FR2585854A1 - METHOD OF FOCUSING MONOCHROMATIC RADIATION AND OPTICAL PHASE DELETING ELEMENT USING THE SAME. - Google Patents

Abstract

THE INVENTION CONCERNS THE CONSTRUCTION OF OPTICAL APPARATUS AND INSTRUMENTS. THE PROCESS, SUBJECT OF THE INVENTION, IS CHARACTERIZED IN THAT THE PHASE MODULATION IS CARRIED OUT AS A FUNCTION OF THE PHASE AND THE INTENSITY OF THE MONOCHROMATIC RADIATION TO BE FOCUSED AND OF THE REQUIRED DISTRIBUTION OF THE INTENSITY IN THE FOCUSING REGION, BY ESTABLISHING A CORRELATION BETWEEN THE POINTS OF THE WAVEFRONT TO BE FOCUSED AND THE POINTS OF THE FOCUS REGION SO THAT EACH POINT OF THE WAVEFRONT TO BE FOCUSED CORRESPONDS ONLY ONE POINT OF THE REGION OF FOCUS. THE OPTICAL ELEMENT FOR THE IMPLEMENTATION OF THE PROCESS IS IN THE FORM OF A REFLECTION OR TRANSMISSION PHASE BLADE1 HAVING ON ONE OF ITS SURFACES ZONES5 EACH OF WHICH HAS A CONTINUOUS GROUND6 AND IS CHARACTERIZED IN THAT THE HEIGHT DUDIT RELIEF6 AND THE SHAPE OF SAID ZONES5 VARY ACCORDING TO THE PHASE AND INTENSITY OF THE MONOCHROMATIC RADIATION TO BE FOCUSED2 AND ACCORDING TO THE DISTRIBUTION OF THE RADIATION INTENSITY FOCUSED IN THE FOCUSING REGIONS3. THE INVENTION MAY BE USED IN LASER TECHNOLOGY IN USE IN INDUSTRY.

Description

The present invention relates to the construction of apparatus and

  optical instruments, in particular the creation of complicated optical elements for transforming monochromatic radiation, and particularly relates to a method of focusing a monochromatic radiation and an optical phase shift element to

the implementation of this method.

  The invention can be used in the laser technology used in industry for technological purposes and for the treatment of materials (heat treatment,

  welding, cutting, marking, perforation), in micro-

  electronics (annealing of semiconductors), photochemistry, medicine (surgery, ophthalmology, including

  correction of complex vision disorders), that is,

  say in all areas where a focus is needed

complicated with radiation.

  The problem of obtaining a large concentration

  The energy of radiation where it is needed has been solved after the advent of lasers, which have lately had many applications in the most diverse fields. However, the laser is not to be considered as an independent element, it is part of a system intended to perform a specific operation. This is to send the laser beam to a certain area and create the desired intensity distribution. Also, does the evolution of the laser technique go hand in hand with

  that of the manipulation of the laser emission.

  The focusing method of the laser emission in which the laser beam is properly directed by means of a lens, a cylindrical lens or a mirror, that is to say based on elements of the classic optics, can not satisfy all the

  variety of imperatives of modern technology. Convenient-

  However, this method does not benefit from one of the main advantages of the laser beam of knowing its amplitude and its phase. It does not achieve the desired intensity distribution in the focusing region. For example, a lens and a cylindrical mirror focus the radiation into a line segment, but the intensity distribution along said line segment depends on that of the beam and is uncontrollable. Also, these elements are unable to create a uniform intensity distribution along the line segment, and in case of Gaussian distribution of the intensity of the radiation to be focused, the intensity of the focused radiation along the line segment differs from the uniform intensity of a few tens to a few hundred times. These elements do not give

  plus adequate focus with arbitrary implications.

  There is a method of focusing a ray-

  monochromatic method based on the use of a scanner which is a complicated electro-mechanical device with mirrors oscillating according to a certain law (Proceedings of the International Conference of Heat Treatment-79, London,

  1980, Trattford O.N.H. et al, Heat Treatment, using a high-

  power laser, pp. 32-38). The movement of the mirrors moves the focused radiation along the desired contour. However, the scanner does not allow to obtain immediately and simultaneously the required distribution of the intensity of the focused radiation. Also, despite their advantages, the sweepers did not find widespread use because of their reduced reliability and their reliability.

high cost.

  A simpler radiation focusing method is the projection method, in which the laser beam is directed towards an object through a mask which, with a lens, forms a focusing region of given shape (see "Promyshlennye primenenia laserov" ("Lasers in Industry") by J. Redy, 1981, "Mir" Editions, Moscow, 459). Although simple and convenient, this process is

  effective, given the prohibitive losses in the mask.

  Another significant drawback of said method is the impossibility

  to control the distribution of the intensity of the

  rayoonement focused along the image obtained.

  The method of focusing a monochromatic radiation with a Gaussian intensity distribution (see Optics Communications, 48, N1, 1983, Y. Kawamura et al., A simple optical device for generating square flat-top irradiation from a gaussian laser beam, pp.44-46) provides a square-shaped focusing region with a uniform distribution of the intensity of the focused radiation. The laser beam is guided towards the focusing region by means of a focusing element which is in the form of four prisms having a common vertex and forming a quadrangular pyramid. The beam is thus divided into four to create an approximately uniform intensity distribution by the superposition effect of said beams in the square. However, this method (as well as other methods based on beam splitting) does not solve the general problem of focusing on an arbitrary intensity distribution region. Even in the case of a square, the difference between the intensity distribution obtained and the uniform distribution is the size of the square, the

  focal length, to the parameters of the radiation to focus.

  It should also be noted that the intersection of the portions of the beam in the focusing region produces an interference image, undesirable in a number of

practical cases.

  A general process of transformation of a rayon

  monochromatic is given by holography. Monochromatic radiation is guided towards the focusing region through a volume or plane hologram, which makes it possible to obtain practically any distribution.

  of intensity in the given region. However, to

  to build a hologram, one must have a standard wavefront, which is of a delicate nature. Holograms

  plans have a low diffraction efficiency (nearly 33%).

  For example, there is a method of treating surfaces with holograms (Soviet Certificate No. 224714, Cl, 21d, 53/00, Bulletin "Discoveries, Inventions, Industrial Models and Trademarks" No. 26, 1968 ) poor performance due to partial energy transition

to the zero diffraction order.

  The creation of volume holograms for CO2 lasers (A = 10.6, p m), the most promising for applications requiring very powerful beams, remains for the moment impossible for lack of an adequate recording medium. There is a method of focusing monochromatic radiation, using various zoned blades, for example Fresnel, Gabor, Rayleigh-Wood, Soret, etc.. (Applied Optics, v6 N 2, 1967, MH Horman et al., Plate Zone Theory Based on Holography, pp. 317-322) and consisting of forming the wavefront of the radiation by phase modulation of a wave at using a zoned phase slide. However, the zoned blades do not make it possible to vary the distribution of the intensity in the

  region of focus, let alone create the distribution of

  required. Since said zoned blades are multifocal, one can concentrate in the main focus only

  small portion of the radiation energy.

  But there is a method of focusing a monochromatic radiation, consisting of phase modulating the wavefront of the radiation, and an optical phase shift element to implement this method, which is in the form of a reflection plate or transmission containing on one of its surfaces areas each of which has a continuous relief (Reports of the Academy of Sciences of the USSR, v. 113, No. 4, 1975, "Optical systems with phase layers" by GG Slusarev, pp. 780-73, Applied Optics, v. 9, No. 8, 1970, Jordan JA et al., Kinoform Lenses, pp. 1883-1887) which direct the radiation to a single focus and have theoretical efficacy. approaching 100%. Although more advantageous than the ordinary lens, the phase shift optical element, like this one, does not make it possible to control the focusing region or the distribution of the intensity of the focused radiation, or to take account of the parameters

beam to focus.

