A solution method and system for phase diversity wavefront sensing

Abstract

The application provides a solving method and system for phase difference wave front detection, and the method comprises the following steps: collecting a plurality of target images with phase difference through an imaging system; obtaining an estimated value of an imaging wave front phase through the target images and a neural network; and obtaining the imaging wave front phase by using a nonlinear algorithm based on the estimated value. The method provided by the application can quickly and accurately solve the optical wave front phase, has the advantages of high solving precision, fast processing speed, good method robustness and strong practicability, can directly give a better estimated value of the imaging wave front phase without iteration operation which consumes a large amount of time, and the trained network also maintains high precision for real images through simulation image training of the neural network, avoids the harsh requirement of collecting a large amount of real images as training data, and has good application feasibility.

Description

Technical Field

[0001] The present invention belongs to the technical field of phase difference wavefront detection, and in particular relates to a method and system for solving phase difference wavefront detection. Background Art

[0002] Optical wavefront detection is crucial for evaluating the quality of imaging systems.

[0003] Phase-difference wavefront detection is an important detection method with advantages such as simple system structure, strong anti-interference capabilities, and ease of implementation. It has found promising applications in many fields. This method, which does not require the addition of complex hardware, acquires several target images through an imaging system. An additional phase, known as phase diversity, is pre-introduced into the imaging channel of each target image. A target evaluation function is established based on the imaging model and imaging parameters, and a nonlinear optimization algorithm is used to search for the optimal solution, thereby recovering the wavefront phase.

[0004] However, how to quickly and accurately obtain the optimal solution is a difficult problem in phase difference wavefront detection. Traditional methods generally use gradient-based nonlinear optimization algorithms to search for the minimum value of the objective function. However, when the objective function is a non-convex function in the solution space, the gradient-based optimization algorithm is prone to falling into local minima or saddle points, and the solution is far from the true value; by increasing the number of initial search points of the optimization algorithm, the probability of obtaining the global optimal solution can be increased, but the processing time increases dramatically. In addition, the steps of most existing methods are relatively cumbersome and require repeated debugging and parameter setting. Summary of the Invention

[0005] In order to overcome the defects of the above-mentioned prior art, the applicant conducted research and found that the difference between the low-frequency Fourier coefficients of the simulated image and the real image is very small. The network that uses the low-frequency Fourier coefficients of the simulated image as feature training can also maintain extremely high accuracy for the real image. Therefore, the present invention proposes a solution method for phase difference wavefront detection, which can quickly and accurately solve the optical wavefront phase, and has the advantages of high solution accuracy, fast processing speed, good method robustness and strong practicality.

[0006] The method comprises:

[0007] Acquire a plurality of target images with phase differences through an imaging system;

[0008] Obtaining an estimated value of the imaging wavefront phase through the target image and the neural network;

[0009] Based on the estimated value, a nonlinear algorithm is used to solve and obtain the imaging wavefront phase.

[0010] Specifically, “obtaining an estimated value of the imaging wavefront phase through the target image and the neural network” includes:

[0011] Calculating a two-dimensional Fourier transform of the target image to obtain a low-frequency Fourier coefficient of each target image;

[0012] All low-frequency Fourier coefficients of the target image are combined into an input vector, and the input vector is used as the input of the neural network to obtain an estimated value of the imaging wavefront phase output by the neural network.

[0013] Furthermore, the neural network is trained in the following manner:

[0014] Generate a series of random wavefront phases;

[0015] Simulating each of the random wavefront phases according to the parameters of the imaging system and Fourier optical imaging theory to obtain a plurality of simulated target images with phase differences;

[0016] Calculating a two-dimensional Fourier transform of the simulated target image to obtain a low-frequency Fourier coefficient of each simulated target image;

[0017] All low-frequency Fourier coefficients of each of the simulated target images corresponding to each of the random wavefront phases form an input vector, and the Zernike coefficients of each of the random wavefront phases form an output vector;

[0018] All the input vectors form an input data set, and all the output vectors form an output data set;

[0019] The neural network is trained using the input data set and the output data set.

