CN103325129A - Method for outputting images by utilization of phase modulator - Google Patents
Method for outputting images by utilization of phase modulator Download PDFInfo
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- CN103325129A CN103325129A CN2012100725469A CN201210072546A CN103325129A CN 103325129 A CN103325129 A CN 103325129A CN 2012100725469 A CN2012100725469 A CN 2012100725469A CN 201210072546 A CN201210072546 A CN 201210072546A CN 103325129 A CN103325129 A CN 103325129A
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Abstract
The invention provides a method for outputting images by the utilization of a phase modulator. The method for outputting the images by the utilization of the phase modulator comprises the steps that (1) an initial inputting optical field is determined; (2) Fourier transform is conducted on the current inputting optical field; (3) amplitude of an objective image is used for replacing amplitude of a result of the Fourier transform in the step (2), wherein the objective image is an image which is obtained after an original objective image is softened; (4) Fourier transform is conducted on the result of the step (3); (5) a component of amplitude of the inputting optical field obtained in the step (1) is used for replacing amplitude of the result of the step (4) in a component mode, so that a new inputting optical field which is iterated next time is obtained; (6) the step (2), the step (3), the step (4), the step (5) are repeated till the condition of stopping iteration is met, and therefore a modulated phase needed by the phase modulator for generating the objective image is obtained; (7) the modulated phase obtained in the step 6 is used for outputting a reconstructed image. The method can effectively restrict reconstruction errors and spots, and is suitable for various complex objective images.
Description
Technical field
The present invention relates to optical technical field, specifically, the present invention relates to a kind of method of utilizing the phase modulator output image.
Background technology
Utilize the phase modulator output image, by phase modulator incoming laser beam is carried out certain phase-modulation with the power density distribution of change laser beam exactly, thereby reconstruct the output image consistent with desired target image.Wherein, phase modulator is a kind of important devices in computer-generated hologram (computergenerated holograms, the CGH) technology.Typical phase modulator comprises the static diffraction optical device of scribing in advance (diffractive optical elements, DOEs) and dynamic spatial light modulator (spatial light modulators, SLM), such as liquid crystal on silicon (liquidcrystal on silicon, LCOS), this two classes phase modulator all can be used for reconstructed image.
Different according to the playback mode of 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 devices 1, in the process of transmission phase modulation device 1, produce phase-modulation, project on the image output plane 4 (also can be described as Fourier plane) by fourier lense 3 through the laser beam behind the phase-modulation, and at image output plane 4 reconstruct output images.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 resulting laser beam through phase-modulation projects reconstruct output image on the image output plane 4 through fourier lense 3 again after the reflection.No matter be to adopt transmission-type or reflective phase modulator, all need to design its phase modulation according to incoming laser beam and target image.Obviously, for the Two-Dimensional Reconstruction image, aforementioned phase modulation refers to the PHASE DISTRIBUTION of a two dimension.
At present, for Fu Lang with take the type phase modulator, the algorithms most in use of design phase modulation is iterative Fourier transform algorithm (Iterative Fourier-transform algorithms, IFTAs).It is a kind of typical iterative Fourier transform algorithm (IFTAs) that lid Shi Beige one spreads gram stone algorithm (the Gerchberg-Saxton algorithm is abbreviated as the GS algorithm).Computation process to phase modulation describes the below as an example of the GS algorithm example.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) | the amplitude component of expression initial input light field,
The phase component of expression initial input light field; In general, incident beam is the parallel beam of collimation, so phase component
Can be approximately constant.
(2) to current input light field g
K-1(x) carry out Fourier transform and obtain G
k(u)=| G
k(u) | expi φ
k(u).Wherein, | G
k(u) | represent the amplitude component of the Fourior plane of the k time iteration, φ
k(u) phase component of the Fourior plane of the k time iteration of expression.
(3) amplitude component of usefulness target image | F (u) | the result's of alternative steps (2) Fourier transform amplitude component | G
k(u) |, obtain G '
k(u)=| F (u) | expi φ
k(u).
(4) to the as a result G ' of step (3)
k(u) carry out inverse Fourier transform and obtain g '
k(x);
Wherein | g '
k(x) | the expression amplitude component,
The expression phase component.