  There is also a method of focusing monochromatic radiation by modulating the phase of its wavefront, made so that the radiation from each point of the wavefront is received by the entire focusing region. The focusing device of a monochromatic radiation embodying said focusing method is in the form of an optical phase shifting element called "kinoform" (IBM J. Res, Oev., March 1969, Lesem LB et al., The Kinoform : new wavefront reconstruction device, pp. 41-51). The "kinoform"

  is associated with a lens that directs the trans-

  put by the "kinoform" towards the focusing region.

  It is in the form of a diffraction element, that is to say that the radiation coming from each point of the

  "kinoform" is received by the entire focusing region.

  The "kinoform" provides an image constituted by a set of discrete points arranged in the same plane parallel to that of the "kinoform". Increasing the number of image points to achieve a focused radiation intensity distribution closer to the uniform distribution leads to a complication of the "kinoform" structure. The "kinoform" sends all the radiation in a single diffraction order that

  receives 78% of the radiation, but the remaining 22% o

  a background noise which is a restriction limiting its applications. The calculation of the "kinoform" by the fast Fourier transformation poses severe dimensional limitations both to the "kinoform" and to the image obtained, and makes the solution of the problem of the focusing of a radiation with the help of a 'kinoform' is

always approximate.

  The "kinoform" can be used for focusing only in normal incidence of the radiation to focus, the image obtained must be in the same plane. The creation of a "kinoform" for C02 lasers (X = 10.6 Hum) raises difficulties because of the fineness of its structure, incompatible with high power densities. The need for a lens which, in the infrared, is either of reduced reliability or high cost, also prevents the use of "kinoform" for focusing

powerful beams.

  The present invention therefore aims at a method of focusing a monochromatic radiation by phase modulation of its wavefront, and an optical phase shifting element implementing said method, which would be designed so that said phase modulation and the shape of the surface of said phase shift optical element would be able to focus the radiation into a given shape curve and into a planar figure so as to obtain the required intensity distribution along the curve and over the area of the planar figure , with complete concentration

Energy.

  This object is achieved by the fact that the method of focusing a monochromatic radiation by phase modulation of its wavefront is characterized, according to the invention, in that the phase modulation is effected according to the phase and the intensity of the monochromatic radiation to be focused, as well as the required intensity distribution in the focusing region, by virtue of a correlation established between the points of the wavefront to be focused and the points of the focusing region of the way at each point of the wavefront to focus

  corresponds to a single point in the focusing region.

  The object described above is also achieved by the fact that the phase shift optical element for focusing monochromatic radiation, in the form of a reflection or transmission plate provided on one of its area surfaces each of which comprises a continuous relief is characterized, according to the invention, in that the height of the relief and the shape of the zones are varied in

  function of the phase and the intensity of the mono-

  chromatic focus and the required distribution of focused radiation intensity in a region of

determined focus.

  It is advantageous that, for focusing in a plane curve, the phase shift optical element is in the form of a reflection plate such that the height of the relief in each of its zones and the shape of the zones are variable according to the expression: Z (u, v) = - (ueosO, v) XA o Z (u, v) is the height of the relief at the point (u, v) of the optical phase shift element disposed in the plane OUV, the OZ axis being perpendicular to the OUV plane, and the OR axis

  being in the opposite direction to the projection of mono-

  chromatic to focus on the plane OUV,

  A is the wavelength of the mono-

  chromatic to focus, m = 1,2,3, ..., M, -F (u, v) is a function satisfying the relation: u2 V2 L _ + Y (u, v): argiin (freeze exp ( 21ft ((uv) + u + v R + 'f2 + (x (t) -u 2+ (yo (t) -v2)) dudv-I) dt), ot is the normal parameter on the plane curve defined by the relations: u = xo (t), V = yot, z = f, o <t4 L, I is the intensity of the focused monochromatic radiation, 9 is the angle between the monochromatic radiation to focus and the axis OZ, L is the length of the plane curve, L / 0, R is the radius of the cross-section of the monochromatic radiation to focus, 6 is the parameter of the Gaussian distribution of the intensity of the monochromatic radiation to be focused,

f is the focal length.

  It is also advantageous that, for focusing in a plane curve, the phase shift optical element is in the form of a transmission blade such that the height of the relief in each of its zones and the shape of the zones vary according to the expression: C 1 '.m XZ (uv) = t (ucosv) mm} ncosg'-cosg' o Z (u, v) is the height of the relief at the point (u, v) of the optical element arranged in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR being of direction opposite to the projection of the monochromatic radiation to be focused on the plane OUV,

  R. is the wavelength of the mono-

  chromatic to focus, m = 1, 2, 3, ..., M, n is the index of refraction of the transmission blade, 9 '= arcsin (sin 9 / n), f (-u, v) is a function according to the relation: 2 2 L u + v (u, v) = argmin ((l fe exp + f DO 2 2 R2 + Vf + (xo (t) -u) 2 + (yo (t) -v ) 2)) dudv2 -1 (dt), ot is the normal parameter on the plane curve defined by the relation: u = xo (t), v = yo (t), z = f, 0 4 t CL, I is the intensity of the focused monochromatic radiation, 9 is the angle between the monochromatic radiation to focus and the axis OZ, L is the length of the plane curve, R is the radius of the cross section of the monochromatic radiation to focus, is the parameter of the Gaussian distribution of intensity of the monochromatic radiation to focus,

f is the focal length.

  It is useful that, for focusing in a line segment, the optical phase shift element is in the form of a reflection plate such that the height of the relief in each of its zones and the shape of the zones vary according to the expression: Z (u,) {- T ucos, v> m 2cosg o Z (u, v) is the height of the relief at the point (u, v) of the optical phase shift element disposed in the plane OUV, OZ axis being perpendicular to the OUV plane, and the OR axis

  being in the opposite direction to the projection of mono-

  chromatic to be focused on the plane OUV, g is the angle between the monochromatic radiation to focus and the axis OZ,

  X is the wavelength of the mono-

  chromatic to focus, m = 1,2,3, ..., M, f (u, v) is the function satisfying the relation:

L _ _

(uv) = argmin (I (I d 2 IM :(, ofro? e

2 R2.

  u + v2 R + V f + (u2 + tcosC -U) 2 + (v + tsino -v) 2)) dud 2_I (t)) 2dt) + 'I 2 (U o0) where is the angle between the line segment and the axis located in the plane OUZ and making an angle q '- o with the axis OZ, I (t) is the intensity of the focused monochromatic radiation, t is the normal parameter on the line segment, 0 <t <L, L is the length of the line segment, LJ 0, (Uo, vo) are the coordinates of the projection of the end of the line segment on the plane OUV, R is the radius of the cross section of the monochromatic radiation to focus, 6 is the parameter of the Gaussian distribution of the intensity of the monochromatic radiation to be focused,

f is the focal length.

  It is effective that, for focusing in a line segment, the optical phase shift element is in the form of a transmission blade such that the height of the relief in each of its zones and the shape of the zones vary according to the expression Z (u, v) t (ucos9, v) 1} mm A-ncosg'-cosO o Z (u, v) is the height of the relief at the point (u, v) of the optical phase shift element placed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR

  being in the opposite direction to the projection of mono-

  chromatic to be focused on the plane OUV, 9 is the angle between the monochromatic radiation to focus and the axis OZ,

  A is the wavelength of the mono-

  chromatic to focus, m = 1,2,3, ..., M, n is the index of refraction of the transmission blade, 9 '= arc sin (sin 9 / n) T (u, v) is a function satisfying the relation: 2 2 L; _ u -v

26'2-

(<u, v) = argmin (exp (

2 2 2

  u + v2 R f2 + (u + otcost-u) 2+ (vo + tsinK-V)) dudvI2 -I (t)) dt), where d is the angle between the line segment and an axis located in the plane OUZ and making an angle 2-9 with the axis OZ, I (t) is the intensity of the focused monochromatic radiation, t is the normal parameter on the line segment. 0 <t <L, L is the length of the line segment, L J 0; (uo, vo) are the coordinates of the projection of the end of the line segment on the plane OUV, R is the radius of the cross section of the monochromatic radiation to focus, CY is the Gaussian radiation intensity distribution parameter monochromatic to focus,

f is the focal length.

