the objective , which results in a disappearance of this point. To this end the

program runs again through the indices po, io, jo, each time testing the condition Ra [po 1 io io 1- z 1. When this condition is satisfied, the program performs: [o, 127,127] 8 Ra [po. 10, JO 1 = Iapp, 0, io. jo = -1000 Japo, 0, io, jo = -1000
7. 10. Position adjustment of objectives.

Un programme génère deux images par la procédure décrite en 7.3.3. 1.: une image spatiale obtenue avec transformation de Fourier, et une image fréquentielle obtenue sans transformation de Fourier. Le programme extrait sur chacune de ces images l'intensité (carré du module des nombres complexes constituant l'image obtenue en 7.3.3.1.). Le programme affiche les images résultantes. The sample to be studied is set up. During this step, only the FRGI and FRD beams are used. The mirror (2282) is used to obtain a centered wave with two directions of propagation. The mirrors (2243) (2232) (2247) are closed. The phase shifter (2251) is used to change the phase of this wave. Optical oil at the nominal index of the objectives is used The wave measured on the right side of the objectives on the sensor (2239) indexed by p = 0 is the equivalent of the reference wave used on the other side.

A program generates two images by the procedure described in 7.3.3. 1 .: a spatial image obtained with Fourier transformation, and a frequency image obtained without Fourier transformation. The program extracts on each of these images the intensity (square of the modulus of the complex numbers constituting the image obtained in 7.3.3.1.). The program displays the resulting images.

The spatial image must be centered.

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On the frequency image, we should observe a clear disk. The adjustment should be made so that the intensity is as high as possible for high frequencies (points far from the center). The observed disc must remain relatively homogeneous.

If a dark ring appears between the outer edge and the central area, the sample is too thick and not all frequencies can be taken into account. The adjustment must then be carried out so as to have a relatively homogeneous disc, with as large a radius as possible. The disc does not reach its maximum size and high frequencies cannot be taken into account. The resolution of the image, mainly in depth, is reduced. The only solution to this problem is to use a specially designed lens, described in paragraph 7.19.

This method of setting the objectives is suited to the case where the sample index differs significantly from the nominal index of the objectives. Otherwise, and in particular if it is desired to use a function Dp defined in 7.16 equal to 1, the adjustment must be carried out from the spatial image alone and so that this image is point and centered.

7.11. Determination of x, y, zL, no
It is necessary to know these parameters in order to be able to compensate for the spherical aberration and the effects of the non-coincidence of the points of origin of the reference waves. These parameters can be determined by not performing step 7.10. and therefore leaving the objectives in the position where they were at the end of the step described in 7.9. 1. The values x, y, z are then those which were determined in 7.9.1. The values of L and n0 may have been measured beforehand by means outside the microscope proper. However, this method has the disadvantage of not allowing a movement of the objectives during the installation of the sample, and of requiring the use of an expensive external measuring system.It is therefore preferable to determine the whole again. of these parameters. This second method allows the displacement of the objectives during the placement of the sample and step 7.10. can therefore be performed.

To apply this second method, one could in principle use the theoretical procedure described in 7.8.1. and using a single image capture, but local variations in the characteristics of the sample in the vicinity of the focal point would distort the result. This is why a series of images are taken and the variation in phase and intensity at the point of direct impact of the illumination beam is measured on each image. From this series of values, we can generate an array equivalent to the Frec array used in 7.8. but in which we have freed ourselves from local variations.

7.11.1. Acquisition
The mirrors (2282) (2247) (2243) (2232) are closed so as to eliminate all the reverse indicator beams, which will no longer be used subsequently The procedure described in 7.9 2. is repeated, with the following modifications: - The sample is now present.

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obtenues de imaxO p , jmcrxOp sont réutilisées. - Dans la boucle 2, les indices P0 et q sont fixés à 0. Les étapes 1à 8 ne sont donc effectuées que pour

l'ensemble des indices ;0 . jo ( po étant fixé à 0). Dans chacune de ces étapes, seuls les éléments correspondant à l'indice q=0 sont acquis ou calculés. - L'étape 8 de la boucle 2 est modifiée comme suit:

Ia[po. q, io, 10]' [po.'?.'o.7o]- Ra[po, io,j 0] ne sont pas recalculés et leurs valeurs précédemment obtenues sont maintenues.

la quantité .R&fo .'o-7o] est calculée comme suit: -si Ra[ Po ' i 0 ' } 0] = alors Rb[ Po ' i a ' j 0] = -sinon-. Rbpo,io,jo= .lf3o rmax3o , jnrzr3o jni(u3() -sinon: /'o.'O'io .lf0ornrax0o, jnmx0o Rapo,TOJo Cette quantité correspond à la variation du faisceau d'éclairage dûe à la présence de l'échantillon et

au déplacement des objectifs, sur le capteur 0, pour l'éclairage caractérisé par les indices i 0' j 0 ' par rapport à une position des objectifs ou le point d'origine des ondes de référence utilisées sur chaque objectif seraient confondus. - Loop 1. which consists in determining imaxO p, jmaxO p is deleted. Previous values

obtained from imaxO p, jmcrxOp are reused. - In loop 2, the indices P0 and q are set to 0. Steps 1 to 8 are therefore only carried out for

the set of indices; 0. jo (po being set to 0). In each of these steps, only the elements corresponding to the index q = 0 are acquired or calculated. - Step 8 of loop 2 is modified as follows:

Ia [in. q, io, 10] '[po.' ?. 'o.7o] - Ra [po, io, j 0] are not recalculated and their previously obtained values are maintained.

the quantity .R & fo .'o-7o] is calculated as follows: -if Ra [Po 'i 0'} 0] = then Rb [Po 'ia' j 0] = -if not-. Rbpo, io, jo = .lf3o rmax3o, jnrzr3o jni (u3 () -if: /'o.'O'io .lf0ornrax0o, jnmx0o Rapo, TOJo This quantity corresponds to the variation of the lighting beam due to the presence of sample and

the displacement of the objectives, on the sensor 0, for the lighting characterized by the indices i 0 'j 0' with respect to a position of the objectives where the point of origin of the reference waves used on each objective would be the same.

- Loop 3 is deleted.

7.1 Incineration of the frequency image.

/a[o. <y, ;n, 7o ] - Ja[p0 ,q,io.jo] des points échantillonnés par le tableau Rb ne correspondent pas à des pixels entiers, une méthode de suréchantillonnage et de filtrage est nécessaire pour générer le tableau Frec' Cette méthode est imparfaite car le pas (par exemple 7o[. q, '. 7] - 7a[. fy, i + I- /1 ) séparant deux échantillons adjacents du tableau Rb peut varier. Néanmoins, pour une réalisation de qualité, cette variation est faible et la méthode de suréchantillonnage-filtrage donne de bons résultats Celle-ci comporte les étapes successives suivantes :

Etape 1: génération d'une représentation fréquentielle suréchantillonnée, de dimensions Art, x !\'c avec par exemple -NI, =4096. Le tableau Fs est initialisé à 0 puis le programme parcourt l'ensemble des indices iJ

en testant la condition Ra[ 0, i, J $ 0 . Lorsque la condition est vraie, il effectue: F E\lal0fi,i,j]-\djà[0fi,i,j]s-} =Rb[0.,.j] F E V - * pix N prx O.I.} ou E(x) désigne le nombre entier le plus proche de x. A second program is then launched. The purpose of this is to generate, from the previous measurements, a Frec table that can be used in the algorithm described in 7.8. Like coordinates

/ a [o. <y,; n, 7o] - Ja [p0, q, io.jo] of the points sampled by the array Rb do not correspond to whole pixels, an oversampling and filtering method is necessary to generate the array Frec 'This method is imperfect because the pitch (for example 7o [. q, '. 7] - 7a [. fy, i + I- / 1) separating two adjacent samples of the array Rb may vary. However, for a quality production, this variation is low and the oversampling-filtering method gives good results.This comprises the following successive steps:

Step 1: generation of an oversampled frequency representation, of dimensions Art, x! \ 'C with for example -NI, = 4096. The array Fs is initialized to 0 then the program traverses all the indices iJ

by testing the condition Ra [0, i, J $ 0. When the condition is true, it performs: FE \ lal0fi, i, j] - \ djà [0fi, i, j] s-} = Rb [0.,. J] FEV - * pix N prx OI} or E ( x) denotes the whole number closest to x.

Step 2: an inverse Fourier transform is applied to the array Fs

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Etape 3: la partie centrale du tableau, de dimensions N plX x N pu.. est extraite et la présence du diaphragme simulée.

Step 3: the central part of the table, of dimensions N plX x N pu .. is extracted and the presence of the diaphragm is simulated.

IV Pa f '.' C F ''. Eo rl = Fl - ur Z + 2c '.) - 2 Jx + for all pairs (i, j) such that C - prx 1 z NI 2 C prx 1 r 2 D + 2 D <D2 or open is the opening of the objectives.

Step 4: the Fourier transform of the Frec array obtained is performed.

7.11.3. Calculation of parameters.

l'indice. Il est possible de simuler cette image en fréquence à partir d'un quintuplet (x,y,z,L, n0 ) et de calculer une grandeur caractéristique max. C'est ce que fait la partie de programme décrite sur la Fig 50 et comprenant les étapes (3509) à (351-1), qui calcule finalement une grandeur caractéristique max que l'on notera max(x,y,z,L, n0). La détermination de la valeur du quintuplet (x,y,z,L, n0) consiste à utiliser un programme de maximisation qui fait varier (x,y,z,L, n0) de manière à déterminer le point correspondant à la valeur la plus élevée de max(x,y,z,L, n0 ). En principe, tout algorithme de maximisation convient. The Frec table obtained at the end of step 4 constitutes the frequency image. equivalent to that whose acquisition is described in 7.8.1., but acquired in a way less sensitive to local variations in

the index. It is possible to simulate this frequency image from a quintuplet (x, y, z, L, n0) and to calculate a characteristic quantity max. This is what the part of the program described in Fig. 50 and comprising steps (3509) to (351-1) does, which finally calculates a characteristic quantity max which we will denote by max (x, y, z, L , n0). The determination of the value of the quintuplet (x, y, z, L, n0) consists in using a maximization program which varies (x, y, z, L, n0) so as to determine the point corresponding to the value la greater than max (x, y, z, L, n0). In principle, any maximization algorithm is suitable.

However, the number of variables and the complexity of the calculations are such that it is necessary to use a specific and optimized algorithm. The program described in 7.8. is therefore used to calculate the parameters from the Frec table which constitutes the frequency image.

7. 12. Two-dimensional image capture.

7.12.1.Princine:
We have seen in the first embodiment how it is possible to produce a two-dimensional frequency representation from several elementary images differing from one another by the phase difference between the illumination beam and the reference beam, as well as by the level of attenuation of the illumination beam. In this mode, phase rotators (2210) (2238) (2241) (2226) are added which make it possible to vary the direction of polarization of the wave and the direction of analysis. Indeed, the diffraction of the illuminating wave is not homogeneous in all directions. For a given direction, the diffracted wave strongly depends on the polarization of the incident beam.

Recall that if a and b are two vectors, then: a # b is the cross product of a and b a.b is the dot product of a and b

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Ilall is the norm of a.

We call: fc: characteristic frequency of a point fe: lighting frequency fo. frequency associated with the optical center of the sensor Fig. 51 shows the arrangement of these frequencies.

Jc /\fe alors le faisceau diffracté par l'objet dans la direction f, n'est pas atténué. S'il est orthogonal à ce vecteur, le faisceau diffracté est atténué d'un facteur cos #. 3 is the angle between the vector fc a / # and the vector fc / \ fo / ie is the angle between the vector fe / \ Jc and the vector fe / \ Jo Q 'is the angle between the vector 17 and the vector fc / \ fo (we omit the index p for the vectors i. j, k) ae is the angle between the vector 17 and the vector fe / \ fo 0 is the angle between the vector fe and the vector fc
If the electric field vector of the illumination beam is parallel, in the object, to the vector

Jc / \ fe then the beam diffracted by the object in the direction f, is not attenuated. If it is orthogonal to this vector, the diffracted beam is attenuated by a factor cos #.

fc . Cette rotation conserve l'angle / . On note (/c /\ fe ) le vecteur ainsi obtenu à partir du vecteur fc /\Je . Dans le cas de l'onde de fréquence fe polarisée parallèlement à fe /\fc la rotation se fait autour de fe a fo et on note le vecteur résultant ( je ^ j On note: (Jc /\fetc = Ilfc /\ Je - (Je /\fc te xe IIfc /\ fe Vc ac +,8c #e = [alpha]e+sse

Dans le plan du capteur, on a donc la configuration indiquée Fig.52, ou les points 0, E, C sont respectivement le centre optique (fréquence fo), le point d'impact direct de l'onde d'éclairage (fréquence fe), et le point ou est mesurée l'onde diffractée (fréquence fc ).

The electric field vector of a beam, when it reaches the sensor, is in the plane of the sensor, which is a plane orthogonal to fo. The mode of passage from the electric field vector in the object to the electric field vector on the sensor is a rotation around the vector fc # fo for the frequency wave

fc. This rotation keeps the angle /. We denote by (/ c / \ fe) the vector thus obtained from the vector fc / \ Je. In the case of the frequency wave fe polarized parallel to fe / \ fc the rotation is done around fe a fo and we denote the resulting vector (i ^ j We denote: (Jc / \ fetc = Ilfc / \ Je - (I / \ fc te xe IIfc / \ fe Vc ac +, 8c #e = [alpha] e + sse

In the plane of the sensor, we therefore have the configuration shown in Fig. 52, where points 0, E, C are respectively the optical center (frequency fo), the point of direct impact of the lighting wave (frequency fe ), and the point where the diffracted wave is measured (frequency fc).

When the electric field vector of the lighting beam (at point F ~ is ..1oi + AJ the resulting electric field vector at the ballast point is' oo40 + Coi, 4i) l + (CIO-40 + Qii) 7 During measurements, we will use:

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diffractées polarisées selon les axes orientés par et y , obtenant les facteurs r00 et C10 - une onde d'éclairage dirigée selon j . Pour cette onde d'éclairage, on mesurera des composantes diffractées polarisées selon les axes orientés par i et j . obtenant les facteurs (C01 et C11
Les facteurs Ckl sont donc les grandeurs mesurées
On néglige içi le fait que les directions de polarisation et d'analyse obtenues ne sont pas rigoureusement orthogonales. - a lighting wave directed along ï. For this lighting wave, we will measure components

diffracted polarized along the axes oriented by and y, obtaining the factors r00 and C10 - an illuminating wave directed along j. For this lighting wave, diffracted components polarized along the axes oriented by i and j will be measured. obtaining the factors (C01 and C11
The factors Ckl are therefore the measured quantities
The fact that the polarization and analysis directions obtained are not strictly orthogonal is neglected here.

If the electric field vector of the lighting beam at point E is parallel to vector #e and the electric field vector of the beam received at point C is parallel to vector #c, there is no attenuation.

vaut: ,\= -cos cospcr00 -sin j9e coscr01 -cos sinç)cCl0 -sin(3d sin ço,CI 1 . This case corresponds to an electric field vector at point E of value Ax = .li Cosipe + j sinrpe and therefore a resulting electric field vector at point C: A [(C 00 cosrpe + Col sinipe) i + (('10 cos ip + Ci sin ip e) 1]. The projection of this vector on the axis oriented by -xc has the value: -A [(('00 cos ip + C0] sin ip e) cos ip c + (('10 cos ip + Ci 1 sin ÇO,) Sili ip, The value which one seeks to integrate in the calculations is the ratio of the algebraic value of the diffracted beam to that of the incident beam in the absence of attenuation due to the angle 0, which therefore corresponds to the above case and

is worth:, \ = -cos cospcr00 -sin j9e coscr01 -cos sinç) cCl0 -sin (3d sin ço, CI 1.

In order to calculate this value, it is necessary to first calculate the cos ip e functions. cosço ,, sin ip e, sin ip c. This is done by using on the one hand the trigonometric relations: cos ip = cos ac cos, 6, - sin a, sin P, sin V, = cos a sin3 c + sin a cos / 3 cos ip = pod cos, 6 , - sin a, sin, 6, sin (p, = cosae sin / 7 + sinae cosy3e and on the other hand the following relations: cos, 6c fc A f, fc ^ Io c IIfc I \ fell'l \ Jc 1 \ fo ci / 7 'c ^ JO / c / 6 1 / c S) n /) ,. = (fcI \ Jo 1 \ Jcl \ fe] fc Sin / 3. l \ Jc 1 \ Jo IIJc 1 \ fe Il 'Ifc il cos, 8, = Ie I \ Jc fe I \ fo e Iife 1 \ fc "Ilfe 1 \ fo sin3e ~ le ^ Io,. / 1 e IIJe I \ fol (l \ I 1 \ fc Il îlfell: - fcl \ Jo cosac = / '11 fc 1 \ fo

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sin a, =y.|j7 T-jT cosae - zoo cosor,, =1.7, - /e A/o smory..-##u Si on utilise les valeurs normalisées des vecteurs fréquence:

= xe1 + yej +Zek avec X2 e + - V2 +Zé = f, = Xe 1+.VI -:" - + z, k avec Xe 2 +yc 2 +ZC = on obtient: COSÇ5C = .11 1 ,Llc 1e 1'Vj'yr - 7C'cYcT xz + x c I"y sinrpc = A 1 llce (-xeYeL y +x 2l' +YoY'1 cos Ç7e le 2 "le (V2k- xeyel xz + X^t - sin9e = I llce 1-xeYel \ y a +xéf' +VeT x Y avec :

T Y' = Ycle - Zc Ye Il =-xcZe bzz t xy =-xcYe +Ycxe .llc 2 = xc 2 +Yc ~1lé = xé + ye 1'2 + ,2 + t,'2 -il,e I z
Toutefois, lorsque les dénominateurs sont nuls, les expressions ci-dessus doivent être remplacées par des valeurs limites. - fc # fo

sin a, = y. | j7 T-jT cosae - zoo cosor ,, = 1.7, - / e A / o smory ..- ## u If we use the normalized values of the frequency vectors:

= xe1 + yej + Zek with X2 e + - V2 + Zé = f, = Xe 1 + .VI -: "- + z, k with Xe 2 + yc 2 + ZC = we obtain: COSÇ5C = .11 1, Llc 1e 1'Vj'yr - 7C'cYcT xz + xc I "y sinrpc = A 1 llce (-xeYeL y + x 2l '+ YoY'1 cos Ç7e le 2" le (V2k- xeyel xz + X ^ t - sin9e = I llce 1-xeYel \ y a + xef '+ VeT x Y with:

TY '= Ycle - Zc Ye Il = -xcZe bzz t xy = -xcYe + Ycxe .llc 2 = xc 2 + Yc ~ 1lé = xé + ye 1'2 +, 2 + t,' 2 -il, e I z
However, when the denominators are zero, the above expressions should be replaced by limit values.

Une représentation fréquentielle bidimensionnelle est un tableau .11,,.lr, de nombres complexes, de dimensions ATpvc x noix - k est l'indice de l'image dans sa série, p est l'indice du capteur sur lequel parvient le faisceau d'éclairage direct (0 ou 1) et q a les valeurs suivantes: 7. 12.2. Algorithm:

A two-dimensional frequency representation is an array .11 ,,. Lr, of complex numbers, of dimensions ATpvc x nut - k is the index of the image in its series, p is the index of the sensor on which the beam d arrives 'direct lighting (0 or 1) and q has the following values:

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q = 0: image received on the sensor where direct lighting arrives q = 1: image received on the other sensor.

Bk,p,q 11, JI indicateur de bruit 7. p o-7] image de référence, correspondant à une représentation fréquentielle bidimensionnelle obtenue pour une direction fixe du faisceau. Cette image de référence a pour objet de pouvoir ultérieurement compenser les modifications de trajet optique dues aux vibrations des miroirs inclus dans le système. Si ces vibrations sont faibles, l'image de référence peut n'être acquise que périodiquement L'image de référence peut aussi être une image simplifiée, les critères de précision étant inférieurs à ceux de

l'image utile Alk,p,91. . Pour simplifier la présentation, on suppose qu'une image de référence H., p,9 y, de mêmes caractéristiques que l'image utile (excepté la direction du faisceau d'éclairage) est acquise pour chaque image utile Jfk,p,q[i. j] . Besides the image itself, this program also generates the tables:

Bk, p, q 11, JI noise indicator 7. p o-7] reference image, corresponding to a two-dimensional frequency representation obtained for a fixed direction of the beam. The object of this reference image is to be able to subsequently compensate for the modifications of optical path due to the vibrations of the mirrors included in the system. If these vibrations are weak, the reference image can only be acquired periodically. The reference image can also be a simplified image, the precision criteria being lower than those of

the useful image Alk, p, 91. . To simplify the presentation, it is assumed that a reference image H., p, 9 y, with the same characteristics as the useful image (except the direction of the illumination beam) is acquired for each useful image Jfk, p, q [i. j].

BHk, p, q [I,}] reference image noise indicator
A series of two-dimensional frequency representations is obtained by calculation from a series of elementary images corresponding to interference figures formed on the CCD sensors The program for acquiring the two-dimensional frequency representations is therefore broken down into an acquisition phase elementary images and a calculation phase. These two phases can be separated, or each image can be the object of a calculation as the acquisition progresses. We place ourselves here in the case where the two phases are separated.

7.12.2.1. acquisition of elementary images.

Ic[k, pl. Je( k, p] déterminant les indices 'symboliques' permettant de calculer pour chaque couple (k,p) le mot de commande du déviateur de faisceau ('0"'1 p.Ie{ k, p,.lck, p . Pendant cette procédure les faisceaux FRG et FRD sont présents en permanence, chaque image élémentaire étant formée sur un capteur par l'interférence de l'onde de référence et de l'onde diffractée par l'échantillon, lui-même éclairé par des ondes d'éclairage de caractéristiques variables. Les miroirs (2282) (2243) (2232) (2247) sont obturés. The series of elementary images can be acquired in one go by the high speed camera, without any calculations being carried out, the commands of the beam modification elements having to be synchronized with the acquisition of images. This is an iteration over the integer k and annuitant ;? The succession of parallel lighting to be used must be specified in the tables.

Ic [k, pl. I (k, p] determining the 'symbolic' indices making it possible to calculate for each pair (k, p) the control word of the beam deflector ('0 "' 1 p.Ie {k, p, .lck, p. During this procedure the FRG and FRD beams are permanently present, each elementary image being formed on a sensor by the interference of the reference wave and of the wave diffracted by the sample, itself illuminated by D waves. lighting of variable characteristics The mirrors (2282) (2243) (2232) (2247) are closed.

For each pair (k, p), the taking of images is broken down into two phases: phase 1: it consists of the acquisition of 36 pairs of elementary images, a pair of images comprising one image coming from each sensor, and the 36 torques differing from each other in the state of all the beam control systems except the beam deflector which keeps a constant state for a given torque (k, p). These 36 pairs of elementary images will be used subsequently to generate a representation

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fréquentielle bidimensionnelle utile A1k,p,q[I,}]. On note une de ces images élémentaires .IOk, pc, d, r , r2 q, i, j . Avant chaque prise d'image élémentaire les rotateurs de phase permettant le contrôle du faisceau d'éclairage (atténuation, décalage de phase,dé\ iation et polarisation) doivent être commandés de manière appropriée.

useful two-dimensional frequency A1k, p, q [I,}]. We denote one of these elementary images .IOk, pc, d, r, r2 q, i, j. Before each elementary image capture, the phase rotators allowing control of the illumination beam (attenuation, phase shift, deflection and polarization) must be appropriately controlled.

l'atténuation correspondant à l'indice, et ou les valeurs aï et 2 sont celles explicitées en 7.2.2 , mesurées en 7.3.2.2., et ou l'atténuateur de faisceau est commandé comme explicité en 7 2.2.

The index c is determined by the following table, or att [c] constitutes an array containing

the attenuation corresponding to the index, and where the values aï and 2 are those explained in 7.2.2, measured in 7.3.2.2., and where the beam attenuator is controlled as explained in 7 2.2.

<tb>
<tb> index <SEP> c <SEP> attenuation <SEP> att [c]
<tb> 0 <SEP> 1
<tb> 1 <SEP> a1
<tb> 2 <SEP> a1 <SEP> a2
<tb>

Les indices d, r, , r, sont déterminés par les tableaux suivants:

The indices d, r,, r, are determined by the following tables:

<tb>
<tb> index <SEP> d <SEP> offset <SEP> of <SEP> phase
<tb> (degrees)
<tb> 0 <SEP> +120 <SEP>
<tb> 1 <SEP> 0
<tb> 2 <SEP> -120 <SEP>
<tb> index <SEP> r2 <SEP> voltage <SEP> applied <SEP> to
<tb> rotators <SEP> (2210) <SEP> and <SEP> (2241)
<tb> 0 <SEP> 5V
<tb> 1 <SEP> -5V
<tb> index <SEP> r, <SEP> voltage <SEP> applied <SEP> to
<tb> rotators <SEP> (2238) <SEP> and <SEP> (2226)
<tb> 0 <SEP> 5V
<tb> 1 <SEP> -5V
<tb>

A pair of elementary images (corresponding to the two values of the index q) is obtained for each combination of the indices c, d, r1, r2 and for each direction of illumination defined by the indices (k, p).

.1 f0k. pc, d r r q, y
Le filtre (2203) doit être réglé de manière à ce que le capteur ne soit jamais saturé, mais se rapproche autant que possible de la limite de saturation. De manière équivalente, il peut être réglé en For each direction of illumination (k, p), we therefore obtain 36 pairs of elementary images noted

.1 f0k. pc, drrq, y
The filter (2203) should be set so that the sensor is never saturated, but comes as close as possible to the saturation limit. Equivalently, it can be adjusted by

<Desc / Clms Page number 128>

the absence of reference wave so that the maximum intensity of the wave reaching the sensor in the absence of attenuation of the beam is a quarter of the maximum level authorized by the digitization of the \ ideo signal, or 64 for a digitizer 8 bits.

- on notera A/R0[A\ /?][c,/,r, ,r2 ][qJ,j] une image élémentaire obtenue. -phase 2: It consists of the acquisition of 36 more elementary images, which will be used to generate the reference image. This phase is identical to phase 1 but:

- we denote by A / R0 [A \ /?] [c, /, r,, r2] [qJ, j] an elementary image obtained.

- the command word used to obtain .lIROk, pc, d, r, r2 q, i, J is CO.-11 p, Id p, i,, j,, Jd p, i,, J., or ir > j. are the coordinates of a constant point located on the side of the sensor, for example the point (3905) in Fig. 56. representing a sensor and on which the contour (3902) represents the limit corresponding to the aperture of the objective, which cannot be exceeded by the illumination beams. This command word therefore does not depend on k. The coordinates ir, jr can be chosen in a relatively arbitrary manner. However, the choice of a strongly eccentric point (3905) allows that points corresponding to total frequency vectors (ft according to the notations used in 5.3.) Of comparable standard can be obtained from each sensor. For samples not exhibiting specific regular structures, such points correspond to comparable complex values on the two sensors, which improves the reliability of the results.

7.12.2.2. Calculation of two-dimensional frequency representations.

Mk ,P,q\'<j\ et B,,, , [i,j] le programme parcourt les indices (k,p) en effectuant pour chaque couple (k,p) les 3 étapes suivantes: étape 1: génération du tableau indicateur d'atténuation.

ce tableau est un tableau d'entiers ,Il 1[q, i, j] généré de la manière suivante: il est initialisé à 0, puis le programme parcourt l'ensemble des indices q,i,j deux fois. After the acquisition phase, a specific program must be used to generate complex number images from these elementary images and the associated noise indicators.

Mk, P, q \ '<j \ and B ,,,, [i, j] the program traverses the indices (k, p) by performing for each pair (k, p) the following 3 steps: step 1: generation of the Mitigation Scoreboard.

this array is an array of integers, Il 1 [q, i, j] generated as follows: it is initialized to 0, then the program traverses the set of indices q, i, j twice.

,f 1[q. +iadd, j + jaddl = 1 pour iadd et jadd variant de -1 à 1, et à condition de ne pas sortir des limites du tableau. - first path: the program calculates max pix = nm (A / 0 [À \ p0, d, r. rz qi j]). If for a given aletir d, r1, r2 of q, i, j max ~ pix is equal to the maximum value of the digitizer, then the program sets this pixel and its immediate neighbors to 1:

, f 1 [q. + iadd, j + jaddl = 1 for iadd and jadd varying from -1 to 1, and on condition of not going beyond the limits of the table.

-second path: the program calculates max pix = iiiax p] [1, 1, ci, r, rz q, i, i. If for a given value d, r1, r2 of q, i, j max ~ pix is equal to the maximum value of the digitizer, then the program sets this pixels and its immediate neighbors to 2:

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,\fl[q.1 +iadd,j +jaddi = 2 pour iadd et jadd variant de -I à 1, et à condition de ne pas sortir des limites du tableau.

A l'issue de cette étape le tableau .111[q,i,j] contient l'indice correspondant à l'atténuation devant être utilisée pour atténuer l'image. étape 2. génération des images complexes correspondant à chaque position des rotateurs.

, \ fl [q.1 + iadd, j + jaddi = 2 for iadd and jadd varying from -I to 1, and on condition of not going beyond the limits of the table.

At the end of this step, the table .111 [q, i, j] contains the index corresponding to the attenuation to be used to attenuate the image. step 2. generation of complex images corresponding to each position of the rotators.

.2 [] [? ,, J] 1 1 ## (2A / 0 [A -. [A /! []. 0,,] [../] att ~ 111q, i, J, 67 + .y ] -ll0k, p ~ 111q, r, J, l, rl.r2] q, r, j-TOk. p.tllq.r. J.2.r.r2] qr J) + j ~ 1 ~,. IOk> pAllg, i, j, l, ri, r2lq, i, t-.TOk, p [.lllq, i, j, 2, r, r = q, e.JJIJ step 3: combination of the images obtained for the various rotator positions.

The object of this step 3 is to calculate AIk, p ,, 11, JI as a function of. \ L2 [r \ .r2] [q, i, j]. This can be done simply without using the polarization variations by performing .Lh., P> qr J ~ 112 [l, l] [q, i, ji the noise then being given by: BJ., Pq [i,}] = # r # r ## iT The quantity AT.> p, q 11, JI thus generated corresponds to that which was used in the first embodiment. However, this method induces inaccuracies on high frequencies and it is preferable to use the principle described in 7.12.1., Where, \ f2 [r, r2] [q, I,}] corresponds to the measured quantity, which was denoted Cr1, r2 in 7.12.1. Other variants of this method will be described in 7 18.

f' = P9 + P9 . ~ l\Íplx j- prx x'c= "o # .: 2,yc= no i' >ZC= 1-xo-Yc 110 n, n, = Iaq,P>Ik,p,Jck, n ,Jc k,p - Npix 2 Jajq, L p,l"fk, "l r7 p,Jck, pli - 2 - Ze = 1- xe - y'e "0 f "0 jr -Kpo -Kpo nv nv

Vyz = YcZe - ZcYe vxz = -XcZe +ZcXe 1 xy =-xcYe +Ycxe Step 3 is therefore carried out here as follows:
For each value of the indices q, l, j the program calculates:

f '= P9 + P9. ~ l \ Íplx j- prx x'c = "o #.: 2, yc = no i '> ZC = 1-xo-Yc 110 n, n, = Iaq, P> Ik, p, Jck, n, Jc k, p - Npix 2 Jajq, L p, l "fk," l r7 p, Jck, pli - 2 - Ze = 1- xe - y'e "0 f" 0 jr -Kpo -Kpo nv nv

Vyz = YcZe - ZcYe vxz = -XcZe + ZcXe 1 xy = -xcYe + Ycxe

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:11 z = x z +Y ,\ f2 e =Xe 2 +Ye Mce = V/Z +V +., Les valeurs de sin Ip c coslp c sin Ipe cos Ipe sont déterminées selon les tableaux d'affectation suivants:

: 11 z = xz + Y, \ f2 e = Xe 2 + Ye Mce = V / Z + V +., The values of sin Ip c coslp c sin Ipe cos Ipe are determined according to the following assignment tables:

<tb>
<tb> A <SEP> @ce <SEP> other
<tb> Mc <SEP> 0 <SEP> other
<tb>

COSe COSCpc 2.. le ryl-x'c'c1+xcl.r)! sinrpc Me xe Mc Z 1 ce (-xcYc1 yz +xc1 z , +ycI xy.

COSe COSCpc 2 .. the ryl-x'c'c1 + xcl.r)! sinrpc Me xe Mc Z 1 ce (-xcYc1 yz + xc1 z, + ycI xy.

<tb>
<tb>

Mce <SEP> 0 <SEP> other
<tb> other
<tb>

cosço, "c '1f2,1.T e ce ,'vell xeyel'c+xela3y \f2M \ }- e e Ay; sinço,, 0 JCc c .ie 21 .rc I \e (~XeVeL-XeT,+yeTzy,J puis les coefficients sont calculés:

coefk, p,q,i, j0,0 = - cos Ip cosse coef k, p,q,i, j0,1 ~ -sinlpecoslpc coefk,p,g,i,1,0=-cospe e sin Ip coef[ k, p, q,i,j ][1,1] = - sin Ipe sin(p,
Ces coefficients ne dépendent pas du résultat des prises d'images et dans le cas ou on répète toujours la même série ils peuvent être stockés dans un tableau plutôt que recalculés à chaque fois. C'est pourquoi on les a içi exprimé sous cette forme. Le programme utilise ensuite ces valeurs pour combiner les images obtenues avec les différentes positions des rotateurs de la manière suivante:

Tk.p,9 l , J ~ .I2r , r2 q, i, jcoef k, p, 9, i, jr . rz ] ').'2 À/2[r1,r2][<7,' j] correspond à la grandeur mesurée, qui était notée Cr en 7.12.1 lifk, p,q [' Y] correspond à la grandeur qui était notée Men 7.12.1 Par ailleurs le programme calcule une amplitude de bruit:

cosço, "c '1f2,1.T e ce,' vell xeyel'c + xela3y \ f2M \} - ee Ay; sinço ,, 0 JCc c .ie 21 .rc I \ e (~ XeVeL-XeT, + yeTzy , J then the coefficients are calculated:

coefk, p, q, i, j0,0 = - cos Ip pod coef k, p, q, i, j0,1 ~ -sinlpecoslpc coefk, p, g, i, 1,0 = -cospe e sin Ip coef [ k, p, q, i, j] [1,1] = - sin Ipe sin (p,
These coefficients do not depend on the result of the images taken and in the case where the same series is always repeated they can be stored in a table rather than recalculated each time. That is why they have been expressed here in this form. The program then uses these values to combine the images obtained with the different positions of the rotators as follows:

Tk.p, 9 l, J ~ .I2r, r2 q, i, jcoef k, p, 9, i, jr. rz] ').' 2 À / 2 [r1, r2] [<7, 'j] corresponds to the quantity measured, which was denoted Cr in 7.12.1 lifk, p, q [' Y] corresponds to the quantity which was noted Men 7.12.1 In addition, the program calculates a noise amplitude:

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Bk,p.rr- att[.Lllq,i,j Ce qui termine l'étape 3.

Bk, p.rr- att [.Lllq, i, j Which ends step 3.

est possible de ne pas utiliser les quatre images générées par la combinaison des indices 1'),1'2 ,comme dans le premier mode de réalisation dans lequel une seule image est générée. Il est également possible de ne pas utiliser l'atténuation de faisceau. La méthode la plus rapide consiste donc à n'utiliser que trois images élémentaires différant entre elles par leur phase. L'image de référence peut également être acquise seulement une fois sur dix (par exemple) de manière à limiter la perte de temps liée à son acquisition, et à condition que les vibrations ne soient pas trop importantes. L'image de référence peut être simplifiée de la même manière que l'image utile, mais cette simplification aura en général moins de conséquences sur la qualité des résultats. Il peut donc être utile de la simplifier d'avantage que l'image utile. When the program has calculated Af ,, p, 9 r, and B, p, 9 r. j it also calculates Hk, q [1, J] el B po ['-] This second calculation is performed in the same way as the previous one, in three steps, but .f0k, pc, d, rt, rz cl, i , j, Mk, pq ['' j] and Bk ,,,, 11.jl are replaced respectively by J \ ffî () [A-./? , j /], Hk ,, r, and BH, p, r, j and in step 3 the assignments of xe and ye are NPIX "VP1X replaced by 1, - Jr 1T ~ replaced by x, = ## # #, = ### - # nv po nv po
The above procedure is the one that allows the maximum precision. However, due to the high number of elementary images required, it may be necessary to use a faster procedure.

It is possible not to use the four images generated by the combination of the indices 1 '), 1'2, as in the first embodiment in which a single image is generated. It is also possible not to use the beam attenuation. The fastest method therefore consists in using only three elementary images differing from one another in their phase. The reference image can also be acquired only once in ten (for example) so as to limit the loss of time associated with its acquisition, and provided that the vibrations are not too great. The reference image can be simplified in the same way as the useful image, but this simplification will generally have less impact on the quality of the results. It may therefore be useful to simplify it more than the useful image.

7. 13. Calculation of order indices.

pixels i, j) et à un capteur/) des indices de commande virtuels Icf p, r, 1]. Jd[ p, i, J]) tels que le mot de commande CO.11(p,Id[p,i,j],Jd[p.i,jl) génère un éclairage éclairant un point aussi proche que possible du point de coordonnées (i,j) sur le capteur p. Ce tableau est généré par l'algorithme de la Fig.53 Dans cette algorithme, E(x) désigne l'entier le plus proche de .v. Avant de lancer cet algorithme, le tableau D doit être initialisé à une valeur élevée, par exemple 100000. A l'issue de ce programme le tableau D contient pour chaque point la distance entre ce point et le point le plus proche obtenu pour le point d'impact direct

d'une onde d'éclairage. La double boucle de l'algorithme. (10 ,}o) et sur (;). /; ) permet de définir des valeurs Idp,i,,Jdp,i, y compris pour des points qui ne correspondent pas exactement au point d'impact du faisceau direct. The order index table is the Id table which allows you to associate with coordinates in

pixels i, j) and to a sensor /) virtual control indices Icf p, r, 1]. Jd [p, i, J]) such that the command word CO.11 (p, Id [p, i, j], Jd [pi, jl) generates a light illuminating a point as close as possible to the coordinate point (i, j) on the sensor p. This table is generated by the algorithm of Fig. 53 In this algorithm, E (x) denotes the integer closest to .v. Before running this algorithm, array D must be initialized to a high value, for example 100000. At the end of this program, array D contains for each point the distance between this point and the closest point obtained for the point direct impact

of a lighting wave. The double loop of the algorithm. (10,} o) and on (;). /; ) allows to define values Idp, i ,, Jdp, i, including for points which do not correspond exactly to the point of impact of the direct beam.

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un cercle de rayon R pixels on peut avoir: fo[ k] = R cos#, .7o[A] = R sin # pour k allant de 0 à zot
Les tableaux définissant les indices de commande en fonction de k et p sont obtenus à partir de Io[k] et Jo[k] par :

Ie[k, p] = Id[p, fo[k), Jo[k]] et .7ck, p] = Jd[p.Io[k), Jo[k]] 7.14. Différence de marche induite sur les ondes issues de l'objet. A trajectory of the direct impact point can be defined by the tables (lo [k], Jo [k]) defining as a function of the index k the coordinates of the desired direct impact point. For example if the trajectory is

a circle of radius R pixels we can have: fo [k] = R cos #, .7o [A] = R sin # for k going from 0 to zot
The tables defining the control indices as a function of k and p are obtained from Io [k] and Jo [k] by:

Ie [k, p] = Id [p, fo [k), Jo [k]] and .7ck, p] = Jd [p.Io [k), Jo [k]] 7.14. Induced rate difference on the waves coming from the object.

A = nodo cos,6 - n,,d, cosa avec n0 sin ss=nv sin a d'ou finalement-

4=nod 1-Cn-" sina 2 -nd, 1-sinza (n0)
La Fig. 55 illustre le calcul de la différence de marche entre une onde issue d'un point O de l'objet et l'onde de référence issue virtuellement du point Ap ou p est l'indice du capteur considéré Les coordonnées de Ap par rapport à un repère centré en 0 et de vecteurs directeurs #p,#p, kpsont

xp, y p , zip et la distance entre O et le bord de l'objet du coté du capteur p est w v . Les vecteurs lp 7 jp, -: ka - sont définis comme indiqué en 7.7. On vérifie que conformément à l'orientation des axes sur la Fig. 55, les vecteurs de base des repères utilisés dans chaque demi-espace repéré par l'indice capteur vérifient

,0 =-T1,]0 =-7).o = -kl. Fig. 54 illustrates the calculation of the path difference of a wave coming from a point 0 of the object with respect to the reference wave coming virtually from a point A of a medium of index nv ( nominal index of objectives). We have: # -n0l0-nvlv

A = nodo cos, 6 - n ,, d, cosa with n0 sin ss = nv sin a hence finally-

4 = nod 1-Cn- "sina 2 -nd, 1-sinza (n0)
Fig. 55 illustrates the calculation of the path difference between a wave coming from a point O of the object and the reference wave coming virtually from the point Ap where p is the index of the considered sensor The coordinates of Ap with respect to a coordinate system centered at 0 and directing vectors # p, # p, kpsont

xp, yp, zip and the distance between O and the edge of the object on the side of the sensor p is wv. The vectors lp 7 jp, -: ka - are defined as indicated in 7.7. It is verified that according to the orientation of the axes in FIG. 55, the base vectors of the reference marks used in each half-space marked by the sensor index verify

, 0 = -T1,] 0 = -7) .o = -kl.

d,, = w p - z sinz a = i2 + / >
Kp ou i,j sont des coordonnées en pixels prises à partir du centre optique du capteur. When ï, = y = 0 we can apply the previous formula = nodo 1-Cn - '' sina 2 n'Id, l - - if a (n0) with do = wp

d ,, = wp - z sinz a = i2 + />
Kp or i, j are coordinates in pixels taken from the optical center of the sensor.

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n,,x P Kp +yp j 1 et on obtient finalement pour la différence de marche totale: (nJ2i2+j2 (14@p i2 +lz C /',. = n W 1- -n (w - z ) 1- - + n x - + y pop 1T0 K2 t K2 p Kp PK En particulier on peut positionner le point O de manière à avoir

\xP'yP'ZP, C2 2 2 ou x,y,z sont les coordonnées déterminées en 7. I 1. On a alors: P =nGwP 1-Cnv 0 2 12 + P J 2 -nV y'P -2l 1 l2 K + P J 2 +n,,C2 K l P + 2 K Y Pour obtenir une représentation fréquentielle de l'objet, les représentations fréquentielles bidimensionnelles devront être corrigées pour compenser cette différence de marche. Dans cette expression, seules les valeurs de w p n'ont pas encore été déterminées. If we also take into account xp, yp we must add to this path difference the quantity:

n ,, x P Kp + yp j 1 and we finally obtain for the total path difference: (nJ2i2 + j2 (14 @ p i2 + lz C / ',. = n W 1- -n (w - z) 1 - - + nx - + y pop 1T0 K2 t K2 p Kp PK In particular we can position the point O so as to have

\ xP'yP'ZP, C2 2 2 where x, y, z are the coordinates determined in 7. I 1. We then have: P = nGwP 1-Cnv 0 2 12 + PJ 2 -nV y'P -2l 1 l2 K + PJ 2 + n ,, C2 K l P + 2 KY To obtain a frequency representation of the object, the two-dimensional frequency representations must be corrected to compensate for this path difference. In this expression, only the values of wp have not yet been determined.

7.14 , il est nécessaire de déterminer préalablement les valcurs \1' p , c'est-à-dire en fait la seule valeur 11'0 puisque w1s'en déduit par w1= L-w0. 7.15. Calculation of wpz
7. 15.1. Principle:
To correct the two-dimensional frequency representations of the phase factor determined in

7.14, it is necessary to determine beforehand the values \ 1 'p, that is to say in fact the only value 11'0 since w1s' deduced from it by w1 = L-w0.

If the average index of the object is close to the nominal index of the objectives, the effect of wp on the value # is negligible and we can for example adopt the value wp = L / 2 and position the sample between the two objectives visually, adjusting this position later to obtain an image of the area of interest of this sample.

It is also possible to add a reflective layer on the side of one of the slats which is in contact with the object, for example that which is on the side of the objective (2217), over an area of reduced dimensions. When the FRD beam and its reverse indicator are used alone and when the reflecting part is positioned to reflect the reverse FRD indicator beam, then the interference pattern formed on the sensor (2239) should be a constant. The position of the sample must then be adjusted to effectively obtain such a constant. When this adjustment has been made, we have w0 = z / 2.

If a sufficiently precise positioner is used, then the position of the sample can be changed in the direction of the optical axis to obtain w0 = L / 2. Finally, the position of the sample must be changed in the

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direction orthogonal to the optical axis so that the reflecting zone of the lamella is outside the field of observation.

However, the two preceding methods impose practical constraints which can be troublesome. One solution making it possible to avoid this difficulty is to carry out the determination of wp from measurements carried out on the sample in its final position.

A frequency representation Fa can be obtained from all the two-dimensional frequency representations coming from sensor 0 (2239) when the point of direct impact of the lighting wave is on this same sensor, and travels over this sensor, for example, the trajectory shown in dotted lines Fig. 56. This representation is obtained in a very similar way to the method used in the first embodiment, with however the following differences: -j2 # - # p / @ - The two-dimensional frequency representation must be multiplied by the correction factor e to cancel the phase shift produced by spherical aberration.

- the value of the coefficient K taken into account must be multiplied by a factor no to take into account nv the average index in the sample.

-In order to limit the aliasing phenomena of the correction function, the frequency representation is oversampled.

- When a point in the frequency space is obtained several times, the value retained is one of the values obtained and not the average of the values obtained.

In principle, the frequency representation thus obtained does not depend on the choice of the value retained when a point in the frequency space is obtained several times. However, this is only true if the correction factor has a correct value.

Fa[I1l,nj, nk] = Fsim, nj, nk evp- 2ni, nj, nkw p Lorsqu'un point de l'espace des fréquences est obtenu plusieurs fois, les valeurs Fsini.nj,rak] et G[I1l,nj,nk] obtenues sont à chaque fois différentes. Pour chaque point, on définit Gmll1[ni.nl,nk] et C1171ax[ni,ni,nkl, valeurs minimale et maximale obtenues pour Cl en ce point. /nnfn/./,/7A] et Fsmax[ni,nj.nk] sont alors les valeurs obtenues pour F\{ m, nj, nk] lorsque (:rai, nj. nk vaut respectivement Ciiiin[ni,nj.nkl et Cnraxnt, nj, rak . -j2 ## p / #
Under these conditions, and taking into account the expression of the correction function e -j2 ## p / #, the value of the two-dimensional frequency representation Fa thus obtained, at a point in the frequency space with coordinates ni, nj , nk, can be written as-

Fa [I1l, nj, nk] = Fsim, nj, nk evp- 2ni, nj, nkw p When a point in the frequency space is obtained several times, the values Fsini.nj, rak] and G [I1l, nj, nk] obtained are each time different. For each point, we define Gmll1 [ni.nl, nk] and C1171ax [ni, ni, nkl, minimum and maximum values obtained for Cl at this point. /nnfn/./,/7A] and Fsmax [ni, nj.nk] are then the values obtained for F \ {m, nj, nk] when (: rai, nj. nk is respectively Ciiiin [ni, nj.nkl and Cnraxnt, nj, rak.

We then obtain the two Sequential representations: Famin [l1l. nj, nk] = Fsmin [11 /, ni, nk] ep (- j2 niinunni, nj, nk] w0) Famax [l1l, nj. nk = Fsmax [l1l, ni, nkl ep- j2tfnmxnr, nj, nkyro

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ecart = L IFamax[ni,n1, nk] - Famll1[ni, nJ ,nk ]12 ni,nj,nk
Toutefois, le bruit n'étant pas constant sur l'ensemble de la représentation fréquentielle, chaque élément de cette somme doit être pondéré par l'inverse du bruit au point considéré et on obtient

ecart /'owoyfM/, nj, '1 - Faniin[ni, rtj, nA'1 eco = / ####'####-'####-#### ecart nt,nJ,nk Btotni,nJ,nk ou Btotni, nJ, nk est une amplitude de bruit définie en chaque point
En développant l'expression de cet écart-type on obtient une expression simplifiée qui facilite le calcul de minimisation. When the value of w0 is correct, these two representations are equal. The calculation of Il'0 consists in minimizing the standard deviation between the two frequency representations Famin and Famax. The standard deviation to be minimized is in principle:

deviation = L IFamax [ni, n1, nk] - Famll1 [ni, nJ, nk] 12 ni, nj, nk
However, the noise not being constant over the whole of the frequency representation, each element of this sum must be weighted by the inverse of the noise at the point considered and we obtain

ecart / 'owoyfM /, nj,' 1 - Faniin [ni, rtj, nA'1 eco = / #### '#### -'#### - #### ecart nt, nJ, nk Btotni , nJ, nk or Btotni, nJ, nk is a noise amplitude defined at each point
By developing the expression of this standard deviation we obtain a simplified expression which facilitates the minimization calculation.

- paramètre de fonctionnement wpixels, par exemple II'pixels=5. 7.15. 2. Algorithm:
The calculation of wpse is done using a program whose algorithm is described in Fig. 57. This program must initially have the following information: - values established in 7.1 I .: x, y, z, L, n0

- wpixels operating parameter, for example II'pixels = 5.

programme calcule les indices de commande correspondants ICIÀ-, pi .lclk, p Le programme effectue alors l'acquisition de la série d'images selon la procédure indiquée en 7.12. La procédure d'acquisition génère les

tableaux .1, p,g [/,./] Toutefois, seuls les tableaux correspondant à des indices q,p nuls seront utilisés ici, soit Mk,0,0[i,j]. The essential steps of this program are as follows: - (4001): acquisition of images. A series of images is obtained by making the path shown in dotted lines in FIG. 56, or (3901) represents the limit of the useful area of the sensor, (3902) represents the limit corresponding to the maximum aperture of the objectives, (3903) represents a circular part of the trajectory and (3904) represents a rectilinear part of path. As indicated in 7.13. we generate the arrays Io [k] Jo [k] according to this trajectory and the

program calculates the corresponding control indices ICIÀ-, pi .lclk, p The program then acquires the series of images according to the procedure indicated in 7.12. The acquisition procedure generates the

arrays .1, p, g [/,./] However, only arrays corresponding to zero indices q, p will be used here, ie Mk, 0,0 [i, j].

