CN102074002B - Method for synthesizing and optimizing kinoform - Google Patents

Abstract

The invention provides a method for synthesizing and optimizing a kinoform, wherein the method is based on a genetic algorithm. The technical scheme provided by the invention comprises the following steps: adding a group of random phase masks to original images; optimizing the masks; and when reaching optimizing conditions,taking the phase mask with minimum cost function as the best mask, and the corresponding kinoform of the best mask as the obtained kinoform. The Kinoforms are indirectly optimized by optimizing the masks. Ihe method, the error of reproduced images is reduced by directly optimizing the random phase masks so as to optimize the Kinoform. In the selection link of the genetic algorithm, an elite retaining method is used to retain excellent solutions of groups and to accelerate the convergence rate, and is easy for realizing. Compared with the traditional optimization method, the method provided by the invention has the advantages of small initial cost function, fast optimizing speed, good optimizing effect and the like.

Description

A kind of kinoform synthesizes optimization method

Technical field

The present invention relates to a kind of kinoform synthetic method, particularly relate to a kind of synthetic optimization method of kinoform that keeps genetic algorithm based on the elite.

Background technology

Kinoform: one type can only be by the wavefront reconstruction element of computing machine generation.Different with other kind computing mechanism holograms is that kinoform is that hypothesis light amplitude in whole record plane is under the condition of constant, only the element of phase information before the marking wave.The great advantage of kinoform is that its diffraction efficiency is high especially, and in the ideal case, kinoform can be used for rebuilding the thing light wave to whole incident lights, so diffraction efficiency can reach 100%.Secondly, the illumination kinoform is had to the single order of diffraction, reproduces single image, does not have conjugate image or spuious image overlay on it.At last, because kinoform is not introduced reference light, needn't consider to separate the problem of reproducing picture.

Genetic algorithm: one type of evolution rule of using for reference organic sphere develops and next randomization searching method, comprises links such as initialization, selection, intersection, variation.Its principal feature is directly structure objects to be operated, and does not have the successional qualification of differentiate and function; Have inherent latent concurrency and good global optimizing ability; Adopt the optimization method of randomization, can obtain and instruct the search volume of optimization automatically, adjust the direction of search adaptively, the rule that need not confirm.These character of genetic algorithm have been widely used in fields such as Combinatorial Optimization, machine learning, signal Processing, adaptive control and artificial life by people.

Kinoform is a kind of computed hologram that can only be produced by computing machine.Kinoform and general hologram different mainly show as following two aspects: (one) holographic technique in the past is to rely on the transmitance of film to change the information of coming recording light, and kinoform only is recorded in the phase information of light wave on the film with relief shape.(2) in the past reconstruction of hologram theory all is to be based upon on the theory of light diffraction basis; And kinoform relies on Fresnel Lenses such; Just through changing the PHASE DISTRIBUTION that optical thickness removes to change the irradiation light wave; Thereby reveal original thing light wave again, so kinoform can be regarded a complex lens by computer manufacture as.

The reproduction process of kinoform is as shown in Figure 1.(μ v) represents kinoform to K, and its reproduced image is that (x, y), size all is a N * N pixel to U.When reproducing, kinoform is placed on the front focal plane, with the directional light irradiation on it, the expression formula of the light wave through kinoform be K (μ, v)=[(μ, v)], wherein (μ v) is the PHASE DISTRIBUTION of kinoform to θ to i θ to exp.In most of application scenarioss, PHASE DISTRIBUTION θ (μ v) need be quantized: θ (μ, v)=2 π (n-1)/L, n=1,2 ..., L.On back focal plane, can obtain the reproduced image of kinoform, U (x y) can be obtained by computes:

$U(x,y)=\frac{1}{N^2}\underset{\mathrm{\μ}=1}{\overset{N}{\mathrm{\Σ}}}\underset{v=1}{\overset{N}{\mathrm{\Σ}}}K(\mathrm{\μ},v)\exp \left[2\mathrm{\πi}\frac{\mathrm{\μx}+\mathrm{vy}}{N}\right]---\left(1\right)$

$=\frac{1}{N^2}\underset{\mathrm{\μ}=1}{\overset{N}{\mathrm{\Σ}}}\underset{v=1}{\overset{N}{\mathrm{\Σ}}}\exp [-2\mathrm{\π\θ}(\mathrm{\μ},v)\frac{\mathrm{\μx}+\mathrm{vy}}{N}]$

Be used for the synthetic method of optimizing kinoform at present and use genetic algorithm mostly.In existing method, all with kinoform as the object of directly optimizing, Fig. 2 has shown a kind of genetic algorithm optimization method of classics, other optimization method is method derivation thus mostly.