[0020] Specifically, the “using a nonlinear algorithm to solve the imaging wavefront phase based on the estimated value” includes:

[0021] Constructing a target evaluation function according to the acquired target image and the parameters of the imaging system;

[0022] The estimated value is used as an initial search point, and the nonlinear algorithm is used to minimize the target evaluation function, thereby solving and obtaining the imaging wavefront phase.

[0023] Preferably, the nonlinear optimization algorithm comprises a Limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm.

[0024] The present invention also proposes a phase difference wavefront detection solution system for implementing the phase difference wavefront detection solution method as described above, the system comprising:

[0025] An acquisition module, configured to acquire a plurality of target images with phase differences through an imaging system;

[0026] An estimated value acquisition module, configured to acquire an estimated value of the imaging wavefront phase through the target image and the neural network;

[0027] A solution module is used to solve the imaging wavefront phase using a nonlinear algorithm.

[0028] Specifically, the estimated value acquisition module includes:

[0029] a computing unit, configured to compute a two-dimensional Fourier transform of the target image;

[0030] an acquisition unit, configured to obtain low-frequency Fourier coefficients of each target image;

[0031] a combining unit, configured to combine all low-frequency Fourier coefficients of the target image into an input vector;

[0032] An output unit is used to use the input vector as an input of the neural network, so that the neural network outputs an estimated value of the imaging wavefront phase.

[0033] Specifically, the solution module includes:

[0034] A construction unit, configured to construct a target evaluation function based on the acquired target image and parameters of the imaging system;

[0035] A solving unit is used to use the estimated value as an initial search point, adopt the nonlinear optimization algorithm to make the target evaluation function obtain a minimum value, and solve to obtain the imaging wavefront phase.

[0036] Specifically, the neural network is trained through the following modules:

[0037] A generation module, used to generate a series of random wavefront phases;

[0038] An image acquisition module is used to simulate each of the random wavefront phases according to the parameters of the imaging system and Fourier optical imaging theory to obtain a plurality of simulated target images with phase differences;

[0039] A coefficient acquisition module, configured to calculate a two-dimensional Fourier transform of the simulated target image and obtain a low-frequency Fourier coefficient of each simulated target image;

[0040] A vector composition module, configured to form an input vector from all low-frequency Fourier coefficients of each of the simulated target images corresponding to each of the random wavefront phases, and to form an output vector from the Zernike coefficients of each of the random wavefront phases;

[0041] A data set composition module, configured to compose all the input vectors into an input data set and all the output vectors into an output data set;

[0042] A training module is used to train the neural network using the input data set and the output data set.

[0043] Preferably, the nonlinear algorithm used by the solution module includes a Limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm.

[0044] The present invention has at least the following beneficial effects:

[0045] This method uses a neural network to directly obtain a good estimate of the wavefront to be measured, and uses this estimate as the initial search point for nonlinear optimization. Compared with the traditional random search initial point, the estimated value is located near the true solution. On the one hand, it can effectively prevent the nonlinear optimization from falling into local extreme values ​​or saddle points, ensuring convergence to the true solution and improving the solution accuracy. On the other hand, starting the search near the true solution greatly accelerates the convergence process and improves the solution speed.

[0046] Furthermore, this method achieves satisfactory results for a wide range of random wavefront phases, statistically demonstrating its robustness. The network trained using the low-frequency Fourier coefficients of simulated images also maintains high accuracy for real images. Furthermore, this method uses computer-simulated images to train the network, eliminating the need for acquiring large numbers of real images, making it highly feasible.