Etape 1. Chaque tableau A/,t.o,o ['>./] obtenu lors de la phase d'acquisition est d'abord suréchantillonné de la manière suivante, en 3 étapes: Etape 1.1.: le programme effectue la transformée de Fourier bidimensionnelle inverse du tableau Mk,0,0 - (4002): calculation of Fsmin, Gmin, Fsmax, Gmax, Btot

Step 1. Each table A /, to, o ['> ./] obtained during the acquisition phase is first oversampled as follows, in 3 steps: Step 1.1 .: the program performs the Fourier transform two-dimensional inverse of the array Mk, 0,0

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Nid x xi (par exemple ]I'd =512). Msk est initialisé à 0 puis le programme parcourt les indices i,l du tableau A/-oo en effectuant: .lTsk '=d +i - .' Prx - fk p,0[rvl Etape 1.3.: une transformée de Fourier directe du tableau Msk est effectuée, ce qui termine la phase de suréchantillonnage. Step 1.2 .: the program completes this table with zeros to obtain an Msk table of dimensions

Nest x xi (for example] I'd = 512). Msk is initialized to 0 then the program traverses the indices i, l of array A / -oo by performing: .lTsk '= d + i -.' Prx - fk p, 0 [rvl Step 1.3 .: a direct Fourier transform of the Msk table is performed, which ends the oversampling phase.

Ais 11, JI .\f . k [ l, 1 - ] - [ Afsdl.1] ,\fsk Il1Iaxk ,jmaxk ou on note: imaxk = ex r d la[0,0, Ic[k,0], Jc[k,0]J jni(rrk Ja[0,0, Ic[k,01, Jc[k,01 /'11 prx jmaxk E\ # - Ja[O,O, Ic[k.0], Jc[k,0]]J .\ plX ou E(x) désigne l'entier le plus proche de x. Step 2: The elements of each Msk table are related to the value obtained at the point of direct impact of the lighting wave:

Ais 11, JI. \ F. k [l, 1 -] - [Afsdl.1], \ fsk Il1Iaxk, jmaxk where we note: imaxk = ex rd la [0,0, Ic [k, 0], Jc [k, 0] J jni (rrk Ja [0,0, Ic [k, 01, Jc [k, 01 / '11 prx jmaxk E \ # - Ja [O, O, Ic [k.0], Jc [k, 0]] J. \ PlX or E (x) denotes the integer closest to x.

dimensions .Vd x nid . A cette fin il parcourt les indices y,k ou et varient entre 0 et Yd -1 en effectuant Bsdl.1] = . ma +2 ( Bk,0,0 [il, j, avec: r = T a <//--2<< <<//-+2 ' ' A y7/--2<y 5 j lr+2 Dans cette équation, lorsque le couple il, j, est en dehors des limites du tableau 8., , le coefficient Bk,o.o i t , j 1 ] est supposé égal à 0. Step 3: When the program has thus generated the set of supersampled arrays Msk it calculates an oversampled noise amplitude in the form of a set of arrays of positive reals Bsk of

dimensions .Vd x nest. To this end it runs through the indices y, k or and vary between 0 and Yd -1 by performing Bsdl.1] =. ma +2 (Bk, 0,0 [il, j, with: r = T a <// - 2 <<<< // - + 2 '' A y7 / - 2 <y 5 j lr + 2 In this equation, when the couple il, j, is outside the limits of Table 8.,, the coefficient Bk, oo it, j 1] is assumed to be 0.

chaque triplet (r,,k) les étapes suivantes, numérotées de 4. 1 à -1.3: étape 4.1.:calcul des indices de la représentation fréquentielle tridimensionnelle Le programme effectue les opérations suivantes: Step 4: The program initializes the Fsmin, Fsmax arrays to 0, it initializes the Gain and Max arrays to 10z and -1020 respectively, and it initializes the Rmll1, Bl1Iax arrays to 1020. These arrays each have dimensions 2, 'dx 2 Ne x 2] If d. The program then traverses the indices i, j, k or i ctjvary from 0 to Nd-1 by performing for

each triplet (r ,, k) the following steps, numbered from 4.1 to -1.3: step 4.1 .: calculation of the indices of the three-dimensional frequency representation The program performs the following operations:

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nj = j - jmax. k + Nd - Jt-H1 Z - Ci - 2d J )2 ( . N d )2 ( no, )2 ( . ' \' d )2 (V .. d )2 r-;;:;':'o 1-2 - 1-2 - 1'-;;:;':'0 Imaxk 1maxk +'\d d avec: r = ,V 'v pu Les valeurs ni,nj,nk correspondent à des coordonnées dans un espace tridimensionnel de fréquences comme dans le premier mode de réalisation. Leur calcul menant à des valeurs non entières, on leur affecte l'entier le plus proche de la valeur obtenue. La valeur de K doit être corrigée pour tenir compte de l'indice de l'échantillon et on utilise donc no/@ K0. Le coefficient r permet la prise en compte du suréchantillonnagc nv étape 4.2 : calcul des valeurs de G et Fs au point courant:

Gval 'If f, tr y1 2.2 rc + jc 2 f, - ic 2 + jc 2 2 - ( rt , 'l z. nnc 2 + jmc 2 - inrc 2 + jnrc 2 Gw/=- - () 11" 2. IC 2 + 1c - . 2 - IC ,2. + 1c 2] - [ lnal 2, IIIIC 2 + 1111c - ' 2 - 11IlC ' 2 + 111lc ' 2 ]} 110 À'o 110 l' 2 ;':'0 .2 r 2 ;':'0 ,2 -2 z rc2+c2 x k 3' 7C ! j j ) I imc2 + jmc2 .t'mc y jmc Fsval -J21l ...{(!... 1C2+]C2 ±'=-+J-r!... 1 mc2+]mc2 ++]mc l1 Fn'fl/ = A/sjt[i,~/Jel rKo rKo 'Ko .. .. r r avec: IC = ; - ##, 1c= / - ##, intc imaxi. # , j1l1C = /ioy,;. - ## 2 2 2 2 Dans les équations ci-dessus, ic,jc,imc,jmc correspondent à des coordonnées ramenées au centre optique et r a la même valeur que dans l'étape précédente.

étape -1.3.: modification éventuelle des valeurs de Gmin, Fsmin, Gmax, Fsmax, Le programme teste la valeur de Gval. ni = i-imaxk + Nd

nj = j - jmax. k + Nd - Jt-H1 Z - Ci - 2d J) 2 (. N d) 2 (no,) 2 (. '\' d) 2 (V .. d) 2 r - ;;:; ':' o 1-2 - 1-2 - 1 '- ;;:;': '0 Imaxk 1maxk +' \ dd with: r =, V 'v pu The values ni, nj, nk correspond to coordinates in a three-dimensional space frequencies as in the first embodiment. Their calculation leading to non-integer values, they are assigned the integer closest to the value obtained. The value of K must be corrected to take into account the index of the sample and we therefore use no / @ K0. The coefficient r allows the taking into account of the oversampling c nv step 4.2: calculation of the values of G and Fs at the current point:

Gval 'If f, tr y1 2.2 rc + jc 2 f, - ic 2 + jc 2 2 - (rt,' l z. Nnc 2 + jmc 2 - inrc 2 + jnrc 2 Gw / = - - () 11 "2 . IC 2 + 1c -. 2 - IC, 2. + 1c 2] - [lnal 2, IIIIC 2 + 1111c - '2 - 11IlC' 2 + 111lc '2]} 110 À'o 110 l'2;':'0 .2 r 2;': '0, 2 -2 z rc2 + c2 xk 3' 7C! Jj) I imc2 + jmc2 .t'mc y jmc Fsval -J21l ... {(! ... 1C2 +] C2 ± '= - + Jr! ... 1 mc2 +] mc2 ++] mc l1 Fn'fl / = A / sjt [i, ~ / Jel rKo rKo' Ko .. .. rr with: IC =; - # #, 1c = / - ##, intc imaxi. #, J1l1C = / ioy,;. - ## 2 2 2 2 In the above equations, ic, jc, imc, jmc correspond to coordinates brought back to the optical center and ra the same value as in the previous step.

step -1.3 .: possible modification of the values of Gmin, Fsmin, Gmax, Fsmax, The program tests the value of Gval.

l3maxnr, nJ, nk = Bsk t, j If CfW7 / C7 / M; nfM; .n /, '1 the program performs: Gmll1 [ni.nj, nk] Gval Fsmll1 [ni, nj, nk] Fsval Bmll1 [ni, n1, nk] = 5st [/, ./] If Gval> ~ Gw (M'f / t /./!/./! 1 the program performs: Gmax [ni, nj, nk] Gval Fsmax [ni, nj, nk] = Fsval

l3maxnr, nJ, nk = Bsk t, j

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Btot[ 111, nj, nkl = 1 Bmax[ni ni, nk]1 + I Bntin[ni, nj, nk 2 (4003): La fonction calculée est en principe égale à: r- r ' t1 l2nGrnrnnr,nl,nky~Fr:a.rrt:,rrj.rrku n -j 2xGmax\ni,nj,nk\w0 ecart = L .l'mm /II ,II} ,Il . -. e J l J 1"" - slllax /11,11} ,11 . e fCr ####'#####"###############r#####,-i###################### ecart = nr.n,nkeE's Btolrti,uj,nkl ou fis est l'ensemble des points en lesquels les valeurs de Gamin et Cnnax différent, soit: Es = {y:!,, GnMfM/.y)/,M1 x Gnti ni,r j,nk? Soit en développant l'expression: ecarl = "'\' 1 FSmill[lIi,,!j,llkl\2 +1 Fsmax[lIi,,!j,lIklI2 ecail t#1, Bof[M;,w,nA'1 Btot[lIi,lif,lIk] y Re Fsnrin tri,r j,nklF.mrnx nr.uj,nk e- j 2rr(Crrnnm,nl,nk-<3maaim,nl, ky,y (nr,n,nk )EEs IBlol[lIi ,Iif ,1Ik)J La première partie de l'expression ne dépend pas de w0 Minimiser t'écart-type revient donc à maximiser la fonction suivante ou Re() désigne la partie réelle:

Re Fsntntrti,rrj,rtk,Fsnrnxrri,nj,rtke-j2m(( mnm,nl.nk-(maxm.nl.nk>wo (m.nj,nk)Es 1 Toutefois cette fonction présente des fréquences élevées causant des repliements de spectre qui perturbent la convergence de l'algorithme. Ceux-ci sont supprimés en utilisant la fonction :

T- fyM;;)f;)w,y)]m<7-):[H),7)/,y;<'1 lit f w,.w ~ "p( - ' 2 .(;m;,,[,,; .".,,' ] - (;max!";.,, .'" ])"'0 J] nr,n,nk)eEs IBtotni,r7j,rtkll #y\[Clnmi\m ,nj ,nk\ Glllax[lIi ,Iif ,lIk ]).'1w) ou y (x) = 0 quand Ixl z et yx = 1 quand |x| < 2 (4004): l'algorithme itère la boucle sur wlarg jusqu'à ce qu'une précision suffisante soit atteinte. Par exemple on peut avoir lim =#/8 wpixels

(4005): La valeur 11'/ affichée correspond à m'o. On a: 11'1 = L - Wj et w0 = 11' La valeur rapport affichée correspond à: Step 5: The program generates an overall noise amplitude. For this purpose it runs through the indices ni, nj, nk by performing for each of these triplets the operation

Btot [111, nj, nkl = 1 Bmax [ni ni, nk] 1 + I Bntin [ni, nj, nk 2 (4003): The calculated function is in principle equal to: r- r 't1 l2nGrnrnnr, nl, nky ~ Fr: a.rrt:, rrj.rrku n -j 2xGmax \ ni, nj, nk \ w0 deviation = L .l'mm / II, II}, Il. -. e J l J 1 "" - slllax / 11.11}, 11. e fCr #### '##### "############### r #####, - i ############## ######### ecart = nr.n, nkeE's Btolrti, uj, nkl or fis is the set of points at which the values of Gamin and Cnnax differ, namely: Es = {y:! ,, GnMfM /.y)/,M1 x Gnti ni, rj, nk? Or by expanding the expression: ecarl = "'\' 1 FSmill [lIi ,,! j, llkl \ 2 +1 Fsmax [lIi ,,! j, lIklI2 ecail t # 1, Bof [M;, w, nA'1 Btot [lIi, lif, lIk] y Re Fsnrin tri, rj, nklF.mrnx nr.uj, nk e- j 2rr (Crrnnm, nl, nk- <3maaim, nl, ky, y (nr, n, nk) EEs IBlol [lIi, Iif, 1Ik) J The first part of the expression does not depend on w0 Minimizing the standard deviation therefore amounts to maximizing the following function or Re () designates the real part:

Re Fsntntrti, rrj, rtk, Fsnrnxrri, nj, rtke-j2m ((mnm, nl.nk- (maxm.nl.nk> wo (m.nj, nk) Es 1 However this function presents high frequencies causing aliases of spectrum which disturbs the convergence of the algorithm. These are removed using the function:

T- fyM ;;) f;) w, y)] m <7 -): [H), 7) /, y; <'1 reads fw, .w ~ "p (-' 2. (; M; ,, [,,;. ". ,, '] - (; max!";. ,,.'"])"'0 J] nr, n, nk) eEs IBtotni, r7j, rtkll #y \ [Clnmi \ m, nj, nk \ Glllax [lIi, Iif, lIk]). '1w) or y (x) = 0 when Ixl z and yx = 1 when | x | <2 (4004): the algorithm iterates the loop on wlarg until sufficient precision is reached, for example we can have lim = # / 8 wpixels

(4005): The displayed value 11 '/ corresponds to m'o. We have: 11'1 = L - Wj and w0 = 11 'The displayed ratio value corresponds to:

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wlarg 2f(W , wlarg ) rapport i4,pixels) rapporl = - [IFsmlll[ni,nj,nk]1 2 +IFsma[ni,nj,nk ]1 (m,n,nkEE's IBtot[1II ,Iij ,nk]\
La valeur rapport affichée caractérise la qualité du recoupement obtenu entre les images calculées à partir des représentations fréquentielles Famin et Famax. Plus elle est proche de 1 meilleur ce recoupement est. Lorsque l'échantillon est hors de la zone d'observation cette valeur se rapproche de 0.

wlarg 2f (W, wlarg) ratio i4, pixels) rapporl = - [IFsmlll [ni, nj, nk] 1 2 + IFsma [ni, nj, nk] 1 (m, n, nkEE's IBtot [1II, Iij, nk] \
The displayed ratio value characterizes the quality of the overlap obtained between the images calculated from the frequency representations Famin and Famax. The closer it is to 1, the better this overlap. When the sample is outside the observation zone, this value approaches 0.

d'observation des objectifs. Lors de ce réglage, les valeurs de rapport et 1I'J doivent être recalculées en permanence. La position de l'échantillon doit être ajustée selon l'axe (2263) de manière à obtenir une valeur suffisamment élevée de rapport. puis elle peut être ajustée plus finement de manière à obtenir par exemple
L wf = @/2. 7. 15.3. Focus
Focus adjustment consists of correctly positioning the sample in the area

observation of objectives. During this adjustment, the ratio values and 1I'J must be constantly recalculated. The position of the sample must be adjusted along the axis (2263) so as to obtain a sufficiently high ratio value. then it can be adjusted more finely so as to obtain for example
L wf = @ / 2.

2
This setting generally allows a first focusing. However, if for example the index no is close to nv, this focusing is very imprecise.

In all cases, this adjustment must subsequently be supplemented by a more precise focusing on the area of interest, as indicated in 7.17.3.

7.16. Obtaining the aberration compensation function.

The function e-j2 # / # in principle making it possible to correct the phase shifts introduced by the object and corresponding to the spherical aberration comprises high frequencies which are filtered by the diaphragm It cannot therefore be used directly and it is necessary to filter it to obtain a usable correction function in the form of an array of dimensions Npix x Npix.

Etape 1: génération des tableaux Ds de dimensions .'1' -''e avec par exemple Ye =-1096: r 1 -j- ". 2 rtys +7 . z I- lcz +7c2 +nv - x lc + y P ,...,. 2" ( nv )2' lC 2 + n IC . + 1c ,2 ( x ic 2 jc Ds [l'l]=exp no -nv(w +nv 2 rK p 2 J-C [.exp- Jl-j --b-,J--{,j I\..p NI Ne N, avec ;c = ! - #-, /c == / - #-, r- AT pix pix -j2#/#/@ le tableau Dsp correspond à la fonction e échantillonnée avec un pas suffisamment fin pour éviter le repliement de spectre. The aberration compensation function, which will be used in the imaging phase, is obtained as follows:

Step 1: generation of tables Ds of dimensions .'1 '-''e with for example Ye = -1096: r 1 -j- ". 2 rtys +7. Z I- lcz + 7c2 + nv - x lc + y P, ...,. 2 "(nv) 2 'lC 2 + n IC. + 1c, 2 (x ic 2 jc Ds [l'l] = exp no -nv (w + nv 2 rK p 2 JC [.exp- Jl-j --b-, J - {, j I \. .p NI Ne N, with; c =! - # -, / c == / - # -, r- AT pix pix -j2 # / # / @ the array Dsp corresponds to the function e sampled with a sufficiently fine pitch to avoid aliasing.

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I)pr.=DspCi-,.x+ ,-'V+.2cJ fL J 1 2 22 2 pour tous les couples (/j) tels que C - !'V prx 1 2 (..IV PIX) 2 ( .V PIX) ou aux est l'ouverture des objectifs. Step 2: inverse Fourier transformation of the Dsp arrays Step 3: extraction of the central part of the array, of dimensions Npx x Npix with simulation of the diaphragm. The program performs:

I) pr. = DspCi - ,. x +, - 'V + .2cJ fL J 1 2 22 2 for all pairs (/ j) such that C -!' V prx 1 2 (..IV PIX) 2 (.V PIX) or aux is the aperture of the lenses.

Step 4: Fourier transformation of table Dp.

The usable correction function is then obtained in the form of the table Dp.

7.17. Realization of three-dimensional images.

7. 17.1. principle
7.17.1.1. Superposition of frequency representations.

We have seen that for a given illuminating beam (index k, p), two two-dimensional images are obtained corresponding to the two sensors and identified by the index q. When the path of FIG. 56 on sensor number 0, a frequency representation can be generated from the two-dimensional images obtained on the two sensors. Fig. 58 shows how a set of two-dimensional frequency representations generates a three-dimensional representation. A two-dimensional representation is composed of a portion of a sphere (4101) obtained on the sensor number 0 and of a portion of a sphere (4102) obtained on the sensor number I. When the point of direct impact moves on a transverse trajectory (3904) the movement of these portions of spheres generates a volume In figure 58, there is shown a set of such portions of spheres, obtained for various positions of the point of direct impact on a transverse trajectory When the point of direct impact moves on the circle (3903) the volume (4104) delimited by (4105) is generated in addition When the point of direct impact is on the sensor number 1, a symmetrical volume is generated.

We distinguish four partial three-dimensional frequency representations that ['we will note
Fp, q or the couple (p, q) designates a couple (sensor receiving the direct illumination wave, sensor from which the two-dimensional representations making it possible to generate Fp, q come from) with p = O for the sensor (2239), p = 1 for (2229), q = 0 when it designates the same sensor as /? and q = 1 when it designates the opposite sensor. The final three-dimensional representation is obtained by superimposing these partial three-dimensional representations.

The complete frequency representation obtained is shown in section in Fig. 59 It is made up of:

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- of a part (4111) obtained by the sensor 0 or 1 receiving the point of direct impact of the beam, and corresponding to the representations Fo, o and F1,0 which occupy the same part of the frequency space, - of a part (4113) obtained by sensor 1 when the point of direct impact of the beam is on sensor 0, and therefore corresponding to the representation F0,1 - of a part (4112) obtained by sensor 0 when point d 'direct impact of the beam is on sensor 1, and therefore corresponding to representation F1.1
To obtain exactly this volume, it is in principle necessary to go through all the possible frequency values, i.e. Npix x Npix values on each sensor, minus the values outside the zone limited by the opening of the objective. . However, using the reduced trajectory of FIG. 56 one obtains a volume not very different from that drawn.

The trajectory of Fig. 56 is however a simple example and various types of trajectory could be used in practice. Some examples are given below: - A circle as in the first embodiment.

- The trajectory of FIG. 56, which makes it possible to obtain images of better definition.

- The trajectory of Fig. 56 made less dense. For example, it is possible to use every other pixel along this path. This has the effect of limiting the thickness of the samples that can be observed under good conditions.

- A complete trajectory, that is to say defined by the tables Io [k] and Jo [k] such that the point of coordinates (Io [k], Jo [k]) traverses the whole of the disc limited by the opening of the lens. This means that each pixel included in the disk bounded by the circle (3902) of Fig. 56 must be reached once and only once. This trajectory provides only a slight improvement in the definition compared to that of FIG. 56 and considerably increases the acquisition time. On the other hand, the normal conditions of use of this microscope require that the diffracted beam remains of low intensity compared to the illuminating beam. The use of a full trajectory makes the system more robust when these conditions of use are not respected.

7. 17.1.2. Phase and intensity reference
In order to be able to combine the two-dimensional frequency representations to obtain the partial three-dimensional frequency representations, it is necessary to establish a common phase and intensity reference for them.

the complex values of the waves received on the directly illuminated sensor can be related to the value of the illuminating wave at its point of direct impact, as in the first embodiment or in the calculation of wp.

- A more elaborate method is necessary for the waves received on the opposite sensor. The reference lights are used to establish a characteristic ratio of the phase variation on each sensor and this ratio is taken into account to cancel these variations before referring to the value of the wave

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lighting at its point of direct impact. This makes it possible to make all the two-dimensional representations corresponding to a given pair p, q, independently of the \ ibrations affecting the system, consistent with each other, and therefore to establish for each pair p, only a three-dimensional frequency representation.

et est: no < # -== ouv ou oui, est l'ouverture de l'objectif. Par exemple pour une ouv erture de 1.4 on obtient 2#2 un indice maximal de l'échantillon de n0 = 1,48. However, this does not make it possible to establish the phase relationship between each of these three-dimensional frequency representations, which it is necessary to know in order to combine them into a single frequency representation. The phase relation between, for example, the three-dimensional frequency representations Fo, o and F0,1 which correspond respectively to the parts (4111) and (4113) of the three-dimensional representation of the whole, can be established when these two parts have a common area (4114). It suffices to choose the phase difference which makes these two representations coincide as well as possible on their common zone. For there to be a common area it is necessary that the opening of the lens is sufficient. The condition of existence of this common area is determined geometrically

and is: no <# - == open or yes, is the aperture of the lens. For example for an opening of 1.4 we obtain 2 # 2 a maximum index of the sample of n0 = 1.48.

partir de Tao seule, ou une représentation de l'objet ne différenciant pas l'indice et l'absorpti ité peut être obtenue à partir de Fo,l seule en extrayant le module de la représentation spatiale obtenue en utilisant seulement F0,1. When the two representations Fo, o and F0,1 do not overlap, it is a priori impossible to determine their phase relation: indeed any phase relation corresponds to a possible frequency representation. A representation of the object in absorptivity and index can however be obtained at

from Tao alone, or a representation of the object not differentiating index and absorptivity can be obtained from Fo, l alone by extracting the modulus of the spatial representation obtained using only F0,1.

7. 17.1.2. Phase shift between two noisy arrays.

d'écart-types respectifs I xl CT-1 [r] et GB[r]. C'est donc une loi gaussienne d'écart-type IxI2G.1[r +GBr) . On a donc: We consider two one-dimensional arrays A [II and B [/] where i varies from 0 to N '1. The elements of, (resp.B) are each affected by an independent Gaussian noise whose standard deviation is contained in an array Cu1 [r] (resp.G5 [/]). These tables .4 and B being assumed to be equal to a constant phase and intensity ratio and up to the noise, we seek to determine this phase and intensity ratio, which we will denote by B [i] x, and which would be valid in the absence of noise x (sounds) noise) - B [i]
The value sought for x is that which maximizes the quantity P (x # A, B), representing the probability of a value of x knowing tables A and B. Maximizing this quantity amounts to maximizing P (B # A, x). For a given value of x, and in the case where the values of B [i] and. 1 [they are sufficiently above the noise level, the law giving B [i] from A [i] is the composite of two Gaussian laws

of respective standard deviations I xl CT-1 [r] and GB [r]. It is therefore a Gaussian law of standard deviation IxI2G.1 [r + GBr). So we have:

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.,)=n{- IB[I]-x4[lf ,1 \! ' n i exp - IXI 2 (C 4[j])2 2 +(GB[llt Dans les cas qui nous intéresseront par la suite Ixl est toujours proche de 1. On a donc: P(B\A . . exp - LLi LL .

.,) = n {- IB [I] -x4 [lf, 1 \! 'ni exp - IXI 2 (C 4 [j]) 2 2 + (GB [llt In the cases which will interest us later Ixl is always close to 1. We therefore have: P (B \ A.. exp - LLi LL.

IB[I] - :1:4[1 ]12 i (GA[I]f +(GB[I])2 I4'f qui vaut. après division par le facteur indépendant de x: 13[lf ]12 y 4'MÎ ~ i (C,,4 [11)2 +(C ,2 i (G.4[I]) +(GB[I]) - i (CrA[I]) +(C18[1]) 2 \4>î y I412 y ~J:(1]I2, +1-'1 2 +(GS[;])2 i (G [,])2 +(C B[j])2 (G.4[I]) +(C18[1]) On vérifie que cette quantité est égale à:

A[i]I3[i] 1 1 y~~ 4['] x- i (G4[1])2 +(G8(I])2 + 1 (GA[I])2 +(GB[I])2 - 1 ((1.-1[1])2 +(GB[I])2 y |412 IA[I]12 - lA (1]1 i (G.4[1])2 + (G8(I]) 1 (GA[I])2 2 + (C 1 ((1..1[1])2 +(GB[11)2 La solution minimisant cette quantité est donc: # A [i]B[i]

i (G.4[1])2 + (GB[I]) x= #A [i]#2 #

(Cjl[@])2 +(C B[11)2 Cette formule simple n'est cependant valable que si les valeurs de B[i] et A[i] sont suffisamment au-dessus du niveau de bruit Une manière d'éviter les valeurs ne respectant pas cette conditions est de limiter les sommations de la manière suivante: # A [i]B[i]

IEE(GA[I])2 + (GB[I])2 I4f G1[j])2 +(C B[j 1) P (BJA.x) "" D e \: p - + (GB [i]) 2 Maximizing this quantity amounts to minimizing the quantity

IB [I] -: 1: 4 [1] 12 i (GA [I] f + (GB [I]) 2 I4'f which is equal after division by the independent factor of x: 13 [lf] 12 y 4 'MÎ ~ i (C ,, 4 [11) 2 + (C, 2 i (G.4 [I]) + (GB [I]) - i (CrA [I]) + (C18 [1]) 2 \ 4> î y I412 y ~ J: (1] I2, + 1-'1 2 + (GS [;]) 2 i (G [,]) 2 + (CB [j]) 2 (G.4 [ I]) + (C18 [1]) We check that this quantity is equal to:

A [i] I3 [i] 1 1 y ~~ 4 ['] x- i (G4 [1]) 2 + (G8 (I]) 2 + 1 (GA [I]) 2 + (GB [I] ) 2 - 1 ((1.-1 [1]) 2 + (GB [I]) 2 y | 412 IA [I] 12 - lA (1] 1 i (G.4 [1]) 2 + (G8 (I]) 1 (GA [I]) 2 2 + (C 1 ((1..1 [1]) 2 + (GB [11) 2 The solution minimizing this quantity is therefore: # A [i] B [ i]

i (G.4 [1]) 2 + (GB [I]) x = #A [i] # 2 #

(Cjl [@]) 2 + (CB [11) 2 This simple formula is however only valid if the values of B [i] and A [i] are sufficiently above the noise level. values not respecting this condition is to limit the summations as follows: # A [i] B [i]

IEE (GA [I]) 2 + (GB [I]) 2 I4f G1 [j]) 2 + (CB [j 1)

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avec 4']~ ~ , 4[! avec = < ####.###'##- Coe - max (GA[j]) 2 + (C B[j]) 2 avec E= i (GA[I])2 + (GB[I])2 ])(])J c'est-à-dire que les sommations sont limitées à l'ensemble E des valeurs de1 telles que

IA[i }B[I]I soit supérieur au produit de sa valeur maximale par un coefficient C'oef qui peut par #######'###soit supérieur pro Ult valeur maxima par coefficient Coc/ qUI peut par (C l + (C B[j])2 exemple être égal à 0,5.

with 4 '] ~ ~, 4 [! with = <####. ### '## - Coe - max (GA [j]) 2 + (CB [j]) 2 with E = i (GA [I]) 2 + (GB [I] ) 2]) (]) J that is to say that the summations are limited to the set E of the values of1 such that

IA [i} B [I] I is greater than the product of its maximum value by a coefficient C'oef which can by ####### '### or greater pro Ult maximum value by coefficient Coc / which can by (C l + (CB [j]) 2 example be equal to 0.5.

This method will frequently be used later, generalized to 2 or 3 dimensions, to determine the phase difference between two frequency representations partially intersecting.

7.17.1.3. Combination of a series of noisy elements.

grandeur qui maximise P(xl.4). Maximiser cette quantité revient à maximiser P(. )jr). Or on a: ( ) n! IX-A(if} PAix = 1 (C 4 [1]) 2 Maximiser cette quantité revient à minimiser la quantité suivante: #x-A [i]#2 # [GA[i])2

Qui vaut. après division par la quantité L l, indépendante de y A[lf 2 1- A[il y~41~ i (GA 1 [1]) x i (GA[I]) 1 x - i ((1.1[1]) 1 + Ixl (G~4 [11) (GA[I])2 (GA[i])2 On vérifie que cette quantité est égale à: 4'] ' Lfrll L 2 x- i (GA[I]) i (C 2 (cet-1 ?(f 1 (GA [1]) (C 4 [11) La solutionx qui la minimise est donc: We consider a one-dimensional array, 4 [il or i varies from 0 to N-1. The elements of A are each affected by an independent Gaussian noise whose standard deviation is contained in an array GA [t] In the absence of noise the elements of .4 are all equal to a value x that we want determine. x is there

magnitude that maximizes P (xl.4). Maximizing this quantity amounts to maximizing P (.) Jr). Now we have: () n! IX-A (if} PAix = 1 (C 4 [1]) 2 Maximizing this quantity amounts to minimizing the following quantity: #xA [i] # 2 # [GA [i]) 2

Which is worth. after division by the quantity L l, independent of y A [lf 2 1- A [there ~ 41 ~ i (GA 1 [1]) xi (GA [I]) 1 x - i ((1.1 [1]) 1 + Ixl (G ~ 4 [11) (GA [I]) 2 (GA [i]) 2 We check that this quantity is equal to: 4 ']' Lfrll L 2 x- i (GA [I]) i (C 2 (cet-1? (F 1 (GA [1]) (C 4 [11) The solutionx which minimizes it is therefore:

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7 Y CJx= H) On vérifie que ceci équivaut à: -L=Y #x2# (GA[i])2 On fera également usage de ce résultat, pour déterminer une représentation fréquentielle à partir de plusieurs représentations partielles se recoupant en certains points. A [i] i (GA [i]) 2 x = 1 # i (GA [t]) 2 The noise on x is then given by the squared addition of the noises on each. 4 [il
2 # (GA [i]) 4

7 Y CJx = H) We check that this is equivalent to: -L = Y # x2 # (GA [i]) 2 We will also use this result, to determine a frequency representation from several partial representations intersecting in certain points.

7. 17.2 algorithm.

A series of images is first acquired as indicated in 7.12., The point of direct impact of the lighting beam traveling on each sensor a path defined as indicated in 7.17. 1. 1. To simplify the explanation, the acquisition phase is separated here from the calculation phase. However, the three-dimensional frequency representations Fp, q can also be generated as the acquisition progresses.

For example, if a complete trajectory is used, the separation of the acquisition and calculation phases requires a very large memory and it is therefore preferable to carry out the calculation as the acquisition progresses.

Afk,p,q [l, 1] , correspondant à la prise de vue principale
Bk,p,q[i,j] indicateur de bruit Hk,p,q [i,j] prise de vue de référence pour la k-ième acquisition, BHk,p,q, [i,j] indicateur de bruit de l'image de référence k indiciant la prise de vue, p le capteur éclairé par le faisceau direct, q indiquant : q=0: capteur éclairé par le faisceau direct q= 1 : capteur opposé. The acquisition phase generates the following tables:

Afk, p, q [l, 1], corresponding to the main shot
Bk, p, q [i, j] noise indicator Hk, p, q [i, j] reference shot for the k-th acquisition, BHk, p, q, [i, j] noise indicator for the reference image k indicating the shot, p the sensor illuminated by the direct beam, q indicating: q = 0: sensor illuminated by the direct beam q = 1: opposite sensor.

imOXk,p,q = Ia[p,q.1c[k,p],.Jc[k,p]] The series of control indices used being defined by tables Ic and Jc, the program also generates the series of coordinates of the points of direct and inverted impact of the lighting beams.

imOXk, p, q = Ia [p, q.1c [k, p] ,. Jc [k, p]]

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jnraxk, p,9 - 0. f?, /c[, ]. c[. ]j
A partir de cet ensemble de données un programme génère une représentation tridimensionnelle spatiale de l'objet étudié. Ce programme comporte les étapes suivantes: Etape l. Cette étape consiste à calculer le rapport caractéristique du décalage de phase et d'amplitude dû aux vibrations et aux fluctuations d'intensité du laser, entre une prise de vue de référence d'indice k=O et la prise de vue de référence courante d'indice k, Ce décalage est caractérisé par les variations de la fonction
Hk,p,q[i,j] qui en l'abscence de vibrations devrait être constante Pour tous les triplets (k,p,q) le programme calcule donc, selon la méthode vue en 7.17.2., le rapport:

HO.P9 U' JIHk.P.9 U' JJ ~~~ (1 J)'EEK ,p,q r l2 r 12 (l'l)EEk,P,q IBHk,P,q[i,lf IBHo,p,q[i,jf k,p,q - Hk'P,q'!]- 1 12 (<./)E I BHk.P.9tt'JJI +I BH.P,9!'JJI avec: P.q (r' , HO,P,9I1' JHk,P,9ll' J ~ ;-> Coef inax. IIIo.P 9 a. bHk,P.9 a, b E.(,.y)###############-Coe/'- max. ###############- ' IBHk,p,q[1.1]1 +JBHo,p,q[i.1f 0=a-N,-1 BH fa, Z -,BK a,bl2 et par exemple Coef =0,5.

jnraxk, p, 9 - 0. f ?, / c [,]. vs[. ] j
From this data set, a program generates a three-dimensional spatial representation of the studied object. This program consists of the following steps: Step l. This step consists in calculating the characteristic ratio of the phase and amplitude shift due to vibrations and fluctuations in laser intensity, between a reference shot of index k = 0 and the current reference shot d 'index k, This shift is characterized by the variations of the function
Hk, p, q [i, j] which in the absence of vibrations should be constant For all the triplets (k, p, q) the program therefore calculates, according to the method seen in 7.17.2., The ratio:

HO.P9 U 'JIHk.P.9 U' JJ ~~~ (1 J) 'EEK, p, qr l2 r 12 (l'l) EEk, P, q IBHk, P, q [i, lf IBHo, p, q [i, jf k, p, q - Hk'P, q '!] - 1 12 (<./) EI BHk.P.9tt'JJI + I BH.P, 9!' JJI with: Pq (r ', HO, P, 9I1' JHk, P, 9ll 'J ~; -> Coef inax. IIIo.P 9 a. bHk, P.9 a, b E. (,. y) ##### ########## - Coe / '- max. ############### -' IBHk, p, q [1.1] 1 + JBHo, p, q [ i.1f 0 = aN, -1 BH fa, Z -, BK a, bl2 and for example Coef = 0.5.

Step 2: this step consists in performing the operation consisting in: - normalizing each two-dimensional representation to compensate for the variations in phase and amplitude shifts due to vibrations, characterized by the quantity Rk, p, q - compensate for the spherical aberration and the poor relative positioning of the objectives, characterized by Dp # 9 + # p [i, j] - reduce to the value of the illuminating wave at its point of direct impact.

,, r..1 'rk. p,9 Ll ' JJnP9+P9 ll' xk,P,R 4. ['.7j= Afk,p,O [ Imaxk,p,o,lmaxk,p,O , ] Dp [, Inlaxk,p,o,lmaxk,p.O ] Rk,p,O .o<:.p.o'7't.p.oj<:.o-7t.p.oj.p,o Bk.P.q Il. j i n ] j DP9+P9 Ll , J]lZk.P.9 Bk,p,q[1.1] = Rk,P,q[I,l] [ . D pq+ pq ] [l, j [ ]Rk ,p,q ] Afk,p.o 1IlIaxk,p,o,jmaxk,p,O Dp nllaxk,p,o,jmaxk,p,O R ,po
L'utilisation du tableau Dp, qui est le résultat des étapes 7.11, 7.15. et 7.16., permet d'améliorer nettement les résultats lorsque l'indice moyen de l'objet diffère de l'indice nominal des objectifs. Toutefois, il est également possible de ne pas effectuer les étapes 7.11, 7.15. et 7.16., Le réglage de position des The program therefore traverses the indices k, p, q, i, j by performing:

,, r..1 'rk. p, 9 Ll 'JJnP9 + P9 ll' xk, P, R 4. ['.7j = Afk, p, O [Imaxk, p, o, lmaxk, p, O,] Dp [, Inlaxk, p, o, lmaxk, pO] Rk, p, O .o <:. p.o'7'tpoj <:. o-7t.p.oj.p, o Bk.Pq Il. jin] j DP9 + P9 Ll, J] lZk.P.9 Bk, p, q [1.1] = Rk, P, q [I, l] [. D pq + pq] [l, j [] Rk, p, q] Afk, po 1IlIaxk, p, o, jmaxk, p, O Dp nllaxk, p, o, jmaxk, p, OR, po
The use of the Dp table, which is the result of steps 7.11, 7.15. and 7.16., can significantly improve the results when the average object index differs from the nominal index of the objectives. However, it is also possible to skip steps 7.11, 7.15. and 7.16., The position adjustment of the

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The objectives described in 7.10 must then be carried out in such a way as to obtain a centered and point spatial image.The Dp table must then be set to 1.

The use of the values Rk, p, q makes it possible to compensate for any vibrations of the optical table.

However, if the optical table is perfectly stable, this compensation is not necessary. The values Rk, p, q must then be set to 1.

bruit gaussien affectant chaque élément du tableau Fpq . Ces tableaux sont de dimensions 2 Y PI): 2 2 N pu x 2 Npix. Chaque point d'une représentation fréquentielle bidimensionnelle correspond à un point de la représentation fréquentielle tridimensionnelle Fp,q,dont les coordonnées doivent être déterminées. Step 3: This step consists in calculating for each pair (p, q) a three-dimensional frequency representation Fp, q, accompanied by an array IBp, q of real numbers, containing the inverse of the square of the standard deviation of

Gaussian noise affecting each element of the Fpq array. These tables have dimensions 2 Y PI): 2 2 N pu x 2 Npix. Each point of a two-dimensional frequency representation corresponds to a point of the three-dimensional frequency representation Fp, q, the coordinates of which must be determined.

When a point is scored more than once, the most probable value is determined.

,<7,,<,/ en effectuant pour chaque quintuplet (p,q,k,r j) les opérations suivantes, numérotées de 1 à 3: opération 1: calcul des indices de la représentation fréquentielle tridimensionnelle Le programme effectue ni =aPll -I111QYk.P.q + N pu nj = a p (1 - jmaxk pq} + N pu 1'2f. , prx1 2f..Y \2 I 2f.? 12 I K,,,2 2i N,,Plx2 ,,)2 ,,)2 'NI tik a p 2 J -aPCj- 2 J - fyr -aPCitltrxk,P,9 J -nyC>111nrk,P,9 2 ±V*
Une distance d'un pixel, mesurée sur le capteur p, correspond à un écart de fréquence réel proportionnel à 1/Kp Les pixels ne représentent donc pas les mêmes écarts de fréquence sur les deux Kp capteurs. On se ramène à une unité commune et proportionnelle aux écarts de fréquence en multipliant les distances obtenues sur le capteur p par le coefficient ap = Ko+K1/2Kp 2Kp

La valeur de h devient alors commune aux deux capteurs et \aut K 0 2 +K 1. Elle doit être corrigée pour tenir compte de l'indice de l'échantillon et on obtient donc K,, =no K0+K1 nv 2 opération 2: modification des indices de la représentation fréquentielle tridimensionnelle dans le cas q-1.

The program initializes the arrays Fp, q, IBp, q, to zero then iterates through all the indices

, <7 ,, <, / by performing for each quintuplet (p, q, k, rj) the following operations, numbered from 1 to 3: operation 1: calculation of the indices of the three-dimensional frequency representation The program performs ni = aPll - I111QYk.Pq + N pu nj = ap (1 - jmaxk pq} + N pu 1'2f., Prx1 2f..Y \ 2 I 2f.? 12 IK ,,, 2 2i N ,, Plx2 ,,) 2, ,) 2 'NI tik ap 2 J -aPCj- 2 J - fyr -aPCitltrxk, P, 9 J -nyC> 111nrk, P, 9 2 ± V *
A distance of one pixel, measured on the sensor p, corresponds to a real frequency difference proportional to 1 / Kp The pixels therefore do not represent the same frequency differences on the two Kp sensors. We come back to a common unit proportional to the frequency differences by multiplying the distances obtained on the sensor p by the coefficient ap = Ko + K1 / 2Kp 2Kp

The value of h then becomes common to both sensors and \ aut K 0 2 + K 1. It must be corrected to take into account the index of the sample and we therefore obtain K ,, = no K0 + K1 nv 2 operation 2: modification of the indices of the three-dimensional frequency representation in the case q-1.

donc/, = fc - fe = -2 fe . La fréquence obtenue par la méthode précédente doit donc être translatée d'un vecteur -2fe ce qui se traduit par les opérations supplémentaires suivantes, effectuées seulement dans le cas q=1: If q = 1, the frequency corresponding to the coordinates inrrrxk, P, 9. jmaxk .p, 1. {is not zero frequency. Indeed we have at this point, by taking the notations used in 5.3. : fc = -fe and

therefore /, = fc - fe = -2 fe. The frequency obtained by the preceding method must therefore be translated by a vector -2fe which results in the following additional operations, carried out only in the case q = 1:

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/?/+ = 2apjn'nXk,p,l nk+ NI p- 2 p 2 2 ( lv H pu: )2 -apClnlaxk,p.1 - '" \.' plX )2 nk+=2 2jÂ' -o, 2 Le calcul des indices ni,nj,nk menant à des valeurs non entières, on leur affecte t'entier le plus proche de la valeur calculée. opération 3 : modification des éléments de tableaux. ni + = 2apimaxk, p, 1

/? / + = 2apjn'nXk, p, l nk + NI p- 2 p 2 2 (lv H pu:) 2 -apClnlaxk, p.1 - '"\.' plX) 2 nk + = 2 2j '-o, 2 The computation of the indices ni, nj, nk leading to non-integer values, we assign them the integer closest to the computed value. operation 3: modification of array elements .

/J,-]+=###### Fp.q[l1I,n1,nk]+= . Jfk,p,q [l, ) ] 2 !Bk,P.q [1. 1]1 Etape .!: Il reste une opération à effectuer pour obtenir la valeur la plus probable sur chaque fréquence. Le programme parcourt donc les indices p,q,ni,n1,nk en effectuant, à chaque fois que IR p,q [l1l,/lj, nk] "* 0 , l'opération: FP.9[nr'njnk= [ nkl Fp,q [ni, nj, nk] Fp,q[11l,n1,nk]= IB p,q [ 111, n1, . nk Etape 5: Les repères dans lesquels ont été évalués les indices i,j et donc ni,nj,nk sont inversés entre les deux capteurs Il est donc nécessaire d'effectuer un changement de repère des représentations correspondant au capteur indicé 1 pour les exprimer dans le même repère que les représentations correspondant au capteur

indicé 0. Le programme effectue donc le changement de variables ni - 2,\' pu: - ni , r7j z 2 X pu -nj , nk # 2Npix -nk dans les tableaux correspondant au capteur indicé afin d'exprimer l'ensemble des fréquences dans le même repère. Les tableaux correspondant une représentation fréquentielle issue du capteur 1 ont un indice p égal à 1 ou 0 et un indice q égal à #. The modified indices having been generated, the program modifies the elements of arrays;

/ J, -] + = ###### Fp.q [l1I, n1, nk] + =. Jfk, p, q [l,)] 2! Bk, Pq [1. 1] 1 Step.!: There remains one operation to perform to obtain the most probable value on each frequency. The program therefore traverses the indices p, q, ni, n1, nk by performing, each time IR p, q [l1l, / lj, nk] "* 0, the operation: FP.9 [nr'njnk = [nkl Fp, q [ni, nj, nk] Fp, q [11l, n1, nk] = IB p, q [111, n1,. nk Step 5: The benchmarks in which the indices i, j and therefore ni, nj, nk are reversed between the two sensors It is therefore necessary to perform a change of reference of the representations corresponding to the indexed sensor 1 to express them in the same reference as the representations corresponding to the sensor

indexed 0. The program therefore performs the change of variables ni - 2, \ 'pu: - ni, r7j z 2 X pu -nj, nk # 2Npix -nk in the tables corresponding to the indexed sensor in order to express the set of frequencies in the same frame. The tables corresponding to a frequency representation from sensor 1 have an index p equal to 1 or 0 and an index q equal to #.

["'-"A"] = .p[2A -,2A -/,2A -] 7[,,] = IBP, p [ 2 ,1P, - nr ,2. P. - nj ,2 N P, - nk To perform these changes of variable, the program traverses the set of indices p, ni, nj, nk by performing:

["'-" A "] = .p [2A -, 2A - /, 2A -] 7 [,,] = IBP, p [2, 1P, - nr, 2. P. - nj, 2 NP, - nk

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FP,O [17r, nj, nkFP., rai, n7, nk Rbp '- ' 7B.,J,M/,nA-i IB,@, [ni, ni, nkl Rbp = \ ' J l p[lBpl,[m,nj,nk] j= IBpA[nt.nj,nk] cE, , FP., [ni, nj nkl z nj nkj j ~~~~.j["/]~~~~~ 11/ n' nk EE + ---- Dans cette expression les sommes sont restreintes à un ensemble Eu constitué des triplets (l1/,nj, nk) vérifiant ./Bpo)M;,M/.MA'l7Bpj[n/,M/.] 0 et IFP,o1 r,nj,nkl'P,ni, i ,nkl Coef . Fp" [a, b, cli,7,l [a, blc] 1 1 0:::;a:::;2 V i ~ /B , [. rj, + IBP, [n/. raj, ] 0<A2A,,-1 IBP, c] /B, , /'. Step 6: The program calculates the characteristic ratio of the phase and amplitude shift between the wave received on the directly illuminated sensor and that received on the unlit sensor. It therefore runs through the indices p = 0, p = 1 by performing, in accordance with the principle seen in 7.17.1.2 .:

FP, O [17r, nj, nkFP., Rai, n7, nk Rbp '-' 7B., J, M /, nA-i IB, @, [ni, ni, nkl Rbp = \ 'J lp [lBpl, [m, nj, nk] j = IBpA [nt.nj, nk] cE,, FP., [ni, nj nkl z nj nkj j ~~~~ .j ["/] ~~~~~ 11 / n 'nk EE + ---- In this expression the sums are restricted to a set Eu made up of triples (l1 /, nj, nk) verifying ./Bpo)M;,M/.MA'l7Bpj Partagern/,M/ .] 0 and IFP, o1 r, nj, nkl'P, ni, i, nkl Coef. Fp "[a, b, cli, 7, l [a, blc] 1 1 0 :::; a ::: ; 2 V i ~ / B, [. rj, + IBP, [n /. raj,] 0 <A2A ,, - 1 IBP, c] / B,, / '.

Fp] [111, nj, nk] = FpA [n;. 77/, nA-]. Rbp Etape 8: Le programme calcule la représentation fréquentielle finale, contenue dans un tableau F de dimensions 2N pix x2''P x 2NPIX - Il initialise à 0 ce tableau puis parcourt les indices ni,nj,nk en testant la condition: LIBp,q[ni,nj,nk] ",,0 p, q Lorsque la condition est réalisée il effectue:

L [ni, nl rrkIBP,9 [111, nj, nkl F[ni,n},nk] = P"7 ,IBP.9nl nl,nk p, q Etape 9 : Le programme effectue une transformation de Fourier tridimensionnelle inverse de la représentation fréquentielle ainsi obtenue pour obtenir une représentation spatiale. * IB p, o [ni.nj, nk] IBP @ L [ni, nj, nk] 0 <b <2Npix - \ {jBpn [ab, c] IB p, l [a, h, c] 0 <c <2, PI with for example Coef = 0.5 Step 7: The program modifies the three-dimensional representations obtained from sensors not directly illuminated. It traverses the indices p, ni, nj, nk by performing:

Fp] [111, nj, nk] = FpA [n ;. 77 /, nA-]. Rbp Step 8: The program calculates the final frequency representation, contained in an array F of dimensions 2N pix x2''P x 2NPIX - It initializes this array to 0 then iterates through the indices ni, nj, nk by testing the condition: LIBp, q [ni, nj, nk] ",, 0 p, q When the condition is fulfilled it performs:

L [ni, nl rrkIBP, 9 [111, nj, nkl F [ni, n}, nk] = P "7, IBP.9nl nl, nk p, q Step 9: The program performs an inverse three-dimensional Fourier transformation of the frequency representation thus obtained to obtain a spatial representation.