In the initialization link, kinoform is encoded as the random phase matrix, representes whole kinoform population with M phasing matrix, and M is the population quantity of genetic algorithm.Each kinoform is the body one by one in the population, and each pixel is a gene of this individuality in the individuality.

Each kinoform can generate a different reproduced image, and reproduced image can be calculated by formula (1).For each reproduced image, utilize cost function to weigh the error of itself and original image.Cost function is more little, and it is good more that it reproduces effect, otherwise, then poor more.A kind of general cost function calculation formula is shown below:

$E=\frac{\underset{x=1}{\overset{N}{\mathrm{\Σ}}}\underset{y=1}{\overset{N}{\mathrm{\Σ}}}{|I_o(x,y)-\mathrm{AI}(x,y)|}^2}{\underset{x=1}{\overset{N}{\mathrm{\Σ}}}\underset{y=1}{\overset{N}{\mathrm{\Σ}}}{\left|I_o(x,y)\right|}^2}---\left(2\right)$

Wherein, and I (x, y) and I _o(x y) be respectively the light distribution of reproduced image and original image, and parameter A is a scale factor, is used for the gross energy of balance reproduced image.

I _o(x，y)＝|U _o(x，y)| ²

I(x，y)＝|U(x，y| ²(3)

$A=\frac{\underset{x=1}{\overset{N}{\mathrm{\Σ}}}\underset{y=1}{\overset{N}{\mathrm{\Σ}}}{I}_o(x,y)}{\underset{x=1}{\overset{N}{\mathrm{\Σ}}}\underset{y=1}{\overset{N}{\mathrm{\Σ}}}I(x,y)}$

Behind the calculation cost function, the size of M kinoform according to cost function sorted.In the selection link of genetic algorithm, the system of selection that can adopt has roulette system of selection, classification system of selection, steady state (SS) system of selection, elitism etc.The selecteed probability of the kinoform that cost function is more little is big more, and the big more abandoned probability of kinoform of cost function is big more.In the intersection link of genetic algorithm, the even number individuality is selected out and is used to produce the son individuality, and it is individual that wherein per two different individualities are selected for two sons.In existing cross method, generate two coordinate points at random, then be the intersection region by the rectangle that this two coordinates determined.Two individual genes that exchange in the intersection region of father, it is individual then to obtain corresponding two sons.In the variation link of genetic algorithm, be applied in certain disturbance through the population after intersecting, be used to keep the diversity of gene.

When optimal conditions did not reach, aforesaid operations was recycled execution.And when optimal conditions is satisfied, then withdrawing from circulation, the minimum individuality of cost function is exactly the kinoform of looking in the population at this moment.

Existing various technology can improve the reproduction quality of kinoform, has been used in the practical application of synthetic kinoform.Yet, utilize in the method that traditional genetic algorithm optimizes kinoform existing, its initial stage convergence is slower, calculates consuming time for a long time, the reproduction weak effect has produced serious restriction to the application of kinoform.Therefore the algorithm of various synthetic optimization kinoforms and then reduction reconstruction error also becomes the focus of research.For the needs of practical application, require optimization method to have good speed of convergence, and can reconstruction error be controlled at a lower scope.

Summary of the invention

The purpose of this invention is to provide that a kind of initial cost function is little, optimal speed is fast, optimize the effective synthetic optimization method of kinoform that keeps genetic algorithm based on the elite.