[0047] Therefore, the present invention provides a method and system for solving phase difference wavefront detection. The method proposed in the present invention can quickly and accurately solve the optical wavefront phase, and has the advantages of high solution accuracy, fast processing speed, good method robustness, and strong practicality. It does not require time-consuming iterative calculations, and can directly give a better estimate of the imaging wavefront phase. By training the neural network through simulated images, the trained network also maintains high accuracy for real images, avoiding the harsh requirement of collecting massive real images as training data, and has good application feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0049] Figure 1 A schematic diagram of the overall process of the phase difference wavefront detection solution method provided in Example 1;

[0050] Figure 2 A schematic diagram of a process for obtaining an estimated value of the imaging wavefront phase;

[0051] Figure 3 This is a flowchart of the neural network training method;

[0052] Figure 4 Schematic diagram of the process of solving the imaging wavefront phase using nonlinear algorithms;

[0053] Figure 5 A schematic diagram of the overall module structure of the phase difference wavefront detection solution system provided in Example 2;

[0054] Figure 6 This is a schematic diagram of the partial module structure of the phase difference wavefront detection solution system;

[0055] Figure 7 A schematic diagram of the module structure of a system for training the neural network;

[0056] Figure 8 Schematic diagram of the optical path structure of the imaging system used in the experiment;

[0057] Figure 9 (a) to (f) are schematic diagrams of phase maps and corresponding acquired images;

[0058] Figure 10 (a) ~ (b) are the data diagrams of the neural network training results, where Figure 10 (a) is the regression R 2 Figure 10(b) is the data diagram of the root mean square error;

[0059] Figure 11 To solve the histogram of the wavefront phase residual error.

[0060] Reference numerals:

[0061] 1-acquisition module; 2-estimated value acquisition module; 3-solution module; 4-generation module; 5-image acquisition module; 6-coefficient acquisition module; 7-vector composition module; 8-dataset composition module; 9-training module; 21-computation unit; 22-acquisition unit; 23-combination unit; 24-output unit; 31-construction unit; 32-solution unit; 40-laser; 41-filter; 42-polarizer; 43-reflector; 44-objective lens; 45-pinhole; 46-beam splitter; 47-spatial light modulator; 48-lens; 49-camera. DETAILED DESCRIPTION

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0063] Example 1

[0064] The present invention provides a phase difference wavefront detection solution method, which combines low-frequency Fourier coefficients and BP neural network to quickly and accurately solve the optical wavefront phase, and has the advantages of high solution accuracy, fast processing speed, good method robustness and strong practicality.

[0065] This method uses a neural network to directly obtain a good estimate of the measured wavefront and uses this estimate as the initial search point for nonlinear optimization. Compared to traditional random search starting points, the estimated value is located near the true solution. This effectively prevents the nonlinear optimization from falling into local extrema or saddle points, ensuring convergence to the true solution and improving solution accuracy. Furthermore, starting the search near the true solution significantly accelerates convergence and improves solution speed.

[0066] Experimental results show that the proposed method can achieve satisfactory results for a large number of different random wavefront phases. Statistically, the method is proven to be robust.

[0067] In recent years, there has been an endless stream of research on the introduction of neural networks, especially deep learning, into wavefront phase detection. However, from a practical application perspective, neural networks require a large number of training samples, which is difficult to achieve for most applications. The applicant's research found that the difference between the low-frequency Fourier coefficients of simulated images and real images is very small. The network trained using the low-frequency Fourier coefficients of simulated images as features also maintains extremely high accuracy for real images. Therefore, this method uses computer simulated images to train the network without the need to obtain a large number of real images, and has strong practical feasibility.

[0068] Please refer to Figure 1 , the method comprising:

[0069] S100: Capture a plurality of target images with phase differences through an imaging system, and proceed to step S200.

[0070] It should be noted that, in this embodiment, the phase difference is obtained by introducing different additional phase differences into the imaging channel of each target image.

[0071] S200: Obtain an estimated value of the imaging wavefront phase through the target image and the neural network, and proceed to step S300.

[0072] S300: Based on the estimated value, a nonlinear algorithm is used to solve and obtain the imaging wavefront phase.

[0073] It should be noted that the imaging channel of the target image has an imaging wavefront phase, and the wavefront phase can be represented by a linear combination of a series of orthogonal polynomials. Zernike polynomials are orthogonal to each other in the circular domain and have simple invariance characteristics. They are widely used in wavefront phase analysis. The coefficients of the linear combination of Zernike polynomials are Zernike coefficients. Generally, a finite number of Zernike polynomials is used to fit the wavefront phase, for example, 1 to 15 items, and the fitting coefficients form a set of Zernike coefficients {z1, z2,…, z 15}.