Step 10: As in the first embodiment, the program can then display the representation thus obtained in the form of sections or possibly stereoscopic projections.

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7.17.4. Focus
The algorithm described in 7.17.2. allows obtaining three-dimensional representations of the sample. Focus adjustment consists of adjusting the position of the object so that these representations are those of an area of interest in the sample. This can be achieved by the operator who moves the sample while observing for example a plane projection or a section of this three-dimensional representation, and moves the object to obtain an image of the area of interest if a displacement of the sample in the direction of the optical axis is performed, this changes the values of wp, and the procedure described in 7. 15.2. must be reiterated to get a correct value for wp.

7. 18. Variants.

The algorithms used in the present embodiment admit numerous variants, some of which are explained below.

l'ensemble des valeurs de k,p. ''co --/,p,o /?of/?.7j,].JctA\j1f,/cfA.1.Jc[A-.)1 .IIk,P,O ',0. ] - #-##########-##########Imaxk O,lmaxk Rk-.P,o Cette valeur peut être introduite dans la formule utilisée à l'étape 2, qui est donc remplacée par: [ 1 .lTk, p.9lr'JDP9+P9lr'JRk,P.9 llk,P.9Lr'J Rn[p,Ick.p,Jc[k.p]]Rb[p,Ick,p.Jc[k,P]lDp intax.,P,Jntaxk,p.o 7.18.2. Utilisation des valeurs précalculées du faisceau d'écJaira1!e direct Rb[ p, 7jA'. pl Jc[k , /)]1 est en principe égal à la fonction obtenue en 7.7. : ;21r À = exp (- ] T 2:r [ nv ( , x K p + y p + z J.: 1 p J K p 2 - i 2 - ] 2 ) + L [ no 1 - (11 n: ##--.J.-#### cette fonction étant toutefois filtrée par le diaphragme. Il est donc possible de remplacer f. 7c-. ]..7c[A. pl] par 7Jw;.o,M;J ou la fonction RB.1i,j] est obtenue de la manière suivante (cette méthode d'obtention est similaire à celle utilisée pour Dp p [l, 1] en 7.16.) Etape 1: génération des tableaux RBp de dimensions 've x Xe avec par exemple 've =4096: -2 ) f,Tz1 , . rr,1 ic' + jc 12 B =exp i 2z tiv -+'-+Z-K, ic je 1 ir 2 ic 2 # 1 - til, IC 2 + ,2 C IC . 2 + ' C 2 ]]1 exp 1Iy X K K P Ic2 - 1/0 - 1/: p2 A-' avec ;c = / - #-, /c = / - #-, 1'=- 2 2 Npix 7. 18.1. Using the pre-stored values of the direct light beam
This variant consists in modifying step 2 of the algorithm described in 7 17 2. so as to use the prerecorded values of the direct lighting. We have in fact, except for a phase factor which is constant over

the set of values of k, p. '' co - /, p, o /?of/?.7j, Danemark.JctA\j1f,/cfA.1.Jc→A-.)1 .IIk, P, O ', 0. ] - # - ########## - ########## Imaxk O, lmaxk Rk-.P, o This value can be introduced in the formula used in step 2, which is therefore replaced by: [1 .lTk, p.9lr'JDP9 + P9lr'JRk, P.9 llk, P.9Lr'J Rn [p, Ick.p, Jc [kp]] Rb [p, Ick, p.Jc [k, P] lDp intax., P, Jntaxk, po 7.18.2. Use of the precomputed values of the direct ecJaira1! E beam Rb [p, 7jA '. pl Jc [k, /)] 1 is in principle equal to the function obtained in 7.7. :; 21r À = exp (-] T 2: r [nv (, x K p + yp + z J .: 1 p JK p 2 - i 2 -] 2) + L [no 1 - (11 n: # # -. J .- #### this function is however filtered by the diaphragm. It is therefore possible to replace f. 7c-.] .. 7c [A. Pl] by 7Jw; .o, M; J or the function RB.1i, j] is obtained as follows (this method of obtaining is similar to that used for Dp p [l, 1] in 7.16.) Step 1: generation of RBp arrays of dimensions' ve x Xe with for example 've = 4096: -2) f, Tz1,. rr, 1 ic' + jc 12 B = exp i 2z tiv - + '- + ZK, ic i 1 ir 2 ic 2 # 1 - til, IC 2 +, 2 C IC. 2 + 'C 2]] 1 exp 1Iy XKKP Ic2 - 1/0 - 1 /: p2 A-'with; c = / - # -, / c = / - # -, 1 ' = - 2 2 Npix

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(,V P1X) 2 (' N P1X) 2 ( N P1X) 1-- + 1-- M Etape 4: transformation de Fourier du tableau RBp. Step 2: inverse Fourier transformation of RBp arrays Step 3: extraction of the central part of the array, of dimensions il! pu x N pix with diaphragm simulation. The program performs: RBp [i, j] = RBp [i-Npix / 2 + Nc / 2, j-Npix / 2 + Nc / 2] for all pairs (i, j) such that

(, V P1X) 2 ('N P1X) 2 (N P1X) 1-- + 1-- M Step 4: Fourier transformation of the RBp array.

u r lI ' J IiÎk,P.9 LI' JDP9+P9 LJ' JRk.P,9 '\!k,p,q Rap,lek, p,.lc[k. p]RBp[Jnlaxk,p,0, jneaxk.P.O]Dp(rnlaxk,p,o. JI)Iaxr.P,,] Ce remplacement est équivalent à un lissage de la fonction définie par le tableau Rb et peut dans certains cas améliorer les résultats, en particulier si l'onde diffractée est forte, sortant des conditions d'utilisation normales de ce microscope. Dans ce cas on combinera cette formule avec l'utilisation d'une trajectoire complète comme définie en 7.17.1.1. We then obtain in the form of the array RBp the function equivalent to the array Rb Step 2 of the algorithm described in 7.17.2. is then replaced by:

ur lI 'J IiÎk, P.9 LI' JDP9 + P9 LJ 'JRk.P, 9' \! k, p, q Rap, lek, p, .lc [k. p] RBp [Jnlaxk, p, 0, jneaxk.PO] Dp (rnlaxk, p, o. JI) Iaxr.P ,,] This replacement is equivalent to a smoothing of the function defined by the array Rb and can in some cases improve the results, in particular if the diffracted wave is strong, going outside the normal conditions of use of this microscope. In this case, this formula will be combined with the use of a complete trajectory as defined in 7.17.1.1.

7. 18.3. Obtaining confocal representations
A confocal microscope makes it possible to obtain three-dimensional spatial representations, which will be called confocal representations. The present microscope makes it possible to obtain a confocal representation strictly equivalent to that which would be obtained using a confocal microscope.

Indeed, the illuminating wave used by a confocal microscope is the sum of the plane waves used in the case where a complete trajectory is used for the acquisition, each plane wave having to be assigned a phase depending on the illuminated point. The wave equivalent to the wave received by a confocal microscope with the same aperture as the present microscope, when the central point is illuminated, can therefore be generated by summing the two-dimensional representations of diffracted waves obtained for all the waves of lighting forming a complete path
It can be shown that the confocal representation of the object is the inverse Fourier transform of a three-dimensional frequency representation obtained by summing the partial two-dimensional frequency representations obtained from each lighting wave, the set of lighting waves traversing a full trajectory.

In addition, a confocal microscope only acquires images on a single objective and only illuminates the sample from one side. In addition, it generates a value which is the intensity of the wave having passed through the object and not its complex value. The confocal representation in intensity is therefore obtained from the waves

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received by a single objective, and by extraditing the square of the modulus from the confocal representation previously obtained. Finally, the confocal microscope does not correct the spherical aberration due to the index of the object.

.fk. P.9 Lr' J 77 .fk,P.9 j Ll' JDP9+P9 LJ' JRk.P,9 j j Ralp, Idk p, JCk , fJl JR p I IIItC7Xk.P,O , .%nICX7Ck,p,O JD [imaxk iPS>.jmaxk p0 ou les tableaux Dp peuvent être mis à 1 si on ne souhaite pas corriger l'aberration sphérique et ou RBp est défini comme en 7.17.3.2.

A confocal representation can therefore be obtained by the present microscope, using for the acquisition a complete trajectory as defined in 7.17.1.1. and by modifying the procedure described in paragraph 17. 2. as follows: (1) Step 2 is modified as follows:

.fk. P.9 Lr 'J 77 .fk, P.9 j Ll' JDP9 + P9 LJ 'JRk.P, 9 jj Ralp, Idk p, JCk, fJl JR p I IIItC7Xk.P, O,.% NICX7Ck, p, O JD [imaxk iPS> .jmaxk p0 or the Dp tables can be set to 1 if one does not wish to correct the spherical aberration and or RBp is defined as in 7.17.3.2.

(2) - operation 3 of step 3 is replaced by Fp, q [/ 1 /, nj, nk] + =: \ Il, pq [l, 1] (3) - steps 4,5, 6.7 are not performed.

(4) - step 8 is replaced by F [I1l, nf, nk = Fa ,,. ,, [ni, l1j.nk] or the choice of indices (po, o) depends on the type of confocal representation that l 'we are trying to generate.

- if (po, qo) = (0,0) or (po, qo) = (1,0) we generate a representation corresponding to that which would be obtained by a confocal microscope by reflection.

- if (po, qo) = (0,1) or (po, qo) = (1,1) we generate a representation corresponding to that which would be obtained by a confocal microscope by transmission.

(5) - the square of the modulus of the spatial representation obtained at the end of step 9 then corresponds to the confocal representation in intensity.

The fact of replacing the calculation of the most probable value of the frequency representation at each point results in an overestimation of the low frequencies compared to the high frequencies, which is equivalent to a filtering of the high frequencies and therefore to a loss of definition.

It is also possible to obtain a confocal representation from the three-dimensional frequency representation obtained in accordance with unmodified paragraph 17: in fact, the three-dimensional representation of the object constitutes the most complete information possible that can be obtained with objectives given aperture and can be used to simulate any type of image that could be generated from any type of microscope using the same objective and the same wavelength.

However, the use of a full trajectory makes the system more robust, in accordance with what was said in 7.17.1.1. If a confocal representation is obtained using a trajectory like that of Fig. 56, it will be disturbed in the case where a significant part of the illuminating wave is diffracted, and this to a greater extent than the confocal representation obtained using a confocal microscope or by using a complete trajectory . It cannot therefore be considered as rigorously equivalent to that generated by a confocal microscope.

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7.18.4. Realization of three-dimensional images with control of the reference wave.

In the methods described above, the phase shifter (2205) is controlled to generate phase shifts #d of the illumination wave dependent on the index d according to the table given in 7.12.2.1.

To achieve the present variant, this discrete phase shift device must be replaced by a device allowing continuous phase shifting. Such a device can be a liquid crystal device placed between two polarizers, marketed for example by the company Newport. By modifying the path of the beam, this device can also be a piezoelectric mirror as in the first embodiment.

phase par décalage phase -Ar Rnp,lc>,-. ..7c p],Rb[p,lc[k. p..Ic[k. p, oti phase 0d par un décalage de phase d=6d -Ara # J # i ou Arg Rk, p,0 désigne l'argument d'un nombre complexe. Ceci permet d'annuler la phase de l'onde d'éclairage en son point d'impact direct et rend non nécessaire la compensation de cette phase. Pendant la phase de calcul décrite en 7.17.2., dans l'étape 2, la formule utilisée peut alors être remplacée par

""lk 1 plq . ?lk>P,91'JP9+P91'JRk,P>9 r Dp p I it)taxk,P>0 J171CIxk,p,O,Rk,P>0 Ce mode revient à contrôler le déphasage des faisceaux d'éclairage par le dispositif de décalage de phase au lieu de le compenser par calcul après l'acquisition. The present variant consists, during the image acquisition provided for in 7.17.2 and carried out as indicated in 7.12.2.1, in controlling the phase shift device so as to replace the shift of

phase by phase shift -Ar Rnp, lc>, -. ..7c p], Rb [p, lc [kp.Ic [k. p, oti phase 0d by a phase shift d = 6d -Ara # J # i or Arg Rk, p, 0 denotes the argument of a complex number. This makes it possible to cancel the phase of the lighting wave at its point of direct impact and makes compensation for this phase unnecessary. During the calculation phase described in 7.17.2., In step 2, the formula used can then be replaced by

"" lk 1 plq. ? lk> P, 91'JP9 + P91'JRk, P> 9 r Dp p I it) taxk, P> 0 J171CIxk, p, O, Rk, P> 0 This mode amounts to controlling the phase shift of the lighting beams by the phase shift device instead of compensating for it by calculation after acquisition.

7. 18.5. Obtaining frequency representations without calculation of the wave received on the reception surface.

w P.9 LI ' .1 Afk,p,q[I.1]Dpq+pq[l.j] iPIlIIIIDCk,P>O..In1(LYk, 0
Pour simplifier les explications, on peut supposer que l'atténuateur de faisceau et les rotateurs de polarisation ne sont pas utilisés. On vérifie alors que chaque représentation fréquentielle Fp,q obtenue dans la procédure décrite en 7.17. peut s'exprimer sous la forme:

FP,9L111,11J,1tC] = 6 (ZFP,q.O[I11,I1j,11k ] - 'P,9, [lll,Rj,iIL] - FP,9,[l7i,llj,ll%i]l I (l'P,e,lnl'n.1>nk-FP,9,z[Yll,nj,nkl If the optical table is of sufficient quality to suppress vibrations, the formula used in 7.18.4. bECOMES:

w P.9 LI '.1 Afk, p, q [I.1] Dpq + pq [lj] iPIlIIIIDCk, P> O..In1 (LYk, 0
To simplify the explanations, it can be assumed that the beam attenuator and the polarization rotators are not used. It is then checked that each frequency representation Fp, q obtained in the procedure described in 7.17. can be expressed in the form:

FP, 9L111,11J, 1tC] = 6 (ZFP, qO [I11, I1j, 11k] - 'P, 9, [lll, Rj, iIL] - FP, 9, [l7i, llj, ll% i] l I (l'P, e, lnl'n.1> nk-FP, 9, z [Yll, nj, nkl

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ou F p,q, d [111, nj, nk] est obtenu comme FP.9 dans la procédure 7.17. non modifiée, mais en remplaçant c a ['- y] par la valeur réelle ,lTOk, p0,d,0.0q,,7 obtenue dans la procédure décrite en 7.12 pour une valeur correspondante de l'indice d indiçant le décalage de phase. Il est donc possible de calculer pour chaque indice d une représentation fréquentielle séparée Fp,q,d, ces représentations étant ensuite superposées pour obtenir la représentation fréquentielle Fp,q, au lieu d'effectuer directement dans la procédure 7.12. la superposition des valeurs correspondant à chaque indice d.

where F p, q, d [111, nj, nk] is obtained as FP.9 in procedure 7.17. not modified, but replacing ca ['- y] by the real value, lTOk, p0, d, 0.0q ,, 7 obtained in the procedure described in 7.12 for a corresponding value of the index d indicating the phase shift. It is therefore possible to calculate for each index d a separate frequency representation Fp, q, d, these representations then being superimposed to obtain the frequency representation Fp, q, instead of performing directly in procedure 7.12. the superposition of the values corresponding to each index d.

It is also possible to perform the superposition of the tables corresponding to each index (1 after passage in the spatial domain by inverse Fourier transform.

et les tableaux lo[k],Jo[k] doivent être remplacés par des tableaux /n[A.../o[A'.<7]. On peut alors calculer comme précédement des tableaux Fp,q,d séparés avant de les superposer pour obtenir les tableaux Fp,q,
Ce mode de calcul n'est pas particulièrement avantageux mais montre qu'il n'est pas indispensable de calculer dans une phase intermédiaire les représentations bidimensionnelles complexes, ni même d'effectuer une acquisition des données correspondant à ces représentations bidimensionnelles complexes. Finally, it is possible not to use the same points of impact of the illumination wave depending on the phase shift applied. In this case, each phase shift corresponds to a distinct trajectory

and the arrays lo [k], Jo [k] must be replaced by arrays /n→A.../o→A'.<7]. We can then calculate as before separate arrays Fp, q, d before superimposing them to obtain the arrays Fp, q,
This method of calculation is not particularly advantageous but shows that it is not essential to calculate in an intermediate phase the complex two-dimensional representations, or even to carry out an acquisition of the data corresponding to these complex two-dimensional representations.

7.18.6. Realization of images with a single value of the phase shift.

This variant consists in modifying the procedure described in 7.12. so as to acquire only the real part of the complex number normally acquired as described in 7.12. This real part can be acquired in a single step, which makes it possible to use a single value of the index d characterizing the phase shift. Since only the real part is acquired, the frequency representation obtained, assuming that the spherical aberration compensation table Dp is set to 1, is the real part of the complex representation. The spatial representation obtained by inverse Fourier transform is then the superposition of the normal image with a conjugate image symmetrical with respect to the point of origin of the reference wave. So that the normal image is not superimposed on its symmetrical, the point of origin of the reference wave must be placed on the side of the diaphragm, slightly outside the opening of the diaphragm, and not in the center of it. this. The aperture of the diaphragm must be reduced by half so as to avoid the aliasing of the spectrum induced by this displacement of the point of origin of the reference background The image finally obtained then comprises the normal image and the symmetrical image, not superimposed and therefore usable. However, so that the real part can be acquired in a single step, it is necessary that the intensity of the reference wave is sufficiently greater than the intensity of the diffracted wave, so as not to induce errors. of the second order. The quality of the image finally obtained therefore depends on the intensity of the reference wave. Too low an intensity induces second order distortions and too high an intensity increases the Gaussian noise.

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In order to best meet the condition of sufficient intensity of the reference wave, the intensity of the reference wave alone must be adjusted not to a quarter of the maximum value of the digitizer as indicated in 7.4. but for example at 80% of this value.

0, = -Arg( Ra[p. I4k p], Jc(k, p]]Rb[p.lc[k. p], Jc(k, pl])
Malgré l'application de ce décalage de phase, la référence de phase peut ne pas être constante en présence de vibrations de la table optique. Ceci détruirait l'image et il est donc nécessaire d'utiliser une table optique de très bonne qualité de manière à supprimer ces vibrations. In order for the real part to be effectively acquired at each image capture, the single phase shift used must make it possible to directly obtain a constant phase reference. This shift will therefore be, in a manner similar to what was done in 7. 18.4 .:

0, = -Arg (Ra [p. I4k p], Jc (k, p]] Rb [p.lc [k. P], Jc (k, pl])
Despite the application of this phase shift, the phase reference may not be constant in the presence of vibrations of the optical table. This would destroy the image and it is therefore necessary to use a very good quality optical table in order to suppress these vibrations.

][q- ~ .1f0(k. p]['\fI[q,i,l ],O,r, ,r }q,i.1]- Iref (pq +'.7] h'-J- att(.lllq,t, j]] Iref(pq+p,i, j] Comme en 7.18.4., mais en tenant compte de l'abscence de vibrations, l'étape 2 de la procédure décrite en 7.17.2. est remplacée par:

ik i~ .J'-./].7] ML'-J ' TT#######Ï P,q['*J\ DP I1!)ilLCk.P,O . Jl))CIXk,P.(7
Cette variante peut être d'avantage simplifiée en n'utilisant qu'une seule position des rotateurs de phase et qu'une seule position de l'atténuateur de faisceau, moyennant quoi les 36 couples d'images élémentaires acquis en 7.12.2.1. peuvent se réduire à un seul, au prix d'une forte diminution de la qualité de l'image. Dans ce cas de simplification extrême , les indices c,d,r ,r2 ne prennent plus qu'une seule valeur et l'ensemble de la procédure décrite en 7 12. 2 se réduit à'

.ilk,P.9 Lr' r j] .110k,p[0,0,0,0](q.i, j]-Iref(Pq+P9i.J] 1 ' Iref[pq+ pi,i, jl
7. 18.7. Méthode simplifiée d'obtention des images tridimensionnelles. The index d therefore takes only one value instead of three and step 2 of the procedure described in 7.12.2.2. is replaced by:

] [q- ~ .1f0 (k. p] ['\ fI [q, i, l], O, r,, r} q, i.1] - Iref (pq +'. 7] h'-J - att (.lllq, t, j]] Iref (pq + p, i, j] As in 7.18.4., but taking into account the absence of vibrations, step 2 of the procedure described in 7.17. 2. is replaced by:

ik i ~ .J '-. /]. 7] ML'-J' TT ####### Ï P, q ['* J \ DP I1!) ilLCk.P, O. Jl)) CIXk, P. (7
This variant can be further simplified by using only one position of the phase rotators and only one position of the beam attenuator, by means of which the 36 pairs of elementary images acquired in 7.12.2.1. can be reduced to one, at the cost of a sharp reduction in image quality. In this case of extreme simplification, the indices c, d, r, r2 take only one value and the whole of the procedure described in 7 12. 2 is reduced to '

.ilk, P.9 Lr 'rj] .110k, p [0,0,0,0] (qi, j] -Iref (Pq + P9i.J] 1' Iref [pq + pi, i, jl
7. 18.7. Simplified method of obtaining three-dimensional images.

pour tout couple (p, q) * (0,0) . La présente méthode est la méthode définie en 7.18..1. mais simplifiée de cette manière, et adaptée au cas ou l'indice moyen de l'échantillon est proche de l'indice nominal des objectifs, et ou la table peut être considérée comme parfaitement stable
Dans ces conditions, on a Rk,0,0 = 1 et D0[i,j] = 1 .

To generate the three-dimensional image of the object, one can limit oneself to the representation F0.0 defined in 7.17. This amounts, in the procedure described in 7.17.2., To adopting tables IBp, q zero

for any pair (p, q) * (0,0). This method is the method defined in 7.18..1. but simplified in this way, and adapted to the case where the average index of the sample is close to the nominal index of the objectives, and where the table can be considered as perfectly stable
Under these conditions, we have Rk, 0,0 = 1 and D0 [i, j] = 1.

The formula: Al k, pq [l, 1] = .IIk, P, 9 r 'JDP9 + P9 r' JR, P, 9 formula Mk, p, q [lJ \ DP [Itlaxi ,, P, o, j , 71axk, p, O] Rk-p ()

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,\Ik.O, [1,1] = lvh,o,o [i, 1] c'est-à-dire que le tableau ,0,0 n'est pas modifié avant d'être utilisé pour générer la représentation tridimensionnelle de l'objet. which was used in 7.18.4. is therefore simplified and we obtain:

, \ Ik.O, [1,1] = lvh, o, o [i, 1] i.e. the array, 0,0 is not modified before being used to generate the representation three-dimensional object.

In this particular case, no algorithmic compensation of the phase shift of the reference beam is necessary, because the device used allows the generation of illumination beams having a constant phase shift with respect to the reference wave.

ad =6d Ar4 Ralp. Idk. pl Jclk, pl]) c'est-à-dire qu'elle ne dépend pas de mesures effectuées préalablement sur l'objet lui-même. Si un objectif de microscope ayant pour indice nominal celui du vide est employé, les mesures préalables peuvent être effectuées en l'abscence de tout objet (en considérant comme un objet la lame transparente). In this particular case, it is also possible to avoid steps 7.10, 7.11, 7.15, 7. 16. The position of the objectives can be adjusted as in 7 9.1, so as to have a punctual and centered image The control of the phase shift device is then defined by:

ad = 6d Ar4 Ralp. Idk. pl Jclk, pl]) that is to say that it does not depend on measurements carried out previously on the object itself. If a microscope objective with a nominal vacuum index is used, the preliminary measurements can be carried out in the absence of any object (considering the transparent slide as an object).

7. 18.8. Realization of an image with a single position of the polarizers.

The present variant consists in not using the possibility of variation of the indices ri and r2. If only images according to the present variant are generated, the polarization rotators (2210) (2241) (2238) (2226) can be omitted. The present variant involves a modification of step 3 of the loop on k, p described in 7.12.2.2., As well as a modification of step 8 of the algorithm described in 7.17.2.

7.18.8.1. Modification of step 3 of the loop on k, p described in 7.12.2.2.

When the polarization rotators are not used, the direction of the electric field vector of the illumination beam and the direction of analysis of the received beam are oriented along the vector j of Fig. 52.

On x j = xe sintpe + ye cosrpe
Lors de la diffraction vers le point C: - la composante suivant xe est transmise sans atténuation, devenant la composante sur le vecteur -#c - la composante suivant est transmise, devenant la composante sur le vecteur -#c, mais est atténuée d'un facteur cos# ou # est l'angle entre le vecteur fe et le vecteur fc. We denote by #e and the vectors deduced respectively from the vectors #e and #c by rotation of 2 in the plane of FIG. 52

We xj = xe sintpe + ye cosrpe
During the diffraction towards the point C: - the following component xe is transmitted without attenuation, becoming the component on the vector - # c - the following component is transmitted, becoming the component on the vector - # c, but is attenuated by a factor cos # or # is the angle between the vector fe and the vector fc.

reçue au point C est donc proportionnel à F =-x sine - cos (p, cors 0. On peut prendre en compte les relations Xc = ï cos rp +y sin tp e ' # e = -i sin tp + j cos tp e . La composante de 7 suivant} est alors proportionnelle à Br = -cosrpe cosse cos 0 - sin ço, sinrp . Ceci constitue un facteur d'atténuation qui For an electric field vector y of the lighting wave, the electric field vector of the wave

received at point C is therefore proportional to F = -x sine - cos (p, cors 0. We can take into account the relations Xc = ï cos rp + y sin tp e '# e = -i sin tp + j cos tp e. The following component of 7} is then proportional to Br = -cosrpe pod cos 0 - sin ço, sinrp. This constitutes an attenuation factor which

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affects the diffracted beam measured at point C along an analysis direction oriented along i when the illumination beam is directed on point E and has its electric field vector oriented along j. If the diffusion could be considered as isotropic, this coefficient would be constant. To compensate for the effect of anisotropy, it is therefore sufficient to divide the measured values by this coefficient Br so as to reduce to a constant coefficient characterizing the isotropic diffusion. Dividing by Br brings up the noise affecting the points where Br is weak, which must also be taken into account.

The factor cos0 is equal to cos 0 = # '". This translates, using the normalized values of the IV, il. Lif, frequency vectors, by: coso = xexe + I Jyy + ZCZI.

sinon, compile, p. q\ = -cos0>c cos<pe cos#-sin#>c sin<z>e Comme les valeurs coef k, p, cl, i, jr , .1'2] utilisées en 7.12., les valeurs comp[k, p, q] constituent un tableau qui peut être précalculé. - le programme calcule finalement.

Step 3 of the procedure 7.12.12. is therefore modified as follows: - the program calculates, in addition to the values already calculated in 7.12., cos0 = xxe + YeYe + zeze - the program calculates the factor comp [k, p, q] for compensation of the attenuation : if - cos ([J c cos ([J e cos 0 - sin ([J e sin ([J <lim then comp [k, p, q] = 1, where lrrn is a very low lim value, for example lim = 10-10

if not, compile, p. q \ = -cos0> c cos <pe cos # -sin #> c sin <z> e Like the values coef k, p, cl, i, jr, .1'2] used in 7.12., the values comp [ k, p, q] constitute an array which can be precomputed. - the program finally calculates.

l'ordre de 1. On a: Uac,7 = 10 z 2 N ou .SVR est le rapport signal sur bruit en décibels et N'est le nombre de bits d'échantillonnage du signal. '1 k. P, 9 r I = .112 1, lq, i. I conrpk, p, q] Bk.P, 9lt 'J conrpk> P, q Bk, pq 1,1 - att, Tl (cr, ll Iref [Pq + P9> l, j where #acq is the deviation- type of sensor noise.Sensors are generally designed so that #acq is
SNRdB

the order of 1. We have: Uac, 7 = 10 z 2 N where .SVR is the signal to noise ratio in decibels and N is the number of signal sampling bits.

7.18.8.2. Modification of step 8 of the algorithm described in 7.17.2.

Multiplying by comp [k, p, q] can increase the noise level considerably, which can distort the image obtained. To avoid this problem, step 8 of the procedure described in 7.17 is modified so as to cancel the components of the frequency representation which are lower in modulus than the noise multiplied by a given constant const.

The cancellation of certain elements of the frequency representation itself generates noise. To obtain a frequency representation of comparable quality to that obtained according to the

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normal procedure, more precise sampling or an additional level of attenuation may be required.

de dimensions 2.,N-px x 2N PIX x 2N pu' Il initialise à 0 ce tableau puis parcourt les indices ni,nj,nk en testant la condition: IBP 9 Ur' NJ' nk, p, q, Lorsque la condition est réalisée il effectue :

Fp,q [/1I,nj nk IBP.9 [ni , ni, nk] F[ni,nJ,nk] = p,q IP,9 nr > rT, nk p. Step 8 of the procedure described in 7.17 is modified as follows: step 8 modified: The program calculates the final frequency representation, contained in an array F

of dimensions 2., N-px x 2N PIX x 2N pu 'It initializes this array to 0 then iterates through the indices ni, nj, nk by testing the condition: IBP 9 Ur' NJ 'nk, p, q, When the condition is carried out it performs:

Fp, q [/ 1I, nj nk IBP.9 [ni, ni, nk] F [ni, nJ, nk] = p, q IP, 9 nr> rT, nk p.

It then tests the condition F [ni, nj, 11 'k] S; const IBP, q ni, nj, nk P.9 When this condition is fulfilled it performs: F [ni, nj, nk] = 0 const is a constant chosen so that in the absence of signal (noise only) the condition is always checked. We can for example use const = 4
A multiplication by a constant of the overall noise level modifies the results of this modified step 8. This is why in 7.18.8.1. an absolute noise level is determined, whereas in 7.12 the noise level was defined to within a constant.

7. 18.9. Obtaining an image of a uniaxial birefringent crystal.

We consider a uniaxial crystal of ordinary index no cut so as to form a plate of reduced thickness, the plane of the plate being orthogonal to the optical axis of the crystal. This slide constitutes the observed sample and is placed between the two objectives, optical oil being used between the objectives and the sample, the objective being designed to use plates of index equal to that of the optical oil. .

The optical axis of the crystal is therefore coincident with the optical axis of the objectives.

This blade is assumed not to be perfect. It can be affected, for example, by point crystallization defects. The objective of this procedure is to obtain a three-dimensional image of these crystallization defects. It may also be an optical memory, the local index variations of which characterize the recorded bits. The present procedure makes it possible to obtain a three-dimensional image characteristic of the variations of the ordinary index no of the sample.

The average ordinary index no is assumed to be known, as well as the thickness of the blade. The sample is introduced without moving the objectives, so that x, y, z are also known. he is also

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possible to obtain no, L, x, y, z by a modified version of the procedure described in 7.11. Such a modified version, applicable in the case of embodiment 4, will be described in 8.4.3.2.

Obtaining the image of the ordinary index supposes a modification of step 8 of procedure 7.17. , which is the one already described in 7.18.8.2. It also assumes a modification of step 3 of the loop on k, p described in 7.12.2.2., Described below by using the notations used in 7.12.

On note: üe = 're Je 1\ fa fc 1\ Jo #e et #c sont donc définis d'après les vecteurs de la Fig.51. Ils sont tous deux dans le plan de la Fig.52 (non représentés). #e est orienté selon la direction de polarisation ordinaire de l'onde d'éclairage parvenant en E. #c est orienté selon la direction de polarisation ordinaire de l'onde diffractée parvenant au point C.

7. 18.9.1. Principle

We note: üe = 're Je 1 \ fa fc 1 \ Jo #e and #c are therefore defined according to the vectors of Fig. 51. They are both in the plane of Fig. 52 (not shown). #e is oriented in the direction of ordinary polarization of the illumination wave arriving at E. #c is oriented in the direction of ordinary polarization of the diffracted wave reaching point C.

On note et yc les vecteurs déduits respectivement des vecteurs x, et x, par rotation de # dans le plan de la Fig. 52
On note l'angle entre le vecteur 1 et le vecteur obtenu à partir de 7 par une symétrie dont l'axe est la position de l'axe neutre des rotateurs de polarisation lorsque cet axe neutre n'est pas parallèle à

j . On a typiquement # 10 degrés. We denote by ve and Vc the vectors deduced respectively from the vectors iïe and ûc by rotation of 1r 2 in the plane of Fig. 52

We denote by yc the vectors deduced respectively from the vectors x, and x, by rotation of # in the plane of FIG. 52
We denote the angle between vector 1 and the vector obtained from 7 by a symmetry whose axis is the position of the neutral axis of the polarization rotators when this neutral axis is not parallel to

j. We typically have # 10 degrees.

When the electric field vector of the lighting beam (at point F is A0T + .- 1 j, the electric field vector measured at point C is (CQ0A0 + C0] Ai) i + ('. 1 + Ci, -1 j.

#m = (('00 cosae +C01 sinae)T + (CIO cosae +('11 1 sin a,)J- On peut utiliser :

1 = üccosac -vcsinac 1 = ücsinac +vccosac d'ou: w," ~ Cao cosae cosa +C01sinûrecostf<:. + ('10 cosae sinac + CI 1 sina , sina,)Ùl +(-Coo cosae sina;e -Col sinae sinac +Cto cosae cosac +CI, sinae cosac)vc La valeur mesurée au point C suivant la direction du vecteur Ùc est donc: Brn= Coo cosa e cosac +Col sinae cosac + CIO cosae sinac + CI sina sinac When an electric field vector #e = # cos [alpha] e + # sinae is used for the illumination wave, the electric field vector measured at point C is therefore:

#m = (('00 cosae + C01 sinae) T + (CIO cosae + ('11 1 sin a,) J- We can use:

1 = üccosac -vcsinac 1 = ücsinac + vccosac from where: w, "~ Cao cosae cosa + C01sinûrecostf <:. + ('10 cosae sinac + CI 1 sina, sina,) Ùl + (- Coo cosae sina; e - Col sinae sinac + Cto cosae cosac + CI, sinae cosac) vc The value measured at point C following the direction of vector Ùc is therefore: Brn = Coo cosa e cosac + Col sinae cosac + CIO cosae sinac + CI sina sinac

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oil + AI] le vecteur champ électrique mesuré au point C est Qoo.9o +QOAI)il +Qto-lo + 011- ll)- avec # = i cos # + j sine. We denote by Qr1, r2 the value measured at point C for the combination r1, r2 of the control indices of the polarization rotators. When the electric field vector of the lighting beam (at point E) is

oil + AI] the electric field vector measured at point C is Qoo.9o + QOAI) il + Qto-lo + 011- ll) - with # = i cos # + j sine.

A07 +,41J =a'.9o COS 1 E +j-:to tan e + cos # le vecteur reçu au point C est donc:

CQoo-o cos 1 E +Qoy-Ao E+AIJâ+CQIOAo cos 1 E +Qy--ao tanE+.I1JJ soit: (QOOAO +Qol(-Ao sinE+.91 COSE))T + QQOAO tan -, + QOI (-Ao sin e tan e +,4, sin e) ' + QX0A0 cose + 011 tin e +.41 Cette expression est l'équivalent de (C,,A, +C0XAx)i +(oo +C1,.A1 , avec: COO =0oo-ôoisinf Col =60! cose CIO = Qoo tan QOI SIn E tari E + Q10 1 - QI I tan E cos #

Cl = QOI sinE+Qll L'expression de Bm se transforme donc comme suit: #Bw = (Çoo ~2oi sinEcosa cosac +Q0X cosESinae cosa +(Q0] sinE+Q1I)sinae sina +CQoo tan-g01 1 sin e tan e + 010 cos 1 E -Ql, tanEJcosae sinac soit :

Bm = (cosa e cos a +cosae e sin a tan-)O00 +(-sinscosae cosac +cosesinae eosa +sinssinae sina -sinEtanEcosae e sinat)O0l +C COS 1 E cosae sinaJQo (COSE +sinae sina -tanEcosae sinac)QII Cette valeur Bm est la valeur mesurée au point C selon la direction du vecteur , lorsque le vecteur champ électrique de l'onde d'éclairage est orienté selon sue. Du fait de la définition des vecteurs ùe et tu, Bm est la The relation defining a is reversed in: # = # 1 / @ = # tan # cos # When the electric field vector of the lighting beam is

A07 +, 41J = a'.9o COS 1 E + j-: to tan e + cos # the vector received at point C is therefore:

CQoo-o cos 1 E + Qoy-Ao E + AIJâ + CQIOAo cos 1 E + Qy - ao tanE + .I1JJ either: (QOOAO + Qol (-Ao sinE + .91 COSE)) T + QQOAO tan -, + QOI ( -Ao sin e tan e +, 4, sin e) '+ QX0A0 cose + 011 tin e +.41 This expression is the equivalent of (C ,, A, + C0XAx) i + (oo + C1, .A1, with: COO = 0oo-ôoisinf Col = 60! cose CIO = Qoo tan QOI SIn E tari E + Q10 1 - QI I tan E cos #

Cl = QOI sinE + Qll The expression of Bm is therefore transformed as follows: #Bw = (Çoo ~ 2oi sinEcosa cosac + Q0X cosESinae cosa + (Q0] sinE + Q1I) sinae sina + CQoo tan-g01 1 sin e tan e + 010 cos 1 E -Ql, tanEJcosae sinac either:

Bm = (cosa e cos a + cosae e sin a tan-) O00 + (- sinscosae cosac + cosesinae eosa + sinssinae sina -sinEtanEcosae e sinat) O0l + C COS 1 E cosae sinaJQo (COSE + sinae sina -tanEcosae sinac) QII This value Bm is the value measured at point C according to the direction of the vector, when the electric field vector of the lighting wave is oriented according to sue. Due to the definition of the vectors ùe and tu, Bm is the

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sens ou ce sont les valeurs QtJ qui sont mesurées, la valeur de l3nr en étant déduite. value of the ordinary diffracted ray for an ordinary illumination beam. The measure of Bm is indirect to the

meaning that it is the QtJ values which are measured, the value of l3nr being deduced therefrom.

We can express the vector üe in the form: üe = xe eos / 3e -Ye sinie During the diffraction towards the point C, on the same principle as in 7.18.8. 1 .: - the next component xe is transmitted without attenuation, becoming the component on the vector - # c - the next component is transmitted, becoming the component on the vector -il., But is attenuated by a factor cos # or 0 is the angle between the vector fe and the vector fc.

1ï\ = -xc cos P, + #c sin,6, caso On peut utiliser: zc = ü cos ic + ïc sin /3c #c = -uc sin P, z cos/7c On en tire donc: M'r cosy, cosfJe -sinfJc smpe COSB)üc +(- sinfl, cos,6, +cosfJc sin,8, cosO)vc La valeur reçue au point C suivant la direction du vecteur Üc est donc: Br =-cos3 cos,6, - sin,6, sin fl, corso Cette valeur Br est le coefficient d'atténuation qui affecte le faisceau diffracté ordinaire reçu au point C lorsque le faisceau d'éclairage est ordinaire. Dans un modèle de diffusion isotrope, le coefficient Br serait constant. De même qu'en 7.18.8.1., cette atténuation peut être compensée en divisant la valeur mesurée bm par le coefficient Br. The sector received at point C is therefore:

1ï \ = -xc cos P, + #c sin, 6, caso We can use: zc = ü cos ic + ïc sin / 3c #c = -uc sin P, z cos / 7c We therefore derive: M'r cosy, cosfJe -sinfJc smpe COSB) üc + (- sinfl, cos, 6, + cosfJc sin, 8, cosO) vc The value received at point C following the direction of vector Üc is therefore: Br = -cos3 cos, 6, - sin, 6, sin fl, corso This Br value is the attenuation coefficient which affects the ordinary diffracted beam received at point C when the illumination beam is ordinary. In an isotropic diffusion model, the coefficient Br would be constant. As in 7.18.8.1., This attenuation can be compensated by dividing the measured value bm by the coefficient Br.

sin,8, = c' 1 ce I, cos,6, = c ce 1 (YcI l" -Xcrr) \{cMce ** McMce V c y- c 1 1 1 sinac =-@/Mcxc cosac =@/Mcyc

sin3e =- ~tl Af 1, cos/je = 3l ll Yel yz +xet'~) e ce e ce
I I sin [alpha]e = 1/Me xe cosae =- ye 7. 18.9.2. Algorithm
Step 3 of the loop on k, p described in 7.12.12. is therefore modified as follows ante- - the program calculates the following quantities, in addition to those calculated in 7.12.12 .. cos # = xcxe + ycye + zcze

sin, 8, = c '1 ce I, cos, 6, = c ce 1 (YcI l "-Xcrr) \ {cMce ** McMce V c y- c 1 1 1 sinac = - @ / Mcxc cosac = @ / Mcyc

sin3e = - ~ tl Af 1, cos / i = 3l ll Yel yz + xet '~) e ce e ce
II sin [alpha] e = 1 / Me xe cosae = - ye

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si .'le =0 0 on utilise ae =-aeet 16, = f3e = si .11, = 0 on utilise ae =-aect fJe =fJe = si Mce = 0 on utilise fJe = fJe = 0 si .\le = 0 et .'le = 0 et .\tee = 0 on utilise a = ae = /jc = fJe = 0 - le programme calcule le facteur comp[k, p, q] de compensation de l'atténuation si - cos,6, cos,8, - sin fl, sin,6, cos < lim alors conip[k. p q] /titi ou hm est une valeur très lm faible, par exemple lim = 10-10

sinon, complk, p, o1 -cos/j COSRe -sin/i 1 sin/je cos0 sinon, comp ., p. J - cos fJ e cos fJ e - sinfJ e sinfJ e cos 0 Le programme calcule les valeurs: coeJk, p, q, i, 0,0 ~ (cosa e cos a c + cosa sin a, tan ecompk. p. q] coefk, p,g,r,0~1 =-sinecosae e cosa +cosssinaa couac e + sin Esin a e sina - sin- tan e cos a, sin a e )comp[ k, p, <?] coeJk. p, q, i, j 1,0 = C CO I S E cos a sinac)comp[k, p.q] vcos- coef [k, p, q, i, j][ 1, il = (sin a, sin a, - tan e cos a, sin a . compk, p, g Comme en 7.12. les valeurs coeJk, p, q,i, ri , r2 et comp\k, 77,(7] constituent des tableaux qui peuvent être précalculés. - le programme calcule finalement:

fk,p.9 r = , f2r , rZ ][7, /, 7]cotez, p, q,i.1]h r2 ] r1, r2

g [', JI CF acq comp[k,p,q] Bk,p,q 1,1 - ",6 0" An.,.]7t+/1 ou 6p9 est l'écart-type du bruit des capteurs défini comme en 7.18.8. 1. For all of these values, appropriate limit values are used when the denominators are zero:

if .'le = 0 0 we use ae = -aeet 16, = f3e = si .11, = 0 we use ae = -aect fJe = fJe = if Mce = 0 we use fJe = fJe = 0 if. \ le = 0 and .'le = 0 and. \ Tee = 0 we use a = ae = / jc = fJe = 0 - the program calculates the factor comp [k, p, q] for compensation of the attenuation si - cos, 6 , cos, 8, - sin fl, sin, 6, cos <lim then conip [k. pq] / titi where hm is a very low lm value, for example lim = 10-10

otherwise, complk, p, o1 -cos / j COSRe -sin / i 1 sin / i cos0 otherwise, comp., p. J - cos fJ e cos fJ e - sinfJ e sinfJ e cos 0 The program calculates the values: coeJk, p, q, i, 0,0 ~ (cosa e cos ac + cosa sin a, tan ecompk. P. Q] coefk, p, g, r, 0 ~ 1 = -sinecosae e cosa + cosssinaa quack e + sin Esin ae sina - sin- tan e cos a, sin ae) comp [k, p, <?] coeJk. p, q, i, j 1,0 = C CO ISE cos a sinac) comp [k, pq] vcos- coef [k, p, q, i, j] [1, il = (sin a, sin a, - tan e cos a, sin a. compk, p, g As in 7.12, the values coeJk, p, q, i, ri, r2 and comp \ k, 77, (7] constitute arrays which can be precomputed. - the program finally calculates:

fk, p.9 r =, f2r, rZ] [7, /, 7] dimension, p, q, i.1] h r2] r1, r2

g [', JI CF acq comp [k, p, q] Bk, p, q 1,1 - ", 6 0" An.,.] 7t + / 1 or 6p9 is the standard deviation of the noise of the defined sensors as in 7.18.8. 1.

.lI2r1. r2 g, i, corresponds to the measured value which was noted 2, -en 7.18.9.1. the calculation of .f, p, 9 r, j is equivalent to the calculation of the ratio defined in 7.18.9.1.

7. 18.10. Study of samples by reflection only
When the two representations Fo, o and F0,1 do not overlap. it is a priori impossible to determine their phase relation: indeed any phase relation corresponds to a representation

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frequency possible. A possible solution is then to obtain the representation of the object from F0.1 alone. However, the data of F0.1 alone does not make it possible to reliably differentiate the index and the absorptivity. Indeed, a representation validly differentiating the index and the absorptivity must occupy a zone of the space of the frequencies symmetrical with respect to the origin. A good quality representation, comparable to that obtained by confocal reflection microscopy but of higher precision, can be obtained by extracting the modulus of the spatial representation obtained using only F0.1
This method can also be applied to the study of the surface area of thick samples through which the beam is poorly transmitted. In this case, the approximation that the illumination is roughly constant in the observed area of the sample is only observed in the superficial area adjacent to the microscope objectives, and when the illumination beam and the wave coming from the object are transmitted by the same objective The only reliable part of the frequency representation obtained is therefore F0.1 if the upper face of the object is observed, or F1.1 If the lower face of the object is observed As previously, we can extract the modulus of the spatial representation obtained by using only F0,1 or / - ,,
Similarly, this method can be used for the study of the surface of strongly opaque objects.

It is also possible to construct a degraded version of the microscope according to this principle. having only one objective and therefore functioning only by reflection. The adjustment phase must then be adapted so as not to require a second objective. It is also possible to use a complete system during the adjustment phase and only then remove the second objective.

7. 19. Use of microscope objectives of suitable nominal index
In all of the embodiments it is possible to use standard microscope objectives. These lenses have a nominal index nv close to that of glass. They are designed to work with an immersion liquid and a coverslip of index nv. These objectives will give good results if the observed sample has an average index close to nv or is thin. If the observed sample consists mainly of water, index 1.33, and if the aperture of the objective is 1.4, then the total thickness of the sample must be sufficiently less than the width total of the generated image. If it is too high, the three-dimensional representation obtained may be distorted. Indeed, the spherical aberration caused by the thickness of the sample can then become such that the wave coming from an objective can only be received by the # objective opposite for a small part of the frequencies used. .

A microscope objective is designed to use an optical liquid of a given index, the index of the optical liquid having here been called the nominal index of the objective. It is also designed to use a coverslip of given index and thickness, the index of the slide not necessarily being equal to the nominal index of the objective. If we assume the average index of the object equal to the nominal index of the objective,

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the objective allows compensation of the spherical aberration due to the coverslip, which is independent of the position of the object.

If, on the other hand, the nominal index of the objective differs from the average index of the object, the variations in position of the object cause a variation in the thickness of the layers corresponding respectively to the object and to the optical liquid. The induced spherical aberration therefore depends on the position of the object and therefore cannot be compensated by the objective, a compensation valid for a position of the object no longer being valid for another position. This problem has no effect on obtaining two-dimensional images, which is usual with conventional microscopes, and in which the index of the sample does not intervene. On the other hand, it is inconvenient for the observation of three-dimensional images of a thick sample.

One solution to this problem is to use an objective whose nominal index is close to the average index of the observed sample.

If the observed sample consists essentially of water, the optical liquid may be water or a liquid with a stabilized index close to that of water. The objective can be designed by usual optical calculation methods, taking into account the index of the optical liquid and the need to compensate for the aberration due to the blade. This design can be facilitated by the use of a coverslip made of Tcflon (polymer manufactured by the company DuPont), the index of which is close to that of Peau and which therefore induces a low aberration.

If the observed sample is a birefringent crystal of high index as in the case of optical memories, the nominal index of the objective should be close to that of the crystal, which implies the use of an optical liquid of high index, the coverslip having to be of index close to that of the crystal observed or possibly being able to be suppressed.

Objects for immersion in water are, for example, manufactured by the company Zeiss.

7. 20. Use of microscope objectives affected by spherical aberration.

Fig. 90 represents the plane (6105) whose image is formed by the microscope objective at (6107) and the image focal plane (6106) of the objective We denote by B ([alpha]) the image point, in the plane focal image of the objective, of a beam forming in the object an angle α with the optical axis.

The present variant consists in using objectives designed so as to verify only the following constraints: (1) - The spherical aberration affecting the image formed in the image plane of the objective must remain less than a fraction of the diameter of this image .

(2) - The image, in the image focal plane, of a beam which is parallel in the observed object, must be point.

(3) - The distance between point B ([alpha]) and point B (0) must be proportional to sin a.

An objective respecting only these constraints is easier to design than a conventional objective. This simplification of the constraints imposed by the objective makes it possible to increase the working distance, which makes it possible to place the object between thick blades. It can also make it possible to increase the openness of the objectives, thus making it easier to respect the condition of overlapping representations.

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partial frequencies. An objective of this type can consist, for example, of an aplanatic / achromatic Nikon 1.4 aperture condenser associated with an achromat making it possible to adjust the magnification thereof. Fig. 89 shows the principle of such an association. The Nikon condenser is intended for parallel incident light. The beam coming from a point (6104) of the observed object is therefore parallel to the output of the condenser (6102). An achromat (6101) is used to make it converge again to a point (6103). If the focal length of the condenser is fc and if the focal length of the achromat is fa then the magnification of the whole is fa / fc and the distance between the achromat and the image plane, where must be placed the
Jc diaphragm, is fa.