The present invention is utilized on the image additional random phase mask can balanced this mathematical characteristic of its amplitude versus frequency characte; Proposed a kind of random phase mask, optimized kinoform indirectly thereby change the method for directly optimizing kinoform in the classic method into direct optimization random phase mask.

The classical synthetic optimized Algorithm of the kinoform based on genetic algorithm (other algorithms all are that classical way develops thus at present) as shown in Figure 2, the concrete steps of this classic algorithm are following:

A. in the initialization link, kinoform is encoded as the random phase matrix, representes whole kinoform population with M phasing matrix, and wherein M is the population quantity in the genetic algorithm.Each kinoform is a chromosome in the population, and each pixel is this chromosomal gene in the chromosome;

B. to an above-mentioned M kinoform, calculate its corresponding reproduced image respectively, calculate the cost function of reproduced image again according to formula (2) (3) respectively according to formula (1);

C. in the selection link of genetic algorithm, the size of M chromosome according to cost function sorted successively, adopt certain system of selection to select the superior and eliminate the inferior, the chromosomal viability that cost function is more little is strong more, and the possibility that promptly is retained is big more;

D. in the intersection link of genetic algorithm, the chromosome that picked at random goes out even number matches to it in twos.Each is utilized the two point cross method to chromosome, determine an intersection region, the gene in these two chromosome exchange intersection regions, thus produce new chromosome;

E. in the variation link of genetic algorithm, in whole population, introduce random disturbance, to guarantee the diversity of gene.

When optimal conditions did not reach, aforesaid operations was recycled execution; And when optimal conditions satisfies, then withdrawing from circulation, the minimum chromosome of cost function is exactly the kinoform of being searched in the population at this moment.

Technical scheme provided by the invention is (flow process is referring to Fig. 3) as follows:

Scheme 1: a kind of kinoform synthesizes optimization method, and this method is characterized in that based on genetic algorithm, adds one group of random phase mask to original image; Optimize this mask; When reaching optimal conditions, the phase mask with minimum cost function is best mask, and its corresponding kinoform is the kinoform of being asked.The present invention reaches the purpose of indirect optimization kinoform through the method for optimizing mask.

Scheme 2: as a kind of optimization implementation of scheme 1; It is characterized in that; Said random phase mask is the random phase matrix, representes whole phase mask population with M phasing matrix, and M is the population quantity of genetic algorithm; Each kinoform is a chromosome in the population, and each pixel is this chromosomal gene in the chromosome.

Scheme 3: as a kind of optimization implementation of scheme 1; It is characterized in that; The acquisition methods of kinoform is: M random phase mask is attached to respectively on the original image, through two dimensional discrete Fourier transform, amplitude normalization, phase quantization, thereby obtains M kinoform; To M kinoform after quantizing, calculate its reproduced image and corresponding cost function respectively.Calculate its reproduced image according to formula (1), calculate its corresponding cost function according to formula (2) (3) again.

Scheme 4: a kind of optimization implementation as scheme 3 is characterized in that said phase quantization grade is 16.In phase quantization, for fear of conjugate image, quantification gradation must be greater than 2, and the big more reproduction effect of quantification gradation is good more simultaneously, but existing manufacturing process is difficult to satisfy excessive quantification gradation.The present invention adopts 16 rank quantification gradations, and the existing effect of reproducing preferably can adapt to the existing processes condition again.M kinoform to after quantizing calculates its reproduced image respectively according to formula (1), calculates its corresponding cost function respectively according to formula (2) (3) again.

Scheme 5: as a kind of optimization implementation of scheme 1; It is characterized in that; In the selection link of genetic algorithm, the size of M mask according to cost function sorted successively, utilize the elitism principle to select; (individuals of N≤M/2) is duplicated the minimum N individuals of cost function and is used to keep population quantity to abandon the maximum N of cost function.Compare with other systems of selection, faster based on the system of selection travelling speed of elitism, and can avoid excellent individual to be abandoned, so can accelerate convergence process.

Scheme 6: as a kind of optimization implementation of scheme 1; It is characterized in that; In the intersection link of genetic algorithm, adopt a kind of novel two point cross method (as shown in Figure 4): generate a coordinate points at random, generate the height and the width of intersection region then at random; If the intersection region surpasses the size of mask at random, then utilize the part that periodically will exceed to transfer to corresponding position.Different with traditional cross method, this cross method can be treated all genes in the individuality fully coequally, so can play better intersection effect.