(5) with the inverse Fourier transform of the amplitude component alternative steps (4) of known initial input light field g ' as a result
k(x) amplitude component obtains the new input light field g for next iteration
k(x),
(6) judge whether to satisfy the condition that stops iteration, if so, enter step (7), if not, make k=k+1, and return execution in step (2); Wherein, the condition that stops iteration can being set as the case may be, for example can be that iterations reaches certain numerical value;
(7) with current input light field g
k(x) phase component
Deduct the phase component of initial input light field
Namely obtain the required phase modulation of reconstructed image
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
Input light field g when stopping iteration exactly
k(x) phase component
In conjunction with Fig. 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.Yet in actual applications, when using the GS algorithm to calculate phase modulation and reconstructed image, output image exists comparatively serious reconstructed error (reconstruction errors) and spot (speckles).Fig. 3 shows one based on the experimental result of GS algorithm reconstructed image, and wherein (a) part is the target image of expectation, and (b) part is the output image of actual reconstruct, can find out that there is obvious spot in actual output image.The detailed explanation of GS algorithm defects is list of references Pasienski M andDeMarco B further, A high-accuracy algorithmfor designing arbitrary holographic atom traps Opt.Express, 162176-90,2008.
For solving based on the problem that has reconstructed error and spot in the GS algorithm, Pasienski M and DeMarco B have proposed a kind of GS algorithm (hereinafter referred to as Pasienski algorithm) of correction in 2008, Pasienski algorithm principal feature is: (1) has adopted the account form of amplitude and Phase Double degree of freedom.This account form distributes to the outer Carrier To Noise Power Density of target image planed signal window and ignores, namely keep the outer Carrier To Noise Power Density distribution of output plane signal window in the iterative process, reference paper F.Wyrowski, J.Opt.Soc.Am.A.7,961,1990.(2) according to the difference of target image, use respectively the conic surface function, the linear gradient function, conical function or their mixed function are as the initial phase of initial input light field.The Pasienski algorithm is better than traditional GS algorithm, however experiment find, still have obvious reconstructed error and spot based on the reconstructed image of Pasienski algorithm.
In sum, current in the urgent need to a kind of can the establishment reconstructed error and the phase modulator that utilizes of spot produce the method for reconstructed image.
Summary of the invention
The objective of the invention is a kind of can the establishment reconstructed error and the phase modulator that utilizes of spot produce the method for reconstructed image.
For achieving the above object, the invention provides a kind of method of utilizing phase modulator to produce reconstructed image, comprising:
1) determines the initial input light field;
2) current input light field is carried out Fourier transform;
3) with target image amplitude alternative steps 2) result's of Fourier transform amplitude; Described target image is that the original object image is carried out resulting image after the softization processing;
4) to step 3) the result carry out inverse Fourier transform;
5) with step 1) the amplitude component alternative steps 4 of the input light field that draws) result's amplitude, obtain the new input light field for next iteration;
6) repeating step 2) to 5) until satisfy the condition that stops iteration, thus obtain as producing the required phase modulation of target image phase modulator;
7) utilize step 6) drawn phase modulation output reconstructed image.
Wherein, described step 1) in, the amplitude component of described initial input light field is the amplitude component through softization processing.
Wherein, described step 3) in, described target image is pressed the correction of SIFTA-2 algorithm by the original object image, carries out softization processing again and obtains.
Wherein, described step 1) in, the initial phase of described initial input light field can produce one roughly uniform, and the essentially identical Fourior plane light distribution of image output plane signal window size, described initial phase obtains by Ray-tracing Method.
Wherein, described Ray-tracing Method comprises the 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 compared with target image of Fourier transform results less than predefined threshold value.
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, stop iteration after, with current step 4) phase place that obtains deducts the phase place of the input light field of actual measurement, namely obtaining is to produce the required phase modulation of target image phase modulator.
Wherein, described softization processing comprises: the input light field amplitude component matrix that representative is comprised sudden change respectively up and down about 4 directions move N pixel, then to the summation of resulting 4N image array, thereby obtain input light field distribution of amplitudes after the softization processing; Perhaps obtain the input light field distribution of amplitudes of softization by the point that inserts several gradual changes at the amplitude jump place that inputs light field; Perhaps the input light field amplitude component that comprises sudden change is carried out High frequency filter; Perhaps simulating with corresponding super-Gaussian function exists amplitude jump evenly to input light field.
