CN103325129B - A kind of method utilizing phase modulator output image - Google Patents
A kind of method utilizing phase modulator output image Download PDFInfo
- Publication number
- CN103325129B CN103325129B CN201210072546.9A CN201210072546A CN103325129B CN 103325129 B CN103325129 B CN 103325129B CN 201210072546 A CN201210072546 A CN 201210072546A CN 103325129 B CN103325129 B CN 103325129B
- Authority
- CN
- China
- Prior art keywords
- target image
- light field
- phase
- amplitude
- input light
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Landscapes
- Optical Modulation, Optical Deflection, Nonlinear Optics, Optical Demodulation, Optical Logic Elements (AREA)
Abstract
The invention provides a kind of method utilizing phase modulator output image, comprising: 1) determine initial input light field; 2) Fourier transform is carried out to current input light field; 3) by target image amplitude alternative steps 2) amplitude of the result of Fourier transform; Described target image is the image obtained after carrying out softization process to original target image; 4) to step 3) result carry out inverse Fourier transform; 5) by step 1) the amplitude component alternative steps 4 of input light field that draws) the amplitude of result, obtain the new input light field for next iteration; 6) step 2 is repeated) to 5) until meet the condition stopping iteration, thus obtain the phase modulation for producing needed for target image phase modulator; 7) step 6 is utilized) phase modulation that draws exports reconstructed image.The present invention can effectively suppress reconstructed error and spot, and is applicable to the target image of various complexity.
Description
Technical field
The present invention relates to optical technical field, specifically, the present invention relates to a kind of method utilizing phase modulator output image.
Background technology
Utilize phase modulator output image, by phase modulator, certain phase-modulation is carried out to change the power density distribution of laser beam to incoming laser beam exactly, thus reconstruct the output image consistent with desired target image.Wherein, phase modulator is a kind of important devices in computer-generated hologram (computergeneratedholograms, CGH) technology.Typical phase modulator comprises the static diffraction optical device (diffractiveopticalelements scribed in advance, and dynamic spatial light modulator (spatiallightmodulators DOEs), SLM), as liquid crystal on silicon (liquidcrystalonsilicon, LCOS), this two classes phase modulator all can be used for reconstructed image.
Different according to the playback mode reading light, phase modulator is divided into reflective and transmission-type.Fig. 1 shows the light path schematic diagram based on transmission-type Fu Lang and Fei type phase modulator reconstruct output image, as shown in Figure 1, laser beam 2 incident phase modulation device 1, phase-modulation is produced in the process of transmission phase modulation device 1, laser beam after phase-modulation is projected on image output plane 4 (also can be described as Fourier plane) by fourier lense 3, and reconstructs output image at image output plane 4.Fig. 2 shows the light path schematic diagram based on reflective Fu Lang and Fei type phase modulator reconstructed image, as shown in Figure 2, laser beam 2 is reflected by phase modulator 1, and the laser beam through phase-modulation obtained after reflection projects on image output plane 4 through fourier lense 3 and reconstructs output image.No matter be adopt transmission-type or reflective phase modulator, all need to design its phase modulation according to incoming laser beam and target image.Obviously, for Two-Dimensional Reconstruction image, aforementioned modulation phase place refers to a two-dimentional PHASE DISTRIBUTION.
At present, for Fu Lang with take type phase modulator, the algorithms most in use of design phase modulation is iterative Fourier transform algorithm (IterativeFourier-transformalgorithms, IFTAs).It is a kind of typical iterative Fourier transform algorithm (IFTAs) that lid Shi Beige mono-spreads a gram stone algorithm (Gerchberg-Saxton algorithm is abbreviated as GS algorithm).Be described for the computation process of GS algorithm to phase modulation below.The flow process of GS algorithm comprises the following steps:
(1) initialization iterations variable k=1, determines initial input light field g
0(x),
wherein | g
0(x) | represent the amplitude component of initial input light field,
represent the phase component of initial input light field; In general, incident beam is the parallel beam of collimation, therefore phase component
constant can be approximately.
(2) to current input light field g
k-1x () is carried out Fourier transform and is obtained G
k(u)=| G
k(u) | expi φ
k(u).Wherein, | G
k(u) | represent the amplitude component of the Fourior plane of kth time iteration, φ
ku () represents the phase component of the Fourior plane of kth time iteration.
(3) with the amplitude component of target image | F (u) | the amplitude component of the result of alternative steps (2) Fourier transform | G
k(u) |, obtain G '
k(u)=| F (u) | expi φ
k(u).
(4) to the result G ' of step (3)
ku () is carried out inverse Fourier transform and is obtained g '
k(x);
wherein | g '
k(x) | represent amplitude component,
represent phase component.
(5) with the inverse Fourier transform result g ' of the amplitude component alternative steps (4) of known initial input light field
kx the amplitude component of (), obtains the new input light field g for next iteration
k(x),
(6) judge whether to meet the condition stopping iteration, if so, enter step (7), if not, make k=k+1, and return execution step (2); Wherein, stopping the condition of iteration to set as the case may be, such as, can be that iterations reaches certain numerical value;
(7) with current input light field g
kthe phase component of (x)
deduct the phase component of initial input light field
namely the phase modulation needed for reconstructed image is obtained
in general, incident beam is the parallel beam of collimation, and the PHASE DISTRIBUTION of incident field can be approximately constant, therefore, and phase modulation
be exactly input light field g when stopping iteration
kthe phase component of (x)
composition graphs 1 or light path illustrated in fig. 2, recycle the phase modulation of above-mentioned GS algorithm design phase modulator
just can reconstruct the output image unanimous on the whole with target image.But, in actual applications, use GS algorithm to calculate phase modulation and reconstructed image time, there is comparatively serious reconstructed error (reconstructionerrors) and spot (speckles) in output image.Fig. 3 shows an experimental result based on GS algorithm reconstructed image, and wherein (a) part is the target image expected, (b) part is the output image of actual reconstruct, can find out that actual output image exists obvious spot.The detailed explanation of the above-mentioned defect of GS algorithm can with further reference to document PasienskiMandDeMarcoB, Ahigh-accuracyalgorithmfordesigningarbitraryholographica tomtrapsOpt.Express, 162176-90,2008.