  It is advantageous for the focusing in a line segment located on the optical axis of the optical phase shift element, the latter is in the form of a reflection plate such that the height of the relief in each of its zones and the shape of the zones vary according to the expression r Z (u, v) => 2 Z (, v = Vl f2 (Z (p) 2- m J2 o Z (u, v) is the height of the relief at point (u, v) of the optical phase shift element disposed in the plane OUV, the axis OZ being perpendicular to the plane OUV, m = 1,2,3, ..., M,

  X is the wavelength of the mono-

  chromatic to focus, r2 = u + v Z (f) is the function defined by the relation j, '7 2 TrQJ (r) dr = I (t) dt, 0 f I (t) is the intensity distribution of the focused monochromatic radiation along a line segment located on the OZ axis, t is the normal parameter on the line segment, f <t <f + L, f is the focal length, 3 (r) is the intensity of the monochromatic radiation to focus,

  L is the length of the line segment.

  It is rational that, for focusing into a set of coplanar segments, the optical element of

  phase shift is in the form of a reflection plate -

  such that the height of the relief in each of its zones and the shape of the zones vary according to the expression Z (u, v) = t- Pj (ucosg, v) m? 2 mX? ç 2cosg for (u cos 0, v ) Gj, (j = 1,2, ..., N), where Z (u, v) is the height of the relief at the point (u, v) of the phase shift optical element disposed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR,

  opposite to the projection of monochromatic radiation

  to focus on the plane OUV, N is the number of segments,

  A is the wavelength of the mono-

  chromatic to focus, g is the angle between the monochromatic radiation to focus and the axis OZ, m = 1,2,3, ..., M, Gj (j = 1, ..., N) is the region in the plane OUV where are points (u, v) such that Sjaretg2 (u, v) C Cj + the arctg2 (u, v) is the angle between the axis OR and the radius vector of the point (u, v) , v), O = O, Oj + 1 = "j + + 21V-Lj / L (j = 1,2, ..., N), L is the length of the j-th straight segment, L is the total length of all

right segments -

(L = L L.),

  Yj (u, v) is a function satisfying the relation:

L U -V

41 - -6 r2 ..

  j (u, v) argmin (| e exp ((r (j (u, v) + j 0 G

+5 J

  + f 2+ (u + t cos "u) 2+ (vj + tjein cj-v) 2) dudv 2_ 2I) 2dt), where Vj is the angle between the jth segment of the line and the axis OR , f is the focal length, (uj, v.) are the coordinates of the projection of the end of the j-th straight segment on the plane OUV, t is the parameter on the j-th straight segment, 0 tj <Lj, I is the intensity of the focused monochromatic radiation, is the parameter of the Gaussian distribution

  the intensity of the monochromatic radiation to focus.

  It is advantageous that, for focusing into a set of coplanar segments, the optical phase shift element is in the form of a transmission plate such that the height of the relief in each of its zones and the shape of the zones vary according to the Expression: Z (u, v). (ucos9, v) 1 m L uJos mX ncosg'-cosg for (u cos 9, v) E Gj, (j = 1,2, ..., N), o Z (u, v) is the height of the relief at the point (u, v) of the optical phase shift element placed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR,

  opposite to the projection of the mono-

  chromatic to be focused on the plane OUV, N is the number of line segments, O is the angle between the monochromatic radiation to be focused and the axis OZ,

  A is the wavelength of the mono-

  chromatic to focus, m = 1,2,3, ..., M, O '= arcsin (sin g / n) n is the index of refraction of the transmission blade, G. is the region in the plane OUV o are points (u, v) such that oQj Q.arctg2 (u, v) <dlj + 1 arctg2 (u, v) is the angle between the OR axis and the vector radius of the point (u, v), a1 = 0, Qj + = j + 2 Lj / L (j = 1,2, ..., N), L. is the length of the jth segment of the line, L is the total length of the set of straight segments

(L = L.),

  j Oj (u, v) is the function satisfying the j relation: 2 2 1 (u, v) = argmin ((L e exp (2Ti ((u, v) + f / + Vf2 + (uj + tjcos <ju ) 2+ (vj + tjsin Xj-v) 2)) dudv 2-I) 2dt), where j is the angle between the j-th segment of the set of segments and the OR axis, f is the distance focal, (uj, vj) are the coordinates of the projection of the end of the j-th segment on the plane OUV, t. is the parameter on the j-th segment, 0 tj <Lj, I is the intensity of the focused monochromatic radiation, & is the parameter of the Gaussian distribution

  intensity of monochromatic radiation to focus.

  It is useful that, for focusing in a set of points, the phase shift optical element is in the form of a phase plate, with a reflection such that the height of the relief in each of its zones and the shape of the zones vary. according to the expression: Z (u, v): usn2 Z (uv) tt l / f2 + (u.) 2+ (v + vj) 2usin3Lj m mA2cosg for <r

for 2 (j-1), arctg2 (ucoso, v) 2lj-

N N

  (j = 1,2, ..., N) where Z (u, v) is the height of the relief at the point (u, v) of the phase shift optical element disposed in the plane OUV, the axis OZ being in opposite sense to the projection of the monochromatic radiation to be focused on the plane OUV, and the axis OZ being perpendicular to the plane OUV, N is the number of points belonging to the set of points, arctg2 (u, v) is the angle between the OR axis and the vector radius of the point (u, v), (u, v.) are the coordinates of the projection of the j-th point of the set of points on the plane OUV, f. is the distance from the j-th point of the set J of the points to the plane OUV,

  X_ is the wavelength of the mono-

chromatic to focus,

  9 is the angle between the mono-

  chromatic to focus and the axis OZ, R is the radius of the cross section of the monochromatic radiation to focus,

m = 1,2,3, ..., M.

  It is effective that, for focusing in a rectangle, the optical phase shift element is in the form of a reflection plate such that the height of the relief in each of its zones and the shape of the zones vary according to the expression: Z (u, v): {t (ucosg, v) mt Zcosg o Z (u, v) is the height of the relief at the point (u, v) of the optical phase shift element placed in the plane OUV, l OZ axis being perpendicular to the plane OUV, and the OR axis being opposite direction to the projection of the monochromatic radiation to be focused on the plane OUV,

  A is the wavelength of the mono-

  chromatic to focus, 9 is the angle between the monochromatic radiation to be focused and the axis OZ, m = 1,2,3, ..., M, (u, v) is the function defined by the expression 4 ( u, v) = argmin (5f (/ 1 J (u, v) exp (2tri (% (u, v) + U2 + v2 R2 + i f2 + (x + u) 2+ (yv) 2)) dud \ 2 (I) 2 dxdy), where J (u, v) is the distribution of the intensity of the monochromatic radiation to focus, I is the intensity of the focused monochromatic radiation, x, y are the coordinates in the plane Z = f, F is the region in the OXY plane occupied by the rectangle; f is the focal length, R is the radius of the cross-section of the

  monochromatic radiation to focus.