[0074] It's also important to note that low-frequency Fourier coefficients refer to the coefficients of the two-dimensional Fourier spectrum at lower frequencies. Performing a two-dimensional Fourier transform on an image yields a two-dimensional Fourier spectrum. The zero-frequency Fourier spectrum represents the image's average grayscale; the Fourier spectrum close to zero frequency is the low-frequency spectrum, representing the image's basic outlines; the Fourier spectrum far from zero frequency is the high-frequency spectrum, representing the image's detailed information. The Fourier spectrum is a complex number, consisting of real and imaginary parts. The real and imaginary coefficients of the low-frequency spectrum are the low-frequency Fourier coefficients.

[0075] Specifically, please refer to Figure 2 , step S200 includes:

[0076] S210: Calculate target image I n The two-dimensional Fourier transform of each target image is used to obtain the low-frequency Fourier coefficients {F} n , where n=1, 2,…, N, proceed to step S220.

[0077] S220: All low-frequency Fourier coefficients of the target image {F} n Combined into an input vector in, the input vector in is used as the input of the neural network, so that the neural network outputs an estimated value of the imaging wavefront phase, where n = 1, 2, ..., N.

[0078] Specifically, the input vector in is input into the neural network BPNN, and the neural network BPNN outputs the estimated value of the wavefront phase Zernike coefficient

[0079] Specifically, please refer to Figure 3 , the neural network training method includes:

[0080] A. Generate a series of random wavefront phases and proceed to step B.

[0081] In this embodiment, M groups of Zernike coefficients {z s} m , where m = 1, 2,…, M.

[0082] B. Based on the parameters of the imaging system and Fourier optical imaging theory, simulate each random wavefront phase to obtain several simulated target images with phase differences, and then proceed to step C.

[0083] In this embodiment, according to the parameters of the imaging system and Fourier optical imaging theory, each set of Zernike coefficients {z s} m Perform simulation and generate N simulated target images Where n = 1, 2,…, N.

[0084] It should be noted that the operations of generating random wavefront phases and simulating random wavefront phases are performed by a computer. The phase difference θ introduced by the imaging channel n This is the same as the phase difference actually introduced by the imaging system.

[0085] C. Calculate the two-dimensional Fourier transform of the simulated target image, obtain the low-frequency Fourier coefficients of each simulated target image, and proceed to step D.

[0086] In this embodiment, for each simulated target image Calculate the two-dimensional Fourier transform to obtain the low-frequency Fourier coefficients {F s} mn .

[0087] D. All low-frequency Fourier coefficients of each simulated target image corresponding to each random wavefront phase form an input vector, and the Zernike coefficients of each random wavefront phase form an output vector, and then proceed to step E.

[0088] In this embodiment, for each set of Zernike coefficients {z s} m Corresponding N simulated target images All low-frequency Fourier coefficients {F s} mn Form an input vector Zernike coefficient {z s} m Form an output vector Where n = 1, 2,…, N.

[0089] It should be noted that combining the low-frequency Fourier coefficients into an input vector simply involves arranging them into a column vector in a specific order. For example, if the low-frequency Fourier spectrum is a 1×2 matrix, the coefficients of its real and imaginary parts are taken and rearranged into a 4×1 column vector. Similarly, the Zernike coefficients are arranged into a column vector in a specific order as the output vector.

[0090]

[0091] E. All input vectors form an input data set, all output vectors form an output data set, and go to step F.

[0092] In this embodiment, all Zernike coefficients [z s} m The input vector Form an input data set IN s , all output vectors Form an output data set OUT s .

[0093] F. Use the input data set and output data set to train the BP neural network.

[0094] In this embodiment, the input data set IN s and output dataset OUT s , train a BP neural network BPNN.

[0095] It should be noted that the BP neural network (Back propagation neural network) is a widely used artificial neural network. Specifically, a BP neural network is a multi-layer feedforward neural network composed of an input layer, an output layer, and one or more hidden layers. It is trained using the BP algorithm. BP neural networks can implement complex nonlinear mapping and have strong nonlinear mapping capabilities, self-learning and self-adaptation capabilities, generalization capabilities, and fault tolerance.