For solving based on the problem that there is reconstructed error and spot in GS algorithm, PasienskiM and DeMarcoB proposed a kind of GS algorithm (hereinafter referred to as Pasienski algorithm) of correction in 2008, Pasienski algorithm principal feature is: (1) have employed the account form of amplitude and Phase Double degree of freedom.This account form is ignored the Carrier To Noise Power Density distribution outside target image planed signal window, namely the Carrier To Noise Power Density distribution in iterative process outside output plane signal window is retained, reference paper F.Wyrowski, J.Opt.Soc.Am.A.7,961,1990.(2) according to the difference of target image, use conic surface function respectively, linear gradient function, conical function or their mixed function are as the initial phase of initial input light field.Pasienski algorithm is better than traditional GS algorithm, but experiment finds, the reconstructed image based on Pasienski algorithm still exists obvious reconstructed error and spot.
In sum, current in the urgent need to a kind of method utilizing phase modulator generation reconstructed image that effectively can suppress reconstructed error and spot.
Summary of the invention
The object of the invention is a kind of phase modulator that utilizes of reconstructed error and spot that can effectively suppress and produce the method for reconstructed image.
For achieving the above object, the invention provides a kind of method utilizing phase modulator to produce reconstructed image, comprising:
1) initial input light field is determined;
2) Fourier transform is carried out to current input light field;
3) by target image amplitude alternative steps 2) amplitude of the result of Fourier transform; Described target image is the image obtained after carrying out softization process to original target image;
4) to step 3) result carry out inverse Fourier transform;
5) by step 1) the amplitude component alternative steps 4 of input light field that draws) the amplitude of result, obtain the new input light field for next iteration;
6) step 2 is repeated) to 5) until meet the condition stopping iteration, thus obtain the phase modulation for producing needed for target image phase modulator;
7) step 6 is utilized) phase modulation that draws exports reconstructed image.
Wherein, described step 1) in, the amplitude component of described initial input light field is through the amplitude component of softization process.
Wherein, described step 3) in, described target image presses the correction of SIFTA-2 algorithm by original target image, then carries out softization process and obtain.
Wherein, described step 1) in, the initial phase of described initial input light field can produce one roughly uniformly, and the Fourior plane light distribution substantially identical with image output plane signal window size, described initial phase is obtained by Ray-tracing Method.
Wherein, described Ray-tracing Method comprises Bryngdahl method, Aleksoff method, Roux method, Romero method, Malyak method or Dresel method.
Wherein, described step 5) in, described stop condition is that iterations reaches certain value, or step 2) the error of Fourier transform results compared with target image be less than the threshold value preset.
Wherein, described error is the root-mean-square error of amplitude density distribution or the root-mean-square error of power density distribution.
Wherein, described step 6) in, after stopping iteration, with current procedures 4) phase place that obtains deducts the phase place of the input light field of actual measurement, namely obtains the phase modulation for producing needed for target image phase modulator.
Wherein, described softization process comprises: the input optical field amplitude Component Matrices that representative is comprised sudden change moves N number of pixel respectively to 4 directions up and down, then to obtained 4N image array summation, thus the input optical field amplitude distribution after softization process is obtained; Or the input optical field amplitude distribution of softization is obtained by the point inserting several gradual change at the amplitude jump place of input light field; Or High frequency filter is carried out to the input optical field amplitude component comprising sudden change; Or use corresponding super-Gaussian function to simulate to there is amplitude jump and evenly input light field.
Compared with prior art, the present invention has following technique effect:
1, reconstructed error and spot can effectively be suppressed.
2, applied widely, the target image of various complexity can be applicable to.