Compared with prior art, the present invention has following technique effect:
1, can establishment reconstructed error and spot.
2, applied widely, can be applicable to the target image of various complexity.
Description of drawings
Fig. 1 shows the light path schematic diagram based on transmission-type Fu Lang and Fei type phase modulator generation reconstructed image;
Fig. 2 shows the light path schematic diagram based on reflective Fu Lang and Fei type phase modulator generation reconstructed image;
Fig. 3 shows an output image that produces based on GS algorithm reconstructed image and the example of target image;
Fig. 4 shows the flow process that phase modulation calculates in the one embodiment of the invention;
Fig. 5 (a) shows the Fourior plane of target image;
Fig. 5 (b) shows the target image of Fig. 5 (a) along the distribution of amplitudes of central, transverse axis;
Fig. 5 (c) shows the output image that has reconstructed error based on the target image reconstruct of Fig. 5 (a);
Fig. 6 (a) shows an original even input light field image that contains sudden change;
Fig. 6 (b) shows the distribution of amplitudes of the original even input light field that contains sudden change of Fig. 6 (a);
Fig. 7 shows the original even input light field that contains sudden change of Fig. 6 (a) through the distribution of amplitudes of softization processing;
Fig. 8 (a) shows the Fourior plane that the target image shown in Fig. 5 (a) is carried out the target image after the softization processing;
Fig. 8 (b) shows the distribution of amplitudes along central, transverse axis of the target image shown in Fig. 5 (a) being carried out the target image after the softization processing;
Fig. 9 shows the contrast of three kinds of different reconstructed images and target image;
Figure 10 shows sphere input function commonly used in the initial phase function of one embodiment of the invention and the prior art;
Figure 11 (a) shows the Fourior plane distribution of amplitudes that the initial phase in the one embodiment of the invention produces;
Figure 11 (b) shows the Fourior plane distribution of amplitudes that the initial phase in the another embodiment of the present invention produces;
Figure 12 (a) show use the sphere input function as initial phase based on 2000 resulting reconstructed image results of iteration;
Figure 12 (b) show use the sphere input function as initial phase based on 10000 resulting reconstructed image results of iteration;
Figure 13 (a) shows and adopts the SIFTA-2 algorithm, but target image does not carry out softization processing, and the initial input light field is not done resulting reconstructed image in the situation of optimization yet;
Figure 13 (b) illustrates reconstructed image shown in Figure 13 (a) along the distribution of amplitudes of Fourior plane central, transverse axis;
Figure 14 (a) shows and adopts the SIFTA-2 algorithm, and target image carries out softization processing, and the initial input light field is not done resulting reconstructed image in the situation of optimization;
Figure 14 (b) illustrates reconstructed image shown in Figure 14 (a) along the distribution of amplitudes of Fourior plane central, transverse axis;
Figure 15 shows the light path schematic diagram that generates reconstructed image based on transmission-type Fresnel type phase modulator.
Embodiment
As mentioned before, there has been the multiple scheme of utilizing the phase modulator output image in prior art.Wherein, the Pasienski algorithm is a kind of comparatively advanced phase modulation computing method in the prior art, and this case inventor starts with from the Pasienski algorithm, and the existing reconstructed error of reconstructed image process and spot problem in the prior art are conducted in-depth research.This case the inventor notice: the Gaussian beam that the Pasienski algorithm has been truncated around having used is as input laser beam, this blocking causes existing on the initial input light field amplitude component spatial domain sudden change, if and the 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 (such as the Pasienski algorithm), when the input light field is done Fourier transform 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 the input light field is sampled and discretize, that is to say, in fact all be to adopt approximate calculation method at present when calculating phase modulation, only have number of pixels when optical diffraction device (such as phase modulator) unlimited when many, actual value is just consistent with theoretical value.And the number of pixels of optical diffraction device is in fact limited, so there are certain deviation in actual value and theoretical value.On the other hand, the sudden change of input light field amplitude component must cause existing in the light field radio-frequency component of very high frequency (refer to the radio-frequency component in the frequency spectrum after the spatial fourier transform, hereinafter repeat no more).Therefore when the corresponding highest frequency of the sudden change of input amplitude has surpassed the threshold frequency that the diffraction element by given number of pixels determines, light beam will lose too much information in diffraction process, and then will cause being difficult to reconstruct desired output image.This is very similar to the nyquist sampling law in the signal theory: if half of sample frequency is lower than signal frequency, the information that so just can't pass through to sample is rebuild original signal.Based on above-mentioned analysis, can find, if the corresponding radio-frequency component of radio-frequency component, especially amplitude jump in the active suppression light field amplitude component can significantly suppress reconstructed error and spot in the output image.