[0096] In the method proposed in this embodiment, the number of nodes in the input layer of the BP neural network matches the input vector, and the number of nodes in the output layer matches the output vector. For example, if the input vector in is a p×1 matrix, then the number of nodes in the input layer is also p; if the output vector out is a q×1 matrix, then the number of nodes in the output layer is also q.

[0097] It is worth noting that for a fixed optical imaging system and imaging target, the imaging model and parameters remain essentially unchanged. Therefore, steps A through F of training the BPNN are performed in advance, and the trained BPNN is saved. In actual application scenarios, the BPNN is retrieved for application, and steps S210 through S220 are executed directly.

[0098] Specifically, please refer to Figure 4 , step S300 includes:

[0099] S310: Construct a target evaluation function based on the acquired target image and the parameters of the imaging system, and proceed to step S320.

[0100] In this embodiment, according to the N target images I collected by the imaging system, n , and the phase difference θ introduced by the imaging channel n , construct the objective function L for evaluating the Zernike coefficients, where n = 1, 2, …, N.

[0101] S320: Using the estimated value as the initial search point, a nonlinear optimization algorithm is used to minimize the target evaluation function, and the imaging wavefront phase is obtained by solving the problem.

[0102] In this embodiment, the Zernike coefficient estimate As the initial search point, the nonlinear optimization algorithm is used to search for the minimum value L of the objective function L min , and get L min The corresponding Zernike coefficient {z}. The imaging wavefront phase is reconstructed using the Zernike coefficient {z}

[0103] Generally speaking, commonly used nonlinear optimization algorithms include gradient descent (GD), conjugate gradient method (CG), Newton method (Newton), quasi-Newton method (Quasi-Newton), etc. The method proposed in this embodiment uses the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm, a quasi-Newton method with the advantages of low memory requirements, fast convergence, and good stability. In addition, the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm is a second-order gradient algorithm and is often more accurate than first-order gradient algorithms such as gradient descent and conjugate gradient method.

[0104] The method proposed in this embodiment is based on a neural network based on low-frequency Fourier coefficients. It can directly provide a good estimate of the imaging wavefront phase without the need for time-consuming iterative calculations. This estimate is located near the true solution. Using this estimate as the initial search point for the nonlinear optimization algorithm can, on the one hand, enable the search to converge smoothly to the true solution, avoid falling into local extreme values ​​or saddle points, and improve the solution accuracy. On the other hand, it can reduce the search time and increase the solution speed. More importantly, in practical applications, it is extremely difficult to obtain a large number of real images to train neural networks, and the difference between the low-frequency Fourier coefficients of simulated images and real images is very small. Therefore, this method uses computer simulated images to train the neural network. The trained network also maintains high accuracy for real images, avoiding the demanding requirement of collecting massive real images as training data, and has good application feasibility. This method can quickly and accurately solve the imaging wavefront phase, and can obtain satisfactory results for a large number of different random phases. The method has good robustness.

[0105] Example 2

[0106] This embodiment proposes a phase difference wavefront detection solution system for implementing the phase difference wavefront detection solution method proposed in Example 1. Figure 5 , the system comprising:

[0107] An acquisition module 1 is used to acquire a plurality of target images with phase differences through an imaging system;

[0108] An estimated value acquisition module 2 is used to obtain an estimated value of the imaging wavefront phase through the target image and the neural network;

[0109] The solution module 3 is used to solve the imaging wavefront phase using a nonlinear algorithm.

[0110] It should be noted that the imaging channel of the target image has an imaging wavefront phase, and the wavefront phase can be represented by a linear combination of a series of orthogonal polynomials. Zernike polynomials are orthogonal to each other in the circular domain and have simple invariance characteristics. They are widely used in wavefront phase analysis. The coefficients of the linear combination of Zernike polynomials are Zernike coefficients. Generally, a finite number of Zernike polynomials is used to fit the wavefront phase, for example, 1 to 15 items, and the fitting coefficients form a set of Zernike coefficients {z1, z2,…, z 15}.