Accompanying drawing explanation
Fig. 1 shows the light path schematic diagram generating reconstructed image based on transmission-type Fu Lang and Fei type phase modulator;
Fig. 2 shows the light path schematic diagram generating reconstructed image based on reflective Fu Lang and Fei type phase modulator;
Fig. 3 shows the example of an output image produced based on GS algorithm reconstructed image and target image;
Fig. 4 shows the flow process that in one embodiment of the invention, phase modulation calculates;
Fig. 5 (a) shows the Fourior plane of target image;
The distribution of amplitudes of the target image that Fig. 5 (b) shows Fig. 5 (a) centrally transverse axis;
Fig. 5 (c) shows the output image that there is reconstructed error that the target image based on Fig. 5 (a) reconstructs;
Fig. 6 (a) shows an original even input light field image containing sudden change;
Fig. 6 (b) shows the distribution of amplitudes of the original even input light field containing sudden change of Fig. 6 (a);
The distribution of amplitudes that the original even input light field containing sudden change that Fig. 7 shows Fig. 6 (a) processes through softization;
Fig. 8 (a) shows the Fourior plane target image shown in Fig. 5 (a) being carried out to the target image after softization process;
Fig. 8 (b) shows the distribution of amplitudes of the centrally transverse axis target image shown in Fig. 5 (a) being carried out to the target image after softization process;
Fig. 9 shows the contrast of three kinds of different reconstructed images and target image;
Figure 10 shows sphere input function conventional in the initial phase function of one embodiment of the invention and prior art;
Figure 11 (a) shows the Fourior plane distribution of amplitudes that the initial phase in one embodiment of the invention produces;
Figure 11 (b) shows the Fourior plane distribution of amplitudes that the initial phase in another embodiment of the present invention produces;
Figure 12 (a) shows the reconstructed image result using sphere input function to obtain based on 2000 iteration as initial phase;
Figure 12 (b) shows the reconstructed image result using sphere input function to obtain based on 10000 iteration as initial phase;
Figure 13 (a) shows and adopts SIFTA-2 algorithm, but target image does not carry out softization process, and initial input light field does not do the reconstructed image obtained when optimizing yet;
Figure 13 (b) illustrates that shown in Figure 13 (a), reconstructed image is along the distribution of amplitudes of Fourior plane central, transverse axis;
Figure 14 (a) shows and adopts SIFTA-2 algorithm, and target image carries out softization process, and initial input light field does not do the reconstructed image obtained when optimizing;
Figure 14 (b) illustrates that shown in Figure 14 (a), reconstructed image is along the distribution of amplitudes of Fourior plane central, transverse axis;
Figure 15 shows the light path schematic diagram generating reconstructed image based on transmission-type Fresnel type phase modulator.
Embodiment
As mentioned before, there is the multiple scheme utilizing phase modulator output image in prior art.Wherein, Pasienski algorithm is a kind of comparatively advanced phase modulation computing method in prior art, and inventor starts with from Pasienski algorithm, conducts in-depth research the reconstructed error in prior art existing for reconstructed image process and spot problem.Inventor notices: Pasienski algorithm employs Gaussian beam that a surrounding is truncated as input laser beam, this blocking causes that initial input optical field amplitude component space territory exists sudden change, if and inventor finds to suppress this sudden change, the reconstructed error of output image and spot will greatly reduce.Its reason is as follows: GS algorithm and its derivative algorithm (as Pasienski algorithm), when doing Fourier transform to input light field and calculating, all use fast fourier transform (FFT) algorithm, and fast fourier transformation algorithm is as a kind of discrete Fourier transform (DFT) algorithm, all need to sample and discretize to input light field, that is, in fact all adopt approximate calculation method at present when calculating phase modulation, only have the number of pixels when optical diffraction device (as phase modulator) unlimited many time, actual value is just consistent with theoretical value.And the number of pixels of optical diffraction device is in fact limited, therefore there is certain deviation in actual value and theoretical value.On the other hand, the sudden change inputting optical field amplitude component must cause the radio-frequency component (refer to the radio-frequency component in the frequency spectrum after spatial fourier transform, hereinafter repeat no more) that there is very high frequency in light field.Therefore when input amplitude sudden change corresponding to highest frequency exceeded the threshold frequency determined by the diffraction element of given number of pixels time, light beam will the too much information of loss in diffraction process, and then cause being difficult to reconstruct desired output image.This is very similar to the nyquist sampling law in signal theory: if the half of sample frequency is lower than signal frequency, so just cannot pass through sampled information reconstruction original signal.Based on above-mentioned analysis, can find, if the radio-frequency component in active suppression optical field amplitude component, the radio-frequency component especially corresponding to amplitude jump, significantly can suppress the reconstructed error in output image and spot.
Based on above-mentioned achievement in research, the present invention proposes a kind of method utilizing phase modulator output image.Light path design scheme of the present invention is consistent with prior art, such as, directly can use Fig. 1 or light path illustrated in fig. 2, so do not repeat at this.The proposed by the invention method of phase modulator output image that utilizes comprises the steps: one, calculates phase modulation; Two, according to calculated phase modulation designed phase modulation device and reconstructed image.Introduce this two steps below respectively.
One, phase modulation is calculated
In GS algorithm and derivative algorithm thereof, need to calculate phase modulation according to initial input light field and target image.Target image is known, and initial input light field then can according to circumstances flexible design.
Fig. 4 shows the flow process calculating phase modulation, and this flow process comprises the following steps:
Step 1, determine initial input light field.
Initial input light field refers to the initial input light field of the iterative computation for subsequent step, and initial input light field is made up of amplitude component and phase component.
In one embodiment, the distribution of amplitudes of the light field utilizing laser beam analyzer to be formed at the position measurement incoming laser beam of phase modulator front end, then the amplitude component that softization process obtains initial input light field is carried out to this distribution of amplitudes.In the prior art, often use the laser beam that blocks as the input beam (namely a part of laser energy drops on beyond the sensitive surface of phase modulator) of phase modulator, this causes incident field distribution of amplitudes to there is obvious radio-frequency component, carries out softization process can suppress this radio-frequency component to incident field amplitude component.Based on discussion above, suppress the radio-frequency component in initial input optical field amplitude component, significantly can suppress the reconstructed error in output image and spot.Certainly, one skilled in the art will readily appreciate that if be carried out spatial filtering and expanded to input laser, and input laser beam is without blocking, input laser is exactly an ideal Gaussian beam not comprising sudden change.If know Gaussian beam size somewhere, laser beam just directly can be calculated in any one size and distribution of amplitudes, and without the need to the distribution of amplitudes in the place of phase modulator actual measurement input light field.