Based on above-mentioned achievement in research, the present invention proposes a kind of method of utilizing the phase modulator output image.Light path design scheme of the present invention is consistent with prior art, for example can directly use Fig. 1 or light path illustrated in fig. 2, does not give unnecessary details so do not do at this.The method of utilizing the phase modulator output image proposed by the invention comprises the steps: one, calculates phase modulation; Two, according to the phase modulation designed phase modulation device and the reconstructed image that calculate.The below introduces respectively this two steps.
One, calculates phase modulation
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 the initial input light field is flexible design according to circumstances then.
Fig. 4 shows the flow process of calculating phase modulation, and this flow process comprises the following steps:
The initial input light field refers to the initial input light field for the iterative computation of subsequent step, and the initial input light field is comprised of amplitude component and phase component.
In one embodiment, utilize laser beam analyzer in the distribution of amplitudes of the formed light field of position measurement incoming laser beam of phase modulator front end, again this distribution of amplitudes is carried out the amplitude component that softization processing obtains the initial input light field.In the prior art, often use the laser beam block as the input beam of phase modulator (be a part of laser energy drop on the sensitive surface of phase modulator beyond), this causes the incident field distribution of amplitudes to have obvious radio-frequency component, the incident field amplitude component is carried out softization processing can suppress this radio-frequency component.Based on the discussion of front, suppress the radio-frequency component in the initial input light field amplitude component, can significantly suppress reconstructed error and spot in the output image.Certainly, one skilled in the art will readily appreciate that if be to carry out spatial filtering and expanding to input laser, and input laser beam is without blocking, input laser is exactly an ideal Gaussian beam that does not comprise sudden change.If know Gaussian beam size somewhere, just can directly calculate laser beam in any one size and distribution of amplitudes, and need not the distribution of amplitudes in the place of phase modulator actual measurement input light field.
The concrete scheme that distribution of amplitudes is carried out softization processing can flexible choice.In one embodiment, the amplitude component of original incident field represents with the form of matrix, its softization processing is: will represent original input light field amplitude component matrix respectively up and down about 4 directions move N pixel (N be generally 1 or 2, if matrix is larger, can correspondingly increase the numerical value of N), then to the summation of resulting 4N image array, thereby obtain input light field amplitude component matrix after the softization processing.It is to be noted, if still be not enough to obtain satisfied reconstructed image after the above-mentioned softization processing, can also on the basis of the input light field amplitude component matrix after the processing of front once softization, repeat above-mentioned softization processing procedure with further softization original image (being original input light field amplitude component).Fig. 6 (a) shows an original incident field image, and Fig. 6 (b) shows above-mentioned incident field along the distribution of amplitudes at center, and wherein horizontal ordinate represents the pixel sequence number, and ordinate represents normalized amplitude.Can find out, this original incident field is an even incident field, and there is sudden change in the boundary in signal area and non-signal area.Fig. 7 shows this original incident field amplitude component is carried out distribution of amplitudes after the softization processing.
In another embodiment, softization disposal route is: insert the point of several gradual changes in sudden change place of the original incident field that comprises sudden change, thereby obtain the distribution of amplitudes of the input light field of softization.
In yet another embodiment, softization disposal route is: the original incident field amplitude component that comprises sudden change is carried out High frequency filter.For example: calculate the Fourier transform of incident light amplitude, clip its radio-frequency component, again it is done inverse Fourier transform.