  In the following will be described, by way of specific and nonlimiting examples, some particular embodiments of the invention, with reference to the accompanying drawings in which: - Figure 1 represents a general view of a

  reflective phase plate that receives mono-

  chromatic focusing in a flat curve, according to the invention; - Figure 2 is a general view of the blade of Figure 1 (cross section), according to the invention; FIG. 3 shows the limits of the zones on a reflecting plate in the case of focusing in an arc of a circle, according to the invention; FIG. 4 shows a focusing region in the form of a circular arc, according to the invention; FIG. 5 shows the limits of the zones on a slide as in FIG. 3, in the case of focusing in conjugated circular arcs, according to the invention; FIG. 6 shows a focusing region in the form of conjugated circular arcs; according to the invention; FIG. 7 shows the boundaries of the zones on a reflecting lare in the case of focusing in a line segment with a uniform distribution of the intensity of the focused radiation, according to the invention; FIG. 8 shows a focusing region in the form of a linear segment with a uniform distribution of the intensity of the focused radiation, according to the invention; - Figure 9 is a view similar to Figure 7, but in case of focusing in a segment with non-uniform distribution of the intensity of the focused radiation, according to the invention; FIG. 10 shows a focusing region in the form of a line segment with non-uniform distribution of the intensity of the focused radiation according to the invention; FIG. 11 shows the limits of the zones on a reflection plate in the case of focusing in a set of line segments forming the letter "T", according to the invention; FIG. 12 shows a focusing region in the form of a letter "T" consisting of line segments, according to the invention; FIG. 13 is a view similar to FIG. 1, but in the case of focusing in a set of line segments forming the number 4, according to the invention; FIG. 14 shows a focusing region in a set of line segments forming the number "4", according to the invention; FIG. 15 shows the limits of the zones on a reflection plate in the case of focusing in a sense of points forming the letter "0", according to the invention; FIG. 16 shows a focus area in the form of "0" consisting of dots, according to the invention; Figure 17 is a view similar to Figure 15, but in the case of focusing into a set of points forming the number "4", according to the invention; FIG. 18 shows a focusing region in a set of points forming the number "4", according to the invention; FIG. 19 shows the limits of the zones on a reflection plate in the case of focusing in a rectangle, according to the invention; FIG. 20 shows a focusing region

  rectangle-shaped, according to the invention.

  The method of focusing a monochromatic radiation and the optical phase shift element for its implementation make it possible to focus the radiation in a given shape curve and in a plane figure so as to obtain the required intensity distribution along the the curve and the area of the planar figure and the complete concentration of the energy whatever the incidence of the radiation to focus on the optical element.

  The process of focusing a mono-

  in chromatic mode, the phase modulation of the wavefront of the monochromatic radiation is performed as a function of the phase and intensity of the monochromatic radiation to be focused and the distribution of the intensity in the focusing region by establishing a correlation between the points of the wavefront to focus and those of the focusing region so as to match each point of the wavefront to

  focus a point in the focus region.

  The phase shift optical element of the focusing region of a monochromatic radiation embodying said focusing method is in the form of a reflection or transmission plate comprising, on one of its surfaces, zones each of which represents a continuous relief, the height of said relief and the shape of the zones varying in accordance with the phase and the intensity of the monochromatic radiation to be focused, as well as the distribution to be obtained from the intensity of the radiation

  focused in the focusing region.

  FIG. 1 represents a reflection plate 1 focusing a monochromatic radiation 2 on the region

focus required 3.

  Since the phase shift optical element only transforms the iconale of the radiation, the characteristics of such an element are determined from the iconale of the monochromatic radiation to focus and the iconale of the focused radiation, that is to say -say of radiation having

  the required intensity distribution.

  Let i 0 (u, v, Z) be the iconale of the radiation received by an element placed in the plane Z = 0, and $ 1 (u, v, Z), the iconale of the radiation with the required intensity distribution; u, v are the coordinates in the plane of the optical element,

  the axis OZ being perpendicular to the plane OUV.

  The equation of the mirror surface Z = Z (u, v) transforming the field to iconal jO (u, v, Z) into a field with iconale l (u, v, Z) takes the form 0o (u, v , Z) - / l (u, v, Z) = constant value ("const")

(1)

  In the case of optical elements at the height of the relief, it is sufficient to know the value of the iconales around the plane Z = 0. In the case of a normal incidence on the phase shift optical element and a reflection close to the normal, we have 0o (u, v, Z) = b (u, v) - Z, l (u, v, Z ) = P (u, v) + Z, the OZ axis being directed in the opposite direction of the incident radiation; b (u, v) = zo (U, V, o), t (01 (u, v) = l (, v, o) Equation (1) provides the equation of the required mirror area: / - (u, v) - b (u, v) (2) Z (u, v) = 2 + const (2)

2

  o Z (u, v) is the height of the mirror at-point (u, v).

  Equation (2) describes a smooth mirror surface for the transformation of the iconals. With the monochromatic radiation of a wavelength, the conventional is known in multiples of L-nearly. Also, by the game of the const, that is to say by choosing differently the values of const. (multiples of _) in different points of the plane OUV, one obtains the height Z (u, v) of the relief and the shape of the zones of the reflection plate 1: (Zy (u, v) - b (uv) mA Z (u, v) _z_ _- m) b} v 2 (3) o {A is the fractional part of the number A, m is the integer parameter that defines the maximum height of the relief of the reflection plate 1. For weak values of m, the maximum value of the relief is equal to m, and for sufficiently large m we have a smooth mirror, that is to say that equation (3)

  describes the same surface as equation (2).

  The boundaries 4 of the zones 5 (FIG. 2) determining the shape of the zones 5 in the plane OUV are defined by the relation (uv) - b (u, v) t_5 = 0 (4) m (s The equation ( 3) describes a smooth relief 6 in each zone 5 allowing precise focusing of the monochromatic radiation on a determined focusing region.In the case of a transmission blade, the boundaries 4 of the zones 5 have the same shape as in that of

the reflection slide 1.

  Said reflection (transmission) blades 1 focus the monochromatic radiation in normal incidence as in oblique incidence on the plate 1. The height of the relief 6 is then determined in the following manner. Assuming that the incident radiation is at an angle g with the axis OZ and that the axis OR is opposite to the projection of the incident ray on the plane OUV, the iconale 0 (u, v, Z) = b ( u, v) -Zcosg of the reflected field then becomes: 91 (u, v, Z) = f (u, v) + ZcosO (5) The equation of the smooth mirror surface takes the form Z (u, v) = - 'P (u, v) - b (u, v) (6) 2 cosg In this case, the height of the relief and the shape of the zones of the reflection plate 1 have the form: Z (uv): { _ (u, v) - b (u, v) jm LZ (uV = 1 m; L 2 cos7 For low values of m, the maximum value of the relief is m, for 2 cos g values of m sufficiently large the area defined by equation (7) coincides with that given by equation (6). Similarly, it can be shown that, for a transmission blade, the height of the relief 6 and the shape of the zones 5 vary according to the expression: Z (uv (u, v) - b (u, v) m - (8) Z (u 'v) = (uv) m X - n cosg' - cosg on is the index of the blade arcsin (sin g / n) (9)

23 2585854

  In this way, said reflection and transmission phase blades realize the desired transformation of the iconale. The iconale -0 (u, v, Z) of the radiation to focus being known, it remains to find the iconale l (u, v, Z); moreover, it suffices to find the function (u, v) = l (u, v, Z). For this purpose, it is necessary to examine the region of focus and the distribution of intensity in this region. It should be noted that the focusing region can be divided so that each part has its intensity distribution. In this case, the blade splits into as many portions as the focusing region and each portion of the blade sends the radiation to the respective portion of the region of

  focusing. The parts of the blade are calculated independently

  with each other. Therefore, without overlooking the generality, we can consider only the region of focus

form a whole.

  It is important to note that the computation of the function t (u, v) (of the iconale) for the normal incidence is valid for the oblique incidence if the focusing is carried out in the same curve or in a

  same region, but is arranged in the plane Z '= f.