Concrete scheme distribution of amplitudes being carried out to softization process can be selected flexibly.In one embodiment, the amplitude component of original incident light field represents with a matrix type, its softization process is: will represent original input optical field amplitude Component Matrices and move N number of pixel respectively to 4 directions up and down (N is generally 1 or 2, if matrix is larger, correspondingly can increase the numerical value of N), then to obtained 4N image array summation, thus the input optical field amplitude Component Matrices after softization process is obtained.It is to be noted, if be still not enough to obtain satisfied reconstructed image after above-mentioned softization process, on the basis of input optical field amplitude Component Matrices after the process of front once softization, above-mentioned softization processing procedure can also be repeated with further softization original image (i.e. original input optical field amplitude component).Fig. 6 (a) shows an original incident light field image, and Fig. 6 (b) shows above-mentioned incident field distribution of amplitudes centrally, and wherein horizontal ordinate represents pixel sequence number, and ordinate represents normalized amplitude.Can find out, this original incident light field is an even incident field, exists suddenly change at the boundary in signal area and non-signal region.Fig. 7 shows and carries out the distribution of amplitudes after softization process to this original incident optical field amplitude component.
In another embodiment, softization disposal route is: the point inserting several gradual change in sudden change place of the original incident light field comprising sudden change, thus the distribution of amplitudes obtaining the input light field of softization.
In yet another embodiment, softization disposal route is: carry out High frequency filter to the original incident optical field amplitude component comprising sudden change.Such as: the Fourier transform calculating incident light amplitude, clip its radio-frequency component, then inverse Fourier transform is done to it.
In a further embodiment, softization disposal route is: but replace original incident light field with the function not comprising sudden change similar with original incident optical field amplitude, such as can use super-Gaussian function to simulate a uniform beam having sudden change.Such as, circular uniform beam can replace with a circular super-Gaussian function:
In formula, I is power density distribution, and r is the coordinate position of light beam, r
0for the radius of uniform beam, n is the exponent number of super-Gaussian function.Similarly, the uniform beam of a rectangle can replace with the super-Gaussian function of a rectangle:
In formula, x, y are the coordinate position of light beam, x
0, y
0for the half of the length of side of rectangular uniform beam.
On the other hand, phase component directly can adopt the conventional constant of existing GS algorithm (namely incident beam is the parallel beam of collimation), also initial phase function conventional in the derivative algorithm of GS algorithm can be adopted, as conic surface function, linear gradient function, conical function or their mixed function.
In a further advantageous embodiment, the phase component of initial input light field can be obtained by Ray-tracing Method based on following condition.Described condition is: this initial phase produces a roughly uniform light distribution substantially identical with image output plane signal window size.Signal window refers to the region in Fourior plane shared by target image outline.Certain signal window generally can slightly larger than target image outline, and to retain certain buffer zone, this is that those skilled in the art are understandable.Because the band of diffraction element is sex-limited, there is power density in the output image of reconstruct is zero, and the point of phase singularity causes there is error between output image and target image.Existing initial phase, as conic surface function, linear gradient function, conical function or their mixed function, the hot spot that (modulation without phase modulator) is substantially identical with signal window size can be exported at Fourior plane, but its light distribution uneven.And in the process of the reconstructed image of reality, input beam projects Fourior plane through discrete Fourier transform (DFT), discrete Fourier transform (DFT) needs to carry out spatial sampling, its spatial sampling frequencies is uniform, namely the amplitude of input light field is sampled equably/sampled, such as every certain distance, such as 5 microns, get the amplitude of a laser beam.After the amplitude of input light field is sampled equably/sampled, obtain the distribution of amplitudes of a discrete input light field, and replace real distribution of amplitudes to carry out subsequent treatment by this discrete distribution of amplitudes.If therefore initial phase can cause the light distribution of Fourior plane output image uneven, the spatial sampling process of discrete Fourier transform (DFT) will be caused to occur error, and then cause the power density of reconstructed image and target image to there are differences (as shown in Figure 12 (a), (b)), cause reconstructed error.And in the present embodiment, the reconstructed image using initial phase to produce is not only basically identical with the size of target image, and reconstructed image is uniform, and therefore, the power density of reconstructed image is consistent with target image power density.
Signal window can be square (as Suo Shi Figure 11 (a)), and rectangle or circle (as Suo Shi Figure 11 (b)) can certainly be other shapes.Solid line in Figure 10 shows an initial phase function obtained by Ray-tracing Method.And the dotted line in Figure 10 represents spherical function initial phase comparatively conventional at present.Figure 11 (a) show in one embodiment of the invention produced by initial phase function (solid line in Figure 10) with the distribution of amplitudes of the square profile of the sizable general uniform of signal window.Figure 11 (b) show another embodiment of the present invention produced by initial phase function (not shown in other accompanying drawing) with the distribution of amplitudes of the circle of the sizable general uniform of signal window.
Described Ray-tracing Method comprises Bryngdahl method, Aleksoff method, Roux method, Romero method, Malyak method, Dresel method etc.Above-mentioned concrete grammar is all with the naming of the first authors.The common feature of these class methods is the distributions that a Gaussian beam can be become the roughly uniform rectangle of power density distribution or circle, and the phase result using these methods to obtain is substantially identical.