In another embodiment, softization disposal route is: but replace original incident field with one with the similar function that does not comprise sudden change of original incident field amplitude, such as simulating a uniform beam that sudden change is arranged with the super-Gaussian function.For example, the uniform beam of a circle can replace with the super-Gaussian function of a circle:
I is power density distribution in the formula, and r is the coordinate position of light beam, r
0Be 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:
X in the formula, y are the coordinate position of light beam, x
0, y
0Be half of the length of side of rectangular uniform light beam.
On the other hand, phase component can directly adopt existing GS algorithm constant commonly used (being that incident beam is the parallel beam of collimation), also can adopt the initial phase function of commonly using in the derivative algorithm of GS algorithm, such as the 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 obtain by Ray-tracing Method based on following condition.Described condition is: this initial phase produces a roughly uniform and essentially identical light distribution of image output plane signal window size.Signal window refers to the shared zone of target image outline in the Fourior plane.Certainly signal window generally can be slightly larger than the target image outline, and to keep certain buffer zone, this is that those skilled in the art are understandable.Because being with of diffraction element is sex-limited, having power density in the output image of reconstruct is zero, and the point of phase singularity causes having error between output image and the target image.Existing initial phase, such as the conic surface function, linear gradient function, conical function or their mixed function, can export at Fourior plane the essentially identical hot spot of (without the modulation of phase modulator) and signal window size, but its light distribution and inhomogeneous.And in the process of actual reconstructed image, input beam projects Fourior plane through discrete Fourier transform (DFT), discrete Fourier transform (DFT) need to be carried out spatial sampling, its spatial sampling frequency is uniform, namely the amplitude of input light field is sampled equably/sampled, for example 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 with this discrete distribution of amplitudes.If therefore initial phase can cause the light distribution of Fourior plane output image inhomogeneous, will cause the spatial sampling process of discrete Fourier transform (DFT) error to occur, and then the power density that causes reconstructed image and target image there are differences (shown in Figure 12 (a), (b)), causes reconstructed error.And in the present embodiment, use not only big or small basically identical with target image of reconstructed image that initial phase produces, and reconstructed image is uniform, therefore, the power density of reconstructed image is consistent with the target image power density.
Signal window can be square (shown in Figure 11 (a)), and rectangle or circle (shown in Figure 11 (b)) can certainly be other shapes.Solid line among Figure 10 has shown an initial phase function that obtains by Ray-tracing Method.And the dotted line among Figure 10 represents spherical function initial phase comparatively commonly used at present.Figure 11 (a) show in the one embodiment of the invention by initial phase function (solid line among Figure 10) that produce with the distribution of amplitudes uniform square profile of the sizable cardinal principle of signal window.Figure 11 (b) shows produced by initial phase function (not shown in other accompanying drawing) and the distribution of amplitudes uniform circle of the sizable cardinal principle of signal window of another embodiment of the present invention.
Described Ray-tracing Method comprises the 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 to become roughly uniformly rectangle or circular distribution of power density distribution to a Gaussian beam, and the phase result of using these methods to obtain is basic identical.
Amplitude component and phase component combination can be obtained the initial input light field, and this initial input light field will be for the iterative computation of subsequent step.Describe for convenient, hereinafter the initial input light field is designated as g
0(x),
Wherein | g
0(x) | the amplitude component of expression initial input light field,
The phase component of expression initial input light field.Initialization iterations variable k=1.X is the volume coordinate near the phase modulator front end.In one embodiment of the invention, what in fact x represented is the two-dimensional space coordinate, and namely x had both represented horizontal ordinate, also represented ordinate, and it also can be write as vector form
The amplitude component of step 3, usefulness 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 the target image expected and obtain, wherein u is the volume coordinate of Fourior plane.
And in a further advantageous embodiment, need to carry out softization processing to target image, | F (u) | represent the amplitude component of the target image after the softization processing.The various concrete grammars of softization processing are narrated in preamble step 1.
Be similar to the processing of softization of input light field amplitude component, softization processing to the target image amplitude component is the highest frequency of wanting the limited target image, be the high spatial frequency component of target image spatial frequency spectrum, this 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 (being the minimum space resolution of target image) between amplitude variations adjacent in the target image and at 2 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 target image suddenly change corresponding minimum space resolution neither be infinitesimal, so suppress the radio-frequency component of target image amplitude component, reduce the highest frequency of target image amplitude component, the too much information of loss when being conducive to avoid to rebuild input light field amplitude and phase information according to the information of target image amplitude.That is to say, the softization processing of target image amplitude component is conducive to reduce reconstructed error and spot.Target image and former target image after certain softization processing are not quite identical, if but without the highest frequency of the target image after the softization processing surpassed optical system can reconstruct highest frequency, so, the precision of the reconstructed image that obtains as new target image with the target image after the softization processing just always can be better than the precision with the reconstructed image that obtains without the target image after the softization processing.In this case, always can improve the present invention in the practical application in each field to the softization processing 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, be provided with buffer zone around the target image, the pixel count of buffer zone is a free parameter, can be every the limit select pixel (the 5-20 pixel for example of some, generally be no more than a length of side direction pixel 10%) as buffer zone, target image and buffer zone form the signal window oral region together, all the other zones are non-signal window oral region, and the total pixel number that the discrete Fourier transformation in the iterative process and inverse transformation are used is 1024x1024.Fig. 5 (b) shows target image along the distribution of amplitudes of central, transverse axis.Fig. 5 (c) shows based on above-mentioned target image and is reconstructed and the reconstructed image that has reconstructed error exported.
Fig. 8 (a), Fig. 8 (b) show the target image after the softization processing.Wherein Fig. 8 (a) shows the Fourior plane of the target image after the softization processing, and Fig. 8 (b) shows target image after the softization processing along the distribution of amplitudes of central, transverse axis.
According to a further advantageous embodiment of the invention, adopt the SIFTA-2 algorithm in this step.As previously mentioned, SIFTA-2 is a kind of GS algorithm of correction, and the difference of it and GS is described step 3 (being this step).Specifically, in the described step 3, substitute the result of Fourier transform with the target image amplitude of revising; Wherein the target image of correction is that the power density distribution in the target image signal window (being the output plane signal window) is carried out over-compensation (over-compensation), the outer Carrier To Noise Power Density of target image signal window (being the output plane signal window) is distributed ignore (namely keeping the outer Carrier To Noise Power Density distribution of output plane signal window in the iterative process).Be expressed as follows with mathematical formulae: in the GS algorithm, directly come the resulting amplitude of Fourier transform in the alternative steps 2, i.e. G with the target image amplitude in the step 3
k' (u)=| F (u) | exp{i φ
k(u) }, wherein | F (u) | be the amplitude of target image.And in the SIFTA-2 algorithm, step 3 is used
ReviseThe output image amplitude substitutes the resulting amplitude of Fourier transform in the first step, namely
Wherein, 2c|F (u) |-| G
k(u) | } exp{i φ k (u) } be the power density distribution in target image (the being output image) signal window is carried out over-compensation.
Namely keep the outer Carrier To Noise Power Density distribution of output plane signal window in the iterative process.
G wherein
k(u), G
k' (u) and F
k Modified(u) physical significance can be referring to Fig. 3, | G
k(u) | for being the k time iteration distribution of amplitudes that in iteration, calculates, | 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
0The expression target image, γ represents signal window.Because target image and signal window difference are very little, the c value difference that is calculated by top two equations is other also very little, is generally between 0.7～1.But, also can in iterative process, use simply c=1.But SIFTA-2 algorithm particular content list of references: Jinsong Liu et al.Symmetrical iterative Fourier-transformalgorithm using both phase and amplitude freedoms, Optics Communications.267,347-355,2006.
One skilled in the art will readily appreciate that and to calculate with the SIFTA-2 algorithm on the basis of phase modulation, the target image of revising is further carried out softization processing.Be in the described step 3, substitute the result of Fourier transform with the target image amplitude of revising; Wherein target image is carried out following correction: the power density distribution in the target image signal window (being the output plane signal window) is carried out over-compensation (over-compensation), keep simultaneously the outer Carrier To Noise Power Density distribution of output plane signal window in the iterative process; Then the target image of revising is further carried out softization processing, the concrete means of softization processing repeat no more as mentioned before.
The amplitude component of step 5, usefulness initial input light field | g
0(x) | the inverse Fourier transform of alternative steps 4 is g ' as a result
k(x) amplitude component | 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 of the process processing that refers to.
Wherein | F (u) | be the distribution of amplitudes of target image, | G
K_N(u) | be the distribution of amplitudes of normalized the k time iteration of calculating.The root-mean-square error of power density distribution can be defined as:
Wherein | I (u) | be the power distribution of target image.
Two, according to the phase modulation designed phase modulation device and the reconstructed image that calculate
After calculating phase modulation, can make or arrange phase modulator according to this phase modulation.At present, typical phase modulator comprises the static diffraction optical device of scribing in advance (diffractive optical elements, DOEs) and dynamic spatial light modulator (spatial lightmodulators, SLM), such as Micro-Opto-Electro-Mechanical Systems (such as Grating light valve) of liquid crystal on silicon (liquid crystal on silicon, LCOS), phase modulation-type etc.
For the diffraction optical element of the in advance etching of static state, can be by the etching depth of control diffraction optical element, thus control optical path difference and phase differential come phase modulation; For LCD space light modulator, general by control liquid crystal molecule direction, come phase modulation thereby control its refractive index; For the Micro-Opto-Electro-Mechanical Systems of phase modulation-type, can control optical path difference and phase differential comes phase modulation by the micro mirror of control Micro-Opto-Electro-Mechanical Systems.
According to the type of phase modulator, design of graphics 1 or light path illustrated in fig. 2.This light path is narrated in preamble, repeats no more herein.Should be noted, the formed input light field of the incoming laser beam that produces in the light path is consistent with the initial input light field that is used for the calculating phase modulation.Generally, the distribution of amplitudes of input light field is given, distribution of amplitudes with the input light field of calculating phase modulation in the preamble can obtain by calculating or measuring (for example measure the power density distribution of input light field, then the power density distribution that records is opened radical sign).The PHASE DISTRIBUTION of designed input light field can realize by laser interferometer.The GPI series digit phase shift interferometer of ZYGO company for example.Certainly, also can allow input laser beam pass through an accurate lens arra, input light to be tested is decomposed into a plurality of converging beams by this lens array is corresponding, each converging beam will focus on the ccd detector.The convergent point of converging beam on CCD of the corresponding lens array of small distortion meeting of certain part of tested wavefront has corresponding skew.Just the PHASE DISTRIBUTION of whole input laser beam can have been obtained by detecting these skews of analysis.The latter can adopt CLAS series wavefront analysis instrument to measure.
After the light path structure is complete, use the laser beam incident phase modulator, can reconstruct the output image consistent with target image.
The below has provided some experimental results based on the method for utilizing the phase modulator output image proposed by the invention.
Being shown in dotted line of Fig. 9 (a) carried out softization processing to the input light field, but target image is not carried out softization processing, adopt the function shown in Figure 10 solid line as the initial phase function, and adopt the SIFTA-2 algorithm to draw phase modulation and with the distribution of amplitudes along the Fourior plane central, transverse axis of this reconstructed image that generates; The dotted line of Fig. 9 (b) and Fig. 9 (c) then shows the input light field is carried out softization processing, target image is also carried out softization processing, adopt the function shown in Figure 10 solid line as the initial phase function, and adopt the SIFTA-2 algorithm to draw phase modulation and with the distribution of amplitudes along the Fourior plane central, transverse axis of this reconstructed image that generates.
Figure 13 (a) shows and adopts the SIFTA-2 algorithm, but target image does not carry out softization processing, and the initial input light field is not done resulting reconstructed image in the situation of optimization.Figure 13 (b) illustrates reconstructed image shown in Figure 13 (a) along the distribution of amplitudes of Fourior plane central, transverse axis.Figure 14 (a) shows and adopts the SIFTA-2 algorithm, and target image carries out softization processing, and the initial input light field is not done resulting reconstructed image in the situation of optimization.Figure 14 (b) illustrates reconstructed image shown in Figure 14 (a) along the distribution of amplitudes of Fourior plane central, transverse axis.Obviously, with respect to Figure 13 (a), (b), spot and reconstructed error obviously reduce in the reconstructed image shown in Figure 14 (a), (b), easily understand, and target image is carried out softization processing can obviously reduce spot and reconstructed error in the reconstructed image.
According to one embodiment of present invention, provide a kind of method that produces reconstructed image with the Fresnel type phase modulator.Figure 15 shows the light path schematic diagram that generates reconstructed image based on transmission-type Fresnel type phase modulator, and laser beam 2 is by phase modulator 1 rear directly projecting on the image output plane 4.For the Fresnel type phase modulator, then can be behind the phase modulation of the Fu Lang that uses algorithm of the present invention to calculate and Fei type phase modulator, with the lens Phase Stacking to the phase modulation that calculates, thereby obtain the required phase modulation of Fresnel type phase modulator, this is that those skilled in the art are understandable.
The present invention can be applicable to phase-modulation and is the photoetching (in order to replace the gray scale mask version) on basis, Materialbearbeitung mit Laserlicht is (such 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.For example:
1. based on the present invention, can develop a kind of three-dimensional continuous microstructure litho machine based on phase-modulation.For instance, at present the manufacture method of competitive three-dimensional continuous microstructure is with laser beam or electron beam the gray scale mask version directly to be write, then exposure.If single-piece just then general is directly directly write matrix.The manufacturing of gray scale mask version relates generally to chemical substance, and certain pollution is arranged.This is not only expensive, and very consuming time.Substitute the gray scale mask version with onesize phase modulator, can greatly reduce cost and save time.
2. the present invention also can be used for high-definition television and compact micro projector etc.These two application are higher than traditional TV and projector efficiency.Adopt the phase-modulation PHASE DISTRIBUTION of the present invention's design, can produce the almost nil high precision image of error.
At last, the above embodiments only are used for illustrating the present invention, and it should not be construed is that protection scope of the present invention is carried out any restriction.And, it will be apparent to those skilled in the art that do not breaking away under above-described embodiment spirit and the principle, the various equivalent variation that above-described embodiment is carried out, modification and in the text not the various improvement of description all within the protection domain of this patent.
Claims (9)
1. method of utilizing the phase modulator output image comprises:
1) determines the initial input light field;
2) current input light field is carried out Fourier transform;
3) with target image amplitude alternative steps 2) result's of Fourier transform amplitude; Described target image is that the original object image is carried out resulting image after the softization processing;
4) to step 3) the result carry out inverse Fourier transform;
5) with step 1) the amplitude component alternative steps 4 of the input light field that draws) result's amplitude, obtain the new input light field for next iteration;
6) repeating step 2) to 5) until satisfy the condition that stops iteration, thus obtain as producing the required phase modulation of target image phase modulator;
7) utilize step 6) drawn phase modulation output reconstructed image.
2. the method for utilizing the 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 the amplitude component through softization processing.
3. the method for utilizing the phase modulator output image according to claim 1 is characterized in that, described step 3) in, described target image is pressed the correction of SIFTA-2 algorithm by the original object image, carries out softization processing again and obtains.
4. the method for utilizing the 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, with the essentially identical Fourior plane light distribution of image output plane signal window size, described initial phase obtains by Ray-tracing Method.
5. the method for utilizing the phase modulator output image according to claim 4 is characterized in that, described Ray-tracing Method comprises the Bryngdahl method, Aleksoff method, Roux method, Romero method, Malyak method or Dresel method.
6. the method for utilizing the 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 compared with target image of Fourier transform results less than predefined threshold value.
7. the method for utilizing the 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 for utilizing the phase modulator output image according to claim 1, it is characterized in that, described step 6) in, after stopping iteration, with current step 4) phase place that obtains deducts the phase place of the input light field of actual measurement, and namely obtaining is to produce the required phase modulation of target image phase modulator.
9. the method for utilizing the phase modulator output image according to claim 1, it is characterized in that, described softization processing comprises: the input light field amplitude component matrix that representative is comprised sudden change respectively up and down about 4 directions move N pixel, then to the summation of resulting 4N image array, thereby obtain input light field distribution of amplitudes after the softization processing; Perhaps obtain the input light field distribution of amplitudes of softization by the point that inserts several gradual changes at the amplitude jump place that inputs light field; Perhaps the input light field amplitude component that comprises sudden change is carried out High frequency filter; Perhaps simulating with corresponding super-Gaussian function exists amplitude jump evenly to input light field.
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