Conditions (2) and (3) must be interpreted as meaning that the deviations from the punctuality or the positional errors of the point in the image focal plane are of an amplitude less than the diameter of the corresponding diffraction spot, which is approximately with:
Npix - Npix the number of sampling pixels of the frequency plane images used.

- D the diameter of the image formed in the image focal plane of the objective.

An objective meeting the constraints (1) to (3) can be designed using an optical computing program. In this case, the program determines the optical paths. In particular, it can determine the length of the optical path of the ray between point a and point B ([alpha]). This length will be denoted chem (sin [alpha]).

( "':' 27r [ 1. ( JV F plX J2 2 . N pu: J2]] exp " Tchem K 2 2
Ce qui peut être réalisé en prenant en compte ce déphasage dans la fonction de compensation des aberrations obtenue en 7.16. Si la grandeur chem(sin[alpha]) ne peut pas être connue par un calcul optique, elle peut également être déterminée par un processus de mesure
Dans les explications qui suivent, la grandeur chem(sin[alpha]) sera toujours utilisée sous forme fonctionnelle. Toutefois il est clair qu'elle peut en pratique se présenter sous forme de tableaux, des méthodes de suréchantillonnage / sous-échantillonnage pouvant être utilisées pour l'obtenir sous forme de The phase shift, in the image focal plane, of the corresponding beam, is then 2 # chem (sin a)
This phase shift can be compensated by multiplying the coordinate point (i, j) of the frequency plane image by:

("':' 27r [1. (JV F plX J2 2. N pu: J2]] exp" Tchem K 2 2
This can be achieved by taking this phase shift into account in the aberration compensation function obtained in 7.16. If the magnitude chem (sin [alpha]) cannot be known by an optical calculation, it can also be determined by a measurement process
In the explanations which follow, the quantity chem (sin [alpha]) will always be used in functional form. However, it is clear that it can in practice be presented in the form of tables, methods of oversampling / subsampling being able to be used to obtain it in the form of

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tables of different dimensions or with different sampling pitches. The objectives (2217) and (2219) must in all cases be identical to each other.

The use of objectives verifying only the conditions (1) (2) (3) implies certain modifications of the method used.

7. 20.1. Modification of the method for calculating the Kp coefficients described in 7.6.

Because there is a large spherical aberration, it is not possible to focus the image on the micrometer as indicated in 7.6. The focusing procedure and the formula for calculating Kp from the micrometer image are therefore eliminated and the Kp coefficients are calculated directly from the frequency image.

The object is a micrometer illuminated by a plane wave and characterized by the Dreel distance between two successive graduations. The wave from the object is of maximum intensity for angles with respect to the optical axis verifying sin [alpha] = n # v where n is an integer. The corresponding spatial frequencies therefore have as a Dreel component along the horizontal axis: n / Dreel Moreover the frequency step on the image S [p, i, j] is Dreel
1 Kp # v
To measure the coefficient Ko, the objective micrometer is used as an object and the FEG and FRD beams are used. From the sensor (2239) an image S [0, i, j] is obtained by the procedure described in 7.5. This image consists of a central point formed by the direct illuminating wave and of a series of aligned points corresponding to the different frequencies for which the wave coming from the object is maximum. These aligned points are better visible if we let the sensor saturate for the central frequency. In this image, we measure the distance in pixels Dfr between two points separated by Nfr intervals.

On a, compte tenu des considérations précédentes: ## = jr soit avec Ko = nreernr La K0#v Dreel #vNfr longueur d'onde à considérer ici est la longueur d'onde dans le matériau, supposé être d'indice égal à l'indice nominal nv de l'objectif soit : #v = # . On a donc finalement: nv nv Drel Dfr K0 =

0 ii Xfr K1 est mesuré par un processus symétrique à partir du capteur (2229). Dfr Nfr Dreel Dfr

We have, taking into account the previous considerations: ## = jr or with Ko = nreernr The K0 # v Dreel #vNfr wavelength to be considered here is the wavelength in the material, supposed to be of index equal to l nominal index nv of the objective is: #v = #. We therefore finally have: nv nv Drel Dfr K0 =

0 ii Xfr K1 is measured by a symmetrical process from the sensor (2229).

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7.20.2. Modification of the procedure for obtaining the relative coordinates of the objectives, described in 7.9.1.

When the procedure described in 7.9.1. is applied, the image obtained on the CCD (2239) is affected by a phase shift double of that which would affect the wave coming from a point of the sample.

Indeed, the FRGI beam crosses two objectives instead of one. This shift, which would be nonexistent if the objectives were devoid of spherical aberration, must be compensated for in order to obtain a Frec function from which the program described in 7 8 can be applied.

2;r lypix ;,lpix 2 Frec['-j] ( 2-chem # J[' 2 H ) 2 ]J Free[l.l] Free[l,l]eXP -2;:chem Ka
7. 20.3. Modification de la procédure de calcul de wpdécrite en 7.15.2. Before determining the x, y, z coordinates using the program described in 7. 8., the resulting Frec array must therefore be modified as follows:

2; r lypix;, lpix 2 Frec ['- j] (2-chem # J [' 2 H) 2] J Free [ll] Free [l, l] eXP -2;: chem Ka
7. 20.3. Modification of the wp calculation procedure described in 7.15.2.

In order to be able to calculate wp, it is essential to compensate, for each plane frequency image, the phase shifts due to the spherical aberrations of the microscope objectives.
In the block (-1002) of Fig. 57, an additional step 1.4. must be added after step 1.3.

,fsk afsk [ 2 21r Npix N d Cr 2d , +CJ )2
7. 20.4. Modification du calcul de la fonction de compensation des aberrations décrit en 7.16. Step 1.4: the program traverses the indices i, j by performing:

, fsk afsk [2 21r Npix N d Cr 2d, + CJ) 2
7. 20.4. Modification of the calculation of the aberration compensation function described in 7.16.

The spherical aberration of the objectives is compensated by a corresponding modification of the aberration compensation function Dp.

P JJ Dsp [1, 2;r JJ N K kr N) 2 # (KpNe #(2) + (2)
7. 20.5. Mesure de la fonction chem
Si la fonction chem n'est pas connue par utilisation d'un programme de calcul optique, elle peut être mesurée par le microscope. Cette mesure doit être effectuée immédiatement après la mesure des coefficients Kp. Pour réaliser cette mesure on utilise les faisceaux FRGI et FRD. On utilise d'abord la procédure décrite en 7.3.3.1pour calculer l'image dans le domaine spatial et évaluer sa ponctualité et la After step 1 of the procedure described in 7.16. it is necessary to add an additional step: step 1a: the program traverses all the indices i, j by performing the operation

P JJ Dsp [1, 2; r JJ NK kr N) 2 # (KpNe # (2) + (2)
7. 20.5. Chem function measurement
If the chem function is not known by using an optical computing program, it can be measured by the microscope. This measurement must be carried out immediately after the measurement of the Kp coefficients. To carry out this measurement, the FRGI and FRD beams are used. We first use the procedure described in 7.3.3.1 to calculate the image in the spatial domain and evaluate its punctuality and the

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.ri 2- , ,N' pix2 NP'A2 50, i , = exp 2 chem Ci - NZ'x l J 2 + - r yx L ' -/J 2;:chem Ko -) 7
A partir du tableau S mesuré il est possible de reconstituer la fonction chem. Une manière simple d'obtenir cette fonction, pour un ensemble de points d'échantillonnage indicés par l'entier p # K, par l'équation

chem p1 1 Ar 2 'j (Kpl 2 21r =1 SCO,i-1+ Nprx 2 ,OJ 21r L.J .S'0,;-I+#,0 l=t O,i pour 1 # p # K et chem(0)=0, ou Arg désigne l'argument et prend des valeurs entre -# et #. position of its center. The position of the objectives is then adjusted to have the most punctual image possible and so that this image is perfectly centered. The image received on the sensor (2239) is then determined using the procedure described in 7. 5. As in 7.20.2., The image is affected by a phase shift double of that which would affect l 'image of a point of the object and we therefore have approximately:

.ri 2-,, N 'pix2 NP'A2 50, i, = exp 2 chem Ci - NZ'x l J 2 + - r yx L' - / J 2;: chem Ko -) 7
From the measured S table it is possible to reconstitute the chem function. A simple way to obtain this function, for a set of sampling points indexed by the integer p # K, by the equation

chem p1 1 Ar 2 'j (Kpl 2 21r = 1 SCO, i-1 + Nprx 2, OJ 21r LJ .S'0,; - I + #, 0 l = t O, i for 1 # p # K and chem (0) = 0, where Arg is the argument and takes values between - # and #.

The values of chem are obtained here only from measurements taken on a horizontal line. It is possible to use more sophisticated methods to reduce the effect of local disturbances by filtering, by taking into account all the points and not only those located on such a straight line.

The chem function thus obtained can be presented in the form of a table and oversampled or downsampled as has been said above.

7. 21. Use of objectives exhibiting spherical aberration and frequency distortion.

The present variant consists in using objectives verifying only the properties (1) and (2) seen in 7.20, i.e.: (I) - The spherical aberration affecting the image formed in the image plane of the objective must remain less than one fraction of the diameter of this image.

(2) - The image, in the image focal plane, of a beam which is parallel in the observed object, must be point.

Such a lens can be made in the same way as the previous one, but it can then be used in wider conditions, for example with a higher number of pixels. It can also be made in a simpler way than the previous one
The fact that we have freed ourselves from the property (3) makes it possible to further facilitate the construction of the objective. On the other hand, the compensation of the aberrations induced by the non-respect of property (3) entails an additional complexity of the algorithms. The non-respect of property (3) results in the fact that the coefficient of proportionality between the coordinates in pixels and the horizontal components of the

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spatial frequency is not constant. The coordinates i and in pixels of the points obtained on the CCD sensor must be multiplied by a coefficient A (r) depending on the distance in pixels r between the point considered and the optical center. The method used therefore differs from that described in 7.20. by the following points: - a specific procedure is used to determine A (r).

- the plane frequency image which was obtained directly from the intensities received at each point of the CCD sensor must be modified before it can be used, this in each step of the procedure where it is used.

optique. On a alors: 4(Dn+Dn+l) ~~ ##(D, - D). Cette équation donne les valeurs de.-1 en un optique. alors.. Div Dn+l - Cette equatlon donne les valeurs DN nombre limités de points et une méthode de suréchantillonnage doit être utilisée pour obtenir la valeur de, en un nombre suffisant de points. 7.21.1. calculation of A (r) @
To determine the coefficient A (r), an objective micrometer is used as an object. The point of direct impact of the illumination beam must imperatively coincide with the optical center. As shown in Fig. 91 the image obtained on the CCD sensor in the absence of a reference wave consists of a central point P0 coincident with the optical center and a series of aligned points of intensity less than Po. We denote Pn those of these points which are on a given half-line originating from P0, the maximum value of the index n being denoted N. We denote by Dn the distance in pixels between the point Pn and the center

optical. We then have: 4 (Dn + Dn + l) ~~ ## (D, - D). This equation gives the values of. -1 in an optic. then .. Div Dn + 1 - This equation gives the DN values a limited number of points and an oversampling method must be used to obtain the value of, at a sufficient number of points.

7. 21.2. Modification of the frequency plane images obtained.

comme indiqué en 7.5. Sbrul L 1 doit être modifié pour générer un tableau Sjm [l, 1] qui correspondra véritablement à l'image plane en fréquence. Cette modification peut être effectuée comme suit

- génération d'un tableau SI, de dimensions NsurX1Ysur avec par exemple Vsur = 2048 . Ce tableau est initialisé à 0 puis le programme effectue, pour i et j allant de 0 à :'prx -1: Sl aCi ; .rur 1 ,C j .sur 1 - Sbrut It. J V ' prx pur - Transformation de Fourier inverse du tableau SI menant à un tableau S2. We denote by Sbrut [i, j] the table representing a plane frequency image obtained for example

as indicated in 7.5. Sbrul L 1 must be modified to generate an array Sjm [l, 1] which will truly correspond to the frequency plane image. This modification can be done as follows

- generation of an SI table, of dimensions NsurX1Ysur with for example Vsur = 2048. This array is initialized to 0 then the program performs, for i and j ranging from 0 to: 'prx -1: Sl aCi; .rur 1, C j. on 1 - Sbrut It. JV 'prx pure - Inverse Fourier transformation of the SI array leading to an S2 array.

S3y, J, - 52Ct ~ Rirx + '' r j ~ t'x + ,'y sur S'3[ sur. 'sur 2 - Extraction of the central part of array S2, to obtain an S3 array of dimensions Npix x .Vpix. The program performs, for i and j going from 0 to Npix - 1:

S3y, J, - 52Ct ~ Rirx + '' rj ~ t'x +, 'y on S'3 [on. 'out of 2

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- transformation de Fourier du tableau 53. Le tableau ainsi obtenu est le tableau S Jin [1, 1] qui constitue l'image plane en fréquence devant être utilisée dans l'ensemble des opérations.

- Fourier transformation of table 53. The table thus obtained is the table S Jin [1, 1] which constitutes the plane frequency image to be used in all the operations.

All the raw frequency plane images obtained in each step of the three-dimensional image adjustment and calculation procedure must be modified in this way before being incorporated into the calculations.

8. Fourth embodiment (preferred mode)
This embodiment is considered to be the best embodiment because in the visible domain it is the one which allows the best performance in terms of speed and image quality.
8.1. Principles
The fourth embodiment differs from the third - by the use of a different beam deflection device - by the introduction of an additional device making it possible to suppress the direct wave reaching the CCDs to avoid or limit the effect. saturation.

- by the fact that the sampling is 'regular', that is to say that the point image of a lighting beam on the CCD coincides with the center of a pixel of the CCD.

The devices for deflecting the beam and suppressing the direct wave are based on the use of a spatial modulator (SLM: spatial light modulator) marketed by the company Displa) tech. This consists of a matrix of 256x256 elements each functioning as an independent polarization rotator. It works in reflection, that is to say that the light incident on the SLM is reflected with a modified polarization, said modification of polarization being different at each point of the matrix It exists in two versions: one intended for the amplitude modulation, in which for one of the control voltages, the neutral axis of the ferroelectric liquid crystal (FLC: ferroelectric liquid crystal) is oriented in the direction defined by one of the axes of the matrix, and another intended for modulation phase, in which the two possible positions of the neutral axis of the FLC are symmetrical with respect to one of the axes of the matrix.

Carrying out regular sampling and having good control of the path of the beam also presupposes an appropriate use of the lenses.

8. 1.1. Control of the beam path.

When a plane beam but not directed along the optical axis moves away from its point of origin, it moves away from the optical axis and can become unusable. Fig. 67 illustrates a method making it possible to control the position of such a beam with respect to the optical axis. A parallel beam (4800) from a plane (4801) must be used in a plane (4804) far from (4801). If it propagates in a straight line, it moves away from the optical axis and becomes unusable (4805).

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The lenses (4802) and (4803) have the same focal length / The plane (4801) is the object focal plane of (4802). (4804) is the image focal plane of (4803). The object focal plane of (4803) is coincident with the image focal plane of (4802) and represented by the dotted lines (4806).

In the plane (4801) the beam (4800) is parallel and centered on the optical axis, that is to say that its intersection with this plane forms a disc centered on the optical axis. Such a plan will be called a space plan and denoted by the letter E.

In the plane (4806) the beam is point, ie its intersection with the plane is practically reduced to a point. Such a plan will be called a frequency plan and denoted by the letter F
In the plane (4804) the beam is again centered and parallel. This plan is therefore a new space plan. It is the image of the plane (4801) by the optical system made up of the lenses (4802) and (4803).

The device makes it possible to reform in the plane (4804) a beam equivalent to that present in the plane (4801), but symmetrized with respect to the optical axis.

By changing the focal length of the second lens as in Fig. 68, it is possible to modify the angle of the beam with respect to the optical axis and its section. The focal length of the first lens is f1, that of the second lens is f2, the distance between the two lenses is f1 + f2. The angle of the beam with respect to the optical axis is multiplied by f1 and the cross section of the beam is multiplied by f2 f2 f1 8.1.2. Beam deflection device
A direction at the output of the deflection device is equivalent to a given spatial frequency and the terms “frequency” or “angle” will be used in the following to define a deflection.

de ps. sin a varie de 0 à - par pas de - soit au total S valeurs possibles en excluant le zéro Ce
2ps Nsps 2 principe est appliqué pour générer un faisceau de direction donnée. Cependant ce dispositif simple n'est pas suffisant pour les raisons suivantes: - On cherche a générer une seule fréquence et il faut donc ensuite supprimer un des deux faisceaux générés, par exemple (4602) - Le faisceau issu de ce système de modulation simple est bruité, en ce sens qu'en plus de la fréquence correspondant au maximum d'éclairement de nombreuses fréquences parasites sont présentes
Pour supprimer les fréquences parasites et le faisceau symétrique, on utilise un système dont le schéma de principe est utilisé Fig.65. Sur ce schéma, on a représenté les SLM comme s'ils fonctionnaient par transmission, et on n'a pas représenté les polariseurs associés à ces SLM. Un faisceau plan (4611) The beam deflection device uses a phase SLM, the entire surface of which is illuminated by a flat beam. When a crenal phase profile (4601) like that shown in Fig 64 is applied to such a surface, the long-distance diffracted intensity is maximum for the angles a and -a or a is such that h = 3/2 is d sin a = # / 2. These two angles define two symmetrical diffracted beams (4602) and (4603) from the SLM. The number of pixels of the SLM used being Ns and the pitch (distance between two pixels) # # N

from ps. sin a varies from 0 to - in steps of - i.e. a total of S possible values excluding zero Ce
2ps Nsps 2 principle is applied to generate a beam of given direction. However, this simple device is not sufficient for the following reasons: - We try to generate a single frequency and we must then remove one of the two beams generated, for example (4602) - The beam from this simple modulation system is noisy, in the sense that in addition to the frequency corresponding to the maximum illumination, many parasitic frequencies are present
To suppress parasitic frequencies and the symmetrical beam, a system is used, the block diagram of which is used in Fig. 65. In this diagram, the SLMs have been represented as if they were operating by transmission, and the polarizers associated with these SLMs have not been represented. A flat beam (4611)

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incident on a phase SLM (4612) operating as indicated above is diffracted in two directions shown in solid and dotted lines. (4612) is in the object focal plane of a lens (4613). In the image focal plane of (4613), an angle beam given at the output of (4612) gives a point image. The object focal plane of the lens (4612) is a space plane, and the image focal plane of (4612) is a frequency plane. In the frequency plane, we place: - a diaphragm (4615) whose function is to stop the symmetrical beam (in dotted lines) - an SLM (4614) whose function is to suppress the parasitic frequencies. When the SLM (4612) is commanded to generate a given frequency, that frequency corresponds to a point on the SLM (4614). This point is controlled to pass the beam, and the other points of the SLM (4614) are controlled to stop the beam. The parasitic frequencies are therefore suppressed.

A second lens (4616) then again transforms the point obtained in the frequency plane into a corresponding direction at the output of the device.

8.1.3. Direct wave suppression device.

The wave having passed through the objective and reaching the CCD presents frequencies of high intensity around the point of direct impact of the beam. In the previous embodiment, this caused saturation of the CCD when low beam attenuation was used.

To eliminate or attenuate this saturation effect, a device is used, the principle of which is shown in FIG. 66, on which the SLM is represented as if it were operating in transmission, and on which the polarizer associated with the SLM is not represented.

The wave coming from the object and having passed through the objective is filtered in an image plane by the diaphragm (4700). A lens (4703) makes it possible to form in its focal plane image, which constitutes a frequency plane, a frequency image of this wave. In the previous embodiment, a CCD was placed directly in this frequency plane. In the present embodiment, an SLM (4704) is placed therein. The direct beam (4702), not deflected by the sample, is shown in dotted lines. Its image on the SLM is punctual. By darkening the corresponding pixel, and possibly a few nearby pixels, this point of intense illumination is eliminated. The other pixels of the SLM are left in the pass-through position, which allows a ray (470 1) of a different frequency to pass through the SLM.

However, the SLM is not a 'perfect' system in the sense that in the area where it is left transparent, it is in fact a 'grid', each pixel being passed but some obscured space being left between two pixels. This grid diffracts the rays passing through it, generating unwanted diffracted rays which are superimposed on the useful beam. A dotted line (4710) shows a possible direction of this beam at the output of the SLM (4704). A lens (4705) allows from the beam having crossed (4704) to reform a space plane identical to that in which is placed (4700). In this plane of space the unwanted rays diffracted by (4704) lie outside the image of the diaphragm (4700). A diaphragm (4706) placed in a plane of space and the opening of which coincides with the image of the opening of the diaphragm (4700) therefore makes it possible to eliminate these diffracted rays.

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A last lens (4708) makes it possible to reform a frequency plane in which the CCD (4709) is placed.

8.1.4. Obtaining regular sampling.

In the third embodiment, the values of ni, nj, nk obtained at the end of operation 1 of step 3 of the imaging procedure described in 7.17.2 are not whole. Integers being necessary in the remainder of the algorithm, the closest integer is taken for each of these values. However, this constitutes an approximation which can result in disturbances on the three-dimensional image generated. In the present embodiment, the optical system is provided so that said values of ni and nj are practically whole, that is to say so that there is regular sampling along the axes ni and nj. The following sampling nk remains non-regular, nevertheless this method greatly reduces the disturbances.

A given lighting wave produced by the beam deflection system produces on the one hand a direct beam going to strike one of the sensors and on the other hand an inverse indicator beam going to strike the other sensor. Conversely, a given pixel of a sensor can be reached by a direct beam produced by one illuminating wave or by an inverse indicator beam produced by another illuminating wave.
For there to be regular sampling, each illumination wave used must produce a direct beam and an inverse beam each arriving at the center of a corresponding pixel of the corresponding CCD, the coordinates of the pixel reached by the direct beam on a CCD being the same as those of the pixel reached by the reverse indicator beam on the other CCD. To each pixel of the CCD which is in the zone delimited by the aperture of the objectives must correspond two lighting beams for which the pixel is reached respectively by the direct beam and the reverse indicator beam
The frequency representation obtained on the CCD can be transformed in various ways due to the inaccuracies in the characteristics of the system.

- by translation. This translation can be compensated by corresponding displacements of mirrors - by homothety. A variation in the focal length of the lens forming the image on the CCD results in a homothety on this image - by rotation. The part of the system comprising the two objectives, consisting of the assembly (4460) of Fig. 62, detailed in Fig. 63, if it is not perfectly constmite, causes a rotation of the image produced on the CCD.

A homothety applied to the image produced on the CCD invalidates the exact correspondence between a pixel of the CCD, which is fixed, and the impact points of the direct or inverted beam, which are modified by the homothety. To avoid such a homothety, it is necessary to control with precision the focal length of the lens forming the image. A suitable system allows the adjustment of this focal length.

The rotation produced by (4460) is applied only to the direct beam. It can be compensated by a corresponding rotation of the CCD. But this operation shifts the pixels of the CCD relative to the impact points of the reverse beam. It is therefore necessary to perform a rotation

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indicator beam corresponding to reverse to cancel this discrepancy. A suitable system allows this rotation.

8.1.4.1. Adjusting the focal length.

To obtain an optical element whose focal length is adjusted with precision around a central value fc, two lenses of focal length / separated by a distance d are combined.

La valeur de/est alors / = /e + /c(/e " ) Une ensemble de focale fc réglable à ±r est donc constitué de deux lentilles de focale/séparées par une distance d avec: d = 4 fcr

f = f, +Cf, (f7d) La distance focale de l'ensemble est ajustée en faisant varier la distance d. The focal length of the whole is then j = f 2 [1 ~ 12] 2 f @ If we want to adjust fc over a width of ± 1%, that is to say r = 0.01, then we must have d / 2f = r with approximately fc = f / 2, the value of d adopted is therefore: d = 4 fcr

The value of / is then / = / e + / c (/ e ") A set of focal length fc adjustable to ± r therefore consists of two lenses of focal length / separated by a distance d with: d = 4 fcr

f = f, + Cf, (f7d) The focal length of the assembly is adjusted by varying the distance d.

Such doublets are used at various points of the device for similar reasons 8.1.4.2. Rotation adjustment.

To adjust a lighting beam in rotation, a device described in FIG. 69, inserted on the path of the lighting beam in an area where this beam is parallel and therefore defined by its wave vector.

This device consists of a set of mirrors (4901) to (4906). The mirrors (4901) (4902) are fixed.

The mirrors (4903) (4904) (4905) (4906) are integral with one another and the assembly (4910) formed by these mirrors is movable in rotation about an axis (4909). The arrows shown in the plane of the figure represent the wave vectors of the beam at each point of the device.

The transformation of a wave vector by a mirror comprises a vector symmetrization with respect to an axis orthogonal to the plane of the mirror and an inversion of the direction of the vector. The number of mirrors being even the inversions cancel each other out and we are interested here in the symmetrization part. The pair of mirrors (4901) (4902) performs two successive symmetrizations of axes orthogonal to each other, which is equivalent to a single symmetry of axis (4907). Likewise, the pair of mirrors (4903) (4904) performs axis symmetry (4908). The mirrors (4905) (4906) perform two vector symmetries of the same axis, which cancel each other out

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each other. The operation performed by the entire device is therefore composed of an axis vector symmetry (4907) and an axis vector symmetry (4908). Fig. 70 shows, in following view..1, the axes (4907) and (4908). When no rotation of (4910) has been performed, these axes are merged and the compound of the two symmetries is the identity. The beam wave vector is not modified by the device
When an angle rotation α is applied to the assembly (4910), the two axes are offset by an angle α as shown in Fig. 70. The composition of the two symmetries is then a vector rotation of angle 2a.

The system therefore makes it possible to apply to a lighting wave a vector rotation compensating for that due to the assembly (4460).

8. 2. Physical description.

An overall diagram of the system is formed by Figs. 61.62.63. In these figures, the elements directly equivalent to corresponding elements of Figures 27 and 28 are numbered by taking the number of the corresponding element in Figures 27 and 28 and replacing the first two digits by 43. For example 2204 gives 4304. Elements having no direct equivalents in Figures 27 and 28 have numbers beginning with 44. The plane of Figs. 61 and 62 is a horizontal plane, the figures constituting a top view. The elements of the system are fixed on an optical table suitably isolated from vibrations. Fig. 63 shows in several views the part of the microscope containing the objectives, which constitutes a three-dimensional structure.

A laser (4300) polarized in the vertical direction generates a beam whose electric field vector is therefore directed along an axis orthogonal to the plane of the figure. This beam passes through a beam expander (4301). The beam from the expander is then divided into a reference beam and an illumination beam by a semi-transparent mirror (4302).

The illumination beam passes through a diaphragm (4348), a filter (4303) for adjusting its intensity, then a phase shift device (4304) and a beam attenuation device (4305).

(4407). Il traverse ensuite un doublet de lentilles (4 11)(-1-110) du type décrit en 8.1.4. 1. Le plan focal objet de ce doublet coïncide avec le plan focal image de (4407). Le SLM d'amplitude (4412) est placé dans le It then passes through a lens (4401). This lens focuses the beam in a plane or is placed a hole (4402) (pinhole in English) large enough not to disturb the beam, which has the function of partially stopping the reflected beams returning in the opposite direction to the laser. The beam is then reflected on one side of a double mirror (4403). The two reflective sides of (4403) form a right angle. The beam then passes through a lens (4404) whose object focal plane coincides with the image focal plane of (4401), and then goes to a phase SLM (4405). The phase SLM (4405) is placed at the image focus of (4404). The beam reflected by (4405) crosses again (4404) and is reflected by the second face of the double mirror (4403). The beam then passes through a diaphragm (4406) placed at the image focus of (4404) for the beam reflected by (4405), which will be called the second image focus of (4404) It then passes through a lens (4407) whose object focus coincides with the image focus of (4404). The beam then passes through a polarizer (4408). It is then reflected on a mirror (4409) placed a little behind the image focal plane of

(4407). It then passes through a pair of lenses (4 11) (- 1-110) of the type described in 8.1.4. 1. The object focal plane of this doublet coincides with the image focal plane of (4407). The amplitude SLM (4412) is placed in the

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focal objet du doublet (4415)(4416) coïncide avec le plan focal image du doublet (-LI10)(.f-tl I). Il est alors dirigé vers le SLM d'amplitude (4417) qui le réfléchit. Il retraverse alors le doublet (4415)(4416), Il est réfléchi par un miroir (4418), traverse un diaphragme (4419) placé au second foyer image du doublet (4415)(4416), puis traverse un polariseur (4420) et une lentille (4421) dont le plan focal objet coïncide avec le second plan focal image du doublet (4415)(4416). Il parvient alors à un miroir semi-réfléchissant (4307) qui le sépare en un faisceau d'éclairage droit FED et un faisceau d'éclairage gauche FEG. focal plane image of this doublet. The beam having passed through this doublet goes towards (4412) which reflects it.It then crosses the doublet again, then passes through a polarizer (4413) and a diaphragm (4414) placed in the second focal plane image of the doublet (44 10) (44 It ). It then crosses a doublet formed by (4415) and (4416). The plan

object focal plane of the doublet (4415) (4416) coincides with the image focal plane of the doublet (-LI10) (. f-tl I). It is then directed towards the amplitude SLM (4417) which reflects it. It then crosses again the doublet (4415) (4416), It is reflected by a mirror (4418), passes through a diaphragm (4419) placed at the second image focal point of the doublet (4415) (4416), then passes through a polarizer (4420) and a lens (4421) whose object focal plane coincides with the second image focal plane of the doublet (4415) (4416). It then arrives at a semi-reflecting mirror (4307) which separates it into a right light beam FED and a left light beam FEG.

The FEG beam is then reflected by a mirror (4432) and passes through a pair of lenses (4433) (4434) which may, depending on the congestion conditions, be located before or after the mirror (4432). The object focal plane of the doublet (4433) (4434) coincides with the image focal plane of (4421). The beam is then reflected by a mirror (4435) then by an assembly (4436) equivalent to the assembly (4910) of FIG. 69, movable around an axis (4450) and consisting of mirrors (4446) (4447) (4448) (4449). The beam then passes through a beam extinguisher (4437). This beam extinguisher is constructed like the beam attenuator described in 7.2.2. but with an angle 0 zero. The beam then passes through a polarization rotator (4341) and is then separated by the semi-transparent mirror (4325) into a main illumination beam directed towards (4324). which we will also denote by FEG, and a reverse indicator beam directed towards (4342). which we will denote by FEGI. The doublet (4433) (4434) therefore has two image focal planes, one in the direction of the main beam and the other in the direction of the reverse indicator beam.

The lens (4324) is placed in front of the image focal plane of the doublet (4433) (4434) so that the image focal plane of this doublet in the direction of the main beam remains virtual. The lens (4324) forms an image of this focal plane, and this image should be in the plane of the diaphragm (4323).

The image focal plane of this doublet in the direction of the FEGI beam coincides with the object focal plane of a lens (4342). The FEGI beam passes through this lens which focuses it on a mirror (4343) which can optionally be closed by a shutter (4359). The beam reflected by this mirror passes through the lens (4342) and is again reflected by (4325). The FEGI beam then passes through a polarization rotator (4326) then a polarizer (4438). It is then reflected by one face of the double mirror (4439). It then crosses the doublet (4440) (4441) and heads towards the amplitude SLM (4442). The object focal plane of the doublet (4440) (4441) must be confused with an image focal plane of the doublet (4433) (4434). The amplitude SLM (4442) is placed in the image focal plane of the doublet (4440) (4441). The beam reflected by the SLM (4442) crosses the doublet (4440) (4441), is reflected by the second face of (4439), and goes towards a diaphragm (4443) placed in the second focal plane image of the doublet (4440 ) (4441). The beam passes through (4443) then a doublet (4444) (4445), a polarizer (4353), and reaches the CCD (4329) mounted on the camera (4330). The object focal plane of (4444) (4445) coincides with the second image focal plane of the doublet (4440) (4441). The CCD (4329) is placed in the image focal plane of (4444) (4445).

réfléchi par les miroirs (4322)(445I)(4452)(4453). Il traverse l'objectif (4319) puis l'échantillon (4318). The FEG beam passes through the lens (4324) and the diaphragm (4323). It is then successively

reflected by mirrors (4322) (445I) (4452) (4453). It passes through the objective (4319) then the sample (4318).

<Desc / Clms Page number 177>

puis l'objectif (4317). Il est alors successivement réfléchi par les miroirs (4454)(4455)(4456)(4 14) et parvient au diaphragme (4313). Le diaphragme (4323) doit être placé dans le plan ou l'objectif (4319) forme normalement l'image de l'échantillon, soit à 160 mm du col de l'objectif pour un objectif standard Le diaphragme (4313) doit être placé dans le plan ou l'objectif (4317) forme normalement l'image de l'échantillon
Le faisceau FEG traverse alors la lentille (4312) qui est placée de telle manière que, dans le cas ou une lame transparente est utilisée (abscence de perturbations par l'objet), et en sortie de cette lentille, le faisceau soit parallèle. Le faisceau traverse alors le rotateur de polarisation (4338), le polariseur (4423), est réfléchi sur une face de (4424), traverse le doublet (4425)(4426), est réfléchi sur le SLM d'amplitude (4427), retraverse le doublet (4425)(4426), est réfléchi sur la deuxième face de (4424), traverse le diaphragme (4428), le doublet (4429)(4430), le polariseur (4352), et parvient au CCD (4339) monté sur la caméra (4384). L'image du diaphragme (4313) par la lentille (4312) est confondue avec le plan focal objet du doublet (4425)(4426). Le SLM (4427) est dans le plan focal image du doublet (4425)(4426). Le diaphragme (4428) est dans le second plan focal image du doublet (4425)(4426). Le plan focal objet du doublet (4430)(4429) coïncide avec le second plan focal image du doublet (4425)(4426).Le CCD (4339) est placé dans le plan focal image du doublet (4430)(4429).

then the objective (4317). It is then successively reflected by the mirrors (4454) (4455) (4456) (4 14) and reaches the diaphragm (4313). The diaphragm (4323) must be placed in the plane where the objective (4319) normally forms the image of the sample, i.e. 160 mm from the neck of the objective for a standard objective The diaphragm (4313) must be placed in the plane where the objective (4317) normally forms the image of the sample
The FEG beam then passes through the lens (4312) which is placed in such a way that, in the case where a transparent plate is used (absence of disturbances by the object), and at the output of this lens, the beam is parallel. The beam then passes through the polarization rotator (4338), the polarizer (4423), is reflected on a face of (4424), passes through the doublet (4425) (4426), is reflected on the amplitude SLM (4427), crosses the doublet (4425) (4426), is reflected on the second face of (4424), crosses the diaphragm (4428), the doublet (4429) (4430), the polarizer (4352), and arrives at the CCD (4339) mounted on the camera (4384). The image of the diaphragm (4313) by the lens (4312) coincides with the object focal plane of the doublet (4425) (4426). The SLM (4427) is in the image focal plane of the doublet (4425) (4426). The diaphragm (4428) is in the second image focal plane of the doublet (4425) (4426). The object focal plane of the doublet (4430) (4429) coincides with the second image focal plane of the doublet (4425) (4426). The CCD (4339) is placed in the image focal plane of the doublet (4430) (4429).

The straight illumination beam FED passes through a lens (443 1) and is reflected by a mirror (4308).

Depending on the space requirements, the position of the lens and the mirror can be reversed. The FED beam then passes through the beam extinguisher (4422) identical to (4437). then the polarization rotator (43 10). It is separated by a semi-transparent mirror (4311) into a main lighting beam, which will still be denoted FED, and an inverse indicator beam, which will be denoted FEDI.

The FEDI beam then passes through the lens (-1331), is reflected by the mirror (4332), crosses again (433 1), is reflected in the direction of (4338) by the semi-transparent mirror (4311). (4332) can optionally be closed by the shutter (4358). (4332) is in a focal plane of (4331), and the other focal plane of (4331) coincides with the image of (4313) through (4312). The FEDI beam then follows between (4311) and (4339) a path symmetrical to that followed by the FEGI beam between (4325) and (4329).

The main lighting beam FED follows between (4311) and (4329) a path symmetrical to that followed by the main lighting beam FEG between (4325) and (4339).

The reference beam, separated from the illumination beam by the partially transparent mirror (4302), is separated into the right reference beam FRD and the left reference beam FRG by the semi-transparent mirror (4335).

The FRD right reference beam is then reflected by the mirror (4344). then passes through the filter (4356) and the diaphragm (4349). It is then separated by the semi-transparent mirror (4345) into a reference beam directed towards the CCD (4339), which will also be denoted FRD, and an inverse indicator beam, which will be denoted FRDI. The FRDI beam passes through the lens (4346), is focused on the mirror (4347) which reflects it, passes through the lens (4346) and is partially reflected in the direction of (4430). The shutter (4357) optionally makes it possible to suppress this reverse indicator beam.

<Desc / Clms Page number 178>

The left reference beam FRG is reflected by the mirrors (4354) (4336) then passes through a filter (4355), a phase shift device (4351), a diaphragm (4350). It is then separated by the semi-transparent mirror (4328) and a reference beam directed towards (4329). which will also be denoted FRG, and an inverse indicator beam which will be denoted FRGI. The FRGI beam passes through the lens (4381), is focused on the mirror (4382) which reflects it, crosses again in the opposite direction (4381), and is partially reflected by (4328). The shutter (4360) optionally makes it possible to suppress this reverse indicator beam.

To help understanding the diagram, the lighting beam has been shown in solid lines. It passes alternately through frequency planes and space planes, in the sense defined in 8.1.1. In a frequency plane, the beam is focused at one point. In a space plane, it is parallel and 'centered', in the sense it illuminates a circular area symmetrical with respect to the optical axis, not depending on its orientation. The letter (E) appended to the number of an element means that this element is in a space plan. In the absence of an optical element, the letter (E) alone can also designate a space plane. Similarly, the letter (F) designates a frequency plane. We put a letter (E) on the diaphragm (4313). although this diaphragm is not exactly a plane of space: it is the image of this diaphragm by the lens (4312) which is a virtual space plane and which must be understood as designated by the letter E Likewise , the diaphragm (4323) does not exactly correspond to a space plane.

Conversely, the reference beam has been shown in dotted lines. The reference beam is concentrated at a point in the space planes. It is parallel and centered in the frequency planes
Space and frequency planes alternate on the beam path. A successive space plane and frequency plane are always separated by a lens or a doublet. Their succession follows the logic set out in 8.1. A space plane and a frequency plane separated by a lens (or a doublet) always occupy two focal planes of this lens (or of this doublet).

The beam deflection device, the principle of which has been described in 8. 1.2. is implemented by elements corresponding to those of Fig. 65. The SLMs (4612) and (4614) are respectively materialized by the SLMs (4405) and (4412). The diaphragm (4615) is materialized by (4406). The device has been adapted to take into account that SLMs operate in reflection, to include polarizers, and to position the diaphragm (4406) in a different plane from the SLM (4412). The SLM (4417) has been added to perform additional filtering of the illumination wave, thus improving the suppression of parasitic frequencies.

The direct wave suppression device described in 8.1.3. is implemented by elements corresponding to those of FIG. 66. The SLM (4704) corresponds to the SLM (4427). The diaphragms (4700) and (4706) correspond respectively to (4313) and (4428). The CCD (4709) corresponds to (4339). The lens (4703) corresponds to the doublet (4425) (4426). The lens (4705) corresponds to the same doublet crossed in the opposite direction. The lens (4708) corresponds to the doublet (4430) (4429). Symmetric correspondences are valid for the symmetrical part of the microscope.

The doublets used allow an application of the principle described in 8.1.4.1. They consist of two lenses which can be moved together, one of the lenses can also be moved relative to the other.

<Desc / Clms Page number 179>

The system constituted by (4436) realizes the principle described in 8. 1.4.2.

On each polarizer, the passing axis is indicated by a line, representing an axis in the plane of the figure, or a circle, representing an axis in a plane orthogonal to the plane of the figure.

On each SLM, a coordinate system is represented which constitutes the one in which the coordinates of the pixels are evaluated. On each amplitude SLM, we also represent the position of the neutral axis which corresponds to an extinction of the beam, with the same convention as for the passing axis of the polarizers The other possible position of the neutral axis is obtained from the extinguishing position by a rotation of about 40 degrees in one direction or another. On the phase SLM (4405) the two positions of the neutral axis are symmetrical with respect to a vertical axis.

On the polarization rotators, a mark has been indicated. A position of the neutral axis, corresponding to an applied voltage of -5V, is the horizontal axis of the mark. In the other position, the neutral axis is approximately directed along a vector of equal coordinates on both axes.

Polarizers (4408) (4413) (4420) can be Glan-Thomson prisms, which have the advantage of low absorption. However, they cause too large a spherical aberration to be used on the path of the wave coming from the object. The polarizers (4423) (4352) (4438) (4353) are preferably dichroic polarizers made up of a dichroic film held between two sufficiently thin glass plates.

The lenses used can be classic lenses or lenses as described in paragraphs 7. 19 to 7.21. The preferred embodiment consists in using lenses of the type described in 7.20 .. which make it possible to improve the working distance and / or the aperture.

All of the lenses used in the system are achromats or compound lenses, minimizing spherical aberration.

Most of the elements are mounted on positioners allowing precise adjustment of their position. The characteristics of these positioners will be given in 8.5. at the same time as the adjustment procedure. The sample, the positioning characteristics of which are not explained in 8. 5., is mounted on a three-axis positioner in translation.

8. 3. Sizing
It is necessary to specify the focal length of each lens and the aperture of each diaphragm to size the system. For the doublets we will specify the focal length of the doublet f, designates the focal length of the lens (or of the doublet) number t, the lenses being numbered as follows:

<tb>
<tb> index <SEP> i <SEP> number <SEP> of <SEP> the <SEP> lens <SEP> on <SEP> the <SEP> diagram, <SEP> or <SEP>, <SEP> between
<tb> parentheses, <SEP> of <SEP> two <SEP> lenses <SEP> constituting <SEP> a <SEP> doublet
<tb> 1 <SEP> 4401
<tb> 2 <SEP> 4404
<tb> 3 <SEP> 4407
<tb>

<Desc / Clms Page number 180>

<tb>
<tb> 4 <SEP> (4410,4411)
<tb>

5 (-l-115,-1-116)

5 (-l-115, -1-116)

<tb>
<tb> 6 <SEP> 4421 <SEP>
<tb> 7 <SEP> 4431 <SEP> or <SEP> (4433,4434)
<tb> 8 <SEP> (4425,4426) <SEP> or <SEP> (4440,4441)
<tb> 9 <SEP> (4430,4429) <SEP> or <SEP> (4444,4445)
<tb> 10 <SEP> 4312 <SEP> or <SEP> 4324
<tb> It <SEP> 4331 <SEP> or <SEP> 4342
<tb> 12 <SEP> 4346 <SEP> or <SEP> 4381
<tb>
l1 denotes the width of diaphragm number i, the diaphragms being numbered as follows

<tb>
<tb> index <SEP> / <SEP> number <SEP> of the <SEP> diaphragm <SEP> on <SEP> the <SEP> diagram
<tb> 0 <SEP> 4349 <SEP> or <SEP> 4350
<tb> 1 <SEP> 4348 <SEP>
<tb> 2 <SEP> 4406 <SEP>
<tb> 3 <SEP> 4414
<tb> 4 <SEP> 4419
<tb> 5 <SEP> 4313 <SEP> or <SEP> 4323 <SEP>
<tb> 6 <SEP> 4428 <SEP> or <SEP> 4443
<tb>
In addition, the following notations are adopted: pc distance between the centers of two adjacent pixels, on CCD sensors ps distance between the centers of two adjacent pixels, on the phase SLM pf distance between the centers of two adjacent pixels, on SLMs amplitude
Npix number of pixels on a CCD sensor or on an amplitude SLM (these numbers are equal).

Number of pixels on the phase SLM. Ideally we should have Ns = 2Npix but SLMs are not available in any size and we can also be satisfied with Ns = Npix with additional attenuation of the lighting beam. o: numerical aperture of a microscope objective g: magnification of a microscope objective f0: focal length of a microscope objective. do: distance between the lens (4312) and the diaphragm (4313).

The width of the reference beam must be at least: l0 = pc Npix

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Pour éviter une perte de puissance inutile il est préférable d'avoir lo = l, et donc - fui = ps ' f1 pcNpix La largeur du diaphragme (4406), qui laisse passer la moitié des fréquences provenant du SLM (4405) sous

un angle a max est : 12 = f2 sin a max soit avec la valeur de sin a max qui résulte de 8.1.2. 12 = J2
2ps

La partie utile du SLM (4412) doit être l'image du diaphragme (4406) ce qui implique: f4 /2 = Pl X pix f3

A partir des deux équations précédentes on obtient: # #f2 = 2ps p Np, f3

L'onde issue de (4412) présente un angle maximal sin,8r,<,, = 2 . Le diaphragme (4414) doit laisser 2PI passer la totalité de ces ondes et vérifie donc : /3 = 2 sin3m j, soit I3 = f. . The illumination width on (4405) is: psNs = f2 / fl1, from which we derive: f2 / f = psNs / t fi f1 l1

To avoid unnecessary power loss it is preferable to have lo = l, and therefore - fui = ps' f1 pcNpix The width of the diaphragm (4406), which lets half of the frequencies coming from the SLM (4405) pass under

an angle a max is: 12 = f2 sin a max that is to say with the value of sin a max which results from 8.1.2. 12 = J2
2ps

The useful part of the SLM (4412) must be the image of the diaphragm (4406) which implies: f4 / 2 = Pl X pix f3

From the two previous equations we get: # # f2 = 2ps p Np, f3

The wave from (4412) has a maximum angle sin, 8r, <,, = 2. The diaphragm (4414) must let 2PI pass all of these waves and therefore verifies: / 3 = 2 sin3m j, or I3 = f. .

Des équations précédentes on tire: f f6 - 2 z PIN pu: f6 2 o La taille d'image sur le SLM (4427) doit être la même que sur le SLM (4417) d'ou: f6 fi = 1 1 f5 f7

La taille d'image sur la caméra est liée à celle sur le SLM (4427) par: p,'lrpu = 'f9 p f ~,rpu soit. 'f9 = # # f8 f8 pf Les SLM (4412 et (4417) étant de mêmes caractéristiques, on a' f4 = f5 La lentille (4312) doit avoir son plan focal objet confondu avec le plan focal image de l'objectif de microscope, et se trouve à une distance d0 de l'image de l'objectif. On vérifie que ceci impliquef10=gfo+do La distance focale de (4331) ou de (4346) doit être suffisante pour éviter l'aberration sphérique. Pf The width of the diaphragm (4419) is equal to that of the diaphragm (4413) i.e. 1, = l3 Its width is transformed into the width of the object diaphragm (43 12) by: 15 = f7 / f6l3 f6 The width of the object diaphragm ( 4312) is equal to: 1. = # g Npix 2 o

From the previous equations we get: f f6 - 2 z PIN pu: f6 2 o The image size on the SLM (4427) must be the same as on the SLM (4417) hence: f6 fi = 1 1 f5 f7

The image size on the camera is linked to that on the SLM (4427) by: p, 'lrpu =' f9 pf ~, rpu either. 'f9 = # # f8 f8 pf Since the SLMs (4412 and (4417) have the same characteristics, we have' f4 = f5 The lens (4312) must have its object focal plane merged with the image focal plane of the microscope objective , and is at a distance d0 from the lens image We verify that this implies f10 = gfo + do The focal length of (4331) or (4346) must be sufficient to avoid spherical aberration.

f2 =f4 =f5 =f6=f7=f8 =fil =fil2 =f Any set of values satisfying the above equations can in principle be suitable. A particularly simple solution is to pose: pfNpix g
2 o and to impose:

f2 = f4 = f5 = f6 = f7 = f8 = fil = fil2 = f

<Desc / Clms Page number 182>

10 = 15 = 1) = 14 = N plX l2 = f#/2ps l0 = Il = pcNpix La largeur du faisceau en sortie de l'élargisseur de faisceau (4301) doit être légèrement supérieure à l0, la limitation étant effectuée plus loin par les diaphragmes. The other focal lengths are then easily obtained: f3 = g / o # / 4ps f pcNpix f1 = f. rice = psNs f9 = pc / pf f f10 = gfo + do and the diaphragm openings:

10 = 15 = 1) = 14 = N plX l2 = f # / 2ps l0 = Il = pcNpix The width of the beam at the exit of the beam expander (4301) must be slightly greater than l0, the limitation being carried out further by the diaphragms.

8.4.Operating mode
The mode of operation is essentially the same as in the third embodiment.

à .'VS - 1 , l'élément :1 [k, I] correspondant au pixel de coordonnées k, et ayant la valeur 0 pour un pixel de phase négative et la valeur 1 pour un pixel de phase positive. L'état des SLM (4412) et (4417) est donné par un tableau de commande B[k,1] dans lequel k et / varient de 0 à X plX - 1 , l'élément n[k,1] correspondant au pixel de coordonnées k,let ayant la valeur 0 pour un pixel éteint et la valeur 1 pour un pixel allumé. It is therefore described by paragraphs 7.4. to 7.17. and by the variants set out in 7.18. In the case where objectives as described in 7.20 or 7.21 are used, the modifications described in these paragraphs must be applied. The preferred mode is to be understood as using the algorithms described by sections 7.4. to 7.17. without the variants set out in 7. 8. However, some of the solutions described by the variants have their own advantages and the qualifier of preferred mode should not be understood too absolutely. A certain number of differences must however be taken into account with respect to the algorithms described in the third embodiment: SA.1. Beam diverter control
The state of the SLM (4405) is given by a control table A [k, l] in which k and l vary from 0

at .'VS - 1, the element: 1 [k, I] corresponding to the pixel of coordinates k, and having the value 0 for a pixel of negative phase and the value 1 for a pixel of positive phase. The state of the SLMs (4412) and (4417) is given by a control table B [k, 1] in which k and / vary from 0 to X plX - 1, the element n [k, 1] corresponding to the pixel of coordinates k, let having the value 0 for an off pixel and the value 1 for an on pixel.