Scheme 7: a kind of optimization implementation as scheme 1 is characterized in that said optimal conditions is that iterations reaches designated value.Beneficial effect of the present invention is following:

1) the present invention is attached to the random phase mask on the original image through direct optimization, reduces the error of reproducing picture, thereby reaches the purpose of optimizing kinoform indirectly;

2) propose to use 16 quantification gradations, the existing effect of reproducing preferably can adapt to the existing processes condition again;

3) the initial random phase mask of utilization makes initial cost function of the present invention much smaller than traditional genetic algorithm, has overcome the slow shortcoming of traditional genetic algorithm initial stage convergence;

4) in the selection link of genetic algorithm, adopt elite's reservation method, it can keep, and population is outstanding to be separated, and can accelerate speed of convergence, and is easy to realize;

5) in the intersection link of genetic algorithm, a kind of periodicity two dimension two point cross method is proposed, it can definitely treat all genes in former generation's chromosome liberally than traditional two point cross method, thus improvement intersection result.

In sum, this method reduces the error of reproducing picture through directly optimizing this random phase mask, thereby reaches the purpose of optimizing kinoform.Compare with traditional optimization that to have an initial cost function little, optimal speed is fast, optimizes advantages such as effective.

Description of drawings

Fig. 1. the reproduction of kinoform.

Fig. 2. classical genetic algorithm optimization method.

Fig. 3. what the present invention proposed keeps the synthetic optimization method of kinoform of genetic algorithm based on the elite.

Fig. 4. based on periodic two point cross method.

Fig. 5. original image.

Fig. 6. the synthetic kinoform that obtains of optimizing of this method.

The convergence process of Fig. 7 .4 kind genetic algorithm, wherein: solid line is classical genetic algorithm, and dotted line is the simulated annealing genetic algorithm, and dotted line adds '+' number and is the layering genetic algorithm, and dotted line adds ' * ' and number is this method.

Fig. 8. (a) reproduced image of classical genetic algorithm, the reproduced image of (b) layering genetic algorithm, (c) reproduced image of simulated annealing genetic algorithm, (d) reproduced image of this method.

Embodiment

With a concrete embodiment the present invention is further specified below:

Adopt Fig. 5 as original image, this bianry image is of a size of 64 * 64.

1) in the initialization link, the stochastic matrix that generates 100 64 * 64 is represented the random phase mask, any point wherein all be uniformly distributed in [0,2 π);

2) these 100 phase masks are attached to respectively on the original image,, thereby obtain 100 kinoforms through two dimensional discrete Fourier transform, amplitude normalization, 16 rank phase quantizations.Calculate 100 reproduced images respectively according to formula (1) again, calculate its corresponding cost function respectively according to formula (2) (3) again;

3) in the selection link of genetic algorithm, the size of 100 phase masks according to cost function sorted successively.Directly abandon 40 maximum chromosomes of cost function, duplicate 40 minimum chromosomes of cost function simultaneously;

4) in the intersection link of genetic algorithm, in 100 phase masks, select 80 at random, these 80 phase masks are matched in twos, thereby obtain 40 pairs.For any a pair of phase mask, confirm the intersection region according to Fig. 4, promptly generate 4 random integers in [1,100], preceding 2 numbers are as the coordinate of the initial pixel of intersection, and back 2 numbers are represented the length and the width of intersection region.This exchanges the part in the intersection region to phase mask, thereby obtains two new phase masks;

5) in the variation link of genetic algorithm, any pixel of arbitrary phase mask all there is 0.7% notion disturbed, interference intensity is 0.1 π.

6) when optimal conditions did not reach, aforesaid operations was recycled execution.And when optimal conditions is satisfied, then withdraw from circulation.The phase mask that has the minimum cost function this moment in the population is best mask, and its corresponding kinoform is the kinoform of being searched for.

To optimize Rule of judgment and be made as iteration 5000 times, the kinoform that then obtains is as shown in Figure 6.And this method and other three kinds of methods convergence process in 5000 iteration is as shown in Figure 7.Fig. 7 shows the initial cost function of this method much smaller than additive method, and on speed of convergence, far surpasses other classic methods.

It is steady basically that optimal conditions is made as convergence process, and the final optimization pass result's of this method that then obtains and other three kinds of methods reproduction is as as shown in Figure 8, and corresponding cost function is as shown in table 1.It is thus clear that the final optimization pass result of this method is better than other classic methods.

The cost function of corresponding reproduced image among table 1. Fig. 8

Based on above some analysis and verify through simulated experiment; The kinoform optimization method that keeps genetic algorithm based on the elite proposed by the invention is in the synthetic Practice of Optimization of Fourier's kinoform; Initial cost function is much smaller than other genetic algorithms; Can just reconstruction error be reduced to 3% less than 1000 iteration, all demonstrate clear superiority in optimal speed and optimization effect.

Claims (7)

1. the synthetic optimization method of kinoform is characterized in that, comprises the steps:

1) in the initialization link, the stochastic matrix that generates 100 64 * 64 is represented the random phase mask, any point wherein all be uniformly distributed in [0,2 π);

2) these 100 phase masks are attached to respectively on the original image,, thereby obtain 100 kinoforms through two dimensional discrete Fourier transform, amplitude normalization, 16 rank phase quantizations; Calculate 100 reproduced images respectively, calculate its corresponding cost function more respectively;

3) in the selection link of genetic algorithm, the size of 100 phase masks according to cost function sorted successively; Directly abandon 40 maximum chromosomes of cost function, duplicate 40 minimum chromosomes of cost function simultaneously;

4) in the intersection link of genetic algorithm, in 100 phase masks, select 80 at random, these 80 phase masks are matched in twos, thereby obtain 40 pairs; For any a pair of phase mask, confirm its intersection region, promptly generate 4 random integers in [1,100], preceding 2 numbers are as the coordinate of the initial pixel of intersection, and back 2 numbers are represented the length and the width of intersection region; This exchanges the part in the intersection region to phase mask, thereby obtains two new phase masks;

5) in the variation link of genetic algorithm, any pixel of arbitrary phase mask all there is 0.7% notion disturbed, interference intensity is 0.1 π;

6) when optimal conditions did not reach, aforesaid operations was recycled execution; And when optimal conditions is satisfied, then withdraw from circulation; The phase mask that has the minimum cost function this moment in the population is best mask, and its corresponding kinoform is the kinoform of being searched for, and will optimize Rule of judgment to be made as iteration 5000 times, the kinoform that then obtains.

2. kinoform as claimed in claim 1 synthesizes optimization method, it is characterized in that, said random phase mask is the random phase matrix, representes whole phase mask population with M phasing matrix.

3. kinoform as claimed in claim 1 synthesizes optimization method; It is characterized in that; The acquisition methods of kinoform is: M random phase mask is attached to respectively on the original image, through two dimensional discrete Fourier transform, amplitude normalization, phase quantization, thereby obtains M kinoform; To M kinoform after quantizing, calculate its reproduced image and corresponding cost function respectively.

4. kinoform as claimed in claim 3 synthesizes optimization method, it is characterized in that, said phase quantization grade is 16.

5. kinoform as claimed in claim 1 synthesizes optimization method; It is characterized in that; In the selection link of genetic algorithm, the size of M mask according to cost function sorted successively, utilize the elitism principle to select; Abandon the maximum N individuals of cost function, duplicate the minimum N individuals of cost function and be used to keep population quantity.

6. kinoform as claimed in claim 1 synthesizes optimization method; It is characterized in that; In the intersection link of genetic algorithm, adopt the two point cross method: generate a coordinate points at random, generate the height and the width of intersection region then at random; If the intersection region surpasses the size of mask at random, then utilize the part that periodically will exceed to transfer to corresponding position.

7. kinoform as claimed in claim 1 synthesizes optimization method, it is characterized in that, said optimal conditions is that iterations reaches designated value.

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