[0111] Specifically, please refer to Figure 6 , the estimated value acquisition module 2 includes:

[0112] The calculation unit 21 is used to calculate the target image I n The two-dimensional Fourier transform of

[0113] The acquisition unit 22 is used to obtain the low-frequency Fourier coefficients {F} of each target image. n , where n = 1, 2, ..., N;

[0114] The combining unit 23 is used to combine all low-frequency Fourier coefficients {F} n Combined into an input vector in, where n = 1, 2, ..., N;

[0115] The output unit 24 is used to take the input vector in as the input of the neural network, so that the neural network outputs an estimated value of the imaging wavefront phase.

[0116] Specifically, the combining unit 23 combines the input vector in, and the output unit 24 inputs the input vector in into the neural network BPNN, and the neural network BPNN outputs the estimated value of the imaging wavefront phase Zernike coefficient

[0117] In the system proposed in this embodiment, the neural network includes a BP neural network. The number of nodes in the input layer of the BP neural network matches the input vector, and the number of nodes in the output layer matches the output vector. For example, if the input vector in is a p×1 matrix, the number of nodes in the input layer is also p; if the output vector out is a q×1 matrix, the number of nodes in the output layer is also q.

[0118] It is worth noting that for a fixed optical imaging system and imaging target, the imaging model and parameters are essentially unchanged. Therefore, steps A to F of training the neural network BPNN are performed in advance, and the trained neural network BPNN is saved. In actual application scenarios, the neural network BPNN is called out for application, and the calculation unit 21, acquisition unit 22, combination unit 23, and output unit 24 are directly executed.

[0119] Please refer again Figure 6 , the solution module 3 includes:

[0120] A construction unit 31 is used to construct a target evaluation function based on the acquired target image and the parameters of the imaging system;

[0121] The solving unit 32 is used to use the estimated value as the initial search point, adopt a nonlinear optimization algorithm to minimize the target evaluation function, and solve to obtain the imaging wavefront phase.

[0122] In this embodiment, the construction unit 31 collects N target images I n , and the phase difference θ introduced by the imaging channel n , construct the objective function L for evaluating the Zernike coefficient, where n = 1, 2, ..., N; the solving unit 32 converts the Zernike coefficient estimate As the initial search point, the nonlinear optimization algorithm is used to search for the minimum value L of the objective function L min , and get L min The corresponding Zernike coefficient {z}. The imaging wavefront phase is reconstructed using the Zernike coefficient {z}

[0123] Specifically, please refer to Figure 7 , the neural network is trained by the following modules:

[0124] A generating module 4 is used to generate a series of random wavefront phases;

[0125] The image acquisition module 5 is used to simulate each random wavefront phase according to the parameters of the imaging system and Fourier optical imaging theory to obtain a plurality of simulated target images with phase differences;

[0126] A coefficient acquisition module 6 is used to calculate the two-dimensional Fourier transform of the simulated target image and obtain the low-frequency Fourier coefficients of each simulated target image;

[0127] A vector composition module 7 is used to form an input vector from all low-frequency Fourier coefficients of each simulated target image corresponding to each random wavefront phase, and to form an output vector from the Zernike coefficients of each random wavefront phase;

[0128] A data set forming module 8 is configured to form an input data set from all input vectors and an output data set from all output vectors;

[0129] The training module 9 is used to train the neural network using the input data set and the output data set.

[0130] In this embodiment, the generating module 4 includes a computer randomly generating M groups of Zernike coefficients {z s} m , where m = 1, 2, ..., M;

[0131] The image acquisition module 5 obtains the Zernike coefficients {z s} m Perform simulation and generate N simulated target images Where n=1,2,…,N;

[0132] The coefficient acquisition module 6 performs the following operations on each simulated target image: Calculate the two-dimensional Fourier transform to obtain the low-frequency Fourier coefficients {F s} mn ;

[0133] Vector composition module 7 for each group of Zernike coefficients {z s} m Corresponding N simulated target images All low-frequency Fourier coefficients {F s} mn Form an input vector Zernike coefficient {z s} m Form an output vector Where n=1,2,…,N;

[0134] Dataset composition module 8 combines all Zernike coefficients {z s} m The input vector Form an input data set IN s , all output vectors Form an output data set OUT s ;

[0135] Training module 9 uses the input data set IN s and output dataset OUT s , train a BP neural network BPNN.