To obtain a frequency characterized by the indices (i, j):

<Desc / Clms Page number 183>

B avec BI) r k ,1] = 0 en tout point sauf en i j ou on a BI} fi, jl = 1 - on applique au SLM (4405) un tableau AI) approprié, soit : Au [k, I] = E .' p,x 1 (ka + 1) + 1(j + 1)) %2 ([Npix @ ou E désigne la partie entière et %2 signifie modulo 2. - we light the pixel with coordinates i, j on the SLMs (4412) and (4417) i.e. we use an array

B with BI) rk, 1] = 0 at all points except in ij where we have BI} fi, jl = 1 - we apply to the SLM (4405) an appropriate table AI), that is: Au [k, I] = E . ' p, x 1 (ka + 1) + 1 (j + 1))% 2 ([Npix @ or E denotes the integer part and% 2 denotes modulo 2.

l'indice p avec/5=0 pour (4339) et p=1 pour (4329). Pour la commande des rotateurs de phase inclus dans les extincteurs de faisceau (4422) et (4437) un bit de commande nul correspondà une tension appliquée de 5V (position ouverte) et un bit de commande à1 correspond à une tension appliquée de -5V (position fermée).

The 'control word' used in the third embodiment is therefore here constituted by the concatenation of the control tables of the SLMs (4405) (4412) (4417) and the control bits of the phase rotators of (4422) and ( 4437). As previously, the directly illuminated sensor is designated by

the index p with / 5 = 0 for (4339) and p = 1 for (4329). For the control of the phase rotators included in the beam extinguishers (4422) and (4437) a zero control bit corresponds to an applied voltage of 5V (open position) and a control bit to 1 corresponds to an applied voltage of -5V ( closed position).

<tb>
<tb> array <SEP> of <SEP> command <SEP> of <SEP> SLM <SEP> (4405) <SEP> Aijk, l] = E <SEP> ({1 / @ (k (i + 1) + l (j + 1))}% 2)
<tb>

A1J[k,l]-E l\, , plX (k(1+I)+I(l+I)) Votableau de commande du SLM (4412) Bu fi, 1] ] = ! BI} [k,l] = 0 si (k,t)":(I'l) mot de commande tableau de commande du SLM (4417) B fi, il = COM[P, ij] BI} [k,l] = 0 si (k,l)":(I'l)

A1J [k, l] -E l \,, plX (k (1 + I) + I (l + I)) Your SLM control panel (4412) Bu fi, 1]] =! BI} [k, l] = 0 if (k, t) ":( I'l) SLM control panel command word (4417) B fi, il = COM [P, ij] BI} [k, l ] = 0 if (k, l) ":( I'l)

<tb>
<tb> bits <SEP> of <SEP> command <SEP> of the <SEP> rotators <SEP> of <SEP> (4422) <SEP>#.<SEP>#
<tb> bits <SEP> of <SEP> command <SEP> of the <SEP> rotators <SEP> of <SEP> (4437) <SEP> p, p
<tb>

The command word thus formed is substituted in all of the 7.4 procedures. to 7.17. to that which was constituted as indicated in 7.2.4.

8. 4.2. Use of the direct wave suppression system.

les mêmes indices p=0 etp= 1. Dans la procédure décrite en 7.12.2.1 , phase l, lors de l'acquisition d'un couple d'images élémentaires, il est nécessaire de commander également ces SLM. La valeur d'un élément C[k,l] du tableau de commande utilisé pour un tel SLM dépend de l'indice du SLM, des indices c et /? de l'image en cours d'acquisition, et des indices i et/ correspondant au point du capteur éclairé directement

par le faisceau d'éclairage soit <-/[,,7c[A,].Jc[A'./)]].-[<y,,/c[A.L7f',. Il est donné par le tableau suivant, our désigne un 'rayon d'extinction' que l'on peut par exemple prendre égal à 2.

The SLMs (4427) and (4442) are respectively associated with the sensors (4339) and (4329) and indexed by

the same indices p = 0 and p = 1. In the procedure described in 7.12.2.1, phase 1, during the acquisition of a pair of elementary images, it is necessary to also control these SLMs. The value of an element C [k, l] of the control panel used for such an SLM depends on the index of the SLM, the indexes c and /? of the image being acquired, and indices i and / corresponding to the point of the sensor directly illuminated

by the lighting beam is <- / [,, 7c [A,]. Jc [A './)]] .- [<y ,, / c [A.L7f' ,. It is given by the following table, our designates an 'extinction radius' which can for example be taken equal to 2.

<tb>
<tb> index <SEP> c <SEP> 2 <SEP> other <SEP> (attenuation <SEP> not <SEP> maximum)
<tb> index <SEP> of <SEP> SLM <SEP> p <SEP> p
<tb>

<Desc / Clms Page number 184>

indices*,/ k -i2 +l -2 > rZ (k -,f +(! - j)2 <r2 valeur de l'élément du tableau C'[k,l] 1 1 0 8.4.3. Utilisation de l'échantillonnage régulier.

indices *, / k -i2 + l -2> rZ (k -, f + (! - j) 2 <r2 value of the element of array C '[k, l] 1 1 0 8.4.3. Using regular sampling.

Ia[q, p,i,j] = rp + (.' px -r -1) p Ja [q,p,i,j]=j II suffit donc de déterminer le tableau Ra[p,i,j]
On utilise les tableaux Io et Jo caractérisant une trajectoire parcourant l'ensemble des points accessibles, c'est-à-dire que (Io[k], Jo[k]) doit parcourir l'ensemble des valeurs telles que

/o[A'] - # 2 +Jo[kl- #- /? ou 7?, est !e rayon du disque Hmité par !'ou\erture de l'objectif sur un capteur, et correspond par exemple au rayon de la zone illuminée sur (4339) lorsque le faisceau FRGI est utilisé seul. Cette trajectoire sera nommée par la suite trajectoire complète . 8.4.3. l.Modification of the procedure 7. 9.2. the coordinates of the lighting beams are known in advance and are:

Ia [q, p, i, j] = rp + (. 'Px -r -1) p Ja [q, p, i, j] = j It is therefore sufficient to determine the array Ra [p, i, j]
We use the tables Io and Jo characterizing a trajectory traversing the set of accessible points, that is to say that (Io [k], Jo [k]) must traverse the set of values such that

/ o [A '] - # 2 + Jo [kl- # - /? or 7 ?, is! the radius of the disc limited by! 'or \ erture of the objective on a sensor, and corresponds for example to the radius of the area illuminated on (4339) when the FRGI beam is used alone. This trajectory will be called hereafter complete trajectory.

A program performs the acquisition defined by these tables, according to the procedure described in 7.12.

acquisition, il suffit d'enregistrer les valeurs A1k.p,q [Io[ k]..fo[k]] et JJk,p,q [1 r' 1 r ] . Since the index no is not known, it is taken equal to nv in procedure 7.12. However, during this

acquisition, it suffices to record the values A1k.p, q [Io [k] .. fo [k]] and JJk, p, q [1 r '1 r].

Ra[p.Io[k],Jo[k]]= L J JJp - 21r ( Io[k] Jo[k] IO[k]2 + JO[k]2 "t,p,()['r.7rj exp -1 -nv Â. li y-+z K 7 ou ir, jrsont les coordonnées du maximum de l'image de référence, comme définies en 7.12. et ou x,y,z sont les coordonnées déterminées en 7.9.1. The program initializes the array Ra to 0 then it traverses the series of indices k, p by performing for each pair k, p:

Ra [p.Io [k], Jo [k]] = LJ JJp - 21r (Io [k] Jo [k] IO [k] 2 + JO [k] 2 "t, p, () ['r. 7rj exp -1 -nv Â. Li y- + z K 7 or ir, j are the coordinates of the maximum of the reference image, as defined in 7.12. And where x, y, z are the coordinates determined in 7.9.1 .

8.4.3.2. Modification of the procedure 7. 11.

d'images '\!k,p,q [i ,1] et Hk, p, ri, je . Toutefois, lors de cette acquisition, il suffit d'enregistrer les valeurs

Mk,pj [M*]" JOH et Hk@pq [1, 1 ir 1 - Le programme parcourt alors la série des indices k. Pour chaque valeur k il effectue: The program performs the series of acquisitions defined by tables Io and Jo defining a complete trajectory, already used in 8.4.3.1., According to the procedure described in 7.12. It thus generates the series

of images' \! k, p, q [i, 1] and Hk, p, ri, i. However, during this acquisition, it suffices to record the values

Mk, pj [M *] "JOH and Hk @ pq [1, 1 ir 1 - The program then traverses the series of indices k. For each value k it performs:

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F,,, [Io[k], .1 fk,o,o lok, Jok, '"l [ ' ' IJ Hk,(),o [i,, 1, Ra[0, Iok, Jok,
Le programme décrit en 7.8. est alors utilisé pour calculer les paramètres x,y,z,L, no à partir du tableau Frec ainsi constitué.

F ,,, [Io [k], .1 fk, o, o lok, Jok, '"l [''IJ Hk, (), o [i ,, 1, Ra [0, Iok, Jok,
The program described in 7.8. is then used to calculate the parameters x, y, z, L, no from the array Frec thus formed.

calcul de x.y.z.L, n0 correspond à la procédure décrite en 7. I2 et modifiée comme indiqué en 7.18.9. The procedure 7.11. thus reformulated can be used directly to calculate x, y, z, L, no in the case of the uniaxial crystal described in 7. 18.9., thus avoiding having to carry out preliminary measurements and making possible the movement of the objectives. In this case, the acquisition mode of the series of images allowing the

calculation of xyzL, n0 corresponds to the procedure described in 7. I2 and modified as indicated in 7.18.9.

8.4.3.3. Modification of the procedure 7. 13.

Id[p, i, jl = ij7 + - i - I)p JP, il J Ic[k, p] = plok +(.'' p, - lo -1 ) p
Jc[k,p] = Jo[k]
8.4.3.4. modification de la procédure 7. 6. In 7.13, we obtain directly without using the program of fig. 53:

Id [p, i, jl = ij7 + - i - I) p JP, il J Ic [k, p] = plok + (. '' P, - lo -1) p
Jc [k, p] = Jo [k]
8.4.3.4. modification of the procedure 7. 6.

The values of the coefficients K1, K2 determined in 7.6. check:
K1 = K2
8. 5. Adjustment:
The position of each element of the system must be precisely adjusted before use.
8. 5.1. devices used
The devices already described in 7.3.3.2. are used.

8. 5.2. Types of images used
During adjustment, various types of images can be used: - images obtained on an auxiliary CCD: auxiliary CCD placed for example in a space plane can make it possible to determine the center of a lighting beam in this plane, or the punctuality in this plane of a reference beam.

- images obtained on one of the CCDs of the microscope these images can be obtained and analyzed as indicated in 7.3.3.1. in the presence of a reference beam. It is also possible to directly observe the images received in the absence of a reference beam.

* - images obtained on the frequency meter CCD: observed directly, they make it possible to check the flatness of a wave or the angle separating two plane waves.

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- images of the surface of an SLM: placing the frequency meter behind the lens which transforms the wave coming from a given point of the SLM into a plane wave, an image of the surface of the SLM is formed on the CCD of the frequency meter, which can be used for example to check that the SLM is illuminated correctly. In order to visualize figures formed by controlling the SLM, a polarizer must additionally be present between the SLM and the CCD of the frequency meter. If it is not already present in the system, the polarizer of the frequency meter can be used.

- pixel-by-pixel images of the surface of an SLM: such an image consists of a two-dimensional array containing the illumination of each pixel. To obtain it, the frequency meter is placed as above, in the presence of a polarizer. The entire SLM is placed in the absorbent position ('black' image). Each pixel is then lit one by one, each time recording the intensity of the corresponding point on the frequency meter. The intensities thus measured for each pixel of the SLM are stored in a table, which constitutes the pixel by pixel image of the SLM. This type of image can be used, for example, to check the point-to-point correspondence between the various SLMs, necessary to obtain correct lighting and regular sampling.

8. 5.3. Adjustment criteria.

The adjustments aim to ensure that: (1) the beams follow the intended path. This can generally be verified using a simple diffuser (2) the lighting beams are parallel in the planes of space. This is verified using the frequency meter.

(3) the reference beams are point in the space planes and the illumination beams are point in the frequency planes. This is verified for example with the aid of an auxiliary CCD.

(4) the polarizers are correctly adjusted. The extinctions of the beam can for example be observed on the frequency meter.

(5) a beam entering parallel to the objective (4317) and directed along the optical axis has a point image and centered on the sensor (4339).

(6) when the control word A1, j is used for the SLM (4405) and when the control word B1, j is used for the SLM (4412) and (4417), the following conditions are met: (i) the coordinate point i, j must be effectively illuminated on SLMs (4412) and (4417) (ii) when FEG and FEGI beams are used, the points illuminated on SLMs (4427) and (4442) and on sensors ( 4339) and (4329) must have as coordinates (i, j) (iii) when the FED and FEDI beams are used, the points illuminated on the SLMs (4427) and (4442) and on the sensors (4339) and (4329 ) must have for coordinates (pix -1-l, j) This condition (6) can be verified using images obtained on the sensors or using pixel-by-pixel images obtained on the CCDs.

The adjustments to be made result from these conditions. The description of the adjustment steps is given as an indication and constitutes an example of the ordering of the adjustment steps.

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8.5.4. Adjustment steps
In the description of the adjustment steps, frequent reference will be made to the optical axis. Due to the many reflections, the optical axis can only be defined locally. It is therefore to this locally defined optical axis that reference will be made.

Prior to any fine adjustment, the entire system is set up with all possible precision by geometric methods, with the exception of elements (4304) (4305) (4422) (4437) (4351) which will be put in place. place being adjusted.

Throughout the adjustment, the position of the neutral axis of the polarization rotators (4310) (4338) (4341) (4326) is maintained in the plane of figure 62. A point will be said to be centered on one of the sensors (-1339) ) or (4329) if its coordinates are (Npix / 2 Npix / 2)
In the first step of adjusting a given element, the type of positioner on which this element is mounted is indicated Step 1. Orientation adjustment of the laser assembly (4300)-beam expander (4301)
This assembly is mounted on an angular positioner to adjust the direction of the beam. A diffuser is used to check the beam path. The position of the assembly (4300,4301) is adjusted so that the beam follows the intended path.

Step 2. Positioning of the phase shift device (4304).

This phase shift device is identical to that described in 7.2.3. and installed as indicated in 7.3.2.3.

Step 3. Positioning of the beam attenuation device (4305).

This beam attenuation device is identical to that described in 7.2.2. and is installed as indicated in 7.3.2.2.

Step 4 .: 2-axis translation adjustment of the 'hole' (4402)
This hole is mounted on a two-dimensional positioner allowing movement in the plane orthogonal to the optical axis.

It is set to maximize the intensity of the beam that has passed through the 'hole'.

Step 5. Adjusting the orientation of the two-sided mirror (4403)
This mirror is mounted on an angular positioner making it possible to adjust its orientation. A diffuser is used to check the path of the beam and the position of the mirror is adjusted so that the beam incident on the SLM (4405) occupies the entire useful area of this SLM.

Step 6.Adjusting the orientation of the SLM (4405)

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This SLM is mounted on an angular positioner allowing its orientation to be adjusted, coupled with a two-axis translational positioner allowing its position to be adjusted in a plane orthogonal to the optical axis.

The SLM is placed in a fully reflective position. A diffuser is used to verify that the wave reflected on the SLM reaches the intended point on the mirror (4403) and goes in the intended direction.

Step 7. Fine adjustment of the orientation of the two-sided mirror (4403), translational adjustment of the SLM (4405), adjustment of the aperture of the diaphragm (4348), and translational adjustment of the lens (4404).

The lens (4404) is mounted on a positioner with a translational axis allowing translational adjustment in the direction of its optical axis.

The purpose of this step is: - to adjust the position of the lens (4404) so that the SLM (4405) is in a space plane - to adjust the orientation of the two-sided mirror (4403) and the translational position of (4405) so that the beam reaching (4405) is centered.

- adjust the aperture of (4348) so that the incident beam on (4405) is as wide as possible, without however going beyond the active surface of the SLM.

It is possible, on an SLM, to independently control the active zone and a peripheral zone called 'apron'. The whole of the active zone is here controlled to carry out a rotation of polarization in a given direction, and the apron is controlled to carry out a rotation of polarization in the opposite direction. The active zone is then modified so that a cross centered in the middle of the active zone is put in the same state as the apron.

The frequency meter is positioned behind (4406). which is wide open.

The aperture of the diaphragm (4348) is slightly greater (by 20% for example) than its nominal aperture calculated in 8.4.

The frequency meter is first positioned in the absence of its polarizer so that an image of the illuminated zone of (4405) is formed on its CCD.

The polarizer of the frequency meter is then introduced and adjusted in rotation so as to reveal on the image a maximum contrast between the peripheral zone ('apron') and the active central zone of the SLM.

The position of (4403) is then adjusted so that the whole of the active zone and of the border with the apron is visible on the image. We should see an illuminated square active area surrounded by a dark area (the apron) and crossed out by a centered cross.

The position of (4404) is adjusted so as to have the best possible contrast.

The diaphragm (4348) is then reduced in opening. We should see in the image an illuminated disk of reduced diameter, intercepting the dark cross. The position of (4403) and that of (4405) in translation are adjusted so that the center of the disc and the center of the cross coincide.

The position of (4404) is again adjusted so as to have the best possible contrast

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The opening of the diaphragm (4348) is then enlarged to the maximum without, however, the illuminated disc reaching the area of the apron.

Step 8. Translation adjustment of the lens (4407)
This lens is mounted on a positioner in translation one axis in the direction of the optical axis
The purpose of this adjustment is to ensure that a parallel beam coming from the laser and entirely reflected by (4405) is again parallel after passing (4407).

The frequency meter is positioned behind (4407). (4406) is wide open. The control panel of (4405) is entirely set to 0. The position of (4407) is adjusted to have an image as punctual as possible on the frequency meter.

Step 9. Rotation adjustment of the polarizer (4408).

The polarizer (4408) is attached to a positioner allowing rotation adjustment about the optical axis.

When the control word A00 is used, the SLM (4405) reflects the beam in a direction DO. When ANpix -1.0 is used, the beam direction is changed and the component on the frequency corresponding to the DO direction must be canceled. The polarizer (4408) is adjusted so as to effectively produce a cancellation of this component.

The frequency meter is positioned behind (4408). The diaphragm (4406) is wide open. Table A00 is first applied to (4405). The illuminated point P on the frequency counter's CCD is identified. The ANpix -1.0 table is then used and the position of (4408) is adjusted to cancel the current received at point P.

Step 10. 2-axis translation adjustment and diaphragm opening (4406)
The diaphragm (4406) has an adjustable opening and is adjustable in translation along two axes orthogonal to the optical axis.

Its position and its opening must be adjusted so that it lets the useful frequencies pass and stops the symmetrical frequencies, its role being that of the diaphragm (4615) described in 8. 1.2.

The frequency meter is used and positioned behind (4408). The axes of the frequency counter CCD must be oriented as indicated by the reference mark (4470). A specific program is used.

-0.0 A 0, ,v A 'pb V .4 mPâ -1 .A Ne 2 2 2 " Le programme somme les intensités obtenues dans chaque cas par le capteur CCD et affiche l'image correspondante. II superpose sur cette image des symboles indiquant le maximum obtenu dans chacun de ces cas. Il itère indéfiniment cette procédure pour que cette image soit mise à jour en permanence pendant le réglage du diaphragme. This program applies successively to the SLM (4405) the tables

-0.0 A 0,, v A 'pb V .4 mPâ -1 .A Ne 2 2 2 "The program sums the intensities obtained in each case by the CCD sensor and displays the corresponding image. It superimposes symbols on this image indicating the maximum obtained in each of these cases.It iterates this procedure indefinitely so that this image is constantly updated during the iris adjustment.

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The diaphragm must be adjusted in position and opening so that the point obtained for the indices (0,0) is not visible (closed by the diaphragm) and so that the other four points are visible (at the limit of the diaphragm), at the positions indicated by Fig. 72 or (5010) represents the limit of the diaphragm.

Step 11. Adjusting the orientation of the mirror (4409)
The mirror (4409) is attached to a positioner allowing its orientation to be adjusted.

We apply to (4405) the table ANpix Npix # A diffuser is used to control the trajectory of the 2 '2 beam. The angular position of (4409) is adjusted so that the beam hits the center of (4412).

Step 12. Adjusting the orientation of the SLM (4412)
The SLM (4412) is attached to a three-axis rotational positioner allowing adjustment of its orientation (axes in the plane of the sensor) and the rotational position (axis orthogonal to the plane of the sensor), coupled with a two-axis positioner in translation allowing displacement in a plane orthogonal to the optical axis.

The ANpix Npix array remains applied to (4405). The control board of (4412) is set to 1. A
2 'diffuser is used to control the beam path. (4412) is adjusted so that the wave reflects back to (4414) and is centered in the middle of this diaphragm.

Step 13. Rotation adjustment of the polarizer (4413)
The control panel of (4412) is set to 1. The frequency meter is positioned behind (4413) so that the image of (4412) is formed on its CCD. The control panel of (4412) is then set to 0. (4413) is then adjusted in rotation so as to cancel the intensity received on the CCD of the frequency meter.

Step 14. Fine adjustment of the orientation of the mirror (4409), adjustment of the position and focal length of the doublet (4410) (4411), and adjustment in rotation and translation of the SLM (4412).

The lens (4410) is mounted on a positioner one axis in the direction of the optical axis. This positioner and the lens (441 1) are themselves mounted on a second positioner one axis in the direction of the optical axis. It is therefore possible either to jointly move the assembly (4410) (4411) or to move (4410) alone to vary the distance between the two lenses of the doublet (4410) (4411)
The SLM (4405) makes it possible to control the direction in which the wave coming from this SLM is diffracted.

To a direction of the beam at the output of the SLM (4405) corresponds a point in a frequency plane and in particular a point in the plane of the SLM (4412).

The position of (4410) (4411) must be adjusted so that the image of the beam from the SLM (4405) is effectively point in the frequency plane where it is (4412). The position of

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est appliqué à (4405) corresponde à un point de coordonnées C 'x , 2'x sur le SLM (4412). La position de (4410)(4411)(4412) doit en outre être réglée pour qu'il ait une correspondance point à point entre les fréquences générées par les tableaux A1,j appliqués à (4405) et les pixels de (4412), c'est-à-dire pour que lorsque le tableau de commande A1,j est appliqué à (4405) le pixel de coordonnées (k.j) soit illuminé sur le SLM (4412), quels que soient les entiers i et j. (4409) and (4412) must be set so that the frequency generated when the ANpix N control panel
2 '

is applied to (4405) corresponds to a point of coordinates C 'x, 2'x on the SLM (4412). The position of (4410) (4411) (4412) must further be set so that it has a point-to-point correspondence between the frequencies generated by the tables A1, j applied to (4405) and the pixels of (4412), that is, so that when the control array A1, j is applied to (4405) the coordinate pixel (kj) is illuminated on the SLM (4412), regardless of the integers i and j.

The series of operations ol to o3 is repeated a sufficient number of times, so as to converge towards the correct position of each element. o1. Adjusting the joint position of (4410) and (4411) to obtain a point frequency image
The frequency meter is positioned behind (4414) The diaphragm (4414) is wide open The ANpix Npix table is applied to (4405) and the control table applied to (4412) is at 1. The position
2 2 joint of the assembly (4410) (4411) is adjusted to have on the CCD sensor of the frequency meter an image as punctual as possible.

02. Angular adjustment of (4409) and translation adjustment of (4412) to obtain a centered frequency image.

ANpix Npix remains applied to (4405). (4409) and (4412) are then set so that the center frequency
2 'generated either in the middle of the SLM (4412). This adjustment is made with the frequency meter and a program for locating the maximum, which will be called the PA program.

The PA program turns on each pixel of the SLM (4412) in turn and measures the corresponding intensity on the frequency meter. The pixel generating the highest intensity corresponds to the maximum.

coordonnées (ij) des pixels sur le SLM (4412), i etj variant de 0 à N'pix - 1 . Pour chaque couple (i,j) cette procédure effectue les étapes suivantes: - elle applique le tableau de commande Bij défini comme en SA,!. au SLM (4412). The basic procedure of the PA program. which we will call PB, go through the set of

coordinates (ij) of the pixels on the SLM (4412), i etj varying from 0 to N'pix - 1. For each pair (i, j) this procedure performs the following steps: - it applies the Bij control panel defined as in SA,!. at SLM (4412).

- it then acquires an image on the CCD of the frequency meter.

- it determines the maximum value of the intensity measured on all the points of this image.

- it stores this value in an array, \ [in M [l, j]
When it has thus traversed the set of indices i, j the procedure determines the point of maximum intensity of table M and its indices i0, j0 which correspond to the maximum. It displays on the screen

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the two-dimensional image corresponding to the array M, possibly enlarged around the maximum, as well as the values of io, jo and the value M [i0, j0].

The PA program consists in iterating the PB procedure indefinitely so as to be able to carry out the corresponding adjustment.

The position of (4409) must be adjusted to have (1 u 7o) = C # -, and to maximize M [80, j0]. o3. Focal adjustment of the doublet (4410) (4411) and adjustment of (4412) in rotation.

The frequency meter, set as previously, is used. A program for displaying the characteristics of the system is used, which will be called the PC 'program.

A N' pu .4 M A , V pu A N pu appliqués à (4405). Ces tableaux de commande sont c'z z'c - N -1-c N -1-c,- numérotés dans cet ordre. c est une constante, par exemple c=20, introduite pour éviter que les points illuminés sortent de la zone active du SLM en cas de mauvais réglage initial. The PC program successively uses four control panels

AN 'pu. 4 MA, V pu AN pu applied to (4405). These control panels are c'z z'c - N -1-c N -1-c, - numbered in this order. c is a constant, for example c = 20, introduced to prevent the illuminated points from leaving the active zone of the SLM in the event of an incorrect initial setting.

.'[1],F[1]=Cc, h2'J r l (.'[2].3[2])=CN ,cJ l (1-[3],3'[3]=C2u r Ci (..[. lty = Pu - 1 -C, P [. f1.Jl.fl) 2
Le réglage a donc pour objectif d'obtenir effectivement ces égalités. Le réglage de la focale du doublet (4410)(4411) permet d'ajuster l'échelle et le réglage en rotation de (4412) permet d'ajuster la position en rotation. For the n-th command word, the program uses the PB procedure already described and stores the coordinates of the maximum obtained in X [n] and Y [n]. When this operation has been carried out for the four control words, the program has therefore obtained the four-element X and Y arrays, corresponding to the pixel coordinates of the successive maxima. When the system is properly adjusted, we must have:

. '[1], F [1] = Cc, h2'J rl (.' [2] .3 [2]) = CN, cJ l (1- [3], 3 '[3] = C2u r Ci (.. [. lty = Pu - 1 -C, P [. f1.Jl.fl) 2
The aim of the adjustment is therefore to actually obtain these equalities. The focal length adjustment of the doublet (4410) (4411) adjusts the scale and the rotational adjustment of (4412) adjusts the rotational position.

N P I1-2c 2 r[lj-.I'[t]) +(rn]-r[4])' + (.'[2J-.-[3))z +(J12]-Jl3J)2} Si fest la distance focale de chaque lentille et si d1 est la distance entre ces lentilles avant réglage,

la distance focale effective de l'ensemble de deux lentilles avant réglage est: f, ~ f 2 1- 1 dr (2f) The program calculates the ratio of the effective distances to the distances that should be obtained with a correct setting:

NP I1-2c 2 r [lj-.I '[t]) + (rn] -r [4])' + (. '[2J -.- [3)) z + (J12] -Jl3J) 2} If the focal length of each lens is fest and if d1 is the distance between these lenses before adjustment,

the effective focal length of the set of two lenses before adjustment is: f, ~ f 2 1- 1 dr (2f)

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-,=2/(1-1- Dans cette équation/et d1 sont mal connus mais on peut utiliser la distance focale 'de conception' du doublet (4410)(4411). Cette distance est celle pour laquelle le doublet a été prévue. On la notera / et elle vaut à peu près f/2.On obtient alors:

d2 -dl = 4fc(l-r) Le programme PC affiche: - la valeur d2-d1, qui permet de corriger en conséquence la distance entre lentilles. similarly the focal length of the assembly after adjustment is: f2 = f / 2 1 / @ 2 1-d2 / @
2f The magnification being proportional to the focal length, it must be adjusted so that: f2 = 1 f1 r which leads, by expanding the calculations, to:

-, = 2 / (1-1- In this equation / and d1 are not well known but we can use the focal length 'of conception' of the doublet (4410) (4411). This distance is that for which the doublet was intended We will denote it / and it is approximately equal to f / 2, we then obtain:

d2 -dl = 4fc (lr) The PC program displays: - the d2-d1 value, which allows the distance between lenses to be corrected accordingly.

-the lines respectively connecting points 1 and 4 and points 2 and 3
X [1] -X [4] - the deviation, which roughly gives the angle in radians whose rotational position needs to be corrected.

-'Ii po: - 2c A-fl1-A [4l -the ratio II which must be equal to 1.

1121 - 1 '[3] Ar! L -. \ F4l
The SLM (4412) is rotated so as to cancel the displayed deviation 1] and the
Npix-2c distance between the lenses of the doublet (4410) (4411) is changed according to the displayed value of d2-d1.

Step 15. Adjustment of the diaphragm (4414) in translation.

The diaphragm (4414) is mounted on a 2-axis positioner in translation allowing it to be moved in a plane orthogonal to the optical axis.

The opening of (4414) is known. It must be adjusted in translation. An auxiliary CCD is placed just behind (4414). The BNpix Nest control panel used for the SLM (4405), i.e. only 2 '2 a central point of this SLM is switched on, the direct reflected beam being stopped by (4406). The SLM control panel (4412) is set to 1 (through position). The image of the lit point of (4405) is then formed in the plane of the diaphragm (4414). (4414) is then set in translation so that its center coincides with the image of the lit point of (4405).

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Step 16. 2-axis translation adjustment of the SLM (4417)
This SLM is mounted on a positioner two axes in translation in the plane of the SLM, coupled with a positioner three axes in rotation allowing to adjust the orientation (axes in the plane of the sensor) and the position in rotation (axis in a plane orthogonal to the sensor).

The control panels A v Net pu B. 1 v pu are used respectively for the SLMs
2 '2 2' 2 (4405) and (4412). A diffuser is used to follow the beam arriving at (4417) and (4417) is set in translation so that the beam arrives at its center.

Step 17. Adjusting the orientation of the SLM (4417).

The same control panels as before are used for the SLMs (4405) (4412) The control panel of the SLM (4417) is set to 1. (4417) is set so that the reflected beam reaches the intended point on (4419) , which is checked using a diffuser.

Step 18. Adjusting the orientation of the mirror (4418)
The mirror (4418) is mounted on an angular positioner for adjusting its orientation (4418) is set to effectively return the beam in the intended direction, which is verified with a diffuser.

Step 19. Translation adjustment of the diaphragm (4419)
The diaphragm (4419) is mounted on a two-axis translational positioner allowing movement in a plane orthogonal to the optical axis.

The opening of (4419) is known. It must be adjusted in translation. The control panel
BNpix Npix is used for the SLM (4405), i.e. only a central point of this SLM is lit, 2 '2 the direct reflected beam being stopped by (4406). The control panels of the SLMs (4412) and (4417) are set to 1 (through position). The image of the lit point of (4405) is then formed in the plane of the diaphragm (4419). (4419) is then set in translation so that its center coincides with the image of the lit point of (4405).

Les tableaux de commande A N N et 8, ,,;R sont appliqués respectivement à (4405) et
2 ' 2 2 ' 2 (4412). Le tableau de commande de (4417) est mis à 1. Le fréquencemètre est placé juste derrière (4420). Step 20. Rotation adjustment of the polarizer (4420)
The polarizer (4420) is mounted on a positioner allowing it to be adjusted in rotation with respect to the optical axis

The ANN and 8, ,,; R control tables are applied to (4405) and
2 '2 2' 2 (4412). The control panel of (4417) is set to 1. The frequency meter is placed just behind (4420).

The image on his CCD is more or less punctual. The control panel of (4417) is then set to 0 The position of (4420) is adjusted to cancel the intensity received on the frequency meter

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Step 21. Adjustment in 2-axis translation and in rotation of the SLM (4417), adjustment of the position and of the focal length of the doublet (4415) (4416).

The lenses (4415) (4416) are mounted on a positioner in translation allowing either their simultaneous displacement in the direction of the optical axis or the displacement of (4415) alone.

SLM (4412) lorsque les tableaux de commande .4,,V^ N et B J v pl'{ v sont appliqués respectivement à 2 ' 2 2, 2 (4405) et (4412) soit effectivement ponctuelle dans le plan de fréquence ou se trouve (4417). La position de (4417) doit être réglée pour que dans ces conditions le point illuminé sur le SLM (4417) ait pour

coordonnées C T x , r2x J . La position de(4415)(44!6)(44!7) doit en outre être réglée pour qu'il ait une correspondance point à point entre les pixels de (4412) et ceux de (4417), c'est-à-dire pour que lorsque les tableaux de commande .4, et Bi,j sont appliqués respectivement à (4405) et (4412) le point éclairé sur (4417) soit le pixel de coordonnées (i,j). quels que soient les entiers i et}. The position of (4415) (4416) must be adjusted so that the image of the beam coming from the

SLM (4412) when the control tables .4,, V ^ N and BJ v pl '{v are applied respectively to 2' 2 2, 2 (4405) and (4412) either effectively point in the frequency plane or are found (4417). The position of (4417) must be adjusted so that under these conditions the illuminated point on the SLM (4417) has the

coordinates CT x, r2x J. The position of (4415) (44! 6) (44! 7) must further be set so that it has a point-to-point correspondence between the pixels of (4412) and those of (4417), that is say so that when the control tables .4, and Bi, j are applied to (4405) and (4412) respectively, the point illuminated on (4417) is the pixel of coordinates (i, j). whatever the integers i and}.

Les tableaux de commande A N N et BN N sont appliqués respectivement aux SLM 2 ' 2 ' (4405) et (4412). Le tableau de commande appliqué à (4417) est mis à 1. La position de l'ensemble (4415) (4416) est ajustée pour avoir sur le capteur CCD du fréquencemètre une image aussi ponctuelle que possible. The frequency meter is positioned behind (4420). The series of operations 0 Il to o13 is repeated a sufficient number of times. ol 1. Adjusting the joint position of (4415) and (4416) to obtain a point frequency image

The ANN and BN N control tables are applied to SLM 2 '2' (4405) and (4412) respectively. The control table applied to (4417) is set to 1. The position of the assembly (4415) (4416) is adjusted to have on the CCD sensor of the frequency meter an image as punctual as possible.

012. Translation adjustment of (4417) to obtain a centered frequency image.

AN pu N pu and BN N remain applied to SLMs (4405) and (4412) respectively. (4417) is
2, 2 2 '2 then set so that the generated center frequency is in the middle of the SLM (4417). This adjustment is made with the frequency meter and the PA program for locating the maximum defined above. However, in this program for locating the maximum, the SLM (4412) is here replaced by the SLM (4417).

013. Adjustment of (4415) to obtain the correct frequency magnification and rotation adjustment of (4417).

The PC program is used. However, in this program: - the SLM (4412) is replaced by the SLM (4417) - when a control word Ai, j is applied to the SLM (4405), the corresponding control word Bi, j is applied to the SLM ( 4412).

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The inter-lens distance correction obtained is applied to the distance between (4415) and (4416) and the rotation adjustment is made on (4417) in rotation with respect to an axis orthogonal to the plane of the sensor Step 22. Adjustment of the '' orientation of the semi-transparent mirror (4307)
The semi-transparent mirror (4307) is mounted on an angular positioner for adjusting its orientation.

commande de (4405) est AN N et le tableau de commande de (5512) et (4417) est B Iv' N La
2, 2 2, 2 position de (4407) est ajustée à l'aide d'un diffuseur de manière à renvoyer le faisceau dans la direction prévue. The SLMs (4405) (4412) (4417) are controlled to generate a center frequency: the control board

command of (4405) is AN N and the command board of (5512) and (4417) is B Iv 'N La
2, 2 2, 2 position of (4407) is adjusted using a diffuser so as to return the beam in the intended direction.

Step 23. Adjusting the orientation of the mirror (4308)
The mirror (4308) is mounted on an angular positioner to adjust its orientation
The ordering of SLMs is unchanged. The position of (4308) is adjusted using a diffuser so as to return the beam in the intended direction.

Step 24. Installation of the beam extinguisher (4422)
The ordering of SLMs is unchanged. This beam extinguisher is fitted according to the procedure indicated in 7.3.2.2.

Step 25. Translation adjustment of the lens (443 1)
The ordering of SLMs is unchanged. The frequency meter is positioned behind (443 1). The position of (443 1) is adjusted to obtain a point image.

Step 26. Adjusting the orientation of the mirror (4332)
This mirror is mounted on a two-axis positioner allowing its orientation to be adjusted.

The ordering of SLMs is unchanged. Between (4311) and (4331), two beams propagating in the opposite direction are superimposed. A diffuser introduced on the side of the beam will be illuminated on both sides. The illuminated parts on each side of the diffuser must be the same: the two beams are then exactly superimposed. Incorrect adjustment of (4332) results in a shift between the position of these two beams. (4332) is set so that between (4311) and (433 1) the beams propagating in both directions are exactly superimposed.

Step 27. Translation adjustment of the lens (4331)
The lens (4331) is mounted on a positioner with a translational axis allowing movement in the direction of the optical axis.

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(4405)(4412)(4417) est définie par les tableaux AN pu . '1 pl1 et B La position de (4332) est réglée de
2, 2 2, 2 manière à ce que FEDI ait une image aussi ponctuelle que possible sur le fréquencemètre. The frequency meter is positioned between (4311) and (4338). Ordering SLMs

(4405) (4412) (4417) is defined by the AN pu tables. '1 pl1 and B The position of (4332) is adjusted
2, 2 2, 2 so that FEDI has as punctual an image as possible on the frequency meter.

Step 28. Adjusting the orientation of the semi-transparent mirror (4311).

This semi-transparent mirror is mounted on a positioner with two rotating axes (the two axes being in the plane of the semi-transparent mirror) allowing its orientation to be adjusted.

The setting of the SLMs is not changed. A diffuser is used to control the path of the beam. (4311) is set so that the FEDI beam follows the intended path.

Step 29. Adjusting the orientation of the two-sided mirror (4424)
The double mirror (4424) is mounted on a positioner with two rotating axes, the two axes being in the plane of the non-reflecting face.

(4424) is set so that FEDI reaches the center of (4427). this is checked using a diffuser Step 30. Adjusting the orientation of the SLM (4427).

This SLM is mounted on a positioner two axes in translation in the plane of the SLM, coupled with a positioner three axes in rotation allowing to adjust the orientation (axes in the plane of the sensor) and the position in rotation (axis in a plane orthogonal to the sensor).

The control tables of the SLMs (4405) (4412) (4417) are not modified. The SLM control panel (4427) is set to 1.

As the beam path is controlled with a diffuser, the angular position of (4427) is adjusted so that the FEDI beam is aimed at the intended point on (4424).

Step 31. Fine adjustment of the orientation of the two-sided mirror (4424), adjustment in rotation and translation of (4427) and adjustment of the focal length and position of the doublet (4425) (4426).

les tableaux de commande A N N et B,vw N sont appliqués respectivement au SLM (4405) et aux
2, 2 2 ' 2 SLM (4412) et (4417), soit effectivement ponctuelle dans le plan de fréquence ou se trouve (4427). La position de (4424) et (4427) doit être réglée pour que dans ces conditions le point illuminé sur le SLM

(4427) ait pour coordonnées C rX , r 2x J . l La position de (4425)(4426)(4427) doit en outre être réglée pour qu'il ait une correspondance point à point entre les pixels de (4417) et ceux de (4427), c'est-à-dire pour que, lorsque les tableaux de commande Ai,j et Bi,j sont appliqués respectivement au SLM (4405) et The position of (4425) (4426) must be adjusted so that the image of the FEDI beam, when

the ANN and B, vw N control tables are applied to the SLM (4405) and to the
2, 2 2 '2 SLM (4412) and (4417), either effectively punctual in the frequency plane where (4427) is located. The position of (4424) and (4427) must be adjusted so that under these conditions the illuminated point on the SLM

(4427) has for coordinates C rX, r 2x J. l The position of (4425) (4426) (4427) must additionally be adjusted so that it has a point-to-point correspondence between the pixels of (4417) and those of (4427), i.e. for that, when the control tables Ai, j and Bi, j are applied respectively to the SLM (4405) and

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at SLMs (4412) and (4417). the point illuminated on (4427) is the pixel with coordinates (i, j). whatever the integers i and j.

The frequency meter is positioned between (4424) and (4428). Its polarizer is in place. The FEDI harness is used. The control panel of (4427) is set to 0 and the frequency meter polarizer is set to cancel the intensity received on the frequency meter CCD. The series of operations o21 to o23 is then repeated a sufficient number of times to converge towards a correct adjustment. o21. Adjusting the joint position of (4425) and (4426) to obtain a point frequency image
The ANpix Npix control table is applied to the SLM (4405) and the 2 1 - @ / 2 2 BNpix Npix control table is applied to the SLM (4412) and (4417). The command table applied to (442 7)
2 2 is set to 1. The position of the assembly (4425) (4426) is adjusted so as to have on the CCD sensor of the frequency meter an image as punctual as possible.

022. Orientation adjustment of (4424) and translation adjustment of (4427) to obtain a centered frequency image.

(4424) and (4427) are set so that the generated center frequency is in the middle of the SLM. This adjustment is made with the frequency meter and the PA program for locating the maximum defined above. However, in this program for locating the maximum, the SLM (4412) is here replaced by the SLM (4427).

023. Adjustment of (4425) to obtain the correct frequency magnification and rotation adjustment of (4427).

The PC program is used. However, in this program: - the SLM (4412) is replaced by the SLM (4427) - when a control word Ai, j is applied to the SLM (4405), the corresponding control word Bi, j is also applied to the SLM (4412) and (4417).

The obtained inter-lens distance correction is applied to the distance between (4425) and (4426) and the rotation adjustment is made to (4427).

Step 32. 2-axis translation adjustment of the diaphragm (4428) (4428) is mounted on a two-axis translational positioner allowing movements in a plane orthogonal to the optical axis.

The opening of (4428) is known. It must be adjusted in translation.

FEDI is used. (4428) is provisionally deleted. An auxiliary CCD is placed just behind (4428). The ANpix Npix control panel is applied to the SLM (4405) and the control panel
2 '2 BNpix Npix command is applied to SLMs (4412) and (4417). The control panel of (4427) is at 1. The
2 '

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center of the illuminated area is marked on the auxiliary CCD. (4428) is then placed so that its center coincides with the center of the illuminated area.

Step 33. Rotation adjustment of the polarizer (4352)
This polarizer is mounted on a positioner with a rotating axis making it possible to adjust its rotational position around its optical axis.

FEDI is used. The control panel of (4427) is set to 0. The control panels of the SLMs (4405) (4412) (4417) are not modified. The rotational position of (4352) is adjusted to cancel the current received on the CCD (4339).

Step 34. Adjusting the orientation of the mirror (4344)
This mirror is mounted on a positioner allowing adjustment of its orientation. The diaphragm (4349) is wide open. A diffuser is used to verify that the FRD beam reaches the CCD (4339) and is centered on that CCD.

Step 35.Adjusting the position and opening of the diaphragm (4349)
This diaphragm is mounted on a positioner with two translational axes allowing movement in the plane of the optical axis, and has an adjustable opening.

Its position is adjusted in the presence of FRD so that the diaphragm image is centered on the CCD and its aperture is adjusted so that this image covers the entire CCD.

Step 36. Adjustment of the focal length and position of the doublet (4430) (4429) and translation and rotation adjustment of the sensor (4339)
The lenses (4430) (4429) are mounted on a positioner in translation making it possible, on the one hand, to move the two lenses together, on the other hand, to move (4429) relative to (4430).

The CCD (4339), integral with the camera (4384) is mounted on a three-axis rotating positioner allowing on the one hand a rotation around the optical axis, on the other hand an adjustment of the orientation of the sensor, coupled with a three-axis positioner in translation.

The positioners of the lenses (4430) (4429) and of the camera (4384) are themselves mounted on a positioner allowing movement of the assembly in the direction of the optical axis.

les tableaux de commande AN pu N pu et B,; N sont appliqués respectivement au SLM (4405) et aux
2, 2 2, 2 SLM (4412) et (4417) et lorsque le tableau de commande de (4427) est mis à 1, soit effectivement ponctuelle dans le plan de fréquence ou se trouve (4339). La position de (4339) doit être réglée pour que

dans ces conditions le point illuminé sur le CCD (4339) ait pour coordonnées # # , # # . La position de (4339)(4429)(4430) doit en outre être réglée pour qu'il ait une correspondance point à point entre les The position of (4430) (4429) must be adjusted so that the image of the FEDI beam, when

the control panels AN pu N pu and B ,; N are applied to the SLM (4405) and the
2, 2 2, 2 SLM (4412) and (4417) and when the control panel of (4427) is set to 1, either effectively point in the frequency plan where is located (4339). The position of (4339) must be adjusted so that

under these conditions the illuminated point on the CCD (4339) has the coordinates # #, # #. The position of (4339) (4429) (4430) must also be adjusted so that it has a point-to-point correspondence between the

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pixels of (4417) and those of (4339), that is, so that. when the Order tables and
Bi, j are applied respectively to the SLM (4405) and to the SLM (4412) and (4417) and when the control panel of (4427) is at 1, the point illuminated on (4339) is the pixel of coordinates (ij) , whatever the integers i and}.

FEDI and FRD beams are used.

Table C applied to (4427) is set to 1.

2-1'2 CCD (4339) est évaluée selon la procédure décrite en 7.3.3.1. La position de l'ensemble (4429) (4430) est ajustée pour avoir une image aussi ponctuelle que possible. The series of operations o31 to o33 is repeated a sufficient number of times 031. Adjustment of the joint position of (4429) and (4430) to obtain a point frequency image
The AN Npix control panel is applied to the SLM (4405) and the control panel
2, 2 BNpix Npix command is applied to SLMs (4412) and (4417). The punctuality of the image generated on the

2-1'2 CCD (4339) is evaluated according to the procedure described in 7.3.3.1. The position of the assembly (4429) (4430) is adjusted to have an image as point as possible.

032. Translation adjustment of (4339) to obtain a centered frequency image.

calculées selon la procédure indiquée en 7.3.3. 1., soient C l'4 p , '' , 033. Réglage de (4429) pour obtenir le bon grandissement en fréquence et réglage en rotation de (4339). The translational position of (4339) is adjusted so that the coordinates of the point image,

calculated according to the procedure given in 7.3.3. 1., let C l'4 p, '', 033. Adjustment of (4429) to obtain the correct frequency magnification and rotation adjustment of (4339).

The PC program is used. However, in this program: - when a control word Ai, j is applied to the SLM (4405). the corresponding control word Bi, j is additionally applied to the SLMs (4412) and (4417).

- Tables X [i] and Y [i] are not obtained by the PB procedure. They correspond to the coordinates of the maximum determined by the procedure described in 7.3.3.1., Without specific action on an SLM.

The obtained inter-lens distance correction is applied to the distance between (4429) and (4430).

The rotation adjustment is performed on (4339) (4384), in rotation about the optical axis.

L'orientation du CCD est réglée pour avoir }l ~ } f l ~ 1
Y [2]-Y[3] Etape 37. Réglage de la position en translation de l'ensemble constitué du CCD (4339) et du doublet (4430)(4429). X [1] -X [4]

The orientation of the CCD is set to have} l ~} fl ~ 1
Y [2] -Y [3] Step 37. Adjustment of the translational position of the assembly consisting of the CCD (4339) and of the doublet (4430) (4429).

The FRDI beam is used. An auxiliary CCD is placed at the location of the diaphragm (4313). The position of said assembly is adjusted so that the FRDI image on the auxiliary CCD is point.

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Step 38. Adjusting the orientation of the mirror (4347)
This mirror is mounted on a two-axis positioner allowing its orientation to be adjusted.
The ordering of SLMs is unchanged. Between (4345) and (4346). two beams propagating in the opposite direction are superimposed. A diffuser introduced on the side of the beam will be illuminated on both sides. The illuminated parts on each side of the diffuser must be the same: the two beams are then exactly superimposed. (4347) is set so that between (4345) and (4346) the beams propagating in both directions are exactly superimposed.

Step 39. Translation adjustment of the lens (4346)
The lens (4346) is mounted on a positioner with a translational axis allowing its position to be adjusted in the direction of the optical axis.

FRDI is used. The frequency meter is positioned on the FRDI trajectory between (4345) and (4430).

The position of the lens (4346) is adjusted so that the image on the frequency counter's CCD is punctual. Step 40. Adjusting the orientation of the semi-transparent mirror (4345)
The semi-transparent mirror (4345) is mounted on a two-axis positioner allowing its orientation to be adjusted.

An auxiliary sensor is provisionally placed behind (4313). The semi-transparent mirror (4313) is adjusted so that the image on this temporary sensor is centered relative to the diaphragm (4313) Step 41. Position adjustment of the objectives (4317) and (4319) in translation.

The lens (4319) is mounted on a focusing device. The objective (4317) is mounted on a positioner with two translational axes allowing movement in a plane orthogonal to the optical axis.

The FRDI beam is used. A temporary CCD sensor is positioned just behind (4323) on FRDI's path. The position of the objectives is adjusted to obtain a centered point image. Step 42. Introduction of a provisional flat lighting beam.

This beam, which will be called 'FEP', is derived from the laser by a semi-transparent mirror placed between (4304) and (4305) and it is brought by a set of mirrors towards the entrance of the microscope objective (4317), on the side of the sample. The objective (4319) should be temporarily deleted for this purpose. When entering the objective, this beam is directed along the optical axis of the objective.