  In this case, the function <(u, v) is given by the relation: f (u, v) = o9 (u cosO, v) - u sing (10) allowing to treat first the case of normal incidence and then oblique incidence; equation (10), associated with equations (7) and (8), makes it possible to calculate the shape of the surface of an oblique incidence reflection or transmission plate if the solution for normal incidence is known. In normal incidence, the focal plane is parallel to the blade. In oblique incidence, when the incident ray makes an angle g with the axis OZ and the axis OR is in the opposite direction of the projection of the incident ray on the plane OUV, the focal plane is constituted by the plane Z '= f , where the axis OZ 'makes an angle g with the axis OZ, and the axis OR',

an angle g with the OR axis.

  In the case of a plane wavelength focusing radiation such that b (u, v) = -u sing, equations (7) and (10) make it possible to find the height of the relief 6 and the shape of the zones 5 of a reflection plate for an angle of incidence 9: Z (u, v) = (u cos9, vmm A 2 cosg (11) and equations (8) and (10), the height of the relief 6 and the shape of the zones 5 of a transmission plate Z (u, v) = (u cosg, v) m X (12) m A n cosg '- cos9 o 0 (u, v) is the iconale of the field reflected, calculated in normal incidence or radiation to focus on the optical element.Lower we search 'P (u, v) in

  normal incidence, and the expressions (11) or (12)

  find the height of the relief in oblique incidence. To calculate the function Y (u, v) we use the scalar integral of Kirchhoff: | 1 J (uv) exp (? <(U, v) +

I _ '-'

  (13) u2 + v24 R2 u 2 d u dv +. Z + (x-u) + (y-v) 2)) dudv = I (x, y, z), where J (u, v) is the distribution of the intensity of the monochromatic radiation to be focused,

  I (x, y, Z) is the intensity of the mono-

  focused chromatic, R is the radius of the cross section of the

  monochromatic radiation to focus ,.

f is the focal length.

  By adopting various variants of the expression (13) one can find Y (u, v) for a number of specific focusing regions and the intensity distributions therein. In the case of a Gaussian distribution of the intensity of the monochromatic radiation to focus, that is to say when J (u, v) - v e24ju (oo 'is the parameter of the Gaussian distribution of the intensity instead of the expression (13), we have: u2 + v2 j 1 5 2 2 texp (2lY ('t (u, v) + u2 + v2 2 R2 (14) + VZ + (xu) + ( yv) L)) dudvt = I (x, y, z) We will examine the focus in a plane curve with a uniform intensity distribution defined as follows: x = xo (t), y = yO (t), Z: f, 0 <Δ L (15) where L is the length of the focal curve, L / O, f is the focal length, x, y are the coordinates in the plane Z = f, the x axis is parallel to the OR axis and the 0Y axis is parallel to the OV axis,

  t is the normal parameter on the plane curve.

  The expression (14) makes it possible to find the intensity at a point on a plane curve of coordinates (xo (t), Y0 (t), f) starting from the expression: 2 2 u + v Se2612 exp (iu V u2 + 2 R2 o 1fi 261exp2 (δ (u, v) + u2 + v2 R2 (16) + V f2 + (x (t) -u) 2 + (y (t) -v) 2)) dudv / 2 = I (t)

  o I (t) is the intensity of the single radiation

  focused chromatic. For a uniform distribution

  the intensity of the focused radiation I (t) = I = const.

  (the value of I is given by the law of conservation of the energy), the function t (u, v) can be drawn from the relation: i J (11 26z 2Wi tf (u, v) = argmin (3 ( | exp (2 i (\ (u, v) + u2 + v2 4 R2 (17) + f + (Xo (t) -u) + (Yo (t) -v)) dudv -I) dt) Relationships ( 11) and (17) make it possible to find the height of the relief 6 and the shape of the zones 5 for a reflection plate> and the relations (12) and (17) for a

transmission blade.

  FIG. 3 schematically shows the boundaries 4 of the zones 5 on the reflection (transmission) plate 1 in the case of focusing in an arc 7 (FIG. 4), and FIG. on the reflection plate (transmission) 1 in case

  focus in conjugated arcs 8 (Figure 6).

  Let's examine the focus in a line segment with the required distribution of the intensity I (t) of the focused radiation along the segment. Consider a line segment in the plane Z = f and forming an angle D <with the axis OR. The value of t, the normal parameter on the segment, varies between 0 and L, where L-is the length of the line segment. The expression (14) makes it possible to find the relation verified by the function T (u, v) in case of focusing in a line segment:

L + V

  (u, v) = argmin (e exp ((2n? (uv) u2 + v2 R2 (18) 2 2 2)) dd122 2 + f + (uo + tcos -u) + (v + tsino (-v)) ) dudv _I (t)) dt o (u0, v) are the coordinates of the projection

  from the end of the line segment on the OUV plane.

  Relationships (11) and (18) make it possible to find the height of the relief 6 and the shape of the zones 5 in the case of a reflection plate, and the relations (12) and (18), in case

a transmission blade.

  For example, the expression Z (u, v) = - 0.09375 u2 + 0.125 v2 - (0.4872 u + + 0.5626 v) arcsine (0.6123 u + 0.7071 v)

R (19)

2 2

  - R2 - (0.6123 u + 0.7071 v2) (0.5305 + 0.2652 (0.6123 u- + 0.7071 v) 2) 0, 01155 R defines the height of the relief 6 and the shape of the zones 5 of the reflection lamina focusing uniform intensity distribution radiation in a line segment with a

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  uniform intensity distribution of the focused radiation for o = 0.005; f = 200; L = 10; g = 30 (all

  above values are given in mm).

  FIG. 7 schematically shows the boundaries 4 of the zones 5 on the reflection (transmission) plate 1 in the case of focusing in a line segment 9 (FIG. 8) with a uniform intensity distribution of the focused radiation along the segment, and FIG. 9, the boundaries 4 of the zones 5 on the reflection (transmission) plate 1 in the case of focusing in a line segment 10 (FIG) with a non-uniform intensity distribution of the

focused radiation.

  For a segment representing the region of

  sation and located in the axis of the blade, that is to say in the axis OZ, f <Z <f + L, where L is the length of the segment,

f being the focal length.

  In order to define the function P (u, v), it should be noted that, for reasons of symmetry, R (u, v) = 0 (r), or = / u2 + v2 The function 0 (r) is determined by the relation: p (r) = .- d P (20) 0j, 2 (z (j) 2 the function Z (p) being defined by the relation:

Z

  _ (R) = = I (t) dt, (21) f o I (t) is the distribution of the intensity of the focused radiation along the line segment. The formulas (20) and (11) make it possible to determine the height of the relief 6 and the shape of the zones 5 of the reflection plate in accordance with the expression:

29 2585854

Z (u, v) = Jr t d P | 1 m X m A 2

O, 7 + Z -

  (22) We will now examine the focus in a set of line segments. The set of focal segments consists of N segments arranged in the plane

  focal point Z = f (the axis OZ is perpendicular to the plane OUV).

  Let L be denoted by the lengths of the segments, and by (u., Vj) and (u, vj), the co-ordinates of the projections of the ends of the segments on the plane OUV (j = 1,2, ..., N ). The surface of the blade is divided into parts Gj (j = 1,2, ..., N). The portion Gj of the blade focuses the received radiation in the j-th segment. For some

  reasons for the uniform distribution of the intensity of

  The division into parts G. is determined so that the radiation energy j dropped on the part Gj is proportional to L. In the case of an axially symmetrical focusing beam distribution beam. in the section of the beam, for example with a Gaussian intensity distribution, this condition is satisfied by a division into sectors such that the central angle of the jth sector is proportional to L. The part G. then comprises the points u, v such than

J 3

A. arctg2 (u, v) C (, + 1

NOT A WORD

  (23) o arctg2 (u, v) is the angle (in radians) between the OR axis and the vector radius of the point (u, 9 v) in the range 0 2'fY], 1 = O, Sj. =: 2j; + 2 t Lj / L (ji = 1.25 ..., N) 1 j + l j / (24) L is the total length of all segments N L = L j = l

Lj, L X 0.

  In this case, the height of the relief 6 and the shape of the zones 5 of the reflection plate vary according to the expression Z (u, v) = tj (uv) 1 m (25) - cosg 25 for (u cos 0 , v) Gj, and of the transmission plate, according to the expression: 1 m Z (u, v): t (uv) n (cosg '- cosO (26) for (u cosg, v) Gj, the function "fj (u, v) satisfies the relation: j (u, v = argmin5 a exp qi (uv) + (27) + V f2 + (uj + tjc os ju) 2+ (vj + tjsin xj-v) 2) ) dudv I 2I) 2dt) where t is the parameter on the jth segment, J 0 <t.

Not a word.

  I is the intensity of the focused monochromatic radiation. For example, the expression

2 2 2

  Z (u, v) = u + v - 0.473 arcsin v - (0.4244 2 +

8 R R2

  +0.8488) R - v joo, for v? 0 (28) Z (u, v) = + 2 0.2365 arcsin R - (0, 2122 + + 0.4244 V R2 _u2 0.01, for v <0 defines the height of the relief 6 and the shape of the zones 5 of the reflective plate focusing radiation of uniform intensity distribution in a set of segments forming the letter "T", with a uniform intensity distribution, = 0.005, f = 200, 9 = 0 (all values below); -above

being given in mm).

  FIG. 11 schematically shows the boundaries 4 of the zones 5 on the reflection (transmission) plate 1 in the case of focusing in a set of segments 11 (FIG. 12) forming the letter "T" and FIG. 13, the boundaries 4 of the zones 5 on the reflection plate (with transmission) 1 when focusing in a set of segments 12 (FIG. 14)

forming the number "4".

  In the case of focusing in a set of points, the desired image comprises N points located respectively at distances fj (j = 1, 2, ..., N) of the plane OUV, the projections of the points on the plane OUV have coordinates uj, vj

  (J = 1,2, ..., N). All points receive the same energy.

  The surface of the blade is divided into parts G. (j = 1, 2, ..., N).

  Each portion of the blade focuses the incident radiation into an isolated image point. The shape of the relief is calculated so that, for a given angle of incidence, all of the radiation received by an isolated portion of the blade is directed towards the chosen image point. The parts are in the form of sectors, that is to say that the part G. has points (u, v) such that J 2 J (j-1) - arctg (u cosg, v) <2 TIi, o arctg2 (u, v)

N N

  is the angle between the OR axis and the vector radius of the point (u, v) taken in the CO interval, 2fr]. This sharing allows a uniform distribution of energy between the points of the image in the case of a distributed beam

  of symmetrical intensity with respect to the axis.

  So that the radiation reflected by the part G of the blade is focused at the jth image point, its iconale in the plane OUV must be (here (u, v) _ Gj): fj (u, v): - fz + (u-uj) 2 + (v-vj) 2 + const. (29) The emission of most powerful laser sources currently used have a plane wavefront. The laser beam forms an angle of incidence O with the axis OZ (the axis OZ is perpendicular to the plane OUV), the axis OR is of direction opposite to the projection of the incident beam on the plane OUV. Hence the iconale of the incident wavefront in the plane OUV b (u, v) = -usinO. The choice of

* the value of const. provides a reflective surface

  of the blade whose relief is limited in height to m> - / 2 cosO. The height of the relief 6 and the shape of the zones 5 of this plate are (here (ucos, v) 6 Gj): Z (u, v): 1 f + (uu) 2+ (v-vj) -usin m 2cos ( 30) where LA is a fractional part of the number A, m is an integer parameter defining the

maximum value of the relief.

  In addition, it is possible to divide into parts G of arbitrary form. It is possible, in this case, to achieve a distribution of any intensity between the focal points for a given distribution of

  the intensity of the radiation to focus.

  FIG. 15 schematically shows the boundaries 4 of the zones 5 on the reflection (transmission) plate 1 when focusing in a set of points 13 (FIG. 16) forming the letter "0", and FIG. 17, the borders 4 zones 5 on the reflection plate (transmission) 1 in the case of focusing in a set of points 14 (FIG. 18) forming the

number "4".

  In the case of focusing in a rectangle, it is the focusing with a uniform distribution of intensity of the focused radiation which is of the greatest interest. In the case of a rectangle arranged in the plane Z- f at coordinates x, y, the axis OX is parallel to the axis OR, the axis OY is parallel to the axis OR, the function I (u, v ) checks the relation (9 (u, v) = arcmin (| (1 AJ (u, v) exp (2 "i (f (u, v) + ó lx

F (31)

2 2 2

  u + v2 R2 + f2 + (x-u) 2+ (y-v) 2)) dudv | 2-I) 2dxdy) where I is the intensity of the focused radiation, F is the region of the plane OXY that is occupied

by the rectangle.

  Expressions (11) and (18) make it possible to find the height of the relief 6 and the shape of the zones 5 of a reflection plate focusing the radiation with a given intensity distribution in a rectangle. For example, the expression

34 2585854

2 2 2

  Z (u, v): u + V - 0.7957u arcsin-u - 0.2652u

L 8 R R2 (32)

2

  -0,5304 2 u2-1,25 0,01 R2 -u2 rR u- describes the height of the relief 6 and the shape of the zones 5 of the reflection plate which focuses a radiation of uniform intensity distribution into a rectangle of which the dimensions are 5x20, for A = 0.005; f = 200; 9 0

  (all values above are given in mm).

  FIG. 19 schematically shows the boundaries 4 of the zones 5 on the reflection plate 1 in

  focusing case in a rectangle 15 (Figure 20).

  As can be seen from all the variations of the reflection or transmission blades described above, the latter direct the energy of the radiation to be focused towards a determined region of the space without loss of energy, which allows the complete concentration of energy. The blades realize the transformation of the iconale of the radiation to focus in iconale of the radiation giving the desired intensity distribution; the phase blades do not change the intensity of the radiation to focus, that is to say that there is no

energy losses.

  Said reflection or transmission slats can be obtained by known methods,

  particular using an intermediate information support

  photographic touch. According to this method, it is first prepared, with a computer-controlled precision masker, a mask called "amplitude" in which the obscuration density is proportional to the height of the relief of the surface. Then, through this mask, we impress by contact or projection a material

2585854

  photosensitive which changes properties depending on the amount of light absorbed. This results in the appearance, on the photosensitive material, of a modulation of the height of the relief. The role of photosensitive material can be filled by gelatin. However, according to the technology for obtaining the optical element, the shape

  smooth relief can be replaced by gradual relief

  multiple. For example, photoengraving allows

  to obtain some ten gradations of the height of the relief.

  The multi-gradation relief zoned blades are less effective compared to continuous relief zoned plates in each zone, but with a large

  number of gradations this difference is not great.

  The phase shift optical elements which have just been described make it possible to obtain an image in the form of a continuous distribution of intensity in the focal region, which can not be obtained with the other devices known at the time. current. The choice of the shape of the relief of the optical element offers the possibility of controlling the distribution of the intensity of the focused radiation and of obtaining any predetermined continuous intensity distribution. Said optical elements make it possible to overcome the problem of focusing in oblique incidence. They will find many applications in the heat treatment of materials and in particular for marking products or for tempering metal surfaces. At the present time, for the heat treatment of surfaces, complicated mechanical scanners are used to ensure the movement of the focused radiation at a point along a line segment. The use of said optical elements makes it possible to build new technological installations for the treatment of surfaces with

simplified scanning.

  The distribution of the intensity of the radiation on the surface to be treated being of great importance for the quenching, we see the particular interest that presents

36 2585854

  the ability to create optical elements capable

  to focus the radiation into a segment with a distribution

  arbitrary intensity, which makes it possible to control the treatment process optimally. Thus, the use of optical elements is advantageous in cases requiring a high homogeneity of the density of

  distribution of focused radiation.

  Said optical elements will be of great use for the marking of products, especially fragile or small products, and also where the marking must be rapid. Currently, there is used for marking, complicated mechanical scanning facilities ensuring the movement of the focused radiation along the contour of the mark. These facilities are

  unable to perform instant marking.

  Most powerful lasers used for marking, quenching, welding, cutting emit in the infrared. The known scanning facilities

  require transparent focusing elements in the infra-

  red, which are either unreliable or expensive

(zinc-selenium elements).

  The use of said phase shift elements makes it possible to dispense with both zinc-selenium elements and

  scanning facilities which are of inadequate reliability

  cient. In addition, the optical elements do not require

  not the use of mirrors or lenses.

  Optical elements used for focusing

  in a straight segment will find many applications

  in medicine, especially in ophthalmology, where

  sweepers is undesirable and even impossible.

  Great applicability exists for said optical elements for focusing a radiation into a line segment in the field of adaptive optics whose methods make it possible to quickly form a specular surface having a complex shape. These methods allow you to readjust

37 2585854

  systems having an adaptive forming element so as to focus on a focus region at different parameters, including different distributions

  the intensity of the focused radiation.

RE V E N D I CA T IONS

___________________________

  1. A method for focusing a monochromatic radiation by phase modulation of its wavefront, characterized in that the phase modulation is performed as a function of the phase and intensity of the monochromatic radiation to focus and the the required distribution of the intensity in the focusing region, by correlating the points of the wavefront to be focused with the points of the focusing region so that at each point of the wavefront to be focused corresponds to a only point of the

focusing region.

  2.- Optical phase shift element for implementing the focusing method of a monochromatic radiation according to claim 1, presented

  in the form of a phase plate with reflection or trans-

  mission (1) having on one of its surfaces areas (each of which has a continuous relief (6) ,.

  characterized in that the height of said relief (6) and the shape of said zones (5) vary according to the phase and the intensity of the monochromatic radiation to be focused (2) and according to the distribution of the desired intensity of the

  focused radiation in focusing regions (3).

  3.- Optical phase shift element according to the

  claim 2, characterized in that for focusing

  in a planar curve, it is in the form of a reflection plate (1) such that the height of the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression: Z (u, V) = t- u Cosgv)) 1m 0 \ 2 c osg9 o Z (u, v) is the height of the relief (6) at the point (u, v) of the phase shift optical element placed in a plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR

  being in the opposite direction to the projection of mono-

  chromatic to focus (2) on the plane OUV,

  A is the wavelength of the mono-

  chromatic to focus (2), m = 1,2,3, ..., M, q (u, v) is a function satisfying the relation:

L,.,

(u, v) = arm in ((e exp (2 i (t (-

  u2 + v2 R2 + 2+ 2 (X (t) -u2 + (y (t) -v) 2)) dudv 2-I) 2dt) where t is the normal parameter on the plane curve

defined by the relations: -

  u = xo (t), v = yo (t), Z = f, O <t <L, I is the intensity of the focused monochromatic radiation,

  0 is the angle between the mono-

  to focus (2) and the axis OZ, L is the length of the plane curve, L & 0, R is the radius of the cross section of the monochromatic radiation to focus (2), is the parameter of the Gaussian distribution of the intensity of the monochromatic radiation to focus

(2)

f is the focal length.

  Optical phase shift element according to Claim 2, characterized in that for focusing

  in a plane curve, it is realized in the form of a blade-

  with transmission such that the height of the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression: Z (u, v) = t (u cosg, V) 1 mA C.'im A n cos9'-cosO o Z (u, v) is the height of the relief (6) at the point (u, v) of the phase shift optical element disposed in a plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR being opposite direction to the projection of the monochromatic radiation to focus (2) on the plane OUV,

  A is the wavelength of the mono-

  chromatic to focus (2), m = 1, 2, 3 ..... M, n is the index of refraction of the transmission blade, O '= arcsin (sin 9 / n), P (u, v ) is a satisfying function to the relation

L _

  (u, v) = argmin (S (ó ed exp / 2 'il (t (uv) + u2 + V2 <R2 + f2 + (xo (t) -u) 2+ (y (t) v) 2)) dudv i 2 -I) 2dt) ooot is the normal parameter on the plane curve defined by the relation u = xo (t), v = y0 o (t), z = f, 0 <t <L, I is the the intensity of the focused monochromatic radiation, 9 is the angle between the monochromatic radiation to focus (2) and the axis OZ, L is the length of the plane curve, R is the radius of the cross section of the monochromatic radiation to be focused (2 ), is the parameter of the Gaussian distribution of the intensity of the monochromatic radiation (2),

f is the focal length.

  Optical phase shift element according to Claim 2, characterized in that, for focusing in a line segment (9, 10), it is designed as a reflection plate (1) such that the height of the relief (6) in each of its zones (5) and the shape of its zones (5) vary according to the expression: Z (u, y) = t (u coso, v)} mX mA Y 2 cosQ o Z (u, v) is the height of the relief (6) at the point (u, v) of the optical phase shift element placed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR being in the opposite direction to the projection of the monochromatic radiation to be focused (2) on the plane OUV,

  9 is the angle between the monochromatic radiation

  2CI tick to focus (2) and the axis OZ,

  AL is the wavelength of the mono-

  chromatic to focus (2), m = 1, 2, 3, .... M, O (u, v) is a function satisfying the relation: L2. 9 (u, v) = argmin ((t [f- Se exp (2 -i_ (9 '(u, v) + fA

2 + V2 R2

  U + v, + Vf2 + (u o + tcos -u) 2+ (vo + tsin -v) 2)) dudv 2-I (t) 2dt) oc is the angle between the line segment (9,10) and the axis arranged in the plane OUZ and making an angle 2 - -g with the axis OZ,

  I (t) is the intensity of the mono-

  focused chromatic, t is the normal parameter on the line segment (9,10), 0 <t <L, L is the length of the line segment (9,10),

L # O,

  (uo, v0) are the coordinates of the projection of the end of the line segment (9,10) on the plane OUV, R is the radius of the cross section of the monochromatic radiation to focus (2), 6 is the parameter the Gaussian distribution of the intensity of the monochromatic radiation to focus (2),

f is the focal length.

  6.- Optical phase shift element according to the

  claim 2, characterized in that for focusing

  in a line segment, it is in the form of a transmission blade such that the height of the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression: Z (u, v) = (u cosO, v) 1 mmtn cosg '-cosg o Z (u, v) is the height of the relief (6) at the point (u, v) of the phase optical element placed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and

  the OR axis being in the opposite direction to the projection of

  monochromatically focusing (2) on the plane OUV,

  9 is the angle between the monochromatic radiation

  to focus (2) and the axis OZ, _ is the wavelength of the monochromatic radiation to focus (2), m = 1, 2, 3, ..., M, n is the index of refraction of the transmission blade, 9 '= arcsin (sinO / n), L (u, v) is a function satisfying the relation: LY (u, v) = argmin (() and exp (2) (i (? (u, v) + o u2 + V2 CR2 + 2 (u o + tcosp <-u) 2+ (vo = tsino (-v) 2)) dudv 2-I (t)) 2dt o O <is the angle between the line segment (9,10) and the axis located in the plane OUZ and making an angle Ir - 0 with the axis OZ,

  I (t) is the intensity of the monochromatic radiation

  focused tick, t is the normal parameter on the line segment (9,10), L is the length of the line segment (9,10),

L 0 0,

  (uo, vo) are the coordinates of the projection of the end of the line segment (9,10) on the plane OUV, R is the radius of the cross section of the monocromatic radiation to focus (2), is the parameter of the Gaussian distribution of the intensity of the monochromatic radiation to focus (2),

f is the focal length.

  7.- Optical phase shift element according to the

  claim 2, characterized in that for focusing

  in a line segment located in the optical axis of the optical phase shift element, it is in the form of a reflection plate (1) such that the height of the relief (6) in each of its zones (5) ) and the shape of the zones (5) vary according to the expression: Z (uv) = - ai 1} o F (z ()) 2 m X 2 o Z (u, v) is the height of the relief (6 ) at the point (u, v) of the phase shift optical element disposed in a plane OUV, the axis OZ being perpendicular to the plane OUV, m 1, 2, 3, ..., M, X is the length of monochromatic radiation wave to focus (2),

2-

  r = u + v Z (R) is a function defined by the relation z 2T 5 J (r) dr = f I (t) dt I (t) is the distribution of the intensity of the focused monochromatic radiation along a line segment arranged on the axis OZ, t is the normal parameter on the line segment, f <t <f + L, f is the focal length,

  J (r) is the intensity of the mono-

chromatic to focus (2),

  L is the length of the line segment.

  8.- phase shift optical element according to claim 2, characterized in that, for focusing in a set of coplanar segments (11, 12), it is in the form of a reflection plate (1) such that the height the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression: Z (u, v) = 'm 2 (u cosO), v) m J mt J 2 cosO for (u cosg, v) E Gj, (j = 1, ..., N), where Z (u, v) is the height of the relief (6) at the point (u, v) of the optical element of phase shift placed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR being of direction opposite to the projection of the monochromatic radiation to be focused on the plane OUV, N is the number of segments of straight line (11 , 12), is the wavelength of the monochromatic radiation to be focused (2),

  0 is the angle between the monochromatic radiation

  to focus (2) and the axis OZ, m = 1, 2, 3, ..., M, Gj (j = 1,2, ...., N) is the region, in the plane OUV, containing points (u, v) such that dl> jj arctg2 (u, v) <S-j + 1, J arctg2 (u, v) is the angle between the OR axis and the vector radius of the point (u, v) , v), J 1 = O, & 2j + 1 = nj + 2 Lj / L (j = 1, 2, ..., N), Lj is the length of the jth segment, L is the total length of the set of segments (11, 12) (L = Lj) j = 1 to (u, v) is the function satisfying the relation: (j (u, v) = argmin ((\ -e exp (2 1i ( (uv) +

0

  + f2 + (uj + tjcos <ju) 2+ (vj + tjsin -v) 2)) dudv2-I) 2dt) where X is the angle between the j-th segment and the OR axis, f is the focal length , (uj, v.) are the coordinates of the projection of the end of the j-th segment on the plane OUV, tj is the parameter on the j-th segment 0 <tj <Lj,

  -5 I is the intensity of the monochromatic radiation

  focused tick, 6 is the parameter of the Gaussian distribution of the intensity of the monochromatic radiation

to focus (2).

  Optical phase shift element according to Claim 2, characterized in that, for the

  focus into a set of straight line segments

  planar (11, 12), it is in the form of a transmission blade such that the height of the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression: Z (u, v) = t (u coso, v) 1 mk Mx mn cosg'-cosg for (u cosg, v) Gj, (j = 1,2, ..., N), where Z (u , v) is the height of the relief (6) at the point (u, v) of the optical phase shift element placed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR being of opposite direction at the projection of the monochromatic radiation to focus (2) on the plane OUV, N is the number of segments of line (11,12)

  9 is the angle between the monochromatic radiation

  to focus (2) and the axis OZ, x is the wavelength of the monochromatic radiation to focus (2), m = 1, 2, 3, ..., M, g '= arcsin (sin 9 / n), n is the index of refraction of the transmission plate, G. is the region in the plane OUV with J of points (u, v) such that ji arctg2 (u, v) <j + that l <actg2 ( 'V arctg2 (u, v) is the angle between the OR axis and the vector radius of the point (u, v), a1 = O, Sj + l 1 = JT-j + 2 fLj / L (j = l , 2, ..., N), L. is the length of the j-th line segment, L is the total length of all segments (11, 12) w (L = t.), J = 1 J j (u, v) is a function satisfying the relation:

The

  fi (u, v) = argmin (1-A e exp (2- 'i ((u, v) + l -t 1222 + u + jo 2j-u) 2dt + Vf2 + (u + tcos u-u) + 2 (vj + t sincXj-v) 2)) dudvl 2-I) 2dt) where j is the angle between the j-th segment of the set of line segments and the OR axis, f is the focal length ( u., v.) are the coordinates of the projection of the end of the j-th line segment on the plane OUV, 0Uv 't. is the parameter on the j-me segment of J right, 0 <tj <Lj, I is the intensity of the monochromatic focused radiation, 6 is the parameter of the Gaussian distribution of the intensity of monochromatic radiation at

focus (2).

  Optical phase shift element according to Claim 2, characterized in that, for focusing in a set of points (13, 14), it is designed as a reflection plate (1) such that the height of the the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression i Z (u, v) = <f. + (u-u.) 2+ (v-v.) 2 - u sing] i3 mcs m 2 cosg for (j-1) $ arctg2 (u cosO, v) <-j

N N

  (j: 1, 2 ..., N) where Z (u, v) is the height of the relief (6) at the point (u, v) of the optical phase shift element placed in the plane OUV, with the OR axis being opposite to the projection of the monochromatic radiation to be focused (2) on the plane OUV, and the axis OZ being perpendicular to the plane OUV, N is the number of points of the set of points (13, 14) , arctg2 (u, v) is the angle between the OR axis and the vector radius of the point (u, v), (uj, vj) are the coordinates of the projection of the j-th point of the set of points (13, 14) on the plane OUV, f. is the distance from the j-th point of J the set of points (13, 14) to the plane OUV, X- is the wavelength of the monochromatic radiation to focus (2),

  9 is the angle between the mono-

  chromatic focusing (2) and axis OZ, R is the radius of the cross section of the monochromatic radiation to focus (2),

m = 1, 2, 3, ..., M.

  Optical phase shift element according to Claim 2, characterized in that, for focusing in a rectangle (15), it is in the form of a reflection plate (1) such that the height of the relief (6) in each of its zones (5) and the shape of the zones (5) vary according to the expression: Z (u, v) = t- O (u cos O, v) v) - 2 cosg o Z (u, v ) is the height of the relief (6) at the point (u, v) of the optical phase shift element disposed in the plane OUV, the axis OZ being perpendicular to the plane OUV, and the axis OR being in the opposite direction to the projecting the monochromatic radiation to be focused (2) on the plane OUV,> is the wavelength of the monochromatic radiation to focus (2),

  9 is the angle between the mono-

  chromatic focusing (2) and axis OZ, m = 1, 2, 3, ..., M.

  t (u, v) is a function defined by the expression:, (u, v) = argmin ((| A fJ (u, v) exp (2 fi uv) +

P 2 2 2

  u2v2 + f2 + (x-u) 2+ (y-v) 2)) dudv [2-I) 2dxdy) where J (u, v) is the distribution of the intensity of the monochromatic radiation to be focused (2),

  I is the intensity of the monochromatic radiation

  focused tick, x, y are the coordinates in the plane Z = f, F is the region, in the plane OXY, which is occupied by the rectangle, f is the focal length, R is the radius of the cross section of the monochromatic radiation to focus (2).