CN111127338B - Automatic aberration correction calculation method based on image sharpness evaluation optimization - Google Patents

Abstract

The invention discloses a method for automatically correcting computed aberration based on image sharpness evaluation optimization, which comprises the following steps: firstly, establishing an aberration correction mathematical model based on image definition evaluation optimization; then establishing a phase filter mathematical model based on image clear evaluation optimization; then solving the aberration correction coefficient value by using the aberration calculation BPSO algorithm: the BPSO algorithm comprises a back propagation optimization algorithm and a particle swarm random optimization algorithm, and the aberration correction coefficient is utilized to solve a clear image after aberration correction. The automatic aberration calculation correction method based on the image definition evaluation optimization has the advantages that the evaluation index can be flexibly selected, the automatic aberration calculation correction is rapidly realized, and the correction result accuracy is high.

Description

Automatic correction method for calculating aberration based on image sharpness evaluation optimization

Technical Field

The invention relates to the field of optical imaging, in particular to a method for calculating automatic aberration correction based on image definition evaluation optimization.

Background

With the technological progress, biomedical imaging techniques, such as ultrasonic imaging, X-ray imaging, CT, and magnetic resonance imaging, play an important role in the research of bioscience, the diagnosis of medical diseases, and the like. Optical Coherence Tomography (OCT) is a new biomedical imaging technology in the last 90 years, which has the characteristics of noninvasive, high resolution and fast imaging on biological samples, and has been widely favored.

However, when the imaging system has aberrations, the impulse response of the system is blurred: the peak value decreases and the main lobe width increases, thereby generating a blurred image with reduced sharpness and contrast. In order to solve this problem, static correction of aberrations can be achieved by appropriate optical design or a complicated lens group, but this method cannot flexibly correct aberrations at all imaging depths, and cannot satisfy adaptability to aberration correction specific to a sample for tomographic optical imaging. While the conventional Hardware-based Adaptive Optics (HAO) provides a means for correcting these aberrations by physically sensing and modifying the wavefront using a wavefront sensor or a spatial light modulator, etc., the HAO method generally has a complex optical structure and requires expensive components; some foreign researchers are dedicated to research different aberration correction mathematical models, wherein the mathematical models mainly include Digital Adaptive Optics (DAO) based on sub-apertures, which perform high-precision aberration correction on wavefronts by partitioning, but the sub-apertures are difficult to splice, the calculation time cost is huge, and images cannot be processed efficiently and quickly; while the mainstream Interference Synthetic Aperture Microscopy (ISAM) corrects the defocus amount by using a method of interpolation resampling in a wave number range, but the ISAM cannot eliminate other aberrations, so that the application of the ISAM is limited to a certain extent; based on a phase correction Model (FM) of an FM (Forward Model, FM), multiplying a defocusing phase correction factor calculated by using parameters of an imaging system to a two-dimensional Fourier equation of a detected signal to correct defocusing aberration, but the specific parameters of the imaging system need to be obtained, so that the method is not suitable for aberration blind correction and cannot eliminate other aberrations; the method can realize automatic correction of image aberration, does not need to acquire specific parameters of an imaging system, has a wide application range, can provide a substitute method for hardware-based Adaptive Optics, provides flexibility of data post-processing, and greatly saves time cost and hardware overhead.

Disclosure of Invention

The invention aims to provide an automatic aberration calculation correction method based on image definition evaluation optimization, which can flexibly select evaluation indexes, realize quick aberration calculation and automatic correction and have high correction result accuracy.

The technical solution for realizing the purpose of the invention is as follows: an automatic correction method for calculating aberration based on image definition evaluation optimization comprises the following steps:

step 1, establishing an aberration correction mathematical model based on image definition evaluation optimization:

an aberration-to-be-corrected image g (x, y) whose aberration is to be corrected is selected, and an aberration correction process therefor is modeled as a phase filtering process of a fourier domain of the aberration-to-be-corrected image g (x, y), that is

h(x,y)＝ifft(G(u,v)e ^-jφ(u,v) ) (1)

Wherein ifft is inverse Fourier transform, G (u, v) is an aberration image to be corrected in a Fourier domain, h (x, y) is a corrected clear image, and phi (u, v) is a phase filter; j is an imaginary part;

step 2, establishing a phase filter mathematical model based on image clear evaluation optimization:

determining the type of image aberration, selecting an aberration correction basis polynomial

Defining aberration correction coefficient values, thereby establishing a mathematical model of the phase filter, i.e.

Wherein the number of different aberration type termsk＝1,...,K，c _k Is a value of a coefficient of the corresponding aberration;

step 3, solving the aberration correction optimal coefficient value by using a calculation aberration BPSO algorithm:

3-1, obtaining an optimal coefficient value of back propagation optimization by using back propagation optimization in the aberration calculation BPSO algorithm, introducing the aberration image G (u, v) to be corrected in the Fourier domain into a back propagation optimization phase filter mask _1, and searching a polynomial of a correction base of the aberration image to be corrected by adopting the back propagation optimization in the aberration calculation BPSO algorithm

The back propagation aberration correction optimum coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And turning to the step 3-2;

step 3-2, taking the clear image h _1(x, y) after the back propagation optimization as an aberration image to be corrected, introducing a particle swarm random optimization phase filter mask _2, and searching a polynomial of an aberration correction base of the aberration image to be corrected by adopting a particle swarm random optimization algorithm in a calculation aberration BPSO algorithm

The particle swarm random optimization aberration correction optimal coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Turning to step 4;

step 4, correcting the optimal coefficient value c _1 ═ c _1 using the aberration ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after correcting the aberration.

Compared with the prior art, the invention has the remarkable advantages that:

(1) compared with other automatic correction methods for calculating aberration, the method can flexibly select clear evaluation indexes of the image, and different image processing requirements are met due to the diversity of the evaluation indexes; starting from a plurality of evaluation indexes, the image aberration correction accuracy can be improved.

(2) The aberration calculation automatic correction method based on the image definition evaluation optimization can realize quick aberration calculation automatic correction, the back propagation optimization algorithm in the BPSO algorithm realizes coarse correction of an aberration image to be corrected, a local optimal solution can be quickly found, the cycle iteration times of the particle swarm random optimization algorithm are reduced, and the time consumption of the algorithm is greatly shortened.