Amplitude component and phase component combination can be obtained initial input light field, and this initial input light field will be used for the iterative computation of subsequent step.For convenience of describing, hereinafter initial input light field is designated as g
0(x),
wherein | g
0(x) | represent the amplitude component of initial input light field,
represent the phase component of initial input light field.Initialization iterations variable k=1.X is the volume coordinate near phase modulator front end.In one embodiment of the invention, what in fact x represented is two-dimensional space coordinate, and namely x both represented horizontal ordinate, also represents ordinate, and it also can be write as vector form
Step 2, to current input light field g
k-1x () is carried out Fourier transform and is obtained G
k(u)=| G
k(u) | expi φ
k(u).Wherein, | G
k(u) | represent the amplitude component of the Fourior plane of kth time iteration, φ
ku () represents the phase component of the Fourior plane of kth time iteration.This step is consistent with existing GS algorithm, repeats no more herein.
The amplitude component of step 3, use target image | F (u) | the amplitude component of alternative steps 2 Fourier transform results | G
k(u) |, obtain G '
k(u)=| F (u) | expi φ
k(u).
The amplitude component of target image | F (u) | can open radical sign (0.5 power) to the power density distribution of expected target image and obtain, wherein u is the volume coordinate of Fourior plane.
And in a further advantageous embodiment, need to carry out softization process to target image, | F (u) | represent the amplitude component of the target image after softization process.The various concrete grammars of softization process describe in step 1 above.
Be similar to the process of input optical field amplitude component softization, processing softization of target image amplitude component is the highest frequency wanting limited target image, the i.e. most high spatial frequency component of target image spatial frequency spectrum, this most high spatial frequency component can be obtained by Fourier transform.Approx, the highest frequency of target image can be understood as the maximal value of the ratio of the space length (i.e. the minimum space resolution of target image) between the amplitude variations of in target image adjacent 2 and at these 2.Because the inverse of the minimum space resolution of target image and the bulk of diffraction element is directly proportional, and the bulk of diffraction element is not infinitely-great, therefore the minimum space resolution corresponding to target image sudden change neither be infinitesimal, so suppress the radio-frequency component of target image amplitude component, reduce the highest frequency of target image amplitude component, be conducive to avoiding losing too much information when inputting optical field amplitude and phase information according to the information reconstruction of target image amplitude.That is, be conducive to reducing reconstructed error and spot to the softization process of target image amplitude component.Target image after the process of certain softization and former target image not quite identical, if but the highest frequency of the target image after processing without softization has exceeded the highest frequency that optical system can reconstruct, so, using the precision of the reconstructed image that the target image after softization process obtains as new target image, just always can be better than with the precision of the reconstructed image obtained without the target image after softization process.In this case, the practical application of the present invention in each field can always be improved to the softization process of target image.
Fig. 5 (a), Fig. 5 (b) show the example of a target image, wherein Fig. 5 (a) shows the Fourior plane of target image, target image is positioned at the 512x512 pixel region of these Fourior plane central authorities, in general, buffer zone is provided with around target image, the pixel count of buffer zone is a free parameter, often can select pixel (the such as 5-20 pixel of some in limit, generally be no more than 10% of the pixel in a length of side direction) as buffer zone, target image forms signal window mouth region together with buffer zone, all the other regions are non-signal window region, the total pixel number that discrete Fourier transformation in iterative process and inverse transformation use is 1024x1024.Fig. 5 (b) shows the distribution of amplitudes of target image centrally transverse axis.Fig. 5 (c) shows and is reconstructed based on above-mentioned target image and the reconstructed image that there is reconstructed error exported.
Fig. 8 (a), Fig. 8 (b) show the target image after softization process.Wherein Fig. 8 (a) shows the Fourior plane of target image after softization process, Fig. 8 (b) show softization process after the distribution of amplitudes of target image centrally transverse axis.
According to a further advantageous embodiment of the invention, SIFTA-2 algorithm is adopted in this step.As previously mentioned, SIFTA-2 is a kind of GS algorithm of correction, and the difference of it and GS is in described step 3 (i.e. this step).Specifically, in described step 3, substitute the result of Fourier transform with the target image amplitude revised; The target image wherein revised carries out over-compensation (over-compensation) to the power density distribution in target image signal window (i.e. output plane signal window), ignores (namely retaining the Carrier To Noise Power Density distribution in iterative process outside output plane signal window) target image signal window (i.e. output plane signal window) Carrier To Noise Power Density distribution outward.Be expressed as follows with mathematical formulae: in GS algorithm, in step 3, direct use target image amplitude carrys out the amplitude that the Fourier transform in alternative steps 2 obtains, i.e. G
k' (u)=| F (u) | exp{i φ
k(u) }, wherein | F (u) | be the amplitude of target image.And in SIFTA-2 algorithm, step 3 uses
reviseoutput image amplitude carrys out the amplitude that the Fourier transform in the alternative first step obtains, namely
Wherein, 2c|F (u) |-| G
k(u) | } exp{i φ k (u) } be and over-compensation is carried out to the power density distribution in target image (i.e. output image) signal window.
Namely the Carrier To Noise Power Density distribution in iterative process outside output plane signal window is retained.
Wherein G
k(u), G
k' (u) and F
k modifiedu the physical significance of () can see Fig. 3, | G
k(u) | for being the kth time iteration distribution of amplitudes calculated in iteration, | G
k' (u) | or | F
k modified(u) | be the distribution of amplitudes of new correction.When
or
the mean square deviation of distribution of amplitudes in signal window can be optimized to minimum value, wherein γ
0represent target image, γ represents signal window.Due to target image and signal window difference very little, the c value difference calculated by two equations is above other also very little, is generally between 0.7 ~ 1.But, also c=1 can be used simply in an iterative process.SIFTA-2 algorithm particular content can list of references: JinsongLiuetal.SymmetricaliterativeFourier-transformalgo rithmusingbothphaseandamplitudefreedoms, OpticsCommunications.267,347-355,2006.