[0136] It should be noted that combining the low-frequency Fourier coefficients into an input vector simply involves arranging them into a column vector in a specific order. For example, if the low-frequency Fourier spectrum is a 1×2 matrix, the coefficients of its real and imaginary parts are taken and rearranged into a 4×1 column vector. Similarly, the Zernike coefficients are arranged into a column vector in a specific order as the output vector.

[0137]

[0138] It's worth noting that for a fixed optical imaging system and imaging target, the imaging model and parameters remain essentially unchanged. Therefore, the BPNN neural network is pre-trained in the neural network training system, and the trained BPNN neural network is saved. In actual application scenarios, the BPNN neural network is retrieved and directly applied in the estimated value acquisition module 2.

[0139] In this embodiment, the nonlinear algorithm used in the solution module 3 includes the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm, which is a quasi-Newton method with the advantages of low memory requirement, fast convergence speed and good stability.

[0140] The method proposed in this invention was tested on an imaging system to prove its feasibility. The optical path structure of the imaging system used in the experiment is as follows: Figure 8 As shown, the laser 40 emits laser light, the neutral density filter 41 is used to adjust the light intensity, the polarization direction is adjusted by the polarizer 42, and after being reflected by the reflector 43, it enters the objective lens 44 and is focused to the pinhole 45. The light wave emitted from the pinhole 45 is collimated into parallel light after passing through the lens 48. The parallel light passes through the beam splitter 46 and is irradiated onto the pure phase spatial light modulator 47 (phase-only SLM). The spatial light modulator 47 modulates the phase of the light beam. After the modulated light beam is reflected by the beam splitter 46, it is focused by the lens 48 to the detection target surface of the camera 49. The camera 49 is used to collect the spot image.

[0141] Phase maps with different grayscale distributions are loaded onto the spatial light modulator 47 to generate different light wavefront phases. By superimposing the phase map with the defocus phase, a defocus phase difference can be generated. In this experiment, 500 sets of different Zernike coefficients were randomly generated and the phase map was reconstructed. Three phase differences (positive defocus, no defocus, and negative defocus) were superimposed on each phase. A total of 500 sets of images were collected, each set of images including three spot images with different defocus, that is, a total of 1500 images were collected.

[0142] Please refer to Figure 9 (a)~(f), Figure 9 (a) to (f) are examples of a set of phase maps and corresponding acquired images, where Figure 9 (a) Figure 9 (b) Figure 9 (c) are the phase diagrams of positive defocus, no defocus, and negative defocus, respectively. Figure 9 (d) Figure 9 (e) Figure 9 (f) are Figure 9 (a) Figure 9(b) Figure 9 (c) The corresponding collected light spot image.

[0143] A computer was used to randomly generate 1,000 sets of Zernike coefficients. Based on the experimental system parameters and Fourier optical imaging theory, 1,000 sets of images were generated through computer simulation. Similar to the experimentally acquired images, each set of images included three spot images with different defocus levels, generating a total of 3,000 simulated images. A two-dimensional Fourier transform was performed on each simulated image to extract the low-frequency Fourier coefficients. The Fourier coefficients of each set of images were combined into an input vector, and the corresponding Zernike coefficients were combined into an output vector. All input vectors formed the input dataset, and all output vectors formed the output dataset. The input and output datasets were used to train a BP neural network, with the training results shown in Figures 10(a) and 10(b).

[0144] A two-dimensional Fourier transform is performed on each set of images collected in the experiment, and the low-frequency Fourier coefficients are extracted and combined into an input vector. The input vector is input into the training network, and the training network outputs an estimated value of the wavefront phase. The estimated value is used as the initial search point of the L-BFGS nonlinear algorithm. The L-BFGS algorithm solves the Zernike coefficients and reconstructs the wavefront phase. For 500 sets of wavefront phases, the minimum, maximum, and average values ​​of the residual root mean square error of the wavefront phase are 0.029λ, 0.045λ, and 0.037λ, respectively. The histogram of the solved wavefront phase residual error is shown below. Figure 11 shown.