(3) The computed aberration automatic correction method based on image definition evaluation optimization has high correction result accuracy, the particle swarm random optimization algorithm in the BPSO algorithm realizes fine correction of an aberration image to be corrected, a local optimal solution can be skipped, a global optimal solution is found, and the aberration correction result accuracy of the image to be corrected is improved.

Drawings

FIG. 1 is a flowchart of an automatic aberration correction method based on image sharpness evaluation optimization according to the present invention.

Fig. 2 is a conceptual diagram of an algorithm for calculating the aberration BPSO.

Fig. 3 is a flowchart of a back propagation optimization algorithm in the algorithm for calculating aberration BPSO.

Fig. 4 is a flowchart of a random optimization algorithm for calculating the particle group in the aberration BPSO algorithm.

FIG. 5 is a simulation experiment chart of an aberration image to be corrected in a simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization.

FIG. 6 is a diagram of a simulation experiment of a standard clear image in a simulation experiment of an automatic aberration correction method based on clear evaluation optimization according to the present invention.

Fig. 7 is a simulation experiment diagram of a standard phase filter in a simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization.

Fig. 8 is a simulation experiment diagram of a back propagation optimized sharp image h _1(x, y) in a simulation experiment of the calculated aberration automatic correction method based on the sharp evaluation optimization.

Fig. 9 is a simulation experiment diagram of a backward propagation optimized phase filter mask _1 in a simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization according to the present invention.

Fig. 10 is a simulation experiment diagram of the evaluation function S _1 changing with the increase of the number of loop iterations in the back propagation optimization in the simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization according to the present invention.

Fig. 11 is a simulation experiment diagram of a clear image h _2(x, y) after random optimization of a particle group in a simulation experiment of the calculated aberration automatic correction method based on clear evaluation optimization according to the present invention.

Fig. 12 is a simulation experiment diagram of a random optimization phase filter mask _2 of a particle group in a simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization according to the present invention.

Fig. 13 is a simulation experiment diagram showing that the evaluation function S _2 changes with the increase of the number of loop iterations in the random optimization of the particle group in the simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization according to the present invention.

Fig. 14 is a simulation experiment diagram of a clear image h (x, y) after correction by a BPSO algorithm in a simulation experiment of the calculated aberration automatic correction method based on clear evaluation optimization according to the present invention.

FIG. 15 is a simulation experiment diagram of the BPSO algorithm corrected phase filter phi (u, v) in the simulation experiment of the calculated aberration automatic correction method based on the clear evaluation optimization.

FIG. 16 is a graph showing the recovery residual error of the BPSO algorithm corrected phase filter φ (u, v) with respect to the standard phase filter in the simulation experiment of the calculated aberration auto-correction method based on the sharpness evaluation optimization according to the present invention.

Detailed Description

In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, embodiments accompanying figures of the present invention are described in detail below.

With reference to fig. 1, a method for calculating an automatic aberration correction based on image sharpness evaluation optimization includes the following steps:

step 1, establishing an aberration correction mathematical model based on image definition evaluation optimization:

an aberration-to-be-corrected image g (x, y) for which aberration is to be corrected is selected, and aberration correction processing therefor is modeled as phase filtering processing of the fourier domain of the aberration-to-be-corrected image g (x, y), that is

h(x,y)＝ifft(G(u,v)e ^-jφ(u,v) ) (1)

Wherein ifft is inverse Fourier transform, G (u, v) is an aberration image to be corrected in a Fourier domain, h (x, y) is a corrected clear image, and phi (u, v) is a phase filter; j is an imaginary part;

step 2, establishing a phase filter mathematical model based on image clear evaluation optimization:

determining the type of image aberration, selecting an aberration correction basis polynomial

Defining aberration correction coefficient values, thereby establishing a mathematical model of the phase filter, i.e.

Wherein, the term number K of different aberration types is 1 _k Is a coefficient value of the corresponding aberration;

aberration correcting base polynomial

Is a Zernike circular domain orthogonal polynomial; the selection of terms of different aberration types corrects four aberrations, namely defocus, astigmatism, coma and spherical aberration.

And 3, solving the aberration correction optimal coefficient value by combining the conceptual diagram of the aberration calculation BPSO algorithm shown in the figure 2:

step 3-1, combining the flowchart of the back propagation optimization algorithm in the aberration calculation BPSO algorithm shown in FIG. 3, obtaining the back propagation optimization optimal coefficient value by using the back propagation optimization in the aberration calculation BPSO algorithm, introducing the aberration image G (u, v) to be corrected in the Fourier domain into a back propagation optimization phase filter mask _1, searching the aberration correction base polynomial of the aberration image to be corrected by using the back propagation optimization in the aberration calculation BPSO algorithm

Is most effective in correcting back-propagating aberrationsThe best coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T The method comprises the following steps:

step 3-1-1, defining coefficient forward deviation weight eta ⁺ Coefficient inverse offset weight η ═ 0.5 ^- Coefficient forward shift maximum boundary value Δ of 1.2 _max Coefficient reverse deviation minimum boundary value delta of 50 _min 0.001, aberration coefficient offset

The evaluation function S _1 is set as the image definition, and the specific expression is as follows:

wherein h is ^* (x, y) is a conjugate matrix of h (x, y).

Further, the maximum number of loop iterations t _1 _max The value is taken for 500 times, and the step 3-1-2 is carried out.