One skilled in the art will readily appreciate that and at use SIFTA-2 algorithm on the basis calculating phase modulation, softization process can also be carried out further to the target image revised.Namely, in described step 3, the result of Fourier transform is substituted with the target image amplitude revised; Wherein target image is revised as follows: over-compensation (over-compensation) is carried out to the power density distribution in target image signal window (i.e. output plane signal window), retain the Carrier To Noise Power Density distribution in iterative process outside output plane signal window simultaneously; Then carry out softization process further to the target image revised, the concrete means of softization process as mentioned before, repeat no more.
Step 4, result G ' to step 3
ku () is carried out inverse Fourier transform and is obtained g '
k(x);
wherein | g '
k(x) | represent amplitude component,
represent phase component.This step is consistent with existing GS algorithm, repeats no more herein.
The amplitude component of step 5, use initial input light field | g
0(x) | the inverse Fourier transform result g ' of alternative steps 4
kthe amplitude component of (x) | g '
k(x) |, obtain the new input light field g for next iteration
k(x),
in this step | g
0(x) | the amplitude component of the initial input light field after softization process referred to.
Step 6, judge whether to meet and stop the condition of iteration, if so, enter step 7, if not, make k=k+1, and return and perform step 2; Wherein, the condition of iteration is stopped to set as the case may be.In one embodiment, the condition of iteration is stopped to be that iterations reaches certain numerical value (as stopped iteration when iterations reaches 1000 times).And in another embodiment, stop the condition of iteration to be: the error between the distribution of amplitudes of the Fourier transform results of calculation procedure 2 and the distribution of amplitudes of target image, think the condition meeting and stop iteration when error is less than the threshold value preset.At present, there is the error that a lot of standard can be used for judging between said two devices, judging as adopted the root-mean-square error of amplitude density distribution or power density distribution.The root-mean-square error of amplitude density distribution can be defined as:
Wherein | F (u) | be the distribution of amplitudes of target image, | G
k_N(u) | be the distribution of amplitudes of the secondary iteration of the normalized kth calculated.The root-mean-square error of power density distribution can be defined as:
Wherein | I (u) | for the power of target image distributes.
Step 7, with current input light field g
kthe phase component of (x)
deduct the phase component of initial input light field
namely the phase modulation needed for reconstructed image is obtained
in general, incident beam is the parallel beam of collimation, and the PHASE DISTRIBUTION of incident field can be approximately constant, therefore, and phase modulation
be exactly input light field g when stopping iteration
kthe phase component of (x)
Two, according to calculated phase modulation designed phase modulation device and reconstructed image
After calculating phase modulation, can make according to this phase modulation or phase modulator is set.At present, typical phase modulator comprises the static diffraction optical device (diffractiveopticalelements scribed in advance, and dynamic spatial light modulator (spatiallightmodulators DOEs), SLM), as the Micro-Opto-Electro-Mechanical Systems (such as Gratinglightvalve) etc. of liquid crystal on silicon (liquidcrystalonsilicon, LCOS), phase modulation-type.
For the diffraction optical element etched in advance of static state, the etching depth controlling diffraction optical element can be passed through, thus control optical path difference and phase differential carry out phase modulation; For LCD space light modulator, general by controlling liquid crystal molecule direction, thus control its refractive index and carry out phase modulation; For the Micro-Opto-Electro-Mechanical Systems of phase modulation-type, can by controlling the micro mirror of Micro-Opto-Electro-Mechanical Systems and control optical path difference and phase differential carrying out phase modulation.
According to the type of phase modulator, design of graphics 1 or light path illustrated in fig. 2.This light path describes in the preceding article, repeats no more herein.It is noted that the input light field that the incoming laser beam produced in light path is formed is consistent with the initial input light field for calculating phase modulation.Under normal circumstances, the distribution of amplitudes of input light field is given, can by calculating or measure acquisition (such as measure the power density distribution of input light field, then open radical sign to the power density distribution recorded) by the distribution of amplitudes of the input light field calculating phase modulation above.The PHASE DISTRIBUTION of designed input light field can be realized by laser interferometer.The GPI series digit Spatial phase-shifting method of such as ZYGO company.Certainly, input laser beam also can be allowed by a Prescription lenses array, input light to be tested is decomposed into multiple converging beam by this lens array is corresponding, and each converging beam will focus on ccd detector.The small distortion of certain part of tested wavefront the convergent point of converging beam on CCD of corresponding lens array can have corresponding skew.Just the PHASE DISTRIBUTION of whole input laser beam can be obtained by detecting these skews of analysis.The latter can adopt CLAS series wave front analyzer to measure.
Light path with laser beam incident phase modulation device, can reconstruct the output image consistent with target image after building.
Shown below is some based on the proposed by the invention experimental result utilizing the method for phase modulator output image.
The dotted line of Fig. 9 (a) shows and carries out softization process to input light field, but softization process is not carried out to target image, adopt the function shown in Figure 10 solid line as initial phase function, and adopt SIFTA-2 algorithm to draw phase modulation and with the distribution of amplitudes along Fourior plane central, transverse axis of this reconstructed image generated; The dotted line of Fig. 9 (b) and Fig. 9 (c) then shows and carries out softization process to input light field, softization process is also carried out to target image, adopt the function shown in Figure 10 solid line as initial phase function, and adopt SIFTA-2 algorithm to draw phase modulation and with the distribution of amplitudes along Fourior plane central, transverse axis of this reconstructed image generated.