[0145] In summary, the present invention provides a method and system for solving phase difference wavefront detection. The method proposed in the present invention can quickly and accurately solve the optical wavefront phase, and has the advantages of high solution accuracy, fast processing speed, good method robustness, and strong practicality. It does not require time-consuming iterative calculations, and can directly give a better estimate of the imaging wavefront phase. By training the neural network with simulated images, the trained network also maintains high accuracy for real images, avoiding the harsh requirement of collecting massive real images as training data, and has good application feasibility.

[0146] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A phase difference wavefront detection solution method, characterized in that: The method comprises: Acquire a plurality of target images with phase differences through an imaging system; Calculating a two-dimensional Fourier transform of the target image to obtain low-frequency Fourier coefficients of each target image; combining all low-frequency Fourier coefficients of the target image into an input vector, using the input vector as an input of a neural network, and obtaining an estimated value of the imaging wavefront phase output by the neural network; A target evaluation function is constructed based on the acquired target image and the parameters of the imaging system; the estimated value is used as the initial search point, a nonlinear algorithm is used to minimize the target evaluation function, and the imaging wavefront phase is obtained by solving the problem.

2. The phase difference wavefront detection solution method according to claim 1, characterized in that: The neural network is trained in the following way: Generate a series of random wavefront phases; Simulating each of the random wavefront phases according to the parameters of the imaging system and Fourier optical imaging theory to obtain a plurality of simulated target images with phase differences; Calculating a two-dimensional Fourier transform of the simulated target image to obtain a low-frequency Fourier coefficient of each simulated target image; All low-frequency Fourier coefficients of each of the simulated target images corresponding to each of the random wavefront phases form an input vector, and the Zernike coefficients of each of the random wavefront phases form an output vector; All the input vectors form an input data set, and all the output vectors form an output data set; The neural network is trained using the input data set and the output data set.

3. The phase difference wavefront detection solution method according to claim 1, characterized in that: The nonlinear algorithm includes a Limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm.

4. A phase difference wavefront detection solution system, used to implement the phase difference wavefront detection solution method according to any one of claims 1 to 3, characterized in that: The system comprises: An acquisition module, configured to acquire a plurality of target images with phase differences through an imaging system; an estimated value acquisition module, configured to calculate a two-dimensional Fourier transform of the target image to obtain low-frequency Fourier coefficients of each target image; combine all low-frequency Fourier coefficients of the target image into an input vector, use the input vector as an input to a neural network, and obtain an estimated value of the imaging wavefront phase output by the neural network; A solution module is used to establish a target evaluation function based on the collected target image and the parameters of the imaging system; use the estimated value as the initial search point, adopt a nonlinear algorithm to make the target evaluation function obtain the minimum value, and solve to obtain the imaging wavefront phase.

5. The phase difference wavefront detection and solution system according to claim 4, characterized in that: The neural network is trained by the following modules: A generation module, used to generate a series of random wavefront phases; An image acquisition module is used to simulate each of the random wavefront phases according to the parameters of the imaging system and Fourier optical imaging theory to obtain a plurality of simulated target images with phase differences; A coefficient acquisition module, configured to calculate a two-dimensional Fourier transform of the simulated target image and obtain a low-frequency Fourier coefficient of each simulated target image; A vector composition module, configured to form an input vector from all low-frequency Fourier coefficients of each of the simulated target images corresponding to each of the random wavefront phases, and to form an output vector from the Zernike coefficients of each of the random wavefront phases; A data set composition module, configured to compose all the input vectors into an input data set and all the output vectors into an output data set; A training module is used to train the neural network using the input data set and the output data set.

6. The phase difference wavefront detection and solution system according to claim 4, characterized in that: The nonlinear algorithm used by the solution module includes a Limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm.

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