Step 3-1-2, optimizing aberration correction coefficient value c _1 ═ c _1 using back propagation ₁ ,c_1 ₂ ,...,c_1 _K ] ^T Selecting aberration correction coefficient c _1 in the following loop iteration _k The specific expression is as follows:

for k＝1:length(c_1)

c_1 _k

do the circle

end (3)

selecting aberration correction coefficient c _1 _k If K meets the above conditions, entering loop iteration, and going to step 3-1-3; otherwise, turning to the step 3-1-10;

step 3-1-3, according to the loop iteration time t _1 and the maximum loop iteration time t _1 _max Relation, judging the iteration condition of the loop when

t_1≥t_1 _max (4)

The loop iteration is stopped to obtain the final selected aberration correction coefficient c _1 _k Backward propagation optimized phase filtermask _1 and clear image h _1(x, y) after back propagation optimization, the step 3-1-2 is carried out, and the aberration correction coefficient c _1 updated in the next loop iteration is selected _k+1 (ii) a Otherwise, the step 3-1-4 is carried out, and the aberration correction coefficient c _1 is continuously updated in a loop iteration mode _k ；

Step 3-1-4, using the aberration correction coefficient c _1 selected in step 3-1-2 _k And aberration coefficient offset

Calculating an evaluation function S _1 to optimize an aberration correction coefficient c _1 ═ c _1 for back propagation ₁ ,c_1 ₂ ,...,c_1 _K ] ^T Partial derivatives of

The specific expression is as follows:

recording partial derivatives

Turning to the step 3-1-5;

step 3-1-5, utilizing the forward deviation weight eta ⁺ Coefficient reverse bias weight η ^- Coefficient forward deviation maximum boundary value delta _max Coefficient is reversely shifted by a minimum boundary value delta _min Amount of deviation of each aberration coefficient

And

computing

Update value that changes as the number of loop iterations t _1 increases

The specific expression is as follows:

turning to the step 3-1-6;

step 3-1 to 6, utilizing

And

updating the selected aberration correction coefficient c _1 _k The specific expression is as follows:

records the updated selected aberration correction coefficient c _1 _k Turning to the step 3-1-7;

step 3-1-7, utilizing the selected aberration correction coefficient c _1 after updating _k And aberration correcting base polynomial

Establishing a back propagation optimization phase filter mask _1, wherein the specific expression is as follows:

recording the updated back propagation optimized phase filter mask _1, and turning to the step 3-1-8;

step 3-1-8, the image g (x, y) of the aberration to be corrected is optimized by using the back propagation optimization phase filter mask _1 obtained by updating in the step 3-1-7, and a clear image h _1(x, y) after back propagation optimization is obtained, wherein the specific expression is as follows:

h_1(x,y)＝ifft{fft{g(x,y)}.*exp(-1*j*mask_1)} (9)

wherein fft is aberration diagram to be correctedThe image g (x, y) is subjected to two-dimensional Fourier transform processing, ift is two-dimensional inverse Fourier transform, and the selected aberration correction coefficient c _1 updated along with the increase of the number t of loop iterations is recorded _k And the phase filter mask _1 is optimized through back propagation, and the step 3-1-9 is carried out;

step 3-1-9, recording the updated partial derivative

Specific numerical value and sign of (2), and aberration coefficient offset amount

Selected aberration correction coefficient c _1 _k And the backward propagation optimization phase filter mask _1 and the backward propagation optimization back clear image h _1(x, y) are subjected to the next loop iteration:

t_1＝t_1+1 (10)

and (4) transferring to the step 3-1-3.

Step 3-1-10, ending the back propagation optimization loop iteration to obtain the final back propagation aberration correction coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And the clear image h _1(x, y) after the back propagation optimization and the back propagation optimization phase filter mask _1 are switched to the step 3-2.

Step 3-2, combining the flow chart of the particle group random optimization algorithm in the aberration calculation BPSO algorithm shown in FIG. 4, taking the clear image h _1(x, y) after back propagation optimization as an aberration image to be corrected, introducing a particle group random optimization phase filter mask _2, and searching a polynomial of the aberration correction base of the aberration image to be corrected by adopting the particle group random optimization algorithm in the aberration calculation BPSO algorithm

The particle swarm random optimization aberration correction optimal coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T The specific algorithm steps are as follows:

step 3-2-1, taking the clear image h _1(x, y) subjected to back propagation optimization as an aberration image to be corrected, initially defining a K-dimensional coefficient search space, and definingMaximum number of particle swarm loop iterations t _2 _max ，t_2 _max The particles form a set, wherein the t _2 th particle represents a vector with K dimensions, c _2 ^(t_2) Represents the value of the t _2 th particle and represents the random optimization aberration correction coefficient value of the particle swarm

c_2 ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) I.e. by

c_2 ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ),t_2＝1,2,...,t_2 _max (12)

T _2 nd particle c _2 ^(t_2) The motion value of (2) is defined as a K-dimensional vector called the update step V ^(t_2) ，

V ^(t_2) ＝(V ₁ ^(t_2) ,V ₂ ^(t_2) ,...,V _K ^(t_2) ),t_2＝1,2,...,t_2 _max (13)

Turning to the step 3-2-2;

3-2-2, calculating the fitness F of each particle in the particle swarm by using the evaluation function S _2 as an evaluation index, and turning to the step 3-2-3;

step 3-2-3, correcting the base polynomial to prevent aberration

Coupling correction occurs between the first particle and the second particle, the t _2 th particle c _2 generates the individual optimum and the global optimum of the particle swarm random optimization aberration correction coefficient according to the fitness ^(t_2) The optimum coefficient value searched by using the evaluation function S _2 as the evaluation index is called an individual optimum solution E _best ，

The optimal coefficient value searched by the whole particle swarm by taking the evaluation function S _2 as an evaluation index is called as a global optimal solution G _best ，

The step 3-2-4 is changed;

step 3-2-4, utilizing E _best And G _best Updating step size V ^(t_2) And randomly optimizing aberration correction coefficient value c _2 by particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) )，

V ^(t-2) ＝W*V ^(t-2) +C ₁ *R ₁ *(E _best -c_2 ^(t-2) )+C ₂ *R ₂ *(G _best -c_2 ^(t-2) ) (16)

c_2 ^(t-2) ＝c_2 ^(t-2) +V ^(t-2) (17)

Wherein, C ₁ Is an acceleration constant, controls the individual optimal solution E _best For update step size V ^(t_2) Has an influence of 1.5, C ₂ Is a learning rate, embodies a global optimal solution G _best For update step size V ^(t_2) With a value of 1, W is an inertia constant with a value of 1, R ₁ 、R ₂ Is [0,1 ]]The random number in the range is transferred to the step 3-2-5;

step 3-2-5, utilizing the updated step size V ^(t_2) And randomly optimizing aberration correction coefficient value c _2 by particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) Calculating the fitness F of the updated particles by taking the evaluation function S _2 as an evaluation index, and turning to the step 3-2-6;

step 3-2-6, randomly optimizing aberration correction coefficient value c _2 by using updated particle fitness F and updated particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) To update the individual optimal solution E _best And global optimal solution G _best And turning to the step 3-2-7;

step 3-2-7, judging the iteration time t _2 and the maximum particle swarm loop iteration time t _2 _max The relationship is such that,when the temperature is higher than the set temperature

t_2＞t_2 _max (18)