Figure 13 (a) shows and adopts SIFTA-2 algorithm, but target image does not carry out softization process, and initial input light field does not do the reconstructed image obtained when optimizing.Figure 13 (b) illustrates that shown in Figure 13 (a), reconstructed image is along the distribution of amplitudes of Fourior plane central, transverse axis.Figure 14 (a) shows and adopts SIFTA-2 algorithm, and target image carries out softization process, and initial input light field does not do the reconstructed image obtained when optimizing.Figure 14 (b) illustrates that shown in Figure 14 (a), reconstructed image is along the distribution of amplitudes of Fourior plane central, transverse axis.Obviously, relative to Figure 13 (a), (b), in reconstructed image shown in Figure 14 (a), (b), spot and reconstructed error obviously reduce, easy understand, carries out softization process to target image and obviously can reduce spot and reconstructed error in reconstructed image.
According to one embodiment of present invention, a kind of method that Fresnel type phase modulator produces reconstructed image is provided.Figure 15 shows the light path schematic diagram generating reconstructed image based on transmission-type Fresnel type phase modulator, and laser beam 2 is by directly projecting on image output plane 4 after phase modulator 1.For Fresnel type phase modulator, then can after the phase modulation of Fu Lang and the Fei type phase modulator using algorithm of the present invention to calculate, lens phase is added on calculated phase modulation, thus the phase modulation obtained needed for Fresnel type phase modulator, this is that those skilled in the art are understandable.
The present invention can be applicable to the photoetching (in order to replace gray scale mask version) based on phase-modulation, Materialbearbeitung mit Laserlicht is (as LASER HEAT TREATMENT, laser bonding, laser roughening etc.), high-definition television, small-sized minitype projection machine, based on Image Reconstruction or the illumination of LED or other light sources, the every field such as medical and beauty treatment.Such as:
1., based on the present invention, a kind of three-dimensional continuous microstructure litho machine based on phase-modulation can be developed.For example, the manufacture method of the most competitive three-dimensional continuous microstructure directly writes gray scale mask version with laser beam or electron beam at present, then exposes.If just single-piece, then generally direct matrix directly to be write.The manufacture of gray scale mask version relates generally to chemical substance, has certain pollution.This is not only expensive, and very consuming time.Substitute gray scale mask version with onesize phase modulator, can greatly reduce costs and save time.
2. the present invention also can be used for high-definition television and compact micro projector etc.This two methods than traditional TV and projector efficiency higher.Adopt the phase-modulation PHASE DISTRIBUTION of the present invention's design, the high precision image that error is almost nil can be produced.
Finally, the above embodiments are only used for the present invention is described, it should not be construed is carry out any restriction to protection scope of the present invention.And, it will be apparent to those skilled in the art that and do not departing under above-described embodiment spirit and principle, the various equivalences carried out above-described embodiment change, modification and the various improvement that do not describe in the text are all within the protection domain of this patent.
Claims (8)
1. utilize a method for phase modulator output image, comprising:
1) initial input light field is determined;
2) Fourier transform is carried out to current input light field;
3) by target image amplitude alternative steps 2) amplitude of the result of Fourier transform; Described target image is the image obtained after carrying out softization process to original target image;
4) to step 3) result carry out inverse Fourier transform;
5) by step 1) the amplitude component alternative steps 4 of input light field that draws) the amplitude of result, obtain the new input light field for next iteration;
6) step 2 is repeated) to 5) until meet the condition stopping iteration, thus obtain the phase modulation for producing needed for target image phase modulator;
7) step 6 is utilized) phase modulation that draws exports reconstructed image;
Wherein, described softization process comprises: the input optical field amplitude Component Matrices that representative is comprised sudden change moves N number of pixel respectively to 4 directions up and down, then to obtained 4N image array summation, thus the input optical field amplitude distribution after softization process is obtained.
2. the method utilizing phase modulator output image according to claim 1, is characterized in that, described step 1) in, the amplitude component of described initial input light field is through the amplitude component of softization process.
3. the method utilizing phase modulator output image according to claim 1, is characterized in that, described step 3) in, described target image presses the correction of SIFTA-2 algorithm by original target image, then carries out softization process and obtain.
4. the method utilizing phase modulator output image according to claim 1, it is characterized in that, described step 1) in, the initial phase of described initial input light field can produce one roughly uniform, the Fourior plane light distribution substantially identical with image output plane signal window size, described initial phase is obtained by Ray-tracing Method.
5. the method utilizing phase modulator output image according to claim 4, is characterized in that, described Ray-tracing Method comprises Bryngdahl method, Aleksoff method, Roux method, Romero method, Malyak method or Dresel method.
6. the method utilizing phase modulator output image according to claim 1, it is characterized in that, described step 5) in, described stop condition is that iterations reaches certain value, or step 2) the error of Fourier transform results compared with target image be less than the threshold value preset.
7. the method utilizing phase modulator output image according to claim 6, is characterized in that, described error is the root-mean-square error of amplitude density distribution or the root-mean-square error of power density distribution.