Step 43. adjustment of the orientation of the mirror (4314) and adjustment in translation of the lens (43 12).

The mirror (4314) is mounted on an angular positioner allowing its orientation to be adjusted The lens (4312) is mounted on a positioner with an axis in translation in the direction of the optical axis
FEP and FRD are used. An image is obtained from the sensor (4339) The punctuality and the coordinates of the FEP image point are evaluated by the procedure described in 7.3.3.1.

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The lens (4312) is adjusted so that the image is point.

The mirror (4314) is adjusted so that the image is centered.

Step 44. Position adjustment of the objectives.

The FEP beam is removed and the objective (4317) is replaced. The FRDI beam is used A temporary CCD sensor is placed behind (4323) on the path of FRDI. The lenses are adjusted so that the image is point-centered and centered with respect to the iris (4323).

Step 45. Translation adjustment of the lens (4324).

DEF is used. It successively passes through the objectives (4317) and (4319), then the lens (4324) and reaches the frequency meter, which is positioned behind (4324). The position of (4324) is adjusted so as to obtain an image which is as punctual as possible on the CCD of the frequency meter.

Step 46. Adjusting the orientation of the mirrors (4432) (4435), first adjusting the rotation of (4436) and first adjusting the orientation of the semi-transparent mirror (4325)
The SLMs (4405) (4412) (4417) are controlled to generate a center frequency. The FEG beam is used. (4325) is in the normal position. The path of the beam is controlled with a diffuser. Each mirror is adjusted so as to have the intended path. The beam must in particular occupy the entire opening of (4323).

Step 47. Installation of the beam extinguisher (4437)
This beam extinguisher is fitted as indicated in 7.3.2.2.

Step 48. Adjustment of the position and focal length of the doublet (4433) (4434), rotation adjustment of the assembly (4436), and adjustment of the orientation of the semi-transparent mirror (4325).

The lens (4434) is mounted on a positioner in translation along the optical axis This positioner and the lens (4433) are themselves mounted on a second positioner in translation along an axis along the optical axis.

les tableaux de commandez et BN N sont appliqués respectivement au SLM (4405) et aux
2 ' 2 2 ' 2 SLM (4412) et (4417) et lorsque le tableau de commande de (4427) est mis à 1, soit effectivement ponctuelle dans le plan de fréquence ou se trouve (4339). La position de (4325) doit être réglée pour que

dans ces conditions le point illuminé sur le CCD (4339) ait pour coordonnées C 'x , 2'x J . La position de (4433)(4434)(4436)(4325) doit en outre être réglée pour qu'il y ait une correspondance point à point entre les pixels de (4417) et ceux de (4339), c'est-à-dire pour que, lorsque les tableaux de commande Ai,j et
Bi,j sont appliqués respectivement au SLM (4405) et aux SLM (4412) et (4417) et lorsque le tableau de The position of (4433) (4434) must be adjusted so that the image of the FEG beam, when

the command tables and BN N are applied respectively to the SLM (4405) and to the
2 '2 2' 2 SLM (4412) and (4417) and when the control panel of (4427) is set to 1, either effectively punctual in the frequency plan where is (4339). The position of (4325) must be adjusted so that

under these conditions, the point illuminated on the CCD (4339) has the coordinates C ′ x, 2 ′ x J. Additionally, the position of (4433) (4434) (4436) (4325) must be adjusted so that there is a point-to-point correspondence between the pixels of (4417) and those of (4339), that is - say so that when the control tables Ai, j and
Bi, j are applied respectively to the SLM (4405) and to the SLM (4412) and (4417) and when the table of

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command of (4427) is at 1, the point illuminated on (4339) is the pixel of coordinates (i, j), whatever the integers i and j.

FRD and FEG beams are used. The control table applied to (4427) is set to 1.

calculées selon la procédure indiquée en 7.3.3.1., soient C rp'z , p o43. Réglage de (4433) pour obtenir le bon grandissement en fréquence et réglage en rotation de (4436). This adjustment is made by performing steps o41 to o43 o41 a sufficient number of times. Adjusting the joint position of (4433) and (4434) to obtain a point frequency image
The ANpix Npix control panel is applied to the SLM (4405) and the control panel
2 'Bnpix Npix command is applied to SLMs (4412) and (4417). The punctuality of the image generated on the CCD
2 '2 (4339) is evaluated according to the procedure described in 7.3.3.1. The position of the assembly (4433) (4434) is adjusted to have an image as point as possible. o42. Angular adjustment of (4325) to obtain a centered frequency image
The angular position of (4325) is adjusted so that the coordinates of the point image,

calculated according to the procedure indicated in 7.3.3.1., or C rp'z, p o43. Adjustment of (4433) to obtain the correct frequency magnification and rotation adjustment of (4436).

The PC program is used. However, in this program: - when a control word Ai, j is applied to the SLM (4405). the corresponding control word Bi, j is applied to the SLMs (4412) and (4417).

- the values X [i] and ni] are not obtained by the PB procedure. They correspond to the coordinates of the maximum determined by the procedure described in 7.3.3.1., Without specific action on an SLM.

The obtained inter-lens distance correction is applied to the distance between (4433) and (4434) and the rotation adjustment is made to (4436).

A 1 v pu. N pu et EN pu N pu des SLM (4405),(4412),(4417) et avec le faisceau FEG II peut être également
2, 2 2, 2 obtenu avec les tableaux de commande ANpix Npix BNpix N et avec le faisceau FEDI.

" "PK "fU ''' 2 ' 2 2 1, @/2 Step 49. Adjusting the rest of the 'left' part of the microscope
Each still unsettled element corresponds to a symmetrical element on the right side of the microscope. The setting of the still unadjusted elements is 'symmetrical' to the setting of the corresponding elements on the right side of the microscope. It is carried out symmetrically, the FEGI beam replacing the FEDI beam. However, the following fact must be taken into account (Npix, Npix) - a point centered on the sensor (4339) can be obtained with control panels

A 1 v pu. N pu and EN pu N pu of the SLMs (4405), (4412), (4417) and with the FEG II beam can also be
2, 2 2, 2 obtained with the ANpix Npix BNpix N control panels and with the FEDI harness.

"" PK "fU '''2' 2 2 1, @ / 2

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4 # nu et B;, # des SLM (4405),(4412),(44 1 7) et avec le faisceau FED. Il peut être également Npa ; "pu #HL-\ 2 ' 2 2 z' obtenu avec les tableaux de commande .9 N Af B N "" N pu et avec le faisceau FEGI. (Npix Npix) - a point centered in (Npix / 2, Npix / 2) on the sensor (4329) can be obtained with control boards

4 # nu and B ;, # of SLMs (4405), (4412), (44 1 7) and with the FED bundle. It can also be Npa; "pu # HL- \ 2 '2 2 z' obtained with the control panels .9 N Af BN""N pu and with the FEGI harness.

2 ' 2 2 ,. eut bzz 2 ' 2 2 ' 2 Etape 50. Mise en place de (4351)
Ce dispositif de décalage de phase est identique à celui décrit en 7.2.3. et mis en place comme indiqué en 7.3.2.3. 2 '2 2' The control words of the SLMs are therefore not perfectly equivalent during the two adjustments The adjustment of the left part of the microscope comprises in particular steps equivalent to steps 3 1 and 36. In these steps, the control panels ANpix Npix and BNpix Npix must be replaced by

2 '2 2,. eut bzz 2 '2 2' 2 Step 50. Installation of (4351)
This phase shift device is identical to that described in 7.2.3. and installed as indicated in 7.3.2.3.

At the end of this set of settings the system is ready to be used.
8. 6. Variation of the mode of use.

We can limit ourselves. to generate the three-dimensional image of the object, to the representation
Fo, defined in 7.17. This amounts, in the procedure described in 7.17.2., To adopting tables IBp, qnuls for any pair (p, q) # (0,0).

It is also assumed here that the object has an average index close to the nominal index of the observed object and that the optical table is completely free of vibrations.

Steps 7.9, 7.10, 7.11, 7. 13, 7. 15, 7.16 can then be deleted. The present method further differs from the previous one by the method used to adjust the position of the objectives before use, by the control tables applied to the beam deflector during image taking, and by the algorithm for superimposing the images.

8. 6.1. Setting goals.

This adjustment can be made in the presence of the object. It can also be performed with a transparent slide provided that the objective is not moved when the object is introduced.If objectives designed to operate without immersion liquid or coverslip are provided (nominal index equal to 1) and if the sample is not very thick or has an average index close to 1, it can also be carried out in the absence of any object.During this adjustment, the FEG and FRD beams are used and the following operations are carried out.

- we set the control panel of the SLM (4405) to 0 - we set the control panels of the other SLMs to 1.

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- The polarizer (4408) is adjusted in rotation so as to cancel the FEG beam received on (4339).

- the BNpix N control panel is applied to the SLM (4405) which is zero at all points except at the point of
2, @ / 2 coordinates (Npix / 2, Npix / 2).

- the punctuality of the image received on the sensor (4339) is evaluated using the procedure described in 7.3.3.1. with Fourier transformation.

- the position of the objectives is adjusted so that the image is perfectly punctual and centered.

- The polarizer (4408) is then brought back to its initial position.

( 1 ( ( N PIX) ( N plX )) lvpix 2 2 0/02
8.6.3.algorithme de calcul de la représentation tridimensionnelle
Les étapes 1 et 2 de l'algorithme décrit en 7.17.2. peuvent être supprimées. En effet, le réglage supplémentaire effectué, le tableau de commande du déviateur de faisceau utilisé, et l'abscence de vibrations permettent d'éviter tout décalage de phase du faisceau d'éclairage En particulier, si la variante décrite en 7.18.5. est utilisée, le dispositif de décalage de phase (4304) n'est pas utilisé, le déphasage #d étant constant et pouvant être choisi comme nul. 8. 6.2. beam diverter control
The Aij control panel used in 8.4.1. for the SLM (4405) is replaced

(1 ((N PIX) (N plX)) lvpix 2 2 0/02
8.6.3. Algorithm for calculating the three-dimensional representation
Steps 1 and 2 of the algorithm described in 7.17.2. can be deleted. Indeed, the additional adjustment carried out, the control panel of the beam deflector used, and the absence of vibrations make it possible to avoid any phase shift of the lighting beam. In particular, if the variant described in 7.18.5. is used, the phase shift device (4304) is not used, the phase shift #d being constant and can be chosen as zero.

9. Fifth embodiment
This embodiment does not allow image acquisition as fast as the previous embodiment and is not, for this reason, the preferred embodiment in the general case. However, in the particular field of UV radiation, it constitutes the preferred embodiment. Indeed, in this field, embodiments 3 and 4 are not feasible due to the non-availability of liquid crystals and polarizers. Taking into account the fact that it can operate with UV radiation of short wavelength, this embodiment is also the one which makes it possible to obtain the best definition on the generated image.

9. 1. Principles.

This fifth embodiment is similar to the second embodiment in that the image is captured in a plane of space and in that the variations in direction of the beam are effected using a mobile mirror. It approximates the third embodiment in that two microscope objectives are used, and in that most of the algorithms are modified forms of those used in the third embodiment. It differs from all the previous embodiments in that the wave of

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reference is not fixed but is modified at the same time as the illumination wave II is described by Figs 73 and 74.

The objective of this fifth embodiment is to improve the resolution by using an ultraviolet laser. There is no ferroelectric liquid crystal working in ultraviolet, and therefore it is necessary to adopt solutions based on more traditional optical components. In particular, the beam deflection device is a moving mirror (5113).

However, the use of a movable mirror in a system close to the first or the second embodiment generates vibrations. After each movement of the mirror, it is necessary to wait for the stabilization of the system before proceeding with the acquisition. In order to overcome the vibrations caused by the mobile mirror, it is necessary to position the latter outside the optical table and to separate the lighting and reference beams on the optical table, after passing the mirror. It follows that the movements of the mirror result in a simultaneous movement of the reference and illumination beams.

In order to take full advantage of the possible ultraviolet resolution, it is necessary to be able to effect, as in the third and fourth embodiments, changes in the orientation of the electric field vector of the lighting beam. These changes are made by separating the wave, by a semi-transparent mirror (5102), in two paths, a phase plate (5111) modifying the polarization being inserted on one of the paths and shutters (5104) and (5109) allowing you to choose the path used. The two waves are then superimposed again by a mirror (5112). The shutters are placed at a point where the light wave occupies only a small spatial extension and can therefore be opened or closed quickly.

For the same reason it is necessary to have several directions of analysis. On each side of the microscope, two CCD sensors are used, one for each direction of analysis. Insofar as it is difficult to have good polarizers in the UV range, the direction of analysis will be modified only by a modification of the direction of polarization of the reference wave, for example by means of wave plates ( 5238) (5239) which modify this polarization differently before each sensor.

The reference wave is mobile and can in particular pass through the object at an angle close to the maximum aperture of the objective. It follows that the spatial frequency received on the sensor can be twice as high as with a system where the reference wave is centered with respect to the optical axis as in the second embodiment. For an equal image size, a sensor of dimensions in pixels twice as large is therefore necessary, compared with the other embodiments.

To eliminate the direct illumination wave, a window (5165) or (5191) is used on which a black point is fixed, placed in a frequency plane. By moving this black point, the suppressed frequency is modified. On the other hand, this method does not make it possible to obtain the value of the wave at the point of direct impact of the lighting wave, on which the three-dimensional reconstructions carried out in the other embodiments are based. Furthermore, the movable mirror does not lend itself well to rapid changes in the illumination wave between very different frequencies. However, these changes were necessary in the third embodiment in order to obtain the reference images which made it possible to phase-shift the

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two-dimensional representations obtained on the sensor opposite to the point of direct impact of the illumination wave. This is why a phase registration method requiring neither a reference image nor acquisition of the point corresponding to the direct illumination must be provided in this embodiment.

Paragraph 9.2. physically describes the microscope used and paragraph 9. 3. gives the applicable sizing principles. Since the microscope is of a material design significantly different from Embodiment 3, its setting and use also differs greatly from the setting and use of the microscope according to Embodiment 3.

The microscope is subject to a set of adjustments made in the absence of the sample: - The position adjustment of the various elements is carried out as described in paragraph 9. 5. This adjustment calls for an acquisition procedure images described in paragraph 9.4.

- The tables allowing the control of the beam deflection mirror are determined as described in paragraph 9.6.

- The panels allowing the control of the windows (5165) and (5191), used to eliminate the direct light beam, are determined as described in paragraph 9.7.

- The constant K, equivalent to that used in the first embodiment, is determined as described in 9.8.

- The position of the CCD sensors must be fine-tuned as described in paragraph 9 10.

- The table characterizing the frequency response of the sensors is determined as described in paragraph 9.11.

- The relative coordinates of the central points of the images obtained on each side of the microscope are determined as described in paragraph 9.12.

- The phases of each light beam are determined as described in paragraph 9. 13,
After placing the sample, the microscope is subject to a set of additional adjustments: - The position of the objectives is adjusted as described in paragraph 9.14.

- The relative coordinates x, y, z of the points of origin of the reference beams associated with each objective, as well as the average index no of the sample and its thickness L, are determined as described in paragraph 9.15.

- The value w0 characterizing the position of the sample is calculated as described in paragraph 9.16. The procedure described in paragraph 9.16. is essentially similar to that described in paragraph 7.15. and in particular comprises a first focusing adjustment.

- The Dp aberration compensation function is obtained as described in paragraph 9 17.

When these settings have been made, the procedure for obtaining three-dimensional images is started. A version of this procedure, similar to that described for the third embodiment, is

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described in 9.18. A specifically adapted version of this procedure is described in 9.19. In all cases, the two-dimensional frequency representations are acquired using a procedure described in paragraph 9.9., Which is also used in certain tuning steps.

Although not recalled, a focusing adjustment similar to that described in 7.17.3. is performed, which may involve a recalculation of w0 and Dp.

A very simplified version of the operation of this microscope is described in 9.20.

By means of algorithmic modifications similar to those described in 7. 20 and 7.21, this embodiment can be adapted to the use of objectives exhibiting aberrations.

9. 2. Physical description.

A general diagram of the system is constituted by figures 73,74,63. The plan of Figs. 73 and 74 is horizontal The assembly (5176), circled in dotted lines in Fig. 74, is identical to the corresponding assembly in the fourth embodiment and is shown in Fig. 63.

A vertically polarized laser (5100) produces a beam whose electric field vector is therefore directed along an axis orthogonal to the plane of the figure. This beam then passes through a beam expander (5101).

The beam is then split in two by a semi-transparent mirror (5102). One of the beams coming from (5102) passes through a lens (5103) then a shutter (5104) placed in the focal plane of this lens. It then passes through a second lens (5105) whose object focal plane coincides with the image focal plane of (5103). then is reflected by a mirror (5106) and a semi-transparent mirror (5112). The part of the beam which is not reflected from (5112) will strike an absorbent surface (5253). The second beam coming from (5102) is reflected by a mirror (5107), passes through a lens (5108) then a shutter (5109) placed in the focal plane of this lens. It then passes through a second lens (5110) whose object focal plane coincides with the image focal plane of (5108). It then passes through a wave plate (5111) then passes through the mirror (5112) On leaving the mirror (5112) the two beams coming from the semi-transparent mirror (5102) are again superimposed. The focal lengths of the lenses (5103) (5105) (5108) (5110) are equal. The wave plate (5111) introduces an optical path difference of half a wavelength between its two neutral axes. It is positioned so as to transform the incoming beam polarized in the vertical direction into a beam polarized in the horizontal direction. The low spatial extension of the beam passing through the shutters (5104) (5109) allows the use of fast mechanical shutters, a small displacement being sufficient to shut off the beam.

The beam coming from (5112) goes towards the mirror (5113) which reflects it. This mirror is mounted on a two-axis positioner (5114) similar to that shown in FIGS. 2 and 3, which makes it possible to control its orientation. It is placed at the image focus of the lenses (5110) and (5105). The beam coming from (5113) then passes through the lens (5250) whose object focus is on (5113), then the lens (5251) whose object focus coincides with the image focus of (5250). It is then reflected by a partially transparent mirror (5115) which produces a reference beam directed towards (5117). The semi-transparent mirror (5117) then separates the reference beam into a straight FRD reference beam and a

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left reference FRG. The beam having passed through (5115) then passes through a partially transparent mirror (5116) which separates a specific beam FS from it. The beam having passed through (5116) is then separated by a semi-transparent mirror (5118) into a right lighting beam FED and a left lighting beam FEG.

The FRD beam first passes through a lens (5120) whose object focus coincides with the image focus of (5251), then a second lens (5121) whose object focus coincides with the image focus of (5120).

It is then reflected by a mirror (5122) placed at the image focus of (5121) and mounted on a piezoelectric 'stack' (5123) producing shifts of the order of the wavelength, which constitutes the shifting device of. phase, on the same principle as the element (122) of FIG. I. It then passes through a filter (5124) making it possible to adjust its intensity, then a lens (5125) whose object focus is on the mirror (5122). It then passes through a pair of lenses (5127) (5126) operating according to the principle explained in 8.1.4.1. , the object focus of the doublet (5127) (5126) being merged with the image focus of (5125). It is then separated into two beams by a partially transparent mirror (5234). One of these beams is then reflected by the mirror (5235), passes through a wave plate (5239). then is reflected in part towards the CCD (5174) by the partially transparent mirror (5236), the unreflected part being stopped by an absorbent surface (5237). The other beam passes through a wave plate (5238). then is reflected in part towards the CCD (5171) by the partially transparent mirror (5232), the unreflected part being stopped by an absorbent surface (5233). The CCDs (5174) and (5171) are respectively mounted on the cameras (5175) and (5172). They are each in an image focal plane of the doublet (5126) (5127).

The FRG beam is reflected by a mirror (5252). It passes through a lens (5145) whose object focus coincides with the image focus of (5251), then a second lens (5146) whose object focus coincides with the image focus of (5145). It is then reflected by a mirror (5147) placed at the image focus of (5146) and mounted on a piezoelectric 'stack' (5148) which constitutes the phase shift device. It then passes through a filter (5149) making it possible to adjust its intensity, then a lens (5150) whose object focus is on the mirror (5147). It then passes through a pair of lenses (5151) (5152) operating according to the principle explained in 8.1.4.1. , the object focus of doublet (5151) (5152) being the same as the image focus of (5150). It then passes through a rotation adjustment device of the type described in 8. 1.4.2. , consisting of mirrors (5219) (5220) and of the assembly (5221) consisting of mirrors (5214) (5215) (5216) (5217), and movable in rotation about an axis passing through the center of the mirrors ( 5220) (5214) (5217). It is then separated into two beams by a partially transparent mirror (5244). One of these beams is then reflected by the mirror (5245). passes through a wave plate (5249), then is reflected in part towards the CCD (5198) by the partially transparent mirror (5246), the unreflected part being stopped by an absorbent surface (5247). The other beam passes through a wave plate (5248), then is partly reflected towards the CCD (5201) by the partially transparent mirror (5242), the unreflected part being stopped by an absorbing surface (5243). The CCDs (5198) and (5201) are respectively mounted on the cameras (5199) and (5202). They are each in an image focal plane of the doublet (5151) (5152).

The FED beam is reflected by a mirror (5141), passes through a filter (5142) allowing its intensity to be adjusted, a lens (5143) whose object focus coincides with the image focus of (5251), a shutter

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(5144), and a lens (5154) whose object focal plane coincides with the image focal plane of (5143) and whose image focal plane coincides with the image of the diaphragm (5158) through the lens (5157). It is reflected by mirrors (5153) and (5155), then it is separated into two beams by a partially transparent mirror (5156). One of the beams, directed towards (5157), is the main beam and will be denoted FED. The other beam, directed towards (5159), constitutes the inverse indicator of FED and will be noted FEDI.

The FED beam passes through the lens (5157), the diaphragm (5158), the device (5176) shown in Fig. 63, passes through the diaphragm (5184) and the lens (5183). A focal plane of the lens (5157) coincides with the image focal plane of the microscope objective (4317) [in the conventional direction of use of the objective, here opposite to the direction of the rays]. A focal plane of the lens (5183) coincides with the image focal plane of the microscope objective (4319). The diaphragms (5158) and (5184) are placed in the planes where the objectives normally form the images of the sample. The beam coming from (5183) passes through the semitransparent mirror (5182). It passes through the lens (5188) whose object focal plane coincides with the image of the diaphragm (5184) through the lens (5183). It then passes through a glass (5191) of small thickness, on which there is an absorbing black point of a few tens of micrometers in diameter. This window is positioned in the image focal plane of the lens (5188) and its function is to stop the direct illumination beam. A diaphragm (5190) placed in approximately the same plane improves the filtering of spatial frequencies performed by the microscope objective. The beam then passes through a doublet (5192) (5193) whose object focal plane coincides with the glass (5191). It is then separated into two beams by a semi-transparent mirror (5240). One of the beams from (5240) reaches the CCD (5198) after passing through the partially transparent mirror (5246). The other beam is reflected by the mirror (5241) and arrives at the CCD (5201) after passing through the partially transparent mirror (5242). The CCDs (5198) and (5201) are each in an image focal plane of the doublet (5192) (5193).

The FEDI beam passes through the lens (5159), a focal plane of which coincides with the image focal plane of the lens (5154). He reaches the mirror (5160). optionally closed by the shutter (5161), which reflects it. It then passes through the lens (5159) and is reflected by the semi-transparent mirror (5156) towards the lens (5162). It passes through the lens (5162) whose object focal plane coincides with the image of the diaphragm (5158) through the lens (5157). It then passes through the partially transparent mirror (5163). It then passes through a glass (5165) of small thickness, on which there is an absorbing black point of a few tens of micrometers in diameter. This window is positioned in the image focal plane of the lens (5162) and its function is to stop the direct illumination beam. An optional diaphragm (5164) placed in approximately the same plane improves the spatial frequency filtering performed by the microscope objective. The beam then passes through a lens (5166) whose object focal plane coincides with the image focal plane of (5162). It is then separated into two beams by a semi-transparent mirror (5230). One of the beams from (5230) reaches the CCD (5174) after passing through the partially transparent mirror (5236). The other beam is reflected by the mirror (5231) and arrives at the CCD (5171) after passing through the partially transparent mirror (5232). The CCDs (5174) and (5171) are each in an image focal plane of the lens (5166).

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The FEG beam is reflected by the mirrors (5119) (5204), passes through a filter (5205) allowing its intensity to be adjusted, a lens (5206) whose object focus coincides with the image focus of (5251), a shutter (5207), a doublet (5179) (5178) whose object focal plane coincides with the image focal plane of (5206) and whose image focal plane coincides with the image of the diaphragm (5184) through the lens (5183) . It then passes through a rotation adjustment device of the type described in 8.1.4.2., Consisting of mirrors (5177) (5180) and of the assembly (5181) consisting of mirrors (5210) (5211) (5212) (5213 ), and movable in rotation about an axis passing through the center of the mirrors (5180) (5210) (5213). It is then separated into two beams by a partially transparent mirror (5182). One of the beams, directed towards (5183), is the main beam and will be denoted FEG. The other beam, directed towards (5185), constitutes the inverse indicator of FEG and will be noted FEGI.

The FEGI beam passes through the lens (5185), a focal plane of which coincides with the image focal plane of the doublet (5178) (5179). It reaches the mirror (5187), optionally closed by the shutter (5186). who reflects it. It then passes through the lens (5185) and is reflected by the semi-transparent mirror (5182) towards the lens (5188).

The FS beam first passes through a filter (5128) then a lens (5129) and is reflected by a mirror (5130). It then passes through a shutter (5254) then a lens (5140) whose object focus coincides with the image focus of (5129). It is then separated by a semi-transparent mirror (5163) into a main beam FS directed towards (5162) and an inverse indicator beam directed towards (5189), which will be denoted FSI. The FSI beam passes through a lens (5189), is reflected on a mirror placed at the object focal point of (5189) and can be closed off by a shutter (5209), passes through the lens (5189) and is again reflected by the semi-transparent mirror ( 5163) towards (5164).

Each lens used is an achromat or a compound lens minimizing optical aberrations.

The beam control principles indicated in 8.1.1. and 8.1.4. remain valid and the space (E) and frequency (F) planes have been indicated in the same way as for the fourth embodiment.

The reference wave is here parallel, like the illumination wave and as in the second embodiment. This is why it is punctual in the frequency planes and parallel in the space planes like the lighting wave. The special beam FS, on the other hand, is punctual in the space planes and parallel in the frequency planes, as was the reference wave in the fourth embodiment.

Many elements are mounted on positioners making it possible to adjust their position in an adjustment phase.

The assemblies (5181) and (5221) are mounted on rotating positioners, in accordance with their mode of operation explained in 8.1.4.2.

The other mirrors, partially transparent mirrors and piezoelectric mirrors are mounted on angular positioners to adjust their orientation.

The lenses that will be adjusted in 9.5. are mounted on positioners one dimension allowing movement in the direction of the optical axis.

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Each doublet consists of two lenses. It transforms a frequency plane located on one side of the doublet into a space plane located on the other side of the doublet. The lens located on the side of the space plane is mounted on a positioner allowing translation in the direction of the optical axis. This positioner is itself mounted on a second positioner also allowing translation in the direction of the optical axis. The second lens is mounted directly on this second positioner
The objective (-1317) is mounted on a two-dimensional positioner allowing positioning in a plane orthogonal to the optical axis. The objective (43 19) is mounted on a focusing device.

The sample (-1318) is mounted on a three-axis positioner in translation.

* The CCDs are mounted on positioners one axis in rotation and three axes in translation, allowing rotation around the optical axis and three degrees of freedom in translation.

The dotted line (5203) separates two areas. The elements located to the left of this line are mounted on a table directly linked to the ground, without damping. The elements to the right of this line or in Fig. 74 are mounted on an optical table suitably isolated from vibrations. The two tables are at the same level The panes (5165) and (5191), the diaphragms (5164) and (5190), and the shutters (5144) (5207) are the only exceptions to this rule. Each of the panes (5165) and (5191) is mounted on a two-axis motorized translational positioner allowing movement in a plane orthogonal to the optical axis, itself mounted on a manual positioner allowing translation in the direction of the optical axis, itself directly linked to the ground. The two-axis translation positioning system must be precise and not cause parasitic rotational movements of the window. Indeed, such displacements would lead to phase variations which may in certain cases be detrimental to the quality of the images produced.

Each of the shutters (5144) (5207) is linked directly to the ground. Each of the diaphragms (5164) (5190) is linked to the ground by means of a positioner 3 axes in translation and 1 axis in rotation about the optical axis.

In order to be able to link the windows and shutters to the ground, a rigid mechanical construction is used to obtain a stable support located above the optical table, linked to the floor and not to the optical table, and to which the shutters and the shutters can be fixed. windows, through their positioners
The diaphragms (5164) and (5190) are made as shown in Fig. 82. The diaphragm (5710) has a circular opening (5711), a part (5712) making it possible to conceal a portion of additional surface in this opening.

On each camera we have indicated the reference which is used to express the coordinates of the pixels of the corresponding CCD. On each wave plate, a mark has been indicated. The directing vector of this frame in the plane of the figure is denoted by 17 and the directing vector of this frame in the plane orthogonal to that of the figure is denoted j. The wave plate (5111) has a neutral axis directed along i + #. The other wave plates have neutral axes directed along # cos # + # sin # / 8.

8 8
In the case where this microscope works in the field of ultraviolet:

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- All of the non-polarizing components crossed by the light, that is to say the lenses, including those of the objectives, the panes, and the substrates of semi-transparent mirrors, can be made of a silica.

Silica or quartz lenses are available from various manufacturers.

- Mirrors and semi-transparent mirrors must be specially designed for UV - The wave plates are for example made of quartz.

- The laser is for example an excimer laser. In pulsed mode, the pulses must be synchronized with the acquisition of images, for example at 1 image per pulse.

9. 3. Sizing.

'èdN.11 critère Nvquist: ## critère de Nyquist: @/2 2 2a On obtient donc: pc # #/4 f2/f1 g/o d'ou : f1/f2 # #/4pc g/o We note: f1: focal length of the lens (5162) or of the lens (5188) f2: focal length of the lens (5166) or of the doublet (5192,5193) f3: focal length of the lens (5157) or of the lens (5183) pc distance between the centers of two adjacent pixels, on CCD sensors 2 Npix: lateral dimension in pixels of a CCD sensor. o: numerical aperture of a microscope objective g: magnification of a microscope objective f0: focal length of a microscope objective. do: distance between the lens (5157) and the diaphragm (5158). l1: width of the diaphragm (5164) or (5190) The lens (5157) must have its object focal plane coincident with the image focal plane of the microscope objective, and is located at a distance do from the image of the objective We check that this implies: f3 = gfo + do The opening of the beam on arrival at the CCD is: a = f1 o f2 g The sampling period required on the CCD must be greater than pc and is valid for each application of

'èdN.11 Nvquist criterion: ## Nyquist criterion: @ / 2 2 2a We thus obtain: pc # # / 4 f2 / f1 g / o hence: f1 / f2 # # / 4pc g / o

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The ratio f1 / f2 must therefore be equal to or slightly less than # / 4pc g / o, each of the values f1 and f2 being f2 4pc o moreover sufficient to avoid spherical aberration
The diaphragm width l1 (5164) should filter out only frequencies above the nominal lens aperture. We must therefore have l1 = 2f @ o / @. g
The diameter of the beam incident on the mirror (5113) must be such that the necessary variations in direction can actually be produced in a reproducible manner using the positioning system of this mirror. We denote by p [alpha] the angular displacement step of the mirror, that is to say the smallest variation in the orientation angle of this mirror which can be carried out, in a reproducible manner. by the positioning system of this mirror. We denote by L) draph the opening diameter of the diaphragm (5158) and
Determine the diameter of the incident beam on the mirror (5113). We then check that the present condition is expressed by: p [alpha] # o / gNpix Ddiaph / Dnur where the sign # means much lower, for example
1 0 Ddiaph P [alpha] <10 gNpix Dnur
Apart from the above criteria, there is quite a bit of freedom in choosing the focal lengths of the other lenses. The sizing criteria applied to the trajectory of the FEG, FED, FRG, FRD beams are as follows: (1). The succession of space and frequency planes must be as specified in the diagram. This succession of space and frequency planes constitutes the method used to control the trajectory and the opening of the beam as specified in 8.1.1.

(2). The lighting and reference beams, in the absence of a diaphragm used between the mirror (5113) and the CCD sensors, must have the same diameter when they arrive at the sensors. Equivalently, they must have the same aperture, the aperture being here the angle between the parallel beams reaching the CCDs for two different positions of the mirror (5113).

(3). The focal lengths of the lenses must be sufficient to avoid spherical aberration (4). The focal lengths of the different lenses are adapted so as to comply with the size constraints.

critère (4) se traduit par 2 fla + 2 fb = L , d'ou on tire fa = - 2 DI + D2 et fb = bzz . For example, if the diameter of the beam is D1 at (5122) and must be D2 when it arrives at the CCD sensor, and if the distance between (5122) and (5174), following the intended path for the beam, is L, then if fa and fb are respectively the focal lengths of the lens (5125) and of the doublet (5126) (5127), and taking into account the principles exposed in 8.1.1., Criterion (1) results in D2 = -and the
D1 fa

criterion (4) results in 2 fla + 2 fb = L, from which we derive fa = - 2 DI + D2 and fb = bzz.

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The whole system will be adjusted so that when the FEG beam enters the objective (4317) while being directed along the optical axis, its direction on arrival at (5174) or (5171) is merged with that of the reference wave. When the mirror (5113) is moved from this central position, the direction of the reference beam will be changed in one direction and the direction of the illumination beam will be changed in the opposite direction, i.e. in one direction. frequency plane the points corresponding to the FEG and FRD beams will remain symmetrical with respect to the point corresponding to the illumination beam when it enters the objective in the direction of the optical axis. Maintaining this symmetry is made possible by - the general configuration of the device. Indeed, using the diagram of FIG. 67, when the beam passes from a space plane (4801) to a second space plane (4804), its direction is reversed. In the configuration adopted, the difference between the number of space planes crossed by the lighting beam and the number of space planes crossed by the reference beam is an odd number, and the lighting beam is therefore inverted relative to the reference beam.

- compliance with condition (3), which means that the displacement of the reference beam and the displacement of the lighting beam are of the same amplitude.

This displacement symmetry simplifies the algorithms and the adjustment procedure.
The sizing criteria applied to the path of the FS beam are as follows - the FS beam must be parallel when it arrives at (5163) - its width when it arrives at (5163) must be equal to that of a beam which would be point in the plane (5158) and the opening of which would be limited by the opening of the lens. This width, when the beam arrives at (5163), is equal to approximately f1 og
9. 4. Obtaining a simple two-dimensional frequency representation and determining the maximum
A simple two-dimensional frequency representation is understood here to mean a representation for which polarizations have not been taken into account, which can be obtained without knowing the values of.: And of the point of direct impact of the lighting wave, at from a single sensor. The steps for producing such a representation, for a given illumination wave, are as follows: Step 1- acquisition: (5104) is open and (5109) is closed, so that the illumination background polarization is fixed. d is defined as follows, the phase shift being performed with the piezoelectric actuators (5123) (5148) previously calibrated:

<tb>
<tb> index <SEP> d <SEP> offset <SEP> of <SEP> phase
<tb> (degrees)
<tb>

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<tb>
<tb> 0 <SEP> +120
<tb> 1 <SEP> 0
<tb> 2 <SEP> -120
<tb>

The image is obtained from any of the CCD sensors. When obtained using (5171) or (5201) the phase plates (5238) and (5248) must be removed.

.lfGr,=6(2.fIO0r,]-.1lllr,]-A2Ir,j+j z.llFlr.]-.'lft2y..1]) Etape 3- transformation de Fourier . We thus obtain the tables MF [d] [i, j] or i and; vary from 0 to 2N pu: -1, Step 2- Calculation of two-dimensional spatial representations. The program performs:

.lfGr, = 6 (2.fIO0r,] -. 1lllr,] - A2Ir, j + j z.llFlr.] -. 'lft2y..1]) Step 3- Fourier transformation.

représentation fréquentielle -,,fHll, Ji ou/? prend les valeurs 0 ou 1 et ou / et varient de 0 à 2N pix - Dans certains cas, cette transformation de Fourier peut ne pas être effectuée : obtient alors une représentation spatiale au lieu d'une représentation fréquentielle. The Fourier transform of table MG according to the indices i and / is carried out. This generates the

frequency representation - ,, fHll, Ji or /? takes the values 0 or 1 and or / and vary from 0 to 2N pix - In some cases, this Fourier transformation may not be performed: then obtains a spatial representation instead of a frequency representation.

tableau -S'a a maintenant pour dimensions 2Npa x 2:'n,x et est le tableau A/77 calculé comme ci-dessus Il obtient ainsi les coordonnées imax,jmax du maximum sur le capteur concerné. L'image est considérée comme centrée si (/w#r,yMoy) = (,'4'p, llÍ plX ) et elle est considérée comme parfaitement ponctuelle lorsque la valeur du maximum obtenue est la plus élevée possible. When the image is roughly point and the coordinates and the maximum value must be known, the maximum calculation program proceeds as described in 7.3.3. 1., except that the

array -S'a now has dimensions 2Npa x 2: 'n, x and is array A / 77 calculated as above. It thus obtains the coordinates imax, jmax of the maximum on the sensor concerned. The image is considered to be centered if (/ w # r, yAvg) = (, '4'p, llÍ plX) and it is considered to be perfectly point when the maximum value obtained is the highest possible.

9. 5. Adjustment of manual positioners
9. 5.1. Adjustment criteria:
FEP denotes a plane illumination beam entering the objective (4317) while being directed along the optical axis and reaching the sensors (5174) (5171).

The adjustments aim to ensure that: (1) the beams follow the intended path.

(2) the illumination and reference beams are point in the frequency planes and parallel in the space planes.

(3) the FS and FSI beams are point in the space planes (4) the FS and FSI beams have point images and centered on the sensors (5171) (5174) (5201) (5198).

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(5) a parallel FEP beam entering a microscope objective (4317) and directed along the optical axis has a point image and centered on the two-dimensional frequency representations obtained by procedure 9.4. from the images received on the sensors (5174) or (5171).

(6) When the image of the FEG beam on the two-dimensional frequency representations obtained by procedure 9.4 from the images received on the sensors (5174) or (5171) is point and centered, then the image of the FEGI beam on the two-dimensional frequency representations obtained by procedure 9.4. from the images received on the sensors (5198) or (5201) is punctual and centered.

(7) Whatever the position of the mirror (5113): - the points corresponding to the FRD, FEDI, FEG, FEP beams on the two-dimensional frequency representations obtained by procedure 9.4. from the images received on the sensors (5174) or (5171) are arranged as shown in Fig. 78 - the points corresponding to the beams FRG, FEGI, FED on the two-dimensional frequency representations obtained by procedure 9.4. from the images received on the sensors (5198) or (5201) are arranged as shown in Fig. 79.

To make this condition more explicit, we will denote in the same way a beam and the corresponding point on one of the sensors and we denote (A, B) the vector connecting the points A and B This condition means that: (i) FRD and FEDI are on the same vertical line.

(ii) FEDI and FEG are on the same horizontal line.

(iii) FEP is the midpoint of FRD and FEG (iv) (FRG, FEGI) = (FRD, FEDI) (v) (FEGI, FED) = (FEG, FEDI)
The adjustments naturally follow from compliance with conditions (1) to (7) The series of adjustment steps detailed below constitutes an example of the ordering of these adjustments.

9. 5.2. Adjustment steps.

In certain adjustment phases, a temporary parallel beam noted FEP will be used.This beam is derived directly from the laser (5100) using a semi-transparent mirror and directed towards the entrance of the objective (4317), to which it arrives while being directed along the optical axis, and that it crosses before heading towards the sensors (5171) and (5174).

The establishment of VET requires the temporary removal of the target (4319). The parts of the system said to be linked to the ground are in reality linked to a flat support usually placed on the ground or on a table without any particular precaution, the optical table itself being placed, by means of shock absorbers, on this flat support. . During all the adjustments described in this paragraph, the optical table will be secured to the flat support, that is to say fixed without damping and without freedom of movement to the flat support, in a position as close as possible to the position of the optical table when it is free on its dampers. The flat support itself will be fixed on a second table

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optical. This device makes it possible to generate interference figures using the FEP beam, which would be impossible due to the vibrations if said flat support were fixed directly to the ground as in the phase of normal operation of the microscope.

The use of the FEG, FED, FEGI, FEDI, FS, FSI harnesses is controlled by the shutters (5144) (5207) (5218) (5209) (5161) (5186) (5254). Shutters, not shown, also make it possible to eliminate the FRD and FRG beams.

t U: ' ptJC / '
Les étapes suivantes constituent un exemple d'ordonnancement des réglages: Etape 1 : Préréglage
Un préréglage est effectué pendant lequel le miroir est positionné en une position centrale et la trajectoire du faisceau est contrôlée avec un diffuseur. Pendant ce préréglage, la position de l'ensemble des éléments est réglée de manière à ce que le faisceau suive approximativement la trajectoire prévue. Par exemple, à la sortie de (5112) on vérifie la bonne superposition spatiale des faisceaux. Entre (5156) et (5159) on vérifie que le faisceau réfléchi a la même extension spatiale que le faisceau arrivant. On an image of dimensions 2Npix x 2Npix a point will be said to be centered if its coordinates are

t U: 'ptJC /'
The following steps are an example of ordering the settings: Step 1: Presetting
A preset is performed during which the mirror is positioned in a central position and the beam path is controlled with a diffuser. During this presetting, the position of all the elements is adjusted so that the beam approximately follows the intended path. For example, at the output of (5112), the correct spatial superposition of the beams is checked. Between (5156) and (5159) it is verified that the reflected beam has the same spatial extension as the incoming beam.

During the entire adjustment that follows, this preset can be constantly checked or refined, always using the diffuser, without being reminded of this. If you work in the field of UV, it is dangerous to directly visualize the light. The diffuser is then replaced by an auxiliary CCD, and the area illuminated on this CCD is observed on a screen instead of directly observing it Step 2: Translation adjustment of the lens (5105)
The frequency meter is positioned behind the lens (5105) and the position of the latter is adjusted to have a point image on the frequency meter.

Step 3: Translation adjustment of the lens (5110)
The frequency meter is positioned behind the lens (5110) and the position of the latter is adjusted to have a point image on the frequency meter.

Step 4: Adjusting the orientation of the semi-transparent mirror (5112),
The frequency meter is used and positioned behind (-il 12). The shutters (5104) and (5106) being open and closed alternately, the integrated image produced on the frequency meter sensor consists of two points coming from each of the superimposed beams. The angular position of (5112) is adjusted so as to superimpose these two points.

Step 5: translational adjustment of the lens (5251)
The frequency meter is positioned behind the lens (5251) and the position of the latter is adjusted to have a point image on the frequency meter.

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Step 6: translational adjustment of the lens (5121)
The frequency meter is positioned behind the lens (5251) and the position of the latter is adjusted to have a point image on the frequency meter.

Step 7-Translation adjustment of the doublet (5127) (5126)
The frequency meter is placed behind (5127) on the path of the beam and the doublet is moved so that the image on the CCD of the frequency meter is point.

Step 8-Translation adjustment of the lens (5146).

This adjustment is carried out using the frequency meter, placed behind (5146). The image on the frequency counter's CCD should be as punctual as possible.

Step 9-Translation adjustment of the doublet (5151) (5152):
The frequency meter is placed behind (5152) on the path of the beam and the adjustment is carried out so that the image on the CCD of the frequency meter is punctual.

Step 10-Translation adjustment of the lens (5140)
The adjustment is carried out using the frequency meter placed behind (5140). The image on the frequency counter's CCD must be punctual.

Step 11-Translation adjustment of the lens (5154)
The frequency meter is placed behind (5154). The image on the frequency counter's CCD must be punctual / / Step 12-Translation adjustment of the doublet (5178) (5179)
The frequency meter is placed for example behind (5213). The image on the frequency counter's CCD must be punctual.

Step 13-Translation adjustment of the lens (5159)
The frequency meter is placed between (5156) and (5162). The position of (5159) is adjusted so that the image of FEDI on the CCD of the frequency meter is punctual.

Step 14-Introduction of a temporary parallel FEP lighting beam.

This beam has the characteristics explained at the beginning of this paragraph.

Step 15-Translation adjustment of the lens (5157)

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The frequency meter is placed between (5156) and (5162). The position of (5157) is adjusted so that the image of FEP on the CCD sensor of the frequency meter is punctual.

Step 16-Adjusting the orientation of the semi-transparent mirror (5156)
The position of (5156) is adjusted so that FEP and FEDT have coincident point images on the frequency meter.

Step 17-Translation adjustment of the lens (5162).

A CCD is provisionally placed at the location of (5158). FS is used. (5162) is set so that the FS image on this temporary CCD is point.

Step 18: Adjust the orientation of the partially transparent mirror (5163)
The CCD remains used with the FS beam. (5163) is set so that the FS image on this temporary CCD is centered relative to the location of the diaphragm.

Step 19-Translation adjustment of the lens (5189)
The frequency meter is positioned between (5163) and (5164). (5189) is adjusted so as to obtain a point image of FSI on the frequency meter.

Step 20-Translation adjustment of the lens (5166)
FEDI is used. The frequency meter is positioned on the path of the beam behind (5166) and the position of (5166) is adjusted so that the image of FEDI on the frequency meter is point.

Step 21-3-axis translation adjustment of the sensors (5174) and (5171).

We use FSI and FRD. A program calculates the two-dimensional frequency representation received on each CCD (5174) or (5171) according to the procedure described in 9.4., But by not performing the Fourier transformation step 3. The position of the CCDs is adjusted to obtain a centered point image from each CCD.

Step 22-Adjust the orientation of the partially transparent mirror (5236)
We use FRD and FEDI. A program calculates the two-dimensional frequency representation received on the CCD (5174) according to the procedure described in 9.4.

The position of (5236) is adjusted so that the two-dimensional frequency representation obtained on each CCD is centered.

Step 23-Adjust the orientation of the partially transparent mirror (5232)
We use FRD and FEDI. A program calculates the two-dimensional frequency representation received on the CCD (5171) according to the procedure described in 9.4.

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The position of (5232) is adjusted so that the two-dimensional frequency representation obtained on each CCD is centered.

Step 24-Adjustment of the focal length of the doublet (5126) (5127) and adjustment in rotation about the optical axis of the sensors (5174) (5171).

FRD, FEP beams are used. A program calculates the two-dimensional frequency representation received on each CCD (5174) or (5171) according to the procedure described in 9.4.

The initial position of the mirror (5113), in which the previous adjustments have been made, is the centered position. It must be registered. We will call it position C.

The mirror (5113) is moved in such a way that, on the two-dimensional frequency representation obtained on each CCD (5174) or (5171), the point corresponding to FEP is eccentric to the maximum. This mirror position is saved and will be reused later. We will call it position E.

The FEDI bundle is introduced
The positions of the different elements are adjusted so that on each of the two representations obtained: - the coordinates of the points associated with FRD (central point) and FEDI are correct with respect to those of the point associated with FEP, that is to say symmetrical with respect to the horizontal axis passing through the point associated with FEP, as indicated in Fig. 78 or (5501) represents the contour of the two-dimensional zone obtained at the end of the procedure described in 9. 4. and or ( 5502) represents the limit defined by the aperture of the lens.

- the images of FEP and FEDI remain punctual More precisely: - the focal length of the assembly (5126) (5127) is adjusted so that the distance between the point associated with FEP and the point associated with FRD is equal to the distance between the point associated with FEP and the point associated with FEDI.

As changes in the position of the doublet lenses can cause defocus, the positions of the doublet lenses are also adjusted so that the image of FEP and FEDI remains punctual - the rotational position of the sensors is adjusted so that the line passing through them. points associated respectively with FRD and FEDI is vertical.

Due to the non-coincidence of the axis of rotation of the CCDs with the central point of these sensors, this rotation adjustment can lead to a loss of the translation adjustment of the CCDs. This is why, at the end of this operation, the mirror is returned to position C and step 21 is carried out again. Steps 21 and 24 can thus be repeated in sequence a certain number of times so as to converge towards a correct adjustment of the sensors in translation and in rotation.

Step 25-Translation adjustment of the position of the objectives (4319) and (43 17)

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The mirror (5113) is returned to its original position (position C), the FEP beam is removed, the objectives are put back in place. A temporary CCD is positioned at the location of (5184). Only the FS beam is used. A transparent slide is used as the object.

The position of the objectives is adjusted to obtain a point and centered image.

Step 26-Translation adjustment of the lens (5183)
The DEF beam is used. The frequency meter is positioned behind (5183) on the trajectory of FED. (5183) is set so that FED has a point image on the frequency meter.

Step 27-Translation adjustment of the doublet (5178) (5179) and adjustment of the orientation of the semitransparent mirror (5182)
FEG and FRD beams are used. A two-dimensional frequency representation is obtained from the CCDs (5174) or (5171) by procedure 9.4.

The joint position of the doublet (5178) (5179) is adjusted so that the representation obtained is point. The semi-transparent mirror (5182) is set so that this image is centered.

Step 28-Adjusting the focal length of the doublet (5178) (5179), adjusting the rotation of the assembly (5181), and adjusting the orientation of the semi-transparent mirror (5182).

FRD, FEG beams are used. A two-dimensional frequency representation is obtained from the CCDs (5174) or (5171) by procedure 9.4. The above operations ol and o2 must be repeated in this order a number of times to converge to a correct setting. ol: The mirror (5113) is placed in position C and the semi-transparent mirror (5182) is adjusted so that the point of the frequency representation corresponding to FEG is centered. o2: The mirror (5113) is placed in position E (off-center).

The various elements are adjusted so that the point corresponding to FEG obtained on the image is correctly positioned in relation to the others. The point corresponding to FEP is known by the adjustment made in step 24. The point corresponding to FEG must be symmetrical to the point corresponding to FRD with respect to the point corresponding to FEP as shown in FIG. 78.

More precisely: the focal length of the doublet (5178) (5179) is adjusted so that the distance between the points corresponding to FRD and FEP is equal to the distance between the points corresponding to FEP and FEG. As changes in the position of the doublet lenses can cause defocus, the positions of the doublet lenses are also adjusted so that the FEG image remains punctual.

- the rotational position of the assembly (5181) is adjusted so that the FRD, FEP and FEG points are aligned.

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Step 29-Translation adjustment of the lens (5185)
The mirror (5113) is returned to position C. The frequency meter is positioned between (5182) and (5188). The position of (5185) is adjusted so that the image of FEGI on the frequency meter is punctual Step 30-Translation adjustment of the lens (5188)
The FS beam is used. The frequency meter is positioned behind (5188). The position of (5188) is set so that FS has a point image on the frequency counter's CCD.

Step 31-Translation adjustment of the doublet (5192) (5193)
FEGI is used. The frequency meter is positioned behind (5193). The joint position of (5192) (5193) is set so that FEGI has a point image on the CCD of the frequency meter.

Step 32-3-axis translation adjustment of the sensors (5198) and (5201).

FS and FRG are used. A program calculates the two-dimensional frequency representation received on each CCD (5198) or (5201) according to procedure 9.4. but by not performing step 3 of Fourier transformation. The position of the CCDs is adjusted to obtain a centered point image from each CCD.

Step 33-Adjust the orientation of the partially transparent mirror (5246)
FRG and FEGI are used. A program calculates the two-dimensional frequency representation received on the CCD (5198) according to procedure 9.3. 1.

The position of (5246) is adjusted so that the two-dimensional frequency representation obtained is centered.

Step 34-Adjust the orientation of the partially transparent mirror (5242)
FRG and FEGI are used. A program calculates the two-dimensional frequency representation received on the CCD (5201) according to procedure 9.3.1.

The position of (5242) is adjusted so that the two-dimensional frequency representation obtained is centered.

Step 35-Adjustment - of the focal length of the doublet (5151) (5152) - of the focal length of the doublet (5192) (5193) - of the assembly (5212) in rotation - of the CCDs (5198) and (5201) in rotation around the optical axis
FRG, FED, FEGI beams are used. The mirror (5113) is returned to position E (off-center).

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A program calculates the two-dimensional frequency representation received on the CCDs (5198) (5201) according to procedure 9.3.1.

The positions of all the elements are adjusted so that: - the coordinates of the points associated with FRG, FED, FEGI are correct, or with the notations used in 9.5.1. : (FRG, FEGI) = (FRD, FEDI) and (FEGI, FED) = (FEG, FEDI) or the positions of the points FRD, FEG, FEDI are those obtained during steps 24 and 28, all these points being shown in Figs. 78 and 79.

- the images of FEP and FEG remain punctual More precisely:
The focal length of the doublet (5192) (5193) is adjusted so that the distance between the points corresponding to FEGI and FED is correct. As changes in the position of the doublet lenses can cause defocus, the positions of the doublet lenses are also adjusted so that the image of FED and FEGI remains punctual.

The rotational position of the CCDs (5198) and (5201) is set so that the FEGI-FED segment is horizontal.

The focal length of the doublet (5151) (5152) and the position of the assembly (5151) (5152) are adjusted so that the distance between FRG and FEGI is correct and so that the line connecting these points is vertical. As changes in the position of the doublet lenses can cause defocus, the positions of the doublet lenses are also adjusted so that the FEGI image remains punctual.

After this adjustment, the mirror (5113) is returned to position C.

Steps 32 to 35 can be repeated in this order a number of times to converge to the correct positions. In fact, step 35 results in a deregulation of the central position of the CCDs and of the orientation of the reference beams used in position C.

Step 36: adjustment of the position of the window (5165) in the direction of the optical axis.

FSI and FRD beams are used. A frequency image is obtained by procedure 9.4.1 from the sensors (5171) (5174). On this frequency image, the black point of the window is visible in dark on a light background. The position of the glass is adjusted so that the black point stands out against the background with the best possible contrast.

Step 37: adjustment of the position of the window (5191) in the direction of the optical axis.

FS and FRG beams are used. A frequency image is obtained by procedure 9.4. from the sensors (5201) (5198). On this frequency image, the black point of the window is visible in dark on a light background. The position of the glass is adjusted so that the black point stands out against the background with the best possible contrast.

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Step 38: in rotation around the optical axis and 2-axis translation of the diaphragms (5164) and (5190)
Prior to this adjustment, the mirror (5113) is returned to the central position.

These diaphragms have the shape shown in Fig. 82. They are adjustable in translation on 3 axes and in rotation around the optical axis. FS, FSI, FRG, FRGI beams are used for their adjustment. A frequency image is obtained by procedure 9.4. from each of the sensors (5174) (5198).

They are adjusted in translation so as to have an image centered on each sensor and as clear as possible without however hampering the movement of the movable window (5165) or (5191) associated with them. They are rotated so that the coordinates of the point obscured by the moving part (5712) are the same on the image obtained from each sensor. These coordinates will then be noted (io.jo). At the end of this adjustment, the program also determines the radius Rouv of the image obtained on each sensor, which characterizes the zone accessible by the beams not stopped by the opening of the objective. It is better to slightly underestimate Rouv.

Following this adjustment procedure, the objectives are positioned so that FS has a point and centered image on each sensor. This setting will not be changed until the sample is introduced.

9. 6. Beam diverter control.

Each mirror position corresponds to a maximum (point FE in Fig. 75) of the frequency image obtained by procedure 9.4. The point FR corresponding to the reference wave is at the center of the image. The point FO corresponding to the optical center is the midpoint of FR and FE. The coordinates of the point FE in a frame centered on FO are the equivalent of the coordinates of the point of direct impact of the reference wave with respect to the optical center in the third embodiment.

The index p will characterize the right or left side of the microscope with p = O for the sensors (5171) (5174) and p = 1 for the sensors (5198) (5201).

The beam deflection mirror positioning system consists of two actuators that do not have hysteresis. For example, positioning by stepper motors can be used as described in the first embodiment. If the assembly is carried out with sufficient care, such a system can exhibit very low hysteresis. The position of the mirror is then characterized by the number of steps taken by each motor from a central point. It is also possible to use piezoelectric positioners equipped with a feedback loop allowing precise control of their elongation, in which case the number of steps of each motor is replaced by the extension of each actuator. It is also possible to use piezoelectric positioners without a feedback loop, however these have a high hysteresis which requires determining the voltages used on a given path, a point-to-point determination of the position values of the mirror, as performed below. below, not being possible.

The motor control is defined by two tables tabl and tab2 where tab1 [p.i.j] (resp. Tab2 [p.i.j]) is the number of steps that actuator 1 (resp.2) must take so that point FF has the

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dans lequel FO a pour coordonnées CNZx , r2J . Les actionneurs sont numérotés de sorte que l'actionneur 1 détermine un mouvement selon l'axe i et l'actionneur 2 détermine un mouvement selon l'axe j. coordinates (i, j) on the image obtained by procedure 9.4. from a sensor indexed by p, in a reference (Npix Npix)

in which FO has the coordinates CNZx, r2J. The actuators are numbered so that actuator 1 determines movement along axis i and actuator 2 determines movement along axis j.

The tables tabl and tab2 are determined in the absence of an object (transparent slide), by a specific program. The program then determines, for each objective point, the corresponding number of steps of each motor from an origin point. Fig. 77 represents an example of an algorithm of such a program. The main steps are: (5407): modification of the shutter control. When p = 0 the beam used must be FEG and when p = 1 the beam used must be FED.

(5401): imax and jmax correspond to the coordinates of the maximum obtained by procedure 9.4 from the sensor receiving the point of direct impact of the lighting wave. We then have: imax x = @
2 jmax (5402): the lim value used depends on the accuracy of the actuators. We can for example have hm = 0.25.

pas 1=(i-x).pa.s~par~pixel 2 pas2=(i-.y).pas~par~pixel,'2 La valeur de position courante est modifiée: pos1 + =pas1 pos2+=pas2 pas~par~pixel est le rapport (nombre de pas de déplacement du moteur)/(nombre de pixels de déplacement de FE sur l'image obtenue en 9.4.). Il doit avoir été préalablement déterminé, de manière similaire à ce qui est fait dans le premier mode de réalisation, mais avec les images maintenant calculées selon la procédure 9.4. et non pas obtenues directement sur le CCD. (5403): the displacement of the motors is worth, in a similar way to what was done in 5.20 .:

step 1 = (ix) .pa.s ~ by ~ pixel 2 pas2 = (i-.y) .pas ~ by ~ pixel, '2 The current position value is modified: pos1 + = step1 pos2 + = step2 not ~ by ~ pixel is the ratio (number of motor displacement steps) / (number of FE displacement pixels on the image obtained in 9.4.). It should have been previously determined, similar to what is done in the first embodiment, but with the images now calculated according to procedure 9.4. and not obtained directly on the CCD.

tab Ifp, 1,1 1=pos1 tab2(p.r,]=po.s2 Toutefois, dans le cas Ci - ,, 2' +\j , 2 > R ouv 2 les valeurs affectées sont par exemple des valeurs négatives signalant une erreur, comme tabl ,i j]=-10000, tab2\p,i,j]= -10000 (5406): les moteurs sont déplacés de -posl, -pos2 de manière à retourner au point d'origine, qui doit rester constant pour éviter de fausser la trajectoire. (5404): the motors are moved, for a number of steps step 1, steps :! of each motor (5405): the current values of the coordinates in motor steps are recorded in a table:

tab Ifp, 1,1 1 = pos1 tab2 (pr,] = po.s2 However, in the case Ci - ,, 2 '+ \ j, 2> R open 2 the affected values are for example negative values indicating an error , like tabl, ij] = - 10000, tab2 \ p, i, j] = -10000 (5406): the motors are moved from -posl, -pos2 so as to return to the point of origin, which must remain constant for avoid distorting the trajectory.

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deux moteurs jusqu'à leurs positions caractérisées respectivement par tabl[p,ijl et tab2[p.t,j]. et on actionnera les obturateurs (5144) et (5207) selon le tableau suivant:

To obtain an illumination wave on the sensor p, at the point of coordinates i, j, we will move the

two motors up to their positions characterized respectively by tabl [p, ijl and tab2 [pt, j]. and the shutters (5144) and (5207) will be actuated according to the following table:

<tb>
<tb> indexed <SEP> position <SEP> of <SEP> (5144) <SEP> position <SEP> of <SEP> (5207)
<tb> 0 <SEP> closed <SEP> open
<tb> 1 <SEP> open <SEP> closed
<tb>

coordonnées 7[/?.;j]. tabv2[p,r,j]. 9. 7. Window control (5165) and (5191)
Each of these panes is for example mounted on a positioner with two translational axes controlled by stepping motors and making it possible to move the pane in a plane orthogonal to the optical axis. For each position of the illumination wave, characterized by indices p, i, j, it is necessary to position the window so as to cancel the direct illumination. This is done by controlling the stepper motors to move the window to a position characterized in number of steps of each motor by the

coordinates 7 [/?.; j]. tabv2 [p, r, j].

Prior to this use of the panes, a program is used to determine the arrays tab, 1 [p, i, jl, tabv2 [p.i, 11. An example of such a program is shown in Fig. 77.

To use the program of Fig. 77 FS, FSI, FRD and FRG beams are required and the object used is a transparent slide. The filter (5128) used on the path of the FS beam is set so that the sensors are saturated on a few pixels around the impact points of the FS and FSI beams.

(5107): La position du miroir (5113) est commandée par les tableaux tab 1[p, 0, 0], tah2[p, 0, 01. (5401): Une image est obtenue par la procédure décrite en 9.4. avec transformation de Fourier à partir d'un capteur situé du coté caractérisé par l'indice p. Le module des éléments de cette image est extrait pour obtenir une image en nombre réels sur laquelle le point occulté par le 'point noir' de la vitre apparaît en clair sur fond noir. L'image ainsi obtenue constitue le tableau S de dimensions 2Npixx2Npix à partir duquel on calcule les coordonnées imax et jmax du maximum, par la procédure décrite en 7.3.3. 1. On a alors : x = imax y jmax (5402): la valeur lim utilisée dépend de la précision du positionneur. On peut par exemple avoir lim=0,25. The main stages of this program are:

(5107): The position of the mirror (5113) is controlled by the tables tab 1 [p, 0, 0], tah2 [p, 0, 01. (5401): An image is obtained by the procedure described in 9.4. with Fourier transformation from a sensor located on the side characterized by the index p. The module of the elements of this image is extracted to obtain an image in real numbers on which the point obscured by the 'black point' of the window appears in clear on a black background. The image thus obtained constitutes the table S of dimensions 2Npixx2Npix from which the coordinates imax and jmax of the maximum are calculated, by the procedure described in 7.3.3. 1. We then have: x = imax y jmax (5402): the lim value used depends on the precision of the positioner. We can for example have lim = 0.25.

pas I=(i-x),pasyaryixel/2 pas2=(j-y),pas. parixel2 La valeur de position courante est modifiée: pos1+=pas1 pos2+=pas2 (5403): the displacement of the motors is worth, in a similar way to what was done in 5.20 .:

not I = (ix), pasyaryixel / 2 pas2 = (jy), not. parixel2 The current position value is modified: pos1 + = pas1 pos2 + = pas2

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step per pixel is the ratio (number of motor displacement steps) / (number of pixels of displacement of the point with coordinates imax, jmax on the image obtained in 9.4.). It must have been determined beforehand, for example by moving the window in one of the directions and by measuring the number of pixels of displacement of the coordinate point (imax, jmax).

tabv3[p,,J)=ps Toutefois, dans le ( ' )2 (AT > R ou, 2 les valeurs affectées sont par exemple des valeurs négatives signalant une erreur, comme tabl[p,i,j]=-10000, tab2[p,r,J]= -10000 (5406): les moteurs sont déplacés de -posl, -pos2 de manière à retourner au point d'origine, qui doit rester constant pour éviter de fausser la trajectoire. (5404): the motors are moved, for a number of steps], step2 of each motor (5405): the current values of the coordinates in motor steps are recorded in a table: tabvl [p, i, j] = pos1

tabv3 [p ,, J) = ps However, in (') 2 (AT> R or, 2 the affected values are for example negative values indicating an error, like tabl [p, i, j] = - 10000, tab2 [p, r, J] = -10000 (5406): the motors are moved from -posl, -pos2 so as to return to the point of origin, which must remain constant to avoid distorting the trajectory.

9. 8. Obtaining the constant K.

distance en pixels D pu: entre deux graduations séparées par une distance réelle Drcel est mesurée. La saleur nv 2Npix de la constante K est alors K = nv/# 2Npix/D@@@ Dreel. The micrometer is introduced as a sample. An image is obtained in the presence of the FED and FRG beams by the procedure described in 9.4. in which the Fourier transformation step 3 is not carried out. The complex value modulus of this image is used to get a real image of the intensity. The position of the sample is adjusted so that this image is properly focused. The

distance in pixels D pu: between two graduations separated by a real distance Drcel is measured. The salt nv 2Npix of the constant K is then K = nv / # 2Npix / D @@@ Dreel.

# Dpix
9. 9. Obtaining a complete two-dimensional frequency representation.

In the third embodiment, a two-dimensional frequency representation was obtained by the procedure described in 7.12. In the present embodiment, the mode of obtaining this representation must be modified.

9. 9.1. Principle
9. 9.1.1. Acquisition.

During acquisition, the index r will designate the open switch, according to the following table:

<tb>
<tb> index <SEP> shutter <SEP> (5109) <SEP> shutter <SEP> (5104)
<tb> 0 <SEP> open <SEP> closed
<tb> 1 <SEP> closed <SEP> open
<tb>
The indicated will designate the right (p = 0) or left (p = 1) side of the microscope where the direct illumination wave arrives and consequently the position of the shutters (5144) and (5207), according to the following table:

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<tb>
<tb> index <SEP> p <SEP> shutter <SEP> (5207) <SEP> shutter <SEP> (5144)
<tb> 0 <SEP> open <SEP> closed
<tb> 1 <SEP> closed <SEP> open
<tb>

The index q will designate the side of the microscope from which the acquired data come, with q = 0 for data coming from the side where the direct illuminating wave arrives and q = 1 for data coming from the opposite side.

We set s = p # + # q. s therefore designates the side of the microscope from which the acquired data come, with s = 0 for the right side and s = 1 for the left side.

The sensors are indexed by (s, t), as follows.

<tb>
<tb> index <SEP> s <SEP> 0 <SEP> 1
<tb> index <SEP> t <SEP> 0 <SEP> 1 <SEP> 0 <SEP> 1
<tb> sensor <SEP> (5174) <SEP> (5171) <SEP> (5198) <SEP> (5201)
<tb>

les données MA[k,p][d,r,t][q,i,] proviennent du capteur indicé par pq + bzz) Pour chaque quintuplet (k,p,q,r,t) on obtient, à partir d' un capteur correspondant, et à partirde trois acquisitions correspondant à des phases différentes de l'onde de référence, une image sous forme d'un tableau bidimensionnel de nombres complexes de dimensions 2 Npix x 2 Npix.

the data MA [k, p] [d, r, t] [q, i,] come from the sensor indexed by pq + bzz) For each quintuplet (k, p, q, r, t) we obtain, from d 'a corresponding sensor, and from three acquisitions corresponding to different phases of the reference wave, an image in the form of a two-dimensional table of complex numbers of dimensions 2 Npix x 2 Npix.

9. 9.1.2. Passage in frequencies
The image thus obtained is in spatial representation. A Fourier transformation is carried out to obtain an image in frequency representation. The representation thus obtained is centered around a point FR corresponding to the reference beam. It must be translated and limited to obtain a representation of dimensions Npixx Npix centered around the point FO corresponding to the optical center.

coordonnées (Np,x,Np,), correspondant à la fréquence de l'onde de référence. Le point noté F/? correspond à la fréquence de l'onde d'éclairage (q=O) ou de son onde inverse (q=1) Le point noté FO correspond au centre optique du système, c'est-à-dire à la fréquence d'une onde traversant l'objet observé dans le sends de l'axe optique. Les contours (5301) et (5303) délimitent la représentation.

Figs. 75 and 76 represent the representations obtained respectively, for a given index p, on the sensors indexed by q = 0 and by q = 1. In these figures, the point denoted FR is the central point, of

coordinates (Np, x, Np,), corresponding to the frequency of the reference wave. The point denoted F /? corresponds to the frequency of the lighting wave (q = O) or of its inverse wave (q = 1) The point denoted FO corresponds to the optical center of the system, that is to say to the frequency of a wave passing through the object observed in the sends of the optical axis. The outlines (5301) and (5303) delimit the representation.

In the case q = O, FR and FF are symmetrical with respect to FO. In the case q = 1, FR and FI 'are symmetrical with respect to a horizontal line passing through FO.

The limited and centered frequency representation is obtained from these figures by extracting the zone of dimensions Npixx Npix centered around the point FO, limited by (5302) or (5304) in the figures

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9. 9.1.3. Combination of different polarizations.

We denote by Dp, s, r, t the complex value measured at a point C of a frequency representation obtained at the end of the procedure described in 9.9.1.2., From the sensor indexed by s, r and t when the direction of the illumination wave is characterized by / ;.

We denote by # s, r, l the electric field vector of the reference wave on the sensor characterized by the indices s, r and t.

In Fig. 80, the different combinations of the indices s, r, t are shown in the form of a table. In each box of the table: - the neutral axis of the phase plate located in front of the sensor concerned is shown in dotted lines.

- the electric field vector of the reference wave before passage of the phase plate, directed along 1 or # is shown in solid lines.

- the electric field vector # s, r, t of the reference wave after passage of the phase plate and reflection on the semi-transparent mirror which superimposes it on the beam coming from the object, directed according to or ~ #, is also shown in solid lines. If s = 0, this vector is deduced from the electric field vector of the wave before passage of the plate by a symmetry whose axis is the neutral axis of the plate. If s = 1, an additional vertical axis symmetry must be performed.

obtenues est, à une constante pres: ,- W s,r,t = - ( 1) srH s( rt ) 1 .,. + - ( l)"Ft 1
La phase de l'onde de référence diffère entre les capteurs (5171) et (5174). On note as le rapport caractéristique du décalage de phase et d'intensité entre les capteurs indicés respectivement par (s, t=0) et (s, t=1). The values of # s, r, t can be deduced from this figure. A formula bringing together all the values

obtained is, up to a constant:, - W s, r, t = - (1) srH s (rt) 1.,. + - (l) "Ft 1
The phase of the reference wave differs between the sensors (5171) and (5174). We denote as the characteristic ratio of the phase shift and intensity between the sensors indexed respectively by (s, t = 0) and (s, t = 1).

The wave detected on a given sensor constitutes a projection of the wave reaching this sensor on an axis oriented like the electric field vector of the reference wave. The unit vector orienting this axis will be noted as the electric field vector of the reference wave.

- une onde d'éclairage dirigée selon (- 1) p ou p est l'indice du capteur vers lequel est dirigée fonde d'éclairage direct. Le facteur (-1)p est dû au fait que la composante horizontale de l'onde d'éclairage, symétrisée par les miroirs qui la dirigent dans deux sens opposés en fonction de l'indice p, est inversée quand la direction de l'onde d'éclairage est elle-même inversée. Pour cette onde d'éclairage, on mesurera

les composantes de l'onde diffractée polarisées selon les axes orientés par ws 0 0 cl w 0 , , obtenant respectivement les facteurs DP,S,o,o et D p,s,O,1 - une onde d'éclairage dirigée selon j . Pour cette onde d'éclairage, on mesurera les composantes de l'onde

diffractée polarisées selon les axes orientés par ws , etw,, ;1 ( . obtenant respectivement les facteurs Dp,sX0<* Dp,s,I,1 For the measurements we use:

- an illumination wave directed according to (- 1) p or p is the index of the sensor towards which the direct illumination base is directed. The factor (-1) p is due to the fact that the horizontal component of the illuminating wave, symmetrized by the mirrors which direct it in two opposite directions according to the index p, is reversed when the direction of the lighting wave is itself inverted. For this lighting wave, we will measure

the components of the diffracted wave polarized along the axes oriented by ws 0 0 cl w 0,, respectively obtaining the factors DP, S, o, o and D p, s, O, 1 - a lighting wave directed along j . For this lighting wave, we will measure the components of the wave

diffracted polarized along the axes oriented by ws, etw ,,; 1 (. obtaining respectively the factors Dp, sX0 <* Dp, s, I, 1

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Lorsque le vecteur champ électrique du faisceau d'éclairage (au point 10 est A0(-\)p +.41.Ï le vecteur champ électrique résultant au point C, sur le coté s du microscope, est donc: 1 r Dp,s,r,t (i + ta s)w s,r,1 r,t
Lorsque le vecteur champ électrique au point E est A0# +A1# le vecteur champ électrique résultant au point C, sur le cotés du microscope, est donc:

r ~ 1 Pt D p,s,r,t (t +fa s)ws,r,t r,t Soit L (- I)pr(( -Irrt+s(rt) ï + (-1(1 .! )(i + ta S )ArD p,s,r,t r,t I Jt Ce qui correspond à l'expression

C'p,s,0,0.9pi +C'p,s,l,p.90) + Cp@s@ol A,17 +C'P,s,1,1.91.1 avec: -,P's'd'r - (-11 pr= C(-l,srt+srt l + (-1)rt d)(i +ta s )D p,s,r,t
1 JI soit:

Cp.s,0,0 =l (~ 1 P( l-1S(Dp>s,o,o +asDp,s.o,1) C 1 -(-l)P(-D 00 +asDP,s,p>1l Cp,s,0,1 =(-1)s(-Dp,s,l,0+asDp,sl,ll Cp,s,I,I = Dp@s@l@o +a sDp,s,I,1 La même expression qu'en 7.12 peut être utilisée à partir de ces valeurs de Cp,s,d,r pour obtenir la grandeur recherchée Mp,s, les indices p,s qui étaient inutile en 7.12. étant rajoutés:

-,.7 =-cosrpe e cos tp c C p,s,o,o - sin tp e cos tp c C p,s,O,1 - cos tp sinrpy'P,s>1>p -sinpe e sin tp cC p,s,I,1 soit A, 1 Ep,s,r,t Dp,s,r,t r,t avec :

, ,0,0 =-1P(-ls cos 7ecosç5c c + costp e sin tp c ) E p,s,O,1 =(-1)Pas(-1)s costpe cos Ç9, - Cos Çoe sintpc) L'p,s,i,o = (-1)' sintp e cos tp c - sin tp e sin tp Ep, S, 1, = a s( -( -1)' sintp e cos tp c - sintpe sin tp c)

When the electric field vector of the lighting beam (at point 10 is A0 (- \) p + .41.Ï the resulting electric field vector at point C, on side s of the microscope, is therefore: 1 r Dp, s , r, t (i + ta s) ws, r, 1 r, t
When the electric field vector at point E is A0 # + A1 # the resulting electric field vector at point C, on the sides of the microscope, is therefore:

r ~ 1 Pt D p, s, r, t (t + fa s) ws, r, tr, t Let L (- I) pr ((-Irrt + s (rt) ï + (-1 (1.! ) (i + ta S) ArD p, s, r, tr, t I Jt Which corresponds to the expression

C'p, s, 0,0.9pi + C'p, s, l, p.90) + Cp @ s @ ol A, 17 + C'P, s, 1,1.91.1 with: -, P's'd'r - (-11 pr = C (-l, srt + srt l + (-1) rt d) (i + ta s) D p, s, r, t
1 JI either:

Cp.s, 0,0 = l (~ 1 P (l-1S (Dp> s, o, o + asDp, so, 1) C 1 - (- l) P (-D 00 + asDP, s, p > 1l Cp, s, 0,1 = (- 1) s (-Dp, s, l, 0 + asDp, sl, ll Cp, s, I, I = Dp @ s @ l @ o + a sDp, s , I, 1 The same expression as in 7.12 can be used from these values of Cp, s, d, r to obtain the desired quantity Mp, s, the indices p, s which were unnecessary in 7.12. Being added:

- ,. 7 = -cosrpe e cos tp c C p, s, o, o - sin tp e cos tp c C p, s, O, 1 - cos tp sinrpy'P, s>1> p -sinpe e sin tp cC p, s, I, 1 or A, 1 Ep, s, r, t Dp, s, r, tr, t with:

,, 0,0 = -1P (-ls cos 7ecosç5c c + costp e sin tp c) E p, s, O, 1 = (- 1) Pas (-1) s costpe cos Ç9, - Cos Çoe sintpc) L 'p, s, i, o = (-1)' sintp e cos tp c - sin tp e sin tp Ep, S, 1, = as (- (-1) 'sintp e cos tp c - sintpe sin tp c )

<Desc / Clms Page number 232>

Beforehand it is necessary to determine the coefficient [alpha] s. Around the point of impact of the lighting patrol, a comparable value is obtained on each sensor for a given index r. We can therefore adopt for this coefficient the value [alpha] s = # Dp, s, r, 0 Dp, s, r, 1 where the sums are on the indices r and on ## Dp, s, r, 1 a number of points reduced around the point of direct impact of the illumination wave.

9. 9.2. Acquisition
As in the third embodiment, the point of direct impact of the illumination wave follows a trajectory indexed by k and characterized by the tables Io [k], Jo [k].

As in 7.12.2.1., The acquisition of elementary images is an iteration over the integers ;? and k designating respectively the sensor to which the direct illumination beam arrives and the order number of the elementary image in the series of images corresponding to a given index p.

/o[A 1 - #- +J,[k]-'Vp- <R2 le programme commande le déplacement du miroir par les tableaux tabl[pJo[k],Jo[k]1, ta62[p.lo[k],Jo[k]] et les obturateurs (5144) et (5207) comme indiquée en 9.6. Il déplace la vitre située du coté opposé au point d'impact direct de l'onde d'éclairage de manière à ce que son point noir soit hors du champ de fréquences utilisée. There is no beam attenuation here. For each pair (k, p) satisfying

/ o [A 1 - # - + J, [k] - 'Vp- <R2 the program controls the displacement of the mirror by the tables tabl [pJo [k], Jo [k] 1, ta62 [p.lo [k ], Jo [k]] and the shutters (5144) and (5207) as indicated in 9.6. It moves the glass located on the side opposite to the point of direct impact of the lighting wave so that its black point is outside the frequency field used.

l'onde d'éclairage de la manière indiquée en 9.7.. par les tableaux '7[p./o[A'L7o[A']]. tabv2[pJo\k]Jo[k]]. It controls the movement of the window located on the side where the point of direct impact of the

the illumination wave as indicated in 9.7 .. by tables '7 [p./o [A'L7o [A']]. tabv2 [pJo \ k] Jo [k]].

However, according to a variant which will be called variant 2, it does not use this window and therefore moves it so that its black point is outside the frequency field used.

To increase the speed, it is necessary to limit as much as possible the number of changes of the index p, which involve manipulation of the shutters (5144) and (5207) which are slower for example than (5104) and (5109). The program therefore performs a first iteration on k, at p = 0, followed by a second iteration on k, at p = 1.

At each value of (k, p) the program performs the acquisition of 12 pairs of elementary images. A pair of elementary images is as in 7.12.2.1. a table indexed - on the one hand by the index with q = 0 if the image is detected on the same side as the point of direct impact of the reference wave, and q = 1 if it is detected on the opposite side.

- on the other hand by the indices and / characterizing the position of the pixel on the sensor concerned
The indices p, q, r, t are defined as indicated in 9.9.1.1. The index d determines the phase shift of the reference wave and is defined by the following table:

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couples d'images élémentaires MA[k,pl [dr, t] [q, ij] Le programme effectue en plus l'acquisition d'une série d'images correspondant à l'image de référence. Il déplace les moteurs jusqu'aux positions pos I[ p, i" J r po.s2 p.lr . J. ou (1 r ,1 r ) sont normalement, les coordonnées (io,jo) du point fixe occulté par les diaphragmes, déterminées dans l'étape 38 de la procédure de réglage 9.5. Toutefois, si la variante 2 est utilisée, (ir,jr) sont les coordonnées d'un autre point fixe, fortement excentré mais non occulté. Le programme effectue alors l'acquisition d'une série

de 6 couples d'images élémentaires, obtenant un tableau MA2[k,p][d,r,t][q,r,J]
Toutefois, selon une variante, que l'on appellera la variante 1, le programme n'effectue pas l'acquisition de cette image de référence. <tb>
<tb> index <SEP> d <SEP> offset <SEP> of <SEP> phase
<tb>#d<SEP> (degrees)
<tb> 0 <SEP> -120 <SEP>
<tb> 1
<tb> 2 <SEP> +120 <SEP>
<tb>
The acquisition of a series of images corresponding to the indices k, p, q, d, r, t thus generates the series of

pairs of elementary images MA [k, pl [dr, t] [q, ij] The program also acquires a series of images corresponding to the reference image. It moves the motors to positions pos I [p, i "J r po.s2 p.lr. J. where (1 r, 1 r) are normally, the coordinates (io, jo) of the fixed point occulted by the diaphragms, determined in step 38 of adjustment procedure 9.5. However, if variant 2 is used, (ir, jr) are the coordinates of another fixed point, strongly eccentric but not obscured. The program then performs l acquisition of a series

of 6 pairs of elementary images, obtaining an array MA2 [k, p] [d, r, t] [q, r, J]
However, according to a variant, which will be called variant 1, the program does not carry out the acquisition of this reference image.

9. 9.3. Calculations.

The calculation of the two-dimensional frequency representation, of the reference image, and of the characteristic tables of the noise on these two images is carried out by the following steps 1 to 8: Step 1 - Calculation of the two-dimensional spatial representations.

.lfBk,pr.iq.r,j]= (2~lL4[k.p][O,r,t r,J-AL9k.pl.r,tq,r.J]-Af,[k.1[2,r,t[q.i.J) +j Z.lLrlk>P>r>tq>i>j-.ILAk,p2,r>tq>i>J Etape 2- Passage en représentation fréquentielle. The program performs on all the data obtained:

.lfBk, pr.iq.r, j] = (2 ~ lL4 [kp] [O, r, tr, J-AL9k.pl.r, tq, rJ] -Af, [k.1 [2, r, t [qiJ) + j Z.lLrlk>P>r>tq>i> j-.ILAk, p2, r>tq>i> J Step 2- Change to frequency representation.

.\fqk, pUr, t ][q, i, j] Etape 3: compensation de la réponse fréquentielle des capteurs. The indices i etj vary from 0 to 2 Npix -1. The program performs the Fourier transform according to these two indices of each of the previously obtained spatial representations. This leads to transformed representations:

. \ fqk, pUr, t] [q, i, j] Step 3: compensation of the frequency response of the sensors.

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This compensation is not essential but it significantly improves the precision of the microscope.

.\fD[ k, p][r, tg. , j] = Rl[i, j)Af(1 k, p][r, tq, i. il Le tableau RI représente la réponse fréquentielle inversée des capteurs. Il est déterminé en 9.11. Toutefois, selon une variante que l'on appellera variante 3, utilisée pour certains réglages, le tableau RI est mis à 1 Etape 4-Translation et limitation de la représentation fréquentielle bidimensionnelle. The program calculates the MD array:

. \ fD [k, p] [r, tg. , j] = Rl [i, j) Af (1 k, p] [r, tq, i. il Table RI represents the inverted frequency response of the sensors. It is determined in 9.11. However, according to a variant that the variant 3 will be called, used for certain adjustments, the table RI is set to 1 Step 4-Translation and limitation of the two-dimensional frequency representation.

ME[k. P ][1', t ][0, /. J] = llDk . pr, t0. +/o[y+Jo]] \#[k, p][r. tf\, i,j]= A1D[k, p][r, t][ 1,1 - IO[k] + N pIX' j + Jo[ k]] ou i et/varient maintenant de 0 à Npix -1. The position of the FO point indicated in 9.9.1.2. is stored in the form of arrays lo [k] Jo [k] The considerations given in 9. 9.1.2. then result in the following operations, performed by the program:

ME [k. P] [1 ', t] [0, /. J] = llDk. pr, t0. + / o [y + Jo]] \ # [k, p] [r. tf \, i, j] = A1D [k, p] [r, t] [1,1 - IO [k] + N pIX 'j + Jo [k]] or i and / now vary from 0 to Npix - 1.

Step 5: Calculation of the as coefficients.

alpha[k, p. q] . Le programme parcourt l'ensemble des triplet (k,p,q). Pour chaque triplet - il initialise à 0 les nombres nom et denom. A coefficient a is determined for each triplet (k, p, q). It is stored in an array of complexes

alpha [k, p. q]. The program traverses the set of triplets (k, p, q). For each triplet - it initializes the numbers name and name to 0.

[i-Io[k])2 + (j - Jo[k 1) slim2 avec par exemple lim=20. - it traverses the set of triples r, u, j by testing the condition:

[i-Io [k]) 2 + (j - Jo [k 1) slim2 with for example lim = 20.

nom+= MELK, pr,0q,, .1 fEk, pr,lq, i, j denom+ = IME[k, p][r, 1][q, @ J]12 - Lorsque la boucle sur r,i,j est terminée il effectue:

a/p/70 ./?. =-### denom Etape 6- Combinaison des valeurs correspondant aux indices r et t

Cette étape a pour objet de calculer Mk,p,q 11, Ji en fonction de .'tfEk , /?][/#. t ][ q, i, . Ceci peut être réalisé très simplement en effectuant l'opération suivante: .\f k,p,q i, jl = ME[ k. p][1 11[q, i, j] . la valeur affectée au bruit étant alors constante et l'étape 5 étant rendue inutile. Si cette méthode doit être utilisée, il est cependant préférable de supprimer les lames de phase (5111) (5238) (5239) (5248) (5249). When the condition is true it performs:

name + = MELK, pr, 0q ,, .1 fEk, pr, lq, i, j denom + = IME [k, p] [r, 1] [q, @ J] 12 - When the loop on r, i, j is finished he performs:

a / p / 70 ./ ?. = - ### denom Step 6- Combination of the values corresponding to the indices r and t

The purpose of this step is to calculate Mk, p, q 11, Ji as a function of .'tfEk, /?] [/ #. t] [q, i,. This can be done very simply by performing the following operation:. \ Fk, p, qi, jl = ME [k. p] [1 11 [q, i, j]. the value assigned to the noise then being constant and step 5 being made unnecessary. If this method is to be used, however, it is preferable to remove phase plates (5111) (5238) (5239) (5248) (5249).

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principe a été indiqué en 9.9.1.3., la quantité VIE[k. p ][1' , t][ q, i, ./ étant la valeur mesurée notée D p,S,1 ,, en 9.9.1.3. L'étape 6 est alors effectuée comme suit:
Pour chaque valeur des indices k,p,q,i,j le programme calcule:

Npix N plX XC = 1- Z , Yc = J- 2 zc IF Xi72 2 no " nv nv Io[k]~Nplx Jo[k]~NpIX /om- - Jo[kl- .~~~~ Xe= 2 ,Ye= 2 ,ze=l-X;-V: no K no nv nv Tfi = YeZe - ZeYe 'xz =-xcZe +Zcxe Yxy =-xcYe +Ycxe Afe 2 = Xc 2 + Ye Ale 2 = Xe 2 + Ye #r/2 T.2 T.2

Les valeurs de sintpc costpc sintpe costpe sont déterminées selon les tableaux d'affectation suivants

In all cases, this method, similar to that used in the second embodiment, induces imperfections in the high frequencies. It is therefore preferable to use the method whose

principle was indicated in 9.9.1.3., the quantity LIFE [k. p] [1 ', t] [q, i, ./ being the measured value denoted by D p, S, 1 ,, in 9.9.1.3. Step 6 is then carried out as follows:
For each value of the indices k, p, q, i, j the program calculates:

Npix N plX XC = 1- Z, Yc = J- 2 zc IF Xi72 2 no "nv nv Io [k] ~ Nplx Jo [k] ~ NpIX / om- - Jo [kl-. ~~~~ Xe = 2 , Ye = 2, ze = lX; -V: no K no nv nv Tfi = YeZe - ZeYe 'xz = -xcZe + Zcxe Yxy = -xcYe + Ycxe Afe 2 = Xc 2 + Ye Ale 2 = Xe 2 + Ye # r / 2 T.2 T.2

The values of sintpc costpc sintpe costpe are determined according to the following assignment tables

<tb>
<tb> Mce <SEP> 0 <SEP> other
<tb> other
<tb>

cos ço, (y c 2 X,Y" ',, ,-r coslpe - Ale Ye llc 21 :IIc (vYy-xcYcT'.rz+xct'.l ,y le sinlpe Ale Xe .1 1 .Ice (~ xcy'cj yz + xc 1 + yct'xy,J

cos ço, (yc 2 X, Y "',,, -r coslpe - Ale Ye llc 21: IIc (vYy-xcYcT'.rz + xct'.l, y le sinlpe Ale Xe .1 1 .Ice (~ xcy 'cj yz + xc 1 + yct'xy, J

<tb>
<tb> Mce <SEP> 0 <SEP> other
<tb> Me <SEP> other
<tb>

cosço, 2l' -X,V,i' +X,r COSlpe - llrc yc l\le 21 .".Ice (Y;f'y'Z -xeYef'x:; +XeTTxy) smg xeve, +x21" e Sinlpe - 21 (-XeYez+x;Vx:;+Yer'xy) Aie Me Alce

cosço, 2l '-X, V, i' + X, r COSlpe - llrc yc l \ le 21. ". Ice (Y; f'y'Z -xeYef'x :; + XeTTxy) smg xeve, + x21" e Sinlpe - 21 (-XeYez + x; Vx:; + Yer'xy) Aie Me Alce

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coefk, p,9,i,J,=-1P(-1)P9+P9 coscp e cos CPc + cos tp e sincp c ) coef[k. p, q,i, 1 ][0.1] = alpha[k, p,q](-I)p - 1) p+jq cosço, cosço, c - costp e sin tp c ) coe/[Â:,/7,ç,(,y][l,0] =(-]')pq+pq sinp, e coscp c - sin tp sin (p, coefk, p,g,i, J1,1=-alphak. p,gl--lPq+P9 sinrpe costpc -sintpe sintpc)
Ces coefficients ne dépendent pas du résultat des prises d'images et dans le cas ou on répète toujours la même série ils peuvent être stockés dans un tableau plutôt que recalculésà chaque fois. Le programme utilise ensuite ces valeurs pour combiner les images obtenues avec les différentes positions des rotateurs de la manière suivante

M k,p,q [l, J] = L AfE[k, p][r. t Hq.i, 1 ]coef[k, p, q,l. 1 ][r. t] r,t

coef [k, p, q, i, j][r. t] correspond à la quantité notée E p,s,r,t en 9.9.1.3 avec s = pq + pq . then the coefficients are calculated:

coefk, p, 9, i, J, = - 1P (-1) P9 + P9 coscp e cos CPc + cos tp e sincp c) coef [k. p, q, i, 1] [0.1] = alpha [k, p, q] (- I) p - 1) p + jq cosço, cosço, c - costp e sin tp c) coe / [Â:, / 7, ç, (, y] [l, 0] = (-] ') pq + pq sinp, e coscp c - sin tp sin (p, coefk, p, g, i, J1,1 = -alphak. P , gl - lPq + P9 sinrpe costpc -sintpe sintpc)
These coefficients do not depend on the result of the images taken and in the case where the same series is always repeated they can be stored in a table rather than recalculated each time. The program then uses these values to combine the images obtained with the different positions of the rotators as follows

M k, p, q [l, J] = L AfE [k, p] [r. t Hq.i, 1] coef [k, p, q, l. 1] [r. t] r, t

coef [k, p, q, i, j] [r. t] corresponds to the quantity noted E p, s, r, t in 9.9.1.3 with s = pq + pq.

- lorsque Rl y + lok, j + Jok, 0 : Bk,p,O [/,1] = IRl[1 + fo[ k l j + Ja[ k]]1 - sinon Bk p0[i, 1] = MAX ou.lfA I'est une valeur élevée. par exempte 1010 Bk,P.I i, J vaut: - lorsque RJ Il - Io[ki + N plx ,j + Jo[k]] '" 0 : Bk,p,l [l, 1] = IRl[1 -Io[k] + N P1X' j + Jo[k]]1 - sinon: Bk, p 11, JI = MAV Etape 8-Calcul de l'image de référence. AyEf./?jf/'.1f(yy] corresponds to the quantity noted D p, s ,,, r in 9.9.1.3 Jfk, p, q [l, 1] corresponds to the quantity noted ~ 1 fp, s in 9.9 1.3. Step 7- The noise amplitude is calculated as follows: Bk, p, 0 [i, j] is equal to:

- when Rl y + lok, j + Jok, 0: Bk, p, O [/, 1] = IRl [1 + fo [klj + Ja [k]] 1 - otherwise Bk p0 [i, 1] = MAX or .lfA I is a high value. for example 1010 Bk, PI i, J is equal to: - when RJ Il - Io [ki + N plx, j + Jo [k]] '"0: Bk, p, l [l, 1] = IRl [1 -Io [k] + N P1X 'j + Jo [k]] 1 - otherwise: Bk, p 11, JI = MAV Step 8-Calculation of the reference image.

utilisant le tableau iL42 au lieu du tableau'\4 et en remplaçant les valeurs 7o[A],Jo[A] par (i r ,j r ). On notera Hk,p,q [1,1] le tableau ainsi généré et BHk,p,q [1,1] l'amplitude de bruit correspondante. Toutefois, dans le cas de la variante 1, cette image de référence n'est pas calculée. The reference image is calculated, in exactly the same way as the main image, but in

using array iL42 instead of array '\ 4 and replacing the values 7o [A], Jo [A] by (ir, jr). We will denote by Hk, p, q [1,1] the table thus generated and BHk, p, q [1,1] the corresponding noise amplitude. However, in the case of variant 1, this reference image is not calculated.

9. 10. Fine adjustment of the position of the sensors.

The purpose of this operation is to ensure precise adjustment with respect to one another of the two sensors corresponding to the same side of the microscope, in particular in the direction of the optical axis. In the absence

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from such an adjustment, the point of origin of the frequency representations generated from each sensor may differ slightly, which subsequently compromises the correct superposition of the portions of the frequency representations coming from each side of the microscope. The fact of not carrying out this adjustment does not prevent the generation of three-dimensional representations of the sample but limits the precision of these representations.

A translational movement of a sensor causes modulation in the frequency domain and therefore a phase shift of the values of the plane waves obtained from this sensor. The adjustment consists of verifying that the plane waves received on each sensor for various directions of the illumination beam are in phase.

initialise à 0 les tableaux AfFs,1 de dimensions 1V p, x '1'p,x . Il effectue une boucle sur les indices s, i et y. The sensors are indexed by the indices s, t with the same convention as in 9.9.1.3. The program

initializes to 0 the arrays AfFs, 1 of dimensions 1V p, x '1'p, x. It loops over the indices s, i and y.

For each triplet s, ij verifying (1 -. '' 1z J + C j -,. 'Lz J <~ Rou "it performs the following operations.

- it operates the shutters so as to use the FEG beam for s = 0 and the FED beam for s = 1.

- it moves the mirror to the point corresponding to tab I [s, i, 1], tab3s, i. j - it generates from each sensor indexed by s a two-dimensional image according to the method described in 9.4., thus obtaining two images MHs, t [k, l] where the indices s andt have been added to characterize the sensor, with the same convention as in 9.9.

9.4., obtenant deux images IfHR,,, [k, 1] . - It moves the mirror towards a fixed point of coordinates (ir, Jr) - it generates from each sensor indexed by s a two-dimensional image according to the method described in

9.4., Obtaining two images IfHR ,,, [k, 1].

, A, f2 <.2y1 - It performs for the pair of integers (ij): AfF, ',. / ==! IIHT, 2r, 2J .IIHRf r 2i, 2J After completing this loop on s, i, j, the program calculates the following deviations: Cl s = L IAfFs, Q [1,1] - AlFs, 1 [1, j] 12 IJ
The translational position of the transducer (5171) must be adjusted to minimize # 0 and the position of the transducer (5201) must be adjusted to minimize # 1. The program must therefore loop through the calculation of these deviations until the adjustment is completed. #s represents the mean square deviation due to phase errors between the frequencies received on the two sensors located on the same side of the microscope.

9. 11. Determination of the frequency response of the sensors
The sensors filter the spatial frequencies that reach them. This filtering is at best equivalent to averaging over the surface of the pixel, however in general it is more important due to defects in CCDs and cameras. In the reception-based embodiments

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in a frequency plane, this filtering simply induces a darkening of the part of the generated image which is far from the center. In this embodiment, this filtering is performed in the space plane and poses more significant problems. It is preferable to use good quality cameras and to compensate for this filtering. This spatial plane filtering is equivalent to a frequency multiplication by an RF array whose inverse RI is used in procedure 9. 9. to perform the compensation. To limit the noise on the frequency response, it is acquired using plane waves rather than from a single spherical wave.

lo\k\ # + ( Jo[ k ] - N ;IX )2 S R;uv ou Rouv est le rayon limité par l'ouverture des objectifs, qui a été obtenu à l'étape 37 de la procédure de réglage 9. 5. Cette trajectoire sera nommée par la suite trajectoire complète . 9.11.1. Acquisition
We use arrays lo and Jo characterizing a trajectory traversing the set of accessible points, that is to say that (Io [k]. Jo [k]) must traverse the set of points such as @

lo \ k \ # + (Jo [k] - N; IX) 2 SR; uv or Rouv is the radius limited by the aperture of the lenses, which was obtained in step 37 of the adjustment procedure 9. 5 This trajectory will be called hereafter complete trajectory.

(ir,Jr) non occulté. Il génère ainsi les séries d'images J[k,p q [l, 1] et Hk,p q [1. J] . L'indice nu n'étant pas connu, il est pris égal à nv dans la procédure 9.9. Toutefois, lors de cette acquisition, il suffit d'enregistrer les valeurs 1I., p,q lok, Jok et llk, p,q i r , jr . 9. 11.2. calcul

Le programme initialise à 0 le tableau RFI de dimensions .V v .''r"z . Il parcourt alors la série des indices k. Pour chaque indice k il effectue:

RFl[Io[k].Jo[k]] = Mk,o,o[Io[k],Jo[k]] k],Jo[k]]l 111 HtA0\<r.Jr] Hk,,,o[', 1, ou i, , j, sont les coordonnées du maximum de l'image de référence, comme définies en 9.9. A program performs the acquisition defined by these tables, according to the procedure described in 9.9. with variants 2 and 3, i.e. without using panes (5165) (5191) and with a coordinate point

(ir, Jr) not obscured. It thus generates the series of images J [k, pq [l, 1] and Hk, pq [1. J]. Since the bare index is not known, it is taken equal to nv in procedure 9.9. However, during this acquisition, it suffices to record the values 1I., P, q lok, Jok and llk, p, qir, jr. 9. 11.2. calculation

The program initializes the RFI array of dimensions .V v. '' R "z to 0. It then traverses the series of indices k. For each index k it performs:

RFl [Io [k] .Jo [k]] = Mk, o, o [Io [k], Jo [k]] k], Jo [k]] l 111 HtA0 \ <r.Jr] Hk ,,, o [', 1, or i,, j, are the coordinates of the maximum of the reference image, as defined in 9.9.

x 2N plX puis en effectuant pour i et j variant de 0 à N pix - 1 :

RF3Cr+N' >J+/ZJ=RF2y,J
Il effectue alors la transformée de Fourier bidimensionnelle inverse du tableau RF3, obtenant le tableau RF correspondant à la réponse fréquentielle des capteurs. It then performs the inverse two-dimensional Fourier transform of the array RF1, obtaining an array RF2. It completes this table with zeros by initializing to 0 the RF3 table of dimensions 2Npix

x 2N plX then by performing for i and j varying from 0 to N pix - 1:

RF3Cr + N '> J + / ZJ = RF2y, J
It then performs the inverse two-dimensional Fourier transform of array RF3, obtaining the RF array corresponding to the frequency response of the sensors.

The program then calculates the inverted frequency response of the sensors as follows:

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-si (i-Np1Xf +(l-Np1Xf <4/?L alors: Rl y, j = 1 -sinon: Rl[,j]=0
Le tableau RI ainsi déterminé est en particulier utilisé en 9.9.

-if (i-Np1Xf + (l-Np1Xf <4 /? L then: Rl y, j = 1 -otherwise: Rl [, j] = 0
The table RI thus determined is used in particular in 9.9.

9. 12. Determination of the relative coordinates of the points of origin of the images obtained from each side of the microscope.

The frequency images obtained from each side of the microscope by procedure 9.9. are equivalent to the frequency images which were obtained in the previous embodiments. They are, in the same way, relative to a point of origin, which no longer depends on the point of origin of the reference wave, but on the position of the sensor. To be able to superimpose these representations it is necessary to know the relative position of the points of origin of the representations obtained on each side of the microscope.

This is done using FS and FSI spherical waves. The spherical wave FS or FSI received on each side of the microscope must in principle be punctual and centered on each receiving surface.The position of the objectives can therefore be adjusted in the presence of the FS, FSI, FRG, FRD beams so that the image, obtained on each sensor by procedure 9.4. used without Fourier transformation, ie perfectly punctual and centered If this adjustment of the position of the objectives is carried out with the greatest care and with sufficiently precise positioners, of sub-micrometric precision. for example, microscope focusing devices of sufficient quality, or positioners with piezoelectric control, then the points of origin of the images obtained from each side of the microscope are the same.

confondus Leurs coordonnées relatives sont donc (x,~y,z)=(0,0,0). The adjustment procedure described in 9.5. However, it is possible to obtain this quality of adjustment by using positioners of medium precision for the objectives. In fact, the fine adjustments are made, in this procedure, by moving the cameras and not the lenses. If the adjustment procedure described in 9.5. is carried out with care, the points of origin of the frequency representations finally obtained are

combined Their relative coordinates are therefore (x, ~ y, z) = (0,0,0).

des capteurs. Il est possible d'utiliser (x,y,z)=(0,0,0) mais une meilleure superposition des images provenant de chaque capteur sera obtenue si un algorithme adapté est utilisé pour calculer une valeur plus précise de ces paramètres. Une détermination précise des positions relatives des points d'origine peut être obtenue par une méthode similaire à celle utilisée en 7.9.1. Cependant: -L'image du faisceau FS ou FSI dans le plan de réception est ponctuelle et non répartie sur l'ensemble de la surface de réception comme en 7.9.1. Les conséquences sont que l'image obtenue est sensible à des défauts locaux des capteurs et qu'elle est fortement bruitée. However, the adjustments obtained by the procedure 9 5. or by re-adjusting the position of the objectives are in general imperfect. In particular they can be influenced by local imperfections

sensors. It is possible to use (x, y, z) = (0,0,0) but a better superposition of the images coming from each sensor will be obtained if a suitable algorithm is used to calculate a more precise value of these parameters. An accurate determination of the relative positions of the points of origin can be obtained by a method similar to that used in 7.9.1. However: -The image of the FS or FSI beam in the reception plane is punctual and not distributed over the entire reception surface as in 7.9.1. The consequences are that the image obtained is sensitive to local sensor faults and that it is highly noisy.

- The focal point of FS or FSI does not correspond to the characteristic point (with the terminology used in 3.16.) Of one of the objectives, whereas in 7.9.1. the focal point of the reference beam corresponded to the characteristic point of a corresponding objective.

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The method used is therefore modified to overcome, as far as possible, these drawbacks.

vérifiant ( k - N ;IX )2 + - #- rayon 2 avec par exemple rayon = 0.8/?.. Le tableau .\f6 de dimensions N plX X ;"1 plX est initialisé à 0 puis le programme effectue, pour chaque couple (A-,/) de l'ensemble EO , les étapes 1 à 7 suivantes: étape positionnement du miroir de déviation du faisceau au point déterminé par tab l[O. A'. /], tab?0, k, 1] étape 2: Une image est acquise de chaque coté du microscope selon la procédure décrite en 9.4. sans effectuer la transformée de Fourier. On notera ces images .10, li, au lieu de A/y/tf.1. l'indice s caractérisant le capteur avec s=0 pour (5174) et s-- 1 pour (5198). étape 3: le programme détermine les coordonnées imaxs , jmaxs de la valeur maximale de chaque tableau

.\f0" [i, j] , Il calcule alors les tableaux 11, li. j] avec: - si (i -imaxs)2 +(j - jmaxs)2 R2mv A/7j/] = A/0,[<.] - sinon Allsr,=0 0 ou R",t, est déterminé pour que le disque de rayon Rmv centré sur imaxs.jm#ci contienne tous les points dont les valeurs hors bruit sont supérieures au niveau de bruit, tout en étant aussi réduit que possible En pratique, Rniv peut être déterminé empiriquement et valoir une dizaine de pixels. étape 4:1c programme effectue la transformée de Fourier bidimensionnelle de chaque tableau Mls[i,j]. obtenant les tableaux M2s[i,j]. étape 4: le programme applique le filtre RI aux tableaux ainsi obtenus:

Xf3s[ij]=M2s[tj]RJ[i,j] étape 5: Le programme calcule le tableau M4 de dimensions N pix a .'4rp, de la manière suivante:

( N )2 ( N P1X) 2 1 Af30[1+k,l +/] -sinon, M4[i,j] = 0 Le tableau M4 représente le décalage de phase entre les deux capteurs dû à la non-coïncidence des points d'origine, partiellement débruité. étape 6 : le programme effectue la transformée de Fourier inverse du tableau M4, obtenant un tableau M5. étape 7 : le programme modifie le tableau M6 de la manière suivante:

z116 JI+ M4[i, j] .\f6[1,}]+ = M4[O,O] The beams used are FS, FSI, FRD, FRG and the object used is a transparent slide. The method used can be broken down into two phases: Acquisition phase: It consists of an iteration on the indices k, l through the set EO of the points

verifying (k - N; IX) 2 + - # - radius 2 with for example radius = 0.8 /? .. The array. \ f6 of dimensions N plX X; "1 plX is initialized to 0 then the program performs, for each torque (A -, /) of the set EO, the following steps 1 to 7: step positioning the beam deflection mirror at the point determined by tab l [O. A '. /], tab? 0, k, 1 ] step 2: An image is acquired from each side of the microscope according to the procedure described in 9.4. without performing the Fourier transform. These images will be noted .10, li, instead of A / y / tf.1. the index. s characterizing the sensor with s = 0 for (5174) and s - 1 for (5198). step 3: the program determines the coordinates imaxs, jmaxs of the maximum value of each table

. \ f0 "[i, j], It then calculates tables 11, li. j] with: - if (i -imaxs) 2 + (j - jmaxs) 2 R2mv A / 7j /] = A / 0, [ <.] - otherwise Allsr, = 0 0 or R ", t, is determined so that the disk of radius Rmv centered on imaxs.jm # ci contains all the points whose non-noise values are greater than the noise level, while being as small as possible In practice, Rniv can be determined empirically and be worth about ten pixels. step 4: 1c program performs the two-dimensional Fourier transform of each array Mls [i, j]. obtaining the arrays M2s [i, j]. step 4: the program applies the IR filter to the tables thus obtained:

Xf3s [ij] = M2s [tj] RJ [i, j] step 5: The program calculates the array M4 of dimensions N pix a .'4rp, as follows:

(N) 2 (N P1X) 2 1 Af30 [1 + k, l + /] - otherwise, M4 [i, j] = 0 Table M4 represents the phase shift between the two sensors due to the non-coincidence of the points of origin, partially denoised. step 6: the program performs the inverse Fourier transform of array M4, obtaining an array M5. step 7: the program modifies table M6 as follows:

z116 JI + M4 [i, j]. \ f6 [1,}] + = M4 [O, O]

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maximale de LIf6r, j) . Il calcule alors rapport = .lf6i iax, jmax Jl \\. calcule alors rapport = # Fd \imax, p jmax\ f étape 2: le programme calcule la grandeur caractéristique maux: max = - y À/6[; , j] - rapport 7 [;. J]IZ (i,j)#Disque

ou la somme est sur l'ensemble des couples (i j) inclus dans le disque de centre (inrax,jmax) et de rayon
Rniv
2
9.13.Détermination des phases des faisceaux
Cette procédure est similaire à la procédure 7.9.2. La position des objectifs est celle qui a été utilisée en 9.12. pour obtenir les coordonnées x,y,z et ne doit pas être modifiée au cours de la présente procédure. Calculation phase: The program calculates table A / 7 which is the Fourier tranfonne of table M6. The program calculates the x, y, z coordinates obtained by the procedure described in 7.8. from table M7, which replaces the table denoted Frec in 7. 8. However, for this step, the procedure described in 7.8. must be modified as indicated in 7.9. 1. to take into account that the index of the object is known. It must also be modified in a second way to take into account the fact that the acquisition mode is different and that the standard deviation # 2 must be calculated in the spatial domain and not in the frequency domain as in 7.8.1 . This second modification consists in replacing steps (3512) to (3514) of FIG. 50 by the following steps, which are carried out in spatial representation and where it is therefore the table M6 (and not M7) which is used: step 1: the program determines the coordinates (imax, jmax) of the point corresponding to the value
M6 [imax, jmax]

maximum of LIf6r, j). It then calculates ratio = .lf6i iax, jmax Jl \\. then calculate ratio = # Fd \ imax, p jmax \ f step 2: the program calculates the characteristic quantity ills: max = - y À / 6 [; , j] - ratio 7 [;. J] IZ (i, j) #Disk

where the sum is over the set of couples (ij) included in the disc of center (inrax, jmax) and radius
Rniv
2
9.13.Determination of beam phases
This procedure is similar to procedure 7.9.2. The position of the objectives is that which was used in 9.12. to get the x, y, z coordinates and should not be changed during this procedure.

We use the Io and Jo tables already used in 9.11. And characterizing a complete trajectory.

Mk.P,q[I,j] et Hk, p,q i, j . L'indice no n'étant pas connu, il est pris égal à nv dans la procédure 9.9. Lors de cette acquisition, il suffit d'enregistrer les valeurs A/- pf7ofÂ]../ofA])et II k,p,(f [1/ .1r ] . A program performs the acquisition defined by these tables, according to the procedure described in 9.9. with variants 2 and 3, that is to say without using the panes (5165) (5191), with a coordinate point (ir, jr) not obscured, and without compensation for the filtering of the sensors. It thus generates the series of images

Mk.P, q [I, j] and Hk, p, qi, j. Since the index no is not known, it is taken equal to nv in procedure 9.9. During this acquisition, it suffices to record the values A / - pf7ofÂ] ../ ofA]) and II k, p, (f [1 / .1r].

Ra[p.lo[k],Jo[k]]= Hk,p,O ['r - ir 1 Il n v Ji Jo[k] IO[k]2 JO[k]2 ou ir,jr sont les coordonnées du maximum de l'image de référence, comme définies en 9.9. et ou x,y,z sont les coordonnées déterminées en 9.12. The program initializes the array Ra to 0 then it traverses the series of indices k, p by performing for each pair k, p:

Ra [p.lo [k], Jo [k]] = Hk, p, O ['r - ir 1 Il nv Ji Jo [k] IO [k] 2 JO [k] 2 where ir, jr are the coordinates of the maximum of the reference image, as defined in 9.9. and where x, y, z are the coordinates determined in 9.12.

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9.14. Position adjustment of the objectives in the presence of the sample.

tab 1 0 -, - , , tab2C0, i' , li' I A partir de l'onde reçue sur le capteur (5198) on génère deux # 2 2 # # 2 images par la procédure décrite en 9.4.: une image spatiale obtenue sans effectuer l'étape 3 et une image fréquentielle obtenue en effectuant l'étape 3. Le module des valeurs complexes est extrait sur chaque image La position des objectifs est ajustée sur le même principe qu'en 7.10.:
L'image spatiale doit être centrée. The sample to be observed is placed. FS and FRG beams are used. The FRG beam used is in the direction of the optical axis, so the deflection mirror is in the central position, defined by

tab 1 0 -, -,, tab2C0, i ', li' IA from the wave received on the sensor (5198) two # 2 2 # # 2 images are generated by the procedure described in 9.4 .: a spatial image obtained without performing step 3 and a frequency image obtained by performing step 3. The complex value modulus is extracted on each image The position of the objectives is adjusted on the same principle as in 7.10 .:
The spatial image must be centered.

On the frequency image, we should observe a clear disk. The adjustment should be made so that the intensity is as high as possible for high frequencies (points far from the center). The observed disc must remain relatively homogeneous.

If a dark ring appears between the outer edge and the central area, the sample is too thick and not all frequencies can be taken into account. The adjustment must then be carried out so as to have a relatively homogeneous disc, with as large a radius as possible. The disc does not reach its maximum size and high frequencies cannot be taken into account. The resolution of the image, mainly in depth, is reduced. The only solution to this problem is to use a specially designed lens, described in paragraph 7.19.

9. 15. Determination of x, y, z, L, n0
This step is similar to that described in procedure 7.11. As in the procedure described in 7.11., This step can be avoided by carrying out a preliminary measurement of the quantities L and il,) and by introducing the sample without moving the objectives, and therefore without carrying out step 9.14., Of so as not to modify the values of x, y, z obtained in 9.12.

3. Il génère ainsi les séries d'images Ar k,p,q [i, 1] et Hk,p.q [l, 1] . Toutefois, lors de cette acquisition, il suffit d'enregistrer les valeurs AI k,p,q [lo[k], .Jo[k]] et fh,p,q [i r' 1 r ] . Le programme parcourt alors la série des indices k. Pour chaque valeur k il effectue :

Frec[lok, .r.i1 A1k,O,o[Io[k].Jo[k]] 1 ' ' k,0,0 r , Jr [0,/]]]
Le programme décrit en 7.8. est alors utilisé pour calculer les paramètres x,y,z,L, no à partir du tableau Frec ainsi constitué. The program performs the series of acquisitions defined by tables Io and Jo defining a complete trajectory, already used in 9.11.2, according to the procedure described in 9.9. used with variants 2 and

3. It thus generates the series of images Ar k, p, q [i, 1] and Hk, pq [l, 1]. However, during this acquisition, it suffices to record the values AI k, p, q [lo [k], .Jo [k]] and fh, p, q [ir '1 r]. The program then traverses the series of indices k. For each value k it performs:

Frec [lok, .r.i1 A1k, O, o [Io [k] .Jo [k]] 1 '' k, 0,0 r, Jr [0, /]]]
The program described in 7.8. is then used to calculate the parameters x, y, z, L, no from the array Frec thus formed.

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9. 16. Calculation of wp and adjustment of focus.

-les tableaux .llk, p.q i.7 obtenus par la procédure 9.9. utilisée sans variante se substituent à ceux précédemment obtenus par la procédure 7.12. This step is carried out as described in 7.15. It can however be avoided if the index of the sample is close to the nominal index of the objectives, in which case one can choose for example wp = L / 2.

-the tables .llk, pq i.7 obtained by procedure 9.9. used without a variant replace those previously obtained by procedure 7.12.

- les valeurs imaxk jmaxk sont maintenant données par: ;m. = -##/o[A']. 7nrax ~ l d Jok . - because the sampling is regular, we use K0 = K1 = K

- the imaxk jmaxk values are now given by:; m. = - ## / o [A ']. 7nrax ~ ld Jok.

(mlax k, jmaxk Les vitres étant utilisées pour arrêter l'onde d'éclairage directe, cette valeur n'est pas disponible Cette étape est donc remplacée par les étapes 2.1et 2.2. suivantes : étape 2. 1. Pour chaque valeur de k, le programme calcule:

1 0,0,0 [f],o,o[;--] k.0,0 = (>.j)eEk (BO,O,O[,j])2 +K,o.o[',y])2 Tl lHk,O 0 Il. j]12 (1, j ) eEk (V['-i])2 +(.o.o['-7])' avec:

Ek = o.o.o['.7].o.o[']! zur Coef - max ,,,[],.,[a.&j! 1 (<,)#############!##Coc/'- max ##############!##h (['-7])' + (Bk,O.O [1. 1]) o'yr-1 (Bo,,m,h2 +(Bk,O,O[a,h])2 0:b: N'pix - et avec par exemple Coef = 0,5 étape 2.2. Pour chaque valeur de k,i,j le programme effectue:

A1Sk ll, 1 JJ<k ,0,0 ' '' l'' J* Ra[0, Io[k], 7o[A']][/o[-]. Jo[k]] ou Frec est le tableau déterminé en 9.15. Npix Npix - Step 2 of the procedure (4002) of Fig. 57 requires the acquisition of the value of the wave at the point

(mlax k, jmaxk The panes being used to stop the direct illumination wave, this value is not available. This step is therefore replaced by the following steps 2.1 and 2.2.: step 2. 1. For each value of k , the program calculates:

1 0,0,0 [f], o, o [; -] k.0,0 = (> .j) eEk (BO, O, O [, j]) 2 + K, oo [', y ]) 2 Tl lHk, O 0 Il. j] 12 (1, j) eEk (V ['- i]) 2 + (. oo [' - 7]) 'with:

Ek = ooo ['. 7] .oo [']! zur Coef - max ,,, [],., [a. & j! 1 (<,) #############! ## Coc / '- max ##############! ## h ([' -7] ) '+ (Bk, OO [1. 1]) o'yr-1 (Bo ,, m, h2 + (Bk, O, O [a, h]) 2 0: b: N'pix - and with par example Coef = 0.5 step 2.2. For each value of k, i, j the program performs:

A1Sk ll, 1 JJ <k, 0,0 '''l''J * Ra [0, Io [k], 7o [A']] [/ o [-]. Jo [k]] or Frec is the array determined in 9.15.

9. 17. Obtaining the aberration compensation function.

This step is carried out as described in 7.16. with K0 = K1 = K
9. 18. Production of three-dimensional images by the method described in the third embodiment.

9. 18.1. without suppression of the direct wave This step is carried out as described in 7.17.2.

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-les tableaux Ak, p,q i, j Hk,P,q r, j Bk,p,q [1,1] BHk,p,q [i, 1] obtenus par la procédure 9.9 utilisée avec la variante 2 se substituent à ceux précédemment obtenus par la procédure 7.12 - du fait que l'échantillonnage est régulier, on utilise Ko = K1 = K, a0 = a1 = 1 .

-the tables Ak, p, qi, j Hk, P, qr, j Bk, p, q [1,1] BHk, p, q [i, 1] obtained by procedure 9.9 used with variant 2 are substituted for those previously obtained by procedure 7.12 - because the sampling is regular, we use Ko = K1 = K, a0 = a1 = 1.

- the values imaxk, p, g, jmax, p, q are now given by: / w. p = Io [k], nmzx, p, 9 = Jo [k]
9. 18.2. with suppression of the direct wave.

l'algorithme décrit en 7.17.2. nécessite l'acquisition de la valeur de l'onde au point (mlax k,p,O, # Jmaxk,p,o) Les vitres étant utilisées pour arrêter l'onde d'éclairage directe, cette valeur n'est pas disponible. Cette étape est donc remplaçée par l'étape 2 suivante, équivalente à celle indiquée en 7. 18. 1 . étape 2: Pour chaque valeur de k,p,q,i,j le programme effectue:

M k r 1] = Ai k,p,q [l, j]D pq+ pq [1,1 ]Rk,p,q rk,P,9i' []o[A-]]F[/oj,Jo]][/o[].Jo[A]]
9. 19. Réalisation d'images tridimensionnelles suivant une méthode rapide avec suppression de l'éclairage direct. The principle is the same as above but the procedure 9.9. is used without variant. In addition, step 2 of

the algorithm described in 7.17.2. requires the acquisition of the value of the wave at the point (mlax k, p, O, # Jmaxk, p, o) The windows being used to stop the direct lighting wave, this value is not available. This step is therefore replaced by the following step 2, equivalent to that indicated in 7. 18. 1. step 2: For each value of k, p, q, i, j the program performs:

M kr 1] = Ai k, p, q [l, j] D pq + pq [1,1] Rk, p, q rk, P, 9i '[] o [A -]] F [/ oj, Jo] ] [/ o []. Jo [A]]
9. 19. Production of three-dimensional images using a rapid method with elimination of direct illumination.

The use of the method described above has the drawback of requiring the acquisition of reference images. At each reference image acquisition, it is necessary to perform a large displacement of the mirror (5113). It is possible to use a reference image to phase-register several successive useful images, and therefore not to acquire a reference image on each elementary image acquisition. Nevertheless, if the system is not perfectly stable on a time scale comparable to the acquisition time of a complete three-dimensional frequency representation, the acquisitions of reference images must be numerous. Due to the large displacement of the mirror that they require, these acquisitions constitute a significant waste of time. To avoid the acquisition of reference images, steps 1 and 2 of paragraph 7.17.2. , whose objective is to perform the phase registration of the two-dimensional frequency representations, can be replaced by the method described below. This method can also be used with the other embodiments but is then only of limited interest.

This method comprises a preliminary phase, which is carried out before any calculation requiring the phase adjustment (ie before the actual imaging phase), then a modification of the steps used in the imaging phase. The acquisition of an image to be processed by this method can be done according to procedure 9. 9. used with variant 1, that is to say without acquisition of reference image and with use of the glass for cancel direct lighting.

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9. 19.1. Preliminary phase.

fréquentielles bidimensionnelles indicées par l'indice 1, les tableaux Kn p,q [ni, n1.1] Fh p,q [ni, n} ,1] . Dans ces tableaux: p indice le coté (gauche ou droit) vers lequel parvient l'onde d'éclairage direct q indice le coté d'ou provient la représentation fréquentielle (opposé ou nonà celui ou parvient l'onde d'éclairage directe) l indice la position du point correspondant à l'onde d'éclairage directe, sur l'image générée par la méthode décrite en 9.9., à partir du coté indicé par q=0. The preliminary phase consists in determining, from a limited number of representations

two-dimensional frequencies indexed by the index 1, the tables Kn p, q [ni, n1.1] Fh p, q [ni, n}, 1]. In these tables: p index the side (left or right) towards which the direct illumination wave arrives q index the side from which the frequency representation comes (opposite or not to that where the direct illumination wave arrives) l index the position of the point corresponding to the direct illumination wave, on the image generated by the method described in 9.9., from the side indexed by q = 0.

The indices (l, p) therefore characterize a lighting wave and the indices (l, p, q) characterize a two-dimensional frequency representation corresponding to this lighting wave and to the sensor indexed by q.

The indices ni, nj are the coordinates on two axes of this frequency representation, after centering with respect to the point of direct impact of the illuminating wave.

The array Knp, q [ni, ni. 1] contains the third coordinate nk of the frequency representation considered, for each pair ni, nj.

The table Fhp, q [ni, nj, l] contains the value of this representation at the point of coordinates ni, nj, nk after resetting in phase with respect to the representation defined by / = 0.

The array Bh p, q [ni, n1 '/] contains the noise on the corresponding elements of Fh, y ni. nj. 1].

aux différents indices l, et caractérisée par les tableaux Knp,q et Fhp,q . These tables therefore characterize the values of the three-dimensional frequency representation of the object at a certain number of points. The table Knp, q characterizes the points at which values are available, and the table Fhp, q characterizes these values themselves. The positions of the direct illumination wave corresponding to the indices / are chosen such that any two-dimensional frequency representation, after re-centering, has a non-empty intersection with the part of the three-dimensional frequency representation of the object constituted by the superposition of the corresponding representations

with the different indices l, and characterized by the tables Knp, q and Fhp, q.

ex 1 IL[j IJL[L The preliminary phase is broken down into three steps: Step 1: Fig. 81 represents the points corresponding to the direct illumination wave, on the image generated by procedure 9.9. from the sensors where this direct illumination wave arrives, for several values of l We denote by IL [l], JL [l] the coordinates of the point indexed by l, with for example:

ex 1 IL [j IJL [L

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0 ' 1 p .?Il plX 2 2 1 N pix - 1 - marge N plX 2 2 N plX N plX - 1- marge

0 '1 p.? Il plX 2 2 1 N pix - 1 - margin N plX 2 2 N plX N plX - 1- margin

<tb>
<tb> 2
<tb>

marge "pu-

margin "pu-

<tb>
<tb> margin <SEP> 2
<tb> 4 <SEP> Npix <SEP> margin
<tb> 2
<tb>
or margin = 1 for example.

programme détermine alors, pour chaque valeur de l, la valeur de k telle que !L[t] Jo[ k] et .7L[l = Jo[ k] Il range cette valeur dans le tableau TK en TK[l]. The points indexed by l must be part of the trajectory defined by tables Io and Jo Le

program then determines, for each value of l, the value of k such that! L [t] Jo [k] and .7L [l = Jo [k] It stores this value in the table TK in TK [l].

Step 2: The second step is to determine the arrays Knp, q and Fhp, q The program first initializes these arrays, for example to a value of -10,000.

ni =l -1n7Qxk,P.9 + N pD: Ylj = j- jnlaXk.P.9 +NPx

( )2 ( N )2 ( ,,)2 (lio )Z )2 ( " )2 C.JrraxA.P~9 I2Jz )2 II prend pour chacun de ces nombres l'entier le plus proche puis il effectue:

Kn p,q [ni,nj, 1] = nk Fhp,q[ni,nj.l] = Mk,p,q[i,1]Dpq+pq[I.1] Bh p,q [ni, nj, /] = Bk,p,q [i, 1 ]ID pq+ J5q [1,1]1 Etape 3 : cette étape consiste en une modification du tableau Fhp,q. Le programme parcourt l'ensemble des (l,p,q). Pour chaque valeur de ce triplet, le programme effectue les opérations 1 à 3 suivantes: opération 1: le programme initialise à 0 les nombres nom et denom opération 2 : le programme parcourt l'ensemble des valeurs de (ni,nj) en testant la condition

Kn [i,M/./]-À fny,M/.0] z <~ lim avec par exemple hm= 1. Lorsque cette condition est réalisée il effectue: The program then traverses the set of quintuplets (l, p, q, i, j). It calculates for each of them k = TK [l]

ni = l -1n7Qxk, P.9 + N pD: Ylj = j- jnlaXk.P.9 + NPx

() 2 (N) 2 (,,) 2 (lio) Z) 2 (") 2 C.JrraxA.P ~ 9 I2Jz) 2 He takes for each of these numbers the closest integer then he performs:

Kn p, q [ni, nj, 1] = nk Fhp, q [ni, nj.l] = Mk, p, q [i, 1] Dpq + pq [I.1] Bh p, q [ni, nj , /] = Bk, p, q [i, 1] ID pq + J5q [1,1] 1 Step 3: this step consists of a modification of the table Fhp, q. The program traverses the set of (l, p, q). For each value of this triplet, the program performs the following operations 1 to 3: operation 1: the program initializes to 0 the numbers name and name operation 2: the program runs through all the values of (ni, nj) by testing the condition

Kn [i, M /./ Danemark- À fny, M / .0] z <~ lim with for example hm = 1. When this condition is fulfilled he performs:

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nonip,q,l Ph p,q [/1/, nj ,0]Fh p,q [ni, n1, 1] none p,q,l + ~ (BhP.9nn'Oz +BhP.9nlW.l)z denom p,q,l + = IFh p,q 2 [ni, nj,/]\2 <7C/!077! o i + #############T############### denom BhP.9nl'n.0)Z + (Bh p,q [ni, n1,1]) opération 3:le programme effectue:

Fhp,q[ni,nJ,I] = nom p,q,1 Fhp,,,[ni,nj,l] yHV denompql
9. 19.2. Phase d'imagerie
La phase d'imagerie diffère de celle utilisée en 7.17.2. par la méthode de recalage de phase. Le recalage en phase est içi effectué par rapport à la partie de la représentation fréquentielle de l'objet caractérisée par les tableaux calculés dans la phase préliminaire, et non par rapport au point image de l'onde d'éclairage, à des valeurs préenregistrées de l'onde d'éclairage ouà des images de référence.

nonip, q, l Ph p, q [/ 1 /, nj, 0] Fh p, q [ni, n1, 1] none p, q, l + ~ (BhP.9nn'Oz + BhP.9nlW.l) z denom p, q, l + = IFh p, q 2 [ni, nj, /] \ 2 <7C /! 077! oi + ############# T ############### denom BhP.9nl'n.0) Z + (Bh p, q [ni, n1,1]) operation 3: the program performs:

Fhp, q [ni, nJ, I] = name p, q, 1 Fhp ,,, [ni, nj, l] yHV denompql
9. 19.2. Imaging phase
The imaging phase differs from that used in 7.17.2. by the phase adjustment method. The phase adjustment is here carried out with respect to the part of the frequency representation of the object characterized by the tables calculated in the preliminary phase, and not with respect to the image point of the illumination wave, at prerecorded values of the illumination wave or to reference images.

* The following steps 1,2,3 replace steps 1 and 2 defined in 7.17.2.

.Ll,,P,9 ' - ,J]['-7] BkP,9l'J k,P.9Ll'JIDP9+P9Lt'JI Etape 2: Cette étape consiste à établir le coefficient complexe caractérisant, pour chaque représentation bidimensionnelle, le décalage de phase et d'intensité entre cette représentation bidimensionnelle et la

portion de représentation tridimensionnelle caractérisée par les tableaux En p,y et Fhp,, . Ce coefficient complexe, pour la représentation caractérisée par les indices k,p,q, s'exprime sous la forme nomk,p,q . Il denomk, p,q

est obtenu en effectuant une boucle sur l'ensemble des indices (À-,p, q, ij, 1). Pour chaque (k-,p, q, ij, 1) : -le programme calcule: II1 = I - illla7Ck, p.9 +'' p ni =} - jmaxk,p,q + N plX

liv 2 -Il teste la condition:

IKn p,q[ni, ni, 1] -nkl2 lim avec par exemple l1m=l. -Si la condition est vraie, le programme effectue alors les opérations Step 1: the program performs, for all the values of k, p, q, i, j:

.Ll ,, P, 9 '-, J] [' - 7] BkP, 9l'J k, P.9Ll'JIDP9 + P9Lt'JI Step 2: This step consists in establishing the characterizing complex coefficient, for each two-dimensional representation , the phase and intensity shift between this two-dimensional representation and the

portion of three-dimensional representation characterized by the tables En p, y and Fhp ,,. This complex coefficient, for the representation characterized by the indices k, p, q, is expressed in the form nomk, p, q. It denomk, p, q

is obtained by carrying out a loop on the set of indices (À-, p, q, ij, 1). For each (k-, p, q, ij, 1): -the program calculates: II1 = I - illla7Ck, p.9 + '' p ni =} - jmaxk, p, q + N plX

liv 2 -It tests the condition:

IKn p, q [ni, ni, 1] -nkl2 lim with for example l1m = l. -If the condition is true, the program then performs the operations

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.Tk,P,9 t ' FhP,9 nt' n' l nOrilk,P,9+ = (B k,p,q [1,J])2 + (Bhp,q[ni,nj,/J) denoMk,,,,, IMk,p,q[l.l]!2 denOmk,p,q+= ( Bk,p,q [. 1,1 ])2 +(BlP.9Lnt'n,l])z Etape 3 : cette étape constitue le recalage en phase proprement dit. Le programme effectue:

nomk,P,a iirk,P.9l'JJ CjeJ7011Ik.P,q irk.P.9I,
9. 20. Réalisation d'images tridimensionnelles suivant une méthode simplifiée.

.Tk, P, 9 t 'FhP, 9 nt' n 'l nOrilk, P, 9 + = (B k, p, q [1, J]) 2 + (Bhp, q [ni, nj, / J) denoMk ,,,,, IMk, p, q [ll]! 2 denOmk, p, q + = (Bk, p, q [. 1,1]) 2 + (BlP.9Lnt'n, l]) z Step 3 : this step constitutes the realignment in phase. The program performs:

nomk, P, a iirk, P.9l'JJ CjeJ7011Ik.P, q irk.P.9I,
9. 20. Production of three-dimensional images using a simplified method.

To generate the three-dimensional image of the object, we can limit ourselves to the representation
Fo, defined in 7.17. This amounts, in the procedure described in 7.17.2., To adopting tables IBp, q that are zero for any pair (p, q) # (0,0).

It is also assumed here that the object has an average index close to the nominal index of the observed object and that the optical table is completely free of vibrations.

Steps 9.11. to 9.17 can then be deleted. The present method further differs from the previous one in the method used to adjust the position of the lenses before use and in the image overlay algorithm.

9.20.1. Adjustment of lenses and mirror (5113).

This adjustment can be carried out with a transparent blade provided that the objective is not moved after adjustment, when the object is introduced. If objectives intended to operate without immersion liquid or a coverslip are provided (nominal index equal to 1) and if the sample is thin or of average index close to 1, it can also be carried out by absence of object. During this step we use the FEG and FRD beams
It is necessary that the mirror (5113) be removable and can be replaced by an absorbent plate at any point except at a central point where a reflector of small size is placed. The dimension of this reflector must be approximately -or D is the diameter of the incident beam on the mirror
2Npix (5113). This plate should be provisionally placed on the mirror so that the reflector occupies approximately the center of the incident beam on the mirror. The mirror positioner must itself be fixed to a three-axis positioner in translation.

This adjustment must be carried out immediately after the series of adjustments described in 9.5. and the objectives should not be moved any more It comprises the following steps: step 1: the mirror is replaced by the absorbent plate

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step 2: using only the FRD beam, the mirror is moved in translation so that the image produced on the CCD (4339) is point and centered. step 3: using only the FEG beam, the objectives are moved so that the image produced on the CCD (4339) is punctual and centered. step 4: we can then put the mirror back in place.

9. 20.2. three-dimensional representation calculation algorithm
Steps 1 and 2 of the algorithm described in 7.17.2. can be deleted. Indeed, the additional adjustment carried out and the absence of vibrations make it possible to avoid any phase shift of the lighting beam.

9.21. Use of lenses with aberrations.

As in the third embodiment, lenses of the type described in 7. 20 or 7.21 can be used. The corresponding modifications of the algorithms are similar to those described in 7. 20 and 7.21. It is of course necessary to adapt them to the mode of obtaining the plane frequency image, which differs notably from the third embodiment.

10. Positioning device for optical elements.

The embodiments described, and in particular embodiment 4, require the use of numerous positioners of good precision. These positioners are costly elements that are poorly suited to mass production and are liable to become out of adjustment over time. These positioners, with the exception of the objective and sample positioners, should in principle only be adjusted once, during the initial adjustment phase.

One solution to this problem is to use removable positioners during the manufacture of the microscope. After positioning, each element can be fixed with a suitable glue. For example, in embodiment 4, the SLMs can be secured using the device of Figs. 83 to 85. The part of the fixing device which is integrated into the microscope comprises three mobile assemblies: assembly 1: it is made up of the following elements, joined together: - a fixing plate (5801) detailed in Fig. 83 and having a surface porous to glue (5802).

- the SLM (5804) fixed on the unglued part (5803) of this plate.

- a plate (5808) of magnetizable material, for example iron, fixed to the rear of the plate (5801) assembly 2: consists of the following elements, joined together: - a plate (5805) detailed in Fig. 84 having a porous surface to be glued (5806) and a recess (5807) in its center - a plate (5809) having a surface to be glued (5817)

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- a plate (5810) of magnetizable material, for example iron, fixed to the plate (5809). set 3: consists of a plate (5811) having a porous surface to be glued (5816)
The removable part of the fixing device comprises the following assemblies: assembly 4: it is composed of an arm (5815) comprising a magnetizable part (5814) and linked to a positioner POS 1, not shown. The part (5814) has an electric wire winding around an iron core, not shown. By powering this winding, (5814) and (5810) are joined and by interrupting the power supply, these elements are disconnected. assembly 5: is composed of an arm (5813) comprising a magnetizable part (5812) and linked to a positioner POS2, not shown. The part (5812) has an electric wire winding around an iron core, not shown. By powering this winding, (5808) and (5812) are joined and by interrupting the power supply, these elements are disconnected.

The fixed part of the positioner POS1 and the element 3 are integral with the optical table. The fixed part of the POS2 positioner is integral with the movable part of the POS 1 positioner. The POS 1 positioner allows one axis to move in the direction of the # axis and one to rotate about the j axis. The positioner POS2 allows a translation along each of the vectors 7 and k and a rotation around the axis i. It also allows, but with a very small adjustment margin, a rotation around the axis.

To position the system, the surfaces to be glued designated above are glued beforehand. The magnets of the parts (5812) and (5814) are supplied so as to secure the removable parts and the non-removable parts. Adjustment is carried out normally with the POS and POS2 positioners. The system is left in place long enough for the glue to dry. Supplying the magnets is then stopped so as to separate the removable parts from the non-removable parts. The adjustment is then final and the removable part can be removed.

The glue used must have a sufficiently long setting time so as not to interfere with the adjustment and must have minimal shrinkage during drying. It is also possible to provide dedicated orifices in the plates (5811) and (5805) for injecting the glue after positioning. This example is given for the positioning of the SLMs but is simply adaptable to all the elements to be positioned in the system. Depending on the number of degrees of freedom required and the type of element to be positioned, the shape of the mobile platforms must be adapted. The principle consisting in using removable positioners and in effecting a definitive fixing by gluing remains however valid.

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11. Support suitable for transporting and maintaining the adjustments made
The microscopes described in Embodiments 3 to 5 consist of an assembly of elements attached to an optical table. During a possible transport, even slight shocks can cause a disruption of the system. During prolonged use, dust may settle on the various optical elements.

In order to overcome these drawbacks, the microscope described can be protected by a system, the principle of which is shown in FIG. 86. The optical table, which can for example be made of granite, constitutes the lower part of a hermetically sealed box (5901 ). The fact that the box (5901) is hermetically sealed protects the assembly against dust. The box (5901) is included in a larger box (5902), without there being direct contact between the two boxes. The two boxes are separated by shock absorbers which may be appropriately inflated rubber balloons (5903), and which are arranged on the 6 sides of the box (5901). This system absorbs shocks and prevents loss of settings during transport, while ensuring good suspension of the optical table during use.

However, it is necessary that the part of the system constituted by the two objectives and their positioners remain accessible. This entails certain adaptations of the shape of the boxes, visible in FIG.

87, adapted here to the example constituted by embodiments 4 and 5. The front wall of the box (5901) constitutes a vertical plane passing in Fig. 63 between the mirrors (4451) and (4452). The box (5901) has a protuberance (5903) allowing the fixing of the mirrors (4454) (4455) (4456) and of the objective (4317) below the plane of the optical table itself. The box (5902) shown in dotted lines has a notch (5904) providing access to the objectives and to the sample.

In order that the mirrors (4453) and (4454) as well as the lens inputs remain inaccessible, and in order to avoid any entry of dust, the shape of the box (5902) must also be adapted locally. This adaptation is detailed in Fig. 88. The box has two protuberances (5905) and (5906) containing the mirrors (4453) and (4454) respectively, and has two openings linked to the entry of the lenses (in fact, to the mounts of these lenses) by rubber sleeves (6001) (6002). The positioners of the objectives and of the sample, not shown, are external to the box (5902).

In Fig. 87, the shock absorbers (5903) have not been shown, but they are present throughout the area between the two boxes.

A closing cover allowing protection of the accessible part (objectives and sample, as well as their positioners) must also be provided.

In the case of Embodiment 5, the outer box (5901) must have an additional compartment to contain items that are not on the optical table.

12. Variants:
Other embodiments are of course possible and the above description is not limiting. In particular, it is possible to use more objectives, or to perform other

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combinations of receiver and beam deflector types, or to modify the phase adjustment algorithms.

13. Possibilities of industrial application:
13.1. References [Thomas]: 4-D imaging software observes living cells, Charles Thomas & John White, Scientific Computing World p.31, December 1996.

[Holton]: Under a Microscope: Confocal A11croscopy Casts New Light on the Dynallics of Life, W. Conard Holton, Photonics Spectra p. 78, February 1995.

l1lultzlayered optical memory, Y.Kawata, R.Juskaitis, T.Tanaka, T. Wilson & S.Kawata, Applied Optics vol.35 no 14 p. 2466, 10 mai 1996 [Parthenopoulos]: Three-dimensional optical storage memory, D.A.Parthenopoulos & P.M.Rentzepis, Science 245, p. 843, 1989 [Strickler]: Three dimensional optical data storage in refractive média by two-photon excitation, J.H. Strickler & W.W.Webb, Optics Letters 16, p.1780, 1991 [McMichael]: Compact holographic storage demonstrator with rapid access, I. McMichael, W. Christian, D.Pletcher, T.Y.Chang & J.H.Hong, Applied Optics vol.35 no 14 p. 2375, 10 mai 1996. [Pike]: Phase measuring scanning optical microscope, JGWalker & ERPike, patent WO 91/07682 [Bertero]: Analytic inversion formulafor confocal scanning microscopy, B. Bertero, C. De Mol, ERPike, Journal of the Optical Society of America vol. 4no.9, September 1987 [Ueki]: Three-dimensional optical memory with a photorefractive crystal, Y.Kawata, H. Ueki, Y.Hashimoto, S.Kawata, Applied Optics vol. 34 no 20 p.4105, July 10, 1995 [Juskaitis]: Differential phase-contrast microscope with a split detector for the readout system of a

l1lultzlayered optical memory, Y. Kawata, R.Juskaitis, T. Tanaka, T. Wilson & S. Kawata, Applied Optics vol. 35 no 14 p. 2466, May 10, 1996 [Parthenopoulos]: Three-dimensional optical storage memory, DAParthenopoulos & PMRentzepis, Science 245, p. 843, 1989 [Strickler]: Three dimensional optical data storage in refractive media by two-photon excitation, JH Strickler & WWWebb, Optics Letters 16, p.1780, 1991 [McMichael]: Compact holographic storage demonstrator with rapid access, I. McMichael , W. Christian, D. Pletcher, TYChang & JHHong, Applied Optics vol. 35 no 14 p. 2375, May 10, 1996.

[Barbarstatis]: Swift multiplexing wirth spherical reference i4,m,es, G. Barbarstatis, M.Levene,D.Psaltis, Applied Optics vol.35 no 14 p.2403, 10 mai 1996
13. 2. Discussion
Les microscopes courants forment par un procédé optique une image bidimensionnelle correspondant à une coupe aggrandie de l'objet observé. Cette image peut le cas échéant être enregistrée par une caméra vidéo afin de pouvoir être restituée ultérieurement. [Bashaw]: Cross-talk considerations for angular and phase-encoded multiplexing in volume holography, MCBashaw, JFHeanue, A.Aharoni, JFWalkup & L. Hesselink, Journal of the Optical Society of America B vol.11 no 9 p. September 1820, 1994

[Barbarstatis]: Swift multiplexing wirth spherical reference i4, m, es, G. Barbarstatis, M.Levene, D.Psaltis, Applied Optics vol.35 no 14 p.2403, May 10, 1996
13. 2. Discussion
Current microscopes form by an optical process a two-dimensional image corresponding to an enlarged section of the observed object. This image can if necessary be recorded by a video camera in order to be able to be reproduced later.

It is possible to generate a three-dimensional image by using one of these microscopes and varying the focus setting. Each adjustment corresponds to a different cutting plane, and a three-dimensional image can be reconstructed from these cutting planes. Some microscopes equipped with a motorized focusing device and appropriate software perform this operation.

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automatically. Such microscopes are described for example in [Thomas]. The major drawback of these microscopes is that the image of a section plane is strongly disturbed by the content of the other planes.

There are also confocal microscopes, in which the illumination is focused on a point and the three-dimensional image is generated by scanning all the points of the object. Such microscopes are described for example in [Holton]. These microscopes make it possible to solve the problem of the systems described in [Thomas], namely that the value detected at a given point is little disturbed by the value of the close points.

Confocal microscopes have the drawback of only being able to detect the intensity of the received wave and not its phase. As many commonly observed objects are essentially characterized by index variations resulting in phase variations of the transmitted wave, this defect causes significant inconvenience for users who have to color the observed samples. This is why efforts have been made to produce confocal microscopes sensitive to the phase of the transmitted wave [Pike]. For various reasons, these microscopes remain ineffective.

The image generated by confocal microscopes does not have the best theoretical definition that can in principle be obtained from the wave received by the objective used. This is linked, as indicated in 7.18.3., To the fact that the confocal microscopy method strongly filters the high frequencies. This is why efforts have been made to improve the resolution of these confocal microscopes [Bertero].

The present microscope overcomes the shortcomings of previous microscopes in terms of resolution and in terms of phase detection. It can be advantageously used as a replacement for these microscopes, in all of their applications.

A new field of application for microscopes is the reading of three-dimensional optical memories.

A first type of optical memories is that where the data are recorded point by point in a three-dimensional material in the form of variations of the local properties of this material ([Ueki].

[Parthenopoulos], [Strickler]). These data must therefore be read by a microscope capable of reading three-dimensional data without the data recorded in several successive layers of material disturbing each other. The disturbance of the image of a point by the rays diffracted by the neighboring points is therefore reflected here by an intersy mbol interference. In general, the authors used few layers at a great distance from each other, which limits this interference.

However, if a larger amount of data were to be recorded in a given volume, conventional microscopy methods would prove insufficient. In particular in the case of [Strickler] and [Ueki] the data are recorded in the form of index variations and the confocal microscope is particularly poorly suited to their reading. Therefore, efforts have been made to improve the data reading system [Juskaitis].

The present microscope constitutes the reading solution allowing a maximum integration of this type of memories. Indeed the image that it allows to obtain takes into account the index and decreases

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strongly intersymbol interference. In the ideal case where the entire beam from the sample would be detected, which can be achieved by increasing the number or the aperture of the objects, the intersymbol interference is entirely eliminated.

Another type of optical memory consists of holographic memories. For example, in the document [McMichael], the data is read by illuminating the object constituted by the optical memory with a parallel beam of variable direction and by detecting the wave coming from the sample for each direction of the illumination beam. . A direction of the illumination beam corresponds to a data page and each point of the two-dimensional frequency representation of the wave coming from the object for a given illumination wave corresponds to a bit stored in the optical memory. Each point of the two-dimensional representation of the wave coming from the object also corresponding to a point of the three-dimensional representation of the object itself, a bit stored in the optical memory therefore corresponds to a point of the three-dimensional frequency representation of this optical memory. An analysis of this type of memories in terms of frequency representations can be found in [Bashaw]
The present microscope can therefore advantageously be used to read such optical memories, the bits stored in the memory corresponding directly to points of the three-dimensional frequency representation obtained by the present microscope from the object constituted by the optical memory. The writing system of the optical memory must however be planned so as not to use the points of the three-dimensional frequency representation which are not obtained by the present microscope, except to increase the number of objectives used to avoid the non-detection of certain frequencies.

Other types of holographic optical memories exist [Barbarstatis]. In general, the present microscope makes it possible to obtain a representation of the observed object which would be perfect in the ideal case where the objectives used would cover the entire space around the object. the representation obtained is perfect, the data stored in memory and detected in the form of a three-dimensional frequency representation of the object can then be restored in any form: it is possible to simulate, using the known representation of l object constituted by the optical memory, the wave which would be obtained from any lighting or by any other reading method (at the wavelength used by the microscope). All the types of optical memory can therefore be read by the present microscope, in the general case by means of additional operations allowing the reconstitution of the data from the frequency representation of the object constituted by the optical memory. In the case where the representation is not perfect, adequate precautions must be taken to take into account the gray areas of the frequency representation of the object.

Claims (7)

CLAIMS (1/2) 1-Microscope comprising. - one or more receivers (118) each allowing digital recording of interference figures, each of said interference figures being formed on a reception surface, by a wave coming from the observed object (112) illuminated by a wave plane illumination, and by a reference wave that has not passed through the observed object, - a device (109) (111) (124) allowing the generation of several of said plane illumination waves, successively illuminating the object observed, and differing from each other by their direction expressed in a reference linked to said receivers, - means for generating a representation of the observed object, characterized in that it comprises means for controlling and / or compensating for the phase shift affecting, in frequency representation, points of the representation of the object obtained from distinct lighting waves. 2- Microscope according to claim 1, characterized in that it comprises means for generating said plane waves and said reference waves so that the phase difference between a plane wave and the reference wave with which it interferes is reproducible. 3- Microscope according to claim 2, characterized in that it comprises means for generating said plane waves and said reference waves so that the phase difference between a plane wave and the reference wave with which it interferes is independent of the plane wave considered. 4- Microscope according to one of claims 1 to 3, characterized in that it comprises means for determining the difference between the phase shifts affecting two sub-representations of the observed object obtained from illumination waves of different direction. 5-Microscope according to claim 4, characterized in that said means for determining said difference between the phase shifts affecting two sub-representations of the object observed comprise means for determining the phase difference between the restrictions of said sub-representations to a set included in the intersection of said sub-representations in frequency representation, or an approximation of this difference. 6-Microscope according to claim 5, characterized in that said set included in the intersection of said frequency sub-representations, defined in claim 5, is constituted by the fixed point of origin of the frequency representation of the object. <Desc / Clms Page number 256> CLAIMS (2/2) 7-Microscope according to one of claims 1 to 5, characterized in that it comprises an objective affected by aberrations such that the image of a point object by said objective has a size greater than the diameter of the diffraction spot which would be obtained if the objective were limited by the diffraction, and by the fact that it comprises calculation means to compensate for these aberrations. 8- Microscope according to one of claims 1 to 7, characterized in that it comprises at least one objective associated with an optical system allowing on the one hand the measurement on a sensor of the wave coming from the sample and having passed through the objective, and on the other hand the formation of an illumination wave which, after passing through the objective, becomes in the sample a plane illumination wave of variable direction. 9-Microscope according to claim 8, characterized in that it comprises several objectives focused on the same part of the sample and each verifying the conditions of claim 8 10-Microscope according to one of claims 1 to 9, characterized by the fact that it comprises calculation means for compensating for the spherical aberration due to the difference between the average index of the observed sample and the index for which the objective was designed.