Switching to the step 3-2-8, otherwise, switching to the step 3-2-4;

step 3-2-8, ending the particle swarm random optimization loop iteration to obtain the particle swarm random optimization aberration correction optimal coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T The aberration correction optimum coefficient value c _2 is randomly optimized by the particle swarm [ c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And aberration correcting base polynomial

Obtaining a particle swarm random optimization phase filter mask _2,

and (3) optimizing the back-propagation optimized clear image h _1(x, y) in the step 3-1-9 by using the particle swarm random optimization phase filter mask _2 to obtain the particle swarm random optimized clear image h _2(x, y), wherein the specific expression is as follows:

h_2(x,y)＝ifft{fft{h_1(x,y)}.*exp(-1*j*mask_2)} (20)

and fft is to perform two-dimensional Fourier transform processing on the clear image h _1(x, y) subjected to the inverse propagation optimization, ifft is to perform two-dimensional inverse Fourier transform, and the step 4 is carried out.

In the step 3-2-2, the evaluation function S _2 is set as an image information entropy, and a specific expression is as follows:

in the step 3-2-2, the fitness F of the particle is calculated by taking the evaluation function S _2 as an evaluation index, and the specific expression is as follows:

F＝S_2 (22)

using aberration correction optimum coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c \u2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after correcting the aberration, which is concretely as follows:

using the back propagation optimum aberration correction coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And randomly optimizing the aberration correction by the particle swarm to obtain the optimal aberration correction coefficient c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Solving aberration correction coefficient value c:

c＝c_1+c_2＝[c_1 ₁ +c_2 ₁ ,c_1 ₂ +c_2 ₂ ,...,c_1 _K +c_2 _K ] ^T (23)

and (3) solving the phase filter phi (u, v) by utilizing a back propagation optimization phase filter mask _1 and a particle swarm random optimization phase filter mask _2, wherein the specific expression is as follows:

φ(u,v)＝mask_1+mask_2 (24)

solving the corrected clear image h (x, y) by utilizing the back propagation optimized clear image h _1(x, y) and the particle swarm random optimized clear image h _2(x, y), wherein the specific expression is as follows:

h(x,y)＝h_2(x,y) (25)

and (5) turning to step 4.

Step 4, correcting the optimal coefficient value c _1 ═ c _1 using the aberration ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after correcting the aberration.

Compared with other automatic correction methods for calculating aberration, the automatic correction method for calculating aberration based on image definition evaluation optimization can flexibly select image definition evaluation indexes, meets different image processing requirements due to the diversity of the evaluation indexes, and can improve the accuracy of image aberration correction starting from a plurality of evaluation indexes; the aberration calculation automatic correction method based on the image definition evaluation optimization can realize quick aberration calculation automatic correction, the back propagation optimization algorithm in the BPSO algorithm realizes coarse correction of an aberration image to be corrected, a local optimal solution can be quickly found, the cycle iteration times of the particle swarm random optimization algorithm are reduced, and the time consumption of the algorithm is greatly shortened; the computed aberration automatic correction method based on image definition evaluation optimization has high correction result accuracy, the particle swarm random optimization algorithm in the BPSO algorithm realizes fine correction of an aberration image to be corrected, a local optimal solution can be skipped, a global optimal solution is found, and the aberration correction result accuracy of the image to be corrected is improved.

Example 1

With reference to fig. 1, an algorithm for calculating aberration automatic correction based on image sharpness evaluation optimization specifically includes the following steps:

step 1, establishing an aberration correction mathematical model based on image definition evaluation optimization:

the aberration-to-be-corrected image g (x, y) for which aberration is to be corrected is selected, and as shown in fig. 5, aberration correction processing thereon is modeled as phase filtering processing in the fourier domain of the aberration-to-be-corrected image g (x, y), that is, processing for phase filtering in the fourier domain

h(x,y)＝ifft(G(u,v)e ^-jφ(u,v) ) (1)

Wherein ifft is inverse Fourier transform, G (u, v) is an aberration image to be corrected in a Fourier domain, h (x, y) is a corrected clear image, and phi (u, v) is a phase filter; j is an imaginary part;

step 2, establishing a phase filter mathematical model based on image clear evaluation optimization:

determining the type of image aberration, selecting an aberration correction basis polynomial

Defining aberration correction coefficient values, thereby establishing a mathematical model of the phase filter, i.e.

Wherein, the term number K of different aberration types is 1 _k Is a value of a coefficient of the corresponding aberration;

and 3, solving the aberration correction optimal coefficient value by combining the conceptual diagram of the aberration calculation BPSO algorithm shown in the figure 2:

step 3-1, combining the flowchart of the back propagation optimization algorithm in the aberration calculation BPSO algorithm shown in fig. 3, obtaining the back propagation optimization optimal coefficient value by using the back propagation optimization in the aberration calculation BPSO algorithm, introducing the aberration image G (u, v) to be corrected in the Fourier domain into a back propagation optimization phase filter mask _1, and searching the aberration correction base polynomial of the aberration image to be corrected by using the back propagation optimization in the aberration calculation BPSO algorithm

Is corrected by the back propagation aberration with the optimum coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And turning to the step 3-2;

step 3-2, combining the flow chart of the particle group random optimization algorithm in the aberration calculation BPSO algorithm shown in FIG. 4, taking the clear image h _1(x, y) after back propagation optimization as an aberration image to be corrected, introducing a particle group random optimization phase filter mask _2, and searching a polynomial of the aberration correction base of the aberration image to be corrected by adopting the particle group random optimization algorithm in the aberration calculation BPSO algorithm

The particle swarm randomly optimizes the optimal aberration correction coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Turning to step 4;

step 4, correcting the optimum coefficient value c _1 by using the aberration [ c _1 ] ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after the image difference is corrected.

In the step 2, the aberration is corrected by the base polynomial

Is a Zernike circular domain orthogonal polynomial; the selection of terms of different aberration types corrects four aberrations, namely defocus, astigmatism, coma and spherical aberration.

Step 3-1, the concrete steps are as follows:

step 3-1-1, defining coefficient forward offset weightη ⁺ Coefficient inverse offset weight η ═ 0.5 ^- Coefficient forward shift maximum boundary value Δ of 1.2 _max Coefficient reverse deviation minimum boundary value delta of 50 _min 0.001, aberration coefficient offset

Turning to the step 3-1-2;

step 3-1-2, optimizing aberration correction coefficient value c _1 ═ c _1 using back propagation ₁ ,c_1 ₂ ,...,c_1 _K ] ^T Selecting aberration correction coefficient c _1 in the following loop iteration _k The specific expression is as follows:

for k＝1:length(c_1)

c_1 _k

do the circle

end (3)

selecting aberration correction coefficient c _1 _k If K meets the above conditions, entering loop iteration, and going to step 3-1-3; otherwise, turning to the step 3-1-10;

step 3-1-3, according to the loop iteration time t _1 and the maximum loop iteration time t _1 _max Relation, judging the iteration condition of the loop when

t_1≥t_1 _max (4)

The loop iteration is stopped to obtain the final selected aberration correction coefficient c _1 _k The backward propagation optimization phase filter mask _1 and the backward propagation optimized clear image h _1(x, y) are switched to the step 3-1-2, and the aberration correction coefficient c _1 updated in the next loop iteration is selected _k+1 (ii) a Otherwise, the step 3-1-4 is carried out, and the aberration correction coefficient c _1 is continuously updated in a loop iteration mode _k ；

Step 3-1-4, using the aberration correction coefficient c _1 selected in step 3-1-2 _k And aberration coefficient offset

Calculating an evaluation function S _1 to optimize an aberration correction coefficient c _1 ═ c _1 for back propagation ₁ ,c_1 ₂ ,...,c_1 _K ] ^T Partial derivative of (2)

The specific expression is as follows:

recording partial derivatives

Turning to the step 3-1-5;

step 3-1-5, utilizing the forward deviation weight eta ⁺ Coefficient reverse bias weight η ^- Coefficient forward deviation maximum boundary value delta _max Coefficient reverse deviation minimum boundary value delta _min Amount of deviation of each aberration coefficient

And

calculating out

Update value that changes as the number of loop iterations t _1 increases

The specific expression is as follows:

turning to the step 3-1-6;

step 3-1-6, utilizing

And

updating the selected aberration correction coefficient c _1 _k In particularThe expression is as follows:

records the updated selected aberration correction coefficient c _1 _k And turning to the step 3-1-7;

step 3-1-7, utilizing the selected aberration correction coefficient c _1 after updating _k And aberration correcting base polynomial

Establishing a back propagation optimization phase filter mask _1, wherein the specific expression is as follows:

recording the updated back propagation optimized phase filter mask _1, and turning to the step 3-1-8;

step 3-1-8, optimizing the aberration image g (x, y) to be corrected by using the back propagation optimized phase filter mask _1 obtained by updating in step 3-1-7 to obtain a back propagation optimized clear image h _1(x, y), wherein the specific expression is as follows:

h_1(x,y)＝ifft{fft{g(x,y)}.*exp(-1*j*mask_1)} (9)

wherein fft is two-dimensional Fourier transform processing of the aberration image g (x, y) to be corrected, ifft is two-dimensional inverse Fourier transform, and records the selected aberration correction coefficient c _1 updated along with the increase of the cycle iteration number t _k And the phase filter mask _1 is optimized through back propagation, and the step 3-1-9 is carried out;

step 3-1-9, recording the updated partial derivative

Specific numerical value and sign of (1), aberration coefficient offset amount

Selected aberration correction coefficient c _1 _k And reversely transmitAnd (3) broadcasting an optimized phase filter mask _1 and a back propagation optimized clear image h _1(x, y), and performing the next loop iteration:

t_1＝t_1+1 (10)

turning to the step 3-1-3;

step 3-1-10, ending the back propagation optimization loop iteration to obtain the final back propagation aberration correction coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And the back propagation optimized clear image h _1(x, y) and the back propagation optimized phase filter mask _1 are switched to step 3-2 as shown in fig. 8-10.

In the step 3-1-1, the evaluation function S _1 is set to be the image definition, and the specific expression is as follows:

wherein h is ^* (x, y) is the conjugate matrix of h (x, y).

In the step 3-1-1, the maximum number of loop iterations t _1 _max The value was 500 times.

Step 3-2, taking the clear image h _1(x, y) after the back propagation optimization as an aberration image to be corrected, introducing a particle swarm random optimization phase filter mask _2, adopting a particle swarm random optimization algorithm in a computed aberration BPSO algorithm, and searching for an aberration correction base polynomial of the aberration image to be corrected

The particle swarm randomly optimizes the optimal aberration correction coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T The specific algorithm comprises the following steps:

step 3-2-1, taking the clear image h _1(x, y) subjected to back propagation optimization as an aberration image to be corrected, initially defining a K-dimensional coefficient search space, and defining the maximum number of particle swarm loop iterations t _2 _max ，t_2 _max The particles form a set, wherein the t _2 th particle represents a vector with K dimensions, c _2 ^(t_2) Represents the value of the t _2 particle and represents the random optimization of the particle swarmAberration correction coefficient value c _2 ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) I.e. by

c_2 ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ),t_2＝1,2,...,t_2 _max (12)

T _2 nd particle c _2 ^(t_2) The moving value of (2) is defined as a K-dimensional vector called as an updating step V ^(t_2) ，

Turning to the step 3-2-2;

3-2-2, calculating the fitness F of each particle in the particle swarm by using the evaluation function S _2 as an evaluation index, and turning to the step 3-2-3;

step 3-2-3, correcting the base polynomial to prevent aberration

Coupling correction occurs between the first particle and the second particle, the t _2 th particle c _2 generates the individual optimum and the global optimum of the particle swarm random optimization aberration correction coefficient according to the fitness ^(t_2) The optimum coefficient value searched by using the evaluation function S _2 as the evaluation index is called an individual optimum solution E _best ，

And the optimal coefficient value searched by the whole particle swarm by taking the evaluation function S _2 as an evaluation index is called as a global optimal solution G _best ，

The step 3-2-4 is changed;

step 3-2-4, utilizing E _best And G _best Update the step size V ^(t_2) And randomly optimizing aberration correction coefficient value c _2 by particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) )，

V ^(t-2) ＝W*V ^(t-2) +C ₁ *R ₁ *(E _best -c_2 ^(t-2) )+C ₂ *R ₂ *(G _best -c_2 ^(t-2) ) (16)

c_2 ^(t-2) ＝c_2 ^(t-2) +V ^(t-2) (17)

Wherein, C ₁ Is an acceleration constant, controls the individual optimal solution E _best For update step size V ^(t_2) Has an influence of 1.5, C ₂ Is a learning rate and embodies a global optimal solution G _best For update step size V ^(t_2) With a value of 1, W is an inertia constant value of 1, R is a value of 1 ₁ 、R ₂ Is [0,1 ]]The random number in the range is transferred to the step 3-2-5;

step 3-2-5, utilizing the updated step length V ^(t_2) And randomly optimizing aberration correction coefficient value c _2 by particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) Calculating the fitness F of the updated particles by taking the evaluation function S _2 as an evaluation index, and turning to the step 3-2-6;

step 3-2-6, randomly optimizing aberration correction coefficient value c _2 by using updated particle fitness F and updated particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) To update the individual optimal solution E _best And global optimal solution G _best And turning to the step 3-2-7;

step 3-2-7, judging the iteration times t _2 and the maximum particle swarm cyclic iteration times t _2 _max Relationship when

t_2＞t_2 _max (18)

Switching to the step 3-2-8, otherwise, switching to the step 3-2-4;

step 3-2-8, ending the random optimization loop iteration of the particle swarm to obtain the particle swarmRandomly optimizing aberration correction optimum coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T As shown in fig. 13, the evaluation function S _2 is changed such that the optimum aberration correction coefficient value c _2 is [ c _2 ] by the particle swarm optimization ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And aberration correcting base polynomial

Obtaining a particle swarm random optimization phase filter mask _2 as shown in FIG. 12

Optimizing the post-optimization clear image h _1(x, y) in the step 3-1-9 by using the particle swarm random optimization phase filter mask _2 to obtain the post-particle swarm random optimization clear image h _2(x, y), as shown in fig. 11, the specific expression is as follows:

h_2(x,y)＝ifft{fft{h_1(x,y)}.*exp(-1*j*mask_2)} (20)

and fft is to perform two-dimensional Fourier transform processing on the clear image h _1(x, y) subjected to the inverse propagation optimization, ifft is to perform two-dimensional inverse Fourier transform, and the step 4 is carried out.

In the step 3-2-2, the evaluation function S _2 is set as an image information entropy, and a specific expression is as follows:

in the step 3-2-2, the fitness F of the particle is calculated by taking the evaluation function S _2 as an evaluation index, and the specific expression is as follows:

F＝S_2 (22)

using aberration correction optimum coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after the image difference is corrected, which comprises the following steps:

optimum aberration correction coefficient using back propagationThe value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And randomly optimizing the aberration correction by the particle swarm to obtain the optimal aberration correction coefficient c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Solving aberration correction coefficient value c:

c＝c_1+c_2＝[c_1 ₁ +c_2 ₁ ,c_1 ₂ +c_2 ₂ ,...,c_1 _K +c_2 _K ] ^T (23)

and (3) solving the phase filter phi (u, v) by utilizing a back propagation optimization phase filter mask _1 and a particle swarm random optimization phase filter mask _2, wherein the specific expression is as follows:

φ(u,v)＝mask_1+mask_2 (24)

solving the corrected clear image h (x, y) by using the back propagation optimized clear image h _1(x, y) and the particle swarm random optimized clear image h _2(x, y), as shown in fig. 14, the specific expression is as follows:

h(x,y)＝h_2(x,y) (25)。

in this embodiment 1, through a series of measures, automatic aberration correction is performed on an aberration image to be corrected, which has an aberration, to obtain a corrected sharp image, and to verify a correction result, as shown in fig. 7 and 14, the corrected sharp image is a standard sharp image and a BPSO algorithm-corrected sharp image, as shown in fig. 6 and 15, the corrected sharp image is a standard phase filter and a BPSO algorithm-corrected phase filter, as shown in fig. 16, a BPSO algorithm-corrected phase filter restored residual image is shown, and an RMS (root mean square) value of the restored residual image is 0.029, and an experimental result shows that an evaluation index can be flexibly selected for the calculated aberration automatic correction algorithm based on image sharpness evaluation optimization: the back propagation optimization and the particle swarm random optimization in the BPSO algorithm respectively select the image definition and the image information entropy as evaluation indexes to optimize the image, so that the accuracy of image aberration correction is improved from the viewpoint of a simulation result; the automatic aberration calculation correction method based on image sharpness evaluation optimization can realize quick automatic aberration calculation correction: the back propagation optimization algorithm in the BPSO algorithm realizes the rough correction of the aberration image to be corrected, reduces the cycle iteration times of the particle swarm random optimization algorithm and greatly shortens the time consumption of the algorithm; the automatic aberration correction calculation method based on image definition evaluation optimization has high correction result accuracy: the particle swarm random optimization algorithm in the BPSO algorithm realizes the fine correction of the aberration image to be corrected, the accuracy of the aberration correction result of the image to be corrected is improved, and the recovery residual RMS value is only 0.029.

Claims (7)

1. A method for automatically correcting calculated aberration based on image sharpness evaluation optimization is characterized by comprising the following steps:

step 1, establishing an aberration correction mathematical model based on image definition evaluation optimization:

an aberration-to-be-corrected image g (x, y) whose aberration is to be corrected is selected, and an aberration correction process therefor is modeled as a phase filtering process of a fourier domain of the aberration-to-be-corrected image g (x, y), that is

h(x,y)＝ifft(G(u,v)e ^-jφ(u,v) ) (1)

Wherein ifft is inverse Fourier transform, G (u, v) is an aberration image to be corrected in a Fourier domain, h (x, y) is a corrected clear image, and phi (u, v) is a phase filter; j is an imaginary part;

step 2, establishing a phase filter mathematical model based on image definition evaluation optimization:

determining the type of image aberration, selecting an aberration correction basis polynomial

Defining aberration correction coefficient values, thereby establishing a mathematical model of the phase filter, i.e.

Wherein, the term number K of different aberration types is 1 _k Is a value of a coefficient of the corresponding aberration;

step 3, solving the aberration correction optimal coefficient value by using a calculation aberration BPSO algorithm:

step 3-1, obtaining the optimal coefficient value of back propagation optimization by using back propagation optimization in the aberration calculation BPSO algorithm, and correcting the aberration map to be corrected in the Fourier domainIntroducing a back propagation optimization phase filter mask _1 into the image G (u, v), and searching a aberration correction base polynomial of the aberration image to be corrected by adopting back propagation optimization in the aberration calculation BPSO algorithm

The back propagation aberration correction optimum coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T The method comprises the following steps:

step 3-1-1, defining coefficient forward deviation weight eta ⁺ 0.5, coefficient inverse offset weight η ^- 1.2, coefficient forward offset maximum boundary value Δ _max Coefficient reverse shift minimum boundary value Δ of 50 _min 0.001, aberration coefficient offset

The evaluation function S _1 is set as the image definition, and the specific expression is as follows:

wherein h is ^* (x, y) is a conjugate matrix of h (x, y);

turning to the step 3-1-2;

step 3-1-2 of optimizing the aberration correction coefficient value c _1 ═ c _1 using back propagation ₁ ,c_1 ₂ ,...,c_1 _K ] ^T Selecting aberration correction coefficient c _1 in the following loop iteration _k The specific expression is as follows:

k＝1:length(c_1) (3)

selecting aberration correction coefficient c _1 _k If K meets the above conditions, entering loop iteration, and going to step 3-1-3; otherwise, turning to the step 3-1-10;

step 3-1-3, according to the loop iteration time t _1 and the maximum loop iteration time t _1 _max Relation, judging the iteration condition of the loop when

t_1≥t_1 _max (4)

The loop iteration is stopped to obtain the final selected aberration correction coefficient c _1 _k The backward propagation optimization phase filter mask _1 and the backward propagation optimized clear image h _1(x, y) are switched to the step 3-1-2, and the aberration correction coefficient c _1 updated in the next loop iteration is selected _k+1 (ii) a Otherwise, the step 3-1-4 is carried out, and the aberration correction coefficient c _1 is continuously updated in a loop iteration mode _k ；

Step 3-1-4, using the aberration correction coefficient c _1 selected in step 3-1-2 _k And aberration coefficient offset

Calculating an evaluation function S _1 to optimize an aberration correction coefficient c _1 ═ c _1 with respect to back propagation ₁ ,c_1 ₂ ,...,c_1 _K ] ^T Partial derivatives of

The specific expression is as follows:

recording partial derivatives

Turning to the step 3-1-5;

step 3-1-5, utilizing the forward deviation weight eta ⁺ Coefficient reverse bias weight η ^- Coefficient forward deviation maximum boundary value delta _max Coefficient is reversely shifted by a minimum boundary value delta _min Amount of deviation of each aberration coefficient

And

computing

Update value that changes as the number of loop iterations t _1 increases

The specific expression is as follows:

turning to the step 3-1-6;

step 3-1 to 6, utilizing

And

updating the selected aberration correction coefficient c _1 _k The specific expression is as follows:

records the updated selected aberration correction coefficient c _1 _k And turning to the step 3-1-7;

step 3-1-7, utilizing the selected aberration correction coefficient c _1 after updating _k And aberration correcting base polynomial

Establishing a back propagation optimization phase filter mask _1, wherein the specific expression is as follows:

recording the updated back propagation optimized phase filter mask _1, and turning to the step 3-1-8;

step 3-1-8, the image g (x, y) of the aberration to be corrected is optimized by using the back propagation optimization phase filter mask _1 obtained by updating in the step 3-1-7, and a clear image h _1(x, y) after back propagation optimization is obtained, wherein the specific expression is as follows:

h_1(x,y)＝ifft{fft{g(x,y)}.*exp(-1*j*mask_1)} (9)

wherein fft is two-dimensional Fourier transform processing of the aberration image g (x, y) to be corrected, ifft is two-dimensional inverse Fourier transform, and the selected aberration correction coefficient c _1 updated along with the increase of the number of loop iterations t is recorded _k And a backward propagation optimization phase filter mask _1, and then the step 3-1-9 is carried out;

step 3-1-9, recording the updated partial derivative

Specific numerical value and sign of (1), aberration coefficient offset amount

Selected aberration correction coefficient c _1 _k And the backward propagation optimization phase filter mask _1 and the backward propagation optimization back clear image h _1(x, y) are subjected to the next loop iteration:

t_1＝t_1+1 (10)

turning to the step 3-1-3;

step 3-1-10, ending the back propagation optimization loop iteration to obtain the final back propagation aberration correction coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T The clear image h _1(x, y) after the back propagation optimization and the back propagation optimization phase filter mask _1 are switched to the step 3-2;

step 3-2, taking the clear image h _1(x, y) after the back propagation optimization as an aberration image to be corrected, introducing a particle swarm random optimization phase filter mask _2, and searching a polynomial of an aberration correction base of the aberration image to be corrected by adopting a particle swarm random optimization algorithm in a calculation aberration BPSO algorithm

The particle swarm random optimization aberration correction optimal coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Turning to step 4;

step 4, correcting the optimal coefficient value c _1 ═ c _1 using the aberration ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after the image difference is corrected.

2. The method for automatically correcting the calculated aberration based on the image sharpness evaluation optimization according to claim 1, wherein: in the step 2, the aberration is corrected by the base polynomial

Is a Zernike circular domain orthogonal polynomial; the selection of terms of different aberration types corrects four aberrations, namely defocus, astigmatism, coma and spherical aberration.

3. The method for automatically correcting the calculated aberration based on the image sharpness evaluation optimization according to claim 1, wherein: in the step 3-1-1, the maximum number of loop iterations t _1 _max The value was 500 times.

4. The automatic correction method for aberration calculation based on image definition evaluation optimization according to claim 1, wherein in step 3-2, the back propagation optimized clear image h _1(x, y) is taken as an aberration image to be corrected, a particle swarm random optimization phase filter mask _2 is introduced, and a particle swarm random optimization algorithm in a calculated aberration BPSO algorithm is adopted to find a base polynomial for aberration correction of the aberration image to be corrected

The particle swarm randomly optimizes the optimal aberration correction coefficient value c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T The specific algorithm comprises the following steps:

step 3-2-1, taking the clear image h _1(x, y) after the back propagation optimization as an aberration image to be corrected, initially defining a K-dimensional coefficient search space,defining maximum iteration times t _2 of particle swarm loop _max ，t_2 _max The particles form a set, wherein the t _2 th particle represents a vector with K dimensions, c _2 ^(t_2) Represents the value of the t _2 th particle and represents the random optimization aberration correction coefficient value c _2 of the particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) I.e. by

c_2 ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ),t_2＝1,2,...,t_2 _max (12)

T _2 nd particle c _2 ^(t_2) The motion value of (2) is defined as a K-dimensional vector called the update step V ^(t_2) ，

Turning to the step 3-2-2;

3-2-2, calculating the fitness F of each particle in the particle swarm by using the evaluation function S _2 as an evaluation index, and turning to the step 3-2-3;

step 3-2-3, correcting the base polynomial to prevent aberration

Coupling correction occurs between the first particle and the second particle, the t _2 th particle c _2 generates the individual optimum and the global optimum of the particle swarm random optimization aberration correction coefficient according to the fitness ^(t_2) The optimum coefficient value searched by using the evaluation function S _2 as the evaluation index is called an individual optimum solution E _best ，

And the optimal coefficient value searched by the whole particle swarm by taking the evaluation function S _2 as an evaluation index is called as a global optimal solution G _best ，

The step 3-2-4 is converted;

step 3-2-4, utilizing E _best And G _best Update the step size V ^(t_2) And randomly optimizing aberration correction coefficient value c _2 by particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) )，

V ^(t-2) ＝W*V ^(t-2) +C ₁ *R ₁ *(E _best -c_2 ^(t-2) )+C ₂ *R ₂ *(G _best -c_2 ^(t-2) ) (16)

c_2 ^(t-2) ＝c_2 ^(t-2) +V ^(t-2) (17)

Wherein, C ₁ Is an acceleration constant, controls the individual optimal solution E _best For update step size V ^(t_2) Has an influence of 1.5, C ₂ Is a learning rate and embodies a global optimal solution G _best For update step size V ^(t_2) With a value of 1, W is an inertia constant with a value of 1, R ₁ 、R ₂ Is [0,1 ]]The random number in the range is transferred to the step 3-2-5;

step 3-2-5, utilizing the updated step size V ^(t_2) And randomly optimizing aberration correction coefficient value c _2 by particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) Calculating the fitness F of the updated particles by taking the evaluation function S _2 as an evaluation index, and turning to the step 3-2-6;

step 3-2-6, randomly optimizing aberration correction coefficient value c _2 by using updated particle fitness F and updated particle swarm ^(t_2) ＝(c_2 ₁ ^(t_2) ,c_2 ₂ ^(t_2) ,...,c_2 _K ^(t_2) ) To update the individual optimal solution E _best And global optimal solution G _best And turning to the step 3-2-7;

step 3-2-7, judging the iteration time t _2 and the maximum particle swarm loop iteration time t _2 _max Relationship when

t_2＞t_2 _max (18)

Switching to the step 3-2-8, otherwise, switching to the step 3-2-4;

step 3-2-8, ending the particle swarm random optimization loop iteration to obtain the optimal aberration correction coefficient value c _2 ═ c _2 of the particle swarm random optimization ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Randomly optimizing the aberration correction optimum coefficient value c _2 ═ c _2 by using a particle swarm ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And aberration correcting base polynomial

Obtaining a particle swarm random optimization phase filter mask _2,

and (3) optimizing the back clear image h _1(x, y) in the step 3-1-9 by using a particle swarm random optimization phase filter mask _2 to obtain the back clear image h _2(x, y) of the particle swarm random optimization, wherein the specific expression is as follows:

h_2(x,y)＝ifft{fft{h_1(x,y)}.*exp(-1*j*mask_2)} (20)

and fft is to perform two-dimensional Fourier transform processing on the clear image h _1(x, y) subjected to the inverse propagation optimization, ifft is to perform two-dimensional inverse Fourier transform, and the step 4 is carried out.

5. The method for automatically correcting the calculated aberration based on the image clarity assessment optimization according to claim 4, wherein: in the step 3-2-2, the evaluation function S _2 is set as an image information entropy, and a specific expression is as follows:

6. the method for automatically correcting the calculated aberration based on the image sharpness evaluation optimization according to claim 4, wherein: in the step 3-2-2, the fitness F of the particle is calculated by taking the evaluation function S _2 as an evaluation index, and the specific expression is as follows:

F＝S_2 (22)。

7. the method according to claim 1, wherein the optimal aberration correction coefficient value c _1 ═ c _1 is used to correct aberration ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T And solving the clear image after the image difference is corrected, which comprises the following steps:

using the back propagation optimum aberration correction coefficient value c _1 ═ c _1 ₁ ,c_1 ₂ ,...,c_1 _K ] ^T And randomly optimizing the aberration correction by the particle swarm to obtain the optimal aberration correction coefficient c _2 ═ c _2 ₁ ,c_2 ₂ ,...,c_2 _K ] ^T Solving aberration correction coefficient value c:

c＝c_1+c_2＝[c_1 ₁ +c_2 ₁ ,c_1 ₂ +c_2 ₂ ,...,c_1 _K +c_2 _K ] ^T (23)

and (3) solving the phase filter phi (u, v) by utilizing a back propagation optimization phase filter mask _1 and a particle swarm random optimization phase filter mask _2, wherein the specific expression is as follows:

φ(u,v)＝mask_1+mask_2 (24)

and (3) solving the corrected clear image h (x, y) by utilizing the back propagation optimized clear image h _1(x, y) and the particle swarm randomly optimized clear image h _2(x, y), wherein the specific expression is as follows:

h(x,y)＝h_2(x,y) (25)。

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