8. the method utilizing phase modulator output image according to claim 1, it is characterized in that, described step 6) in, after stopping iteration, with current procedures 4) phase place that obtains deducts the phase place of the input light field of actual measurement, namely obtains the phase modulation for producing needed for target image phase modulator.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210072546.9A CN103325129B (en) | 2012-03-19 | 2012-03-19 | A kind of method utilizing phase modulator output image |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210072546.9A CN103325129B (en) | 2012-03-19 | 2012-03-19 | A kind of method utilizing phase modulator output image |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN103325129A CN103325129A (en) | 2013-09-25 |
| CN103325129B true CN103325129B (en) | 2016-04-20 |
Family
ID=49193852
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201210072546.9A Active CN103325129B (en) | 2012-03-19 | 2012-03-19 | A kind of method utilizing phase modulator output image |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN103325129B (en) |
Families Citing this family (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP5842851B2 (en) * | 2013-03-29 | 2016-01-13 | トヨタ自動車株式会社 | Welded part inspection device and inspection method |
| JP6788504B2 (en) | 2014-05-15 | 2020-11-25 | エムティティ イノベーション インコーポレイテッドＭｔｔ Ｉｎｎｏｖａｔｉｏｎ Ｉｎｃｏｒｐｏｒａｔｅｄ | Optimizing drive scheme for multiple projector systems |
| CN116260951A (en) | 2014-06-03 | 2023-06-13 | Mtt创新公司 | Method and apparatus for displaying video data and image data |
| CN104112250A (en) * | 2014-07-08 | 2014-10-22 | 淮安信息职业技术学院 | Blind-information hiding/decryption method |
| EP3175282B1 (en) * | 2014-07-31 | 2021-06-09 | Mtt Innovation Incorporated | Numerical approaches for free-form lensing: area parameterization free-form lensing |
| CN104777612B (en) * | 2015-04-28 | 2017-01-25 | 中南大学 | Iterative method for performing shaping on amplitude and phase of light beam simultaneously |
| CN106937044B (en) * | 2016-12-14 | 2020-10-23 | 北京信息科技大学 | Algebraic iteration method and device for reconstructing light field by focusing stack under incomplete data |
| JP7578139B2 (en) | 2020-06-07 | 2024-11-06 | ソニーグループ株式会社 | Signal processing device, signal processing method, program, and lighting device |
| CN114863036B (en) * | 2022-07-06 | 2022-11-15 | 深圳市信润富联数字科技有限公司 | Data processing method and device based on structured light, electronic equipment and storage medium |
| CN115145024A (en) * | 2022-07-06 | 2022-10-04 | 南开大学 | Adjusting and controlling method for shaping laser |
| WO2024201883A1 (en) * | 2023-03-30 | 2024-10-03 | ナルックス株式会社 | Method for manufacturing microlens array |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1996034307A1 (en) * | 1995-04-28 | 1996-10-31 | Forskningscenter Risø | Phase contrast imaging |
| GB2438026A (en) * | 2006-05-11 | 2007-11-14 | Univ Cambridge Tech | Phase retrevial in hologram generation using amplitude and phase feedback |
-
2012
- 2012-03-19 CN CN201210072546.9A patent/CN103325129B/en active Active
Non-Patent Citations (4)
| Title |
|---|
| 《基于改进GS算法的衍射光学光束整形元件的设计》;邹杰宇等;《红外与激光工程》;20061031;第35卷;全文 * |
| 《基于相位恢复技术的大型光学镜面面形在位检测技术》;吴宇列等;《机械工程学报》;20090228;第45卷(第2期);全文 * |
| 《改进的自适应加法算法及其在衍射光学元件设计中的应用》;温昌礼等;《光学学报》;20100930;第30卷(第9期);全文 * |
| 《连续相位板优化设计》;阳泽健等;《激光与光电子学进展》;20100228(第2期);摘要第1－3行 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN103325129A (en) | 2013-09-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103325129B (en) | A kind of method utilizing phase modulator output image | |
| KR102127588B1 (en) | Pupil Expansion | |
| EP1346252B1 (en) | A method and an apparatus for generating a phase-modulated wave front of electromagnetic radiation | |
| CN101949765B (en) | Atmospheric turbulence light wave front simulation system | |
| CN203964879U (en) | Based on LCD space light modulator aspheric surface calculation holographic interference checking device | |
| Khonina et al. | Analysis of the wavefront aberrations based on neural networks processing of the interferograms with a conical reference beam | |
| Zlokazov | Methods and algorithms for computer synthesis of holographic elements to obtain a complex impulse response of optical information processing systems based on modern spatial light modulators | |
| Berdeu et al. | Reconstruction of in-line holograms: combining model-based and regularized inversion | |
| CN103425035A (en) | Printing system of holographic stereogram and with abnormal-shaped mask plate | |
| Su et al. | Computer generated hologram null test of a freeform optical surface with rectangular aperture | |
| Davis et al. | Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm | |
| TW201825932A (en) | Pupil equalization | |
| CN102323721A (en) | Method for obtaining space image of non-ideal lithography system based on Abbe vector imaging model | |
| Xu et al. | Two-dimensional Hanning self-convolution window for enhancing Moiré fringe alignment in lithography | |
| Zhang et al. | A simple determination approach for zero-padding of FFT method in focal spot calculation | |
| Tsai et al. | Enhancing performance of LCoS-SLM as adaptive optics by using computer-generated holograms modulation software | |
| Kumar et al. | Improvement in wavefront measurement accuracy in grating array-based zonal wavefront sensors by modulating the intensity profile of the incident beam | |
| Eriksson | Development of a Software Tool for Mid-Spatial Frequency Analysis | |
| Neto et al. | Implementation of Fresnel full complex-amplitude digital holograms | |
| Alieva et al. | The linear canonical transformations in classical optics | |
| Gulses et al. | Laser beam shaping with computer-generated holograms for fiducial marking | |
| Gorelaya et al. | Holographic wavefront sensor, based on diffuse Fourier holography | |
| Guo et al. | High-speed fringe projection for robot 3D vision system | |
| George | Fourier optics | |
| Burgi et al. | Exploiting redundant phase information of a reflection matrix |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant |