Hybrid wavefront reconstruction method and system based on orthogonal matching pursuit and deep learning

Abstract

This invention relates to a hybrid wavefront reconstruction method and system based on orthogonal matching pursuit and deep learning, belonging to the field of adaptive optics technology. It includes: acquiring an image of the spot array corresponding to the distorted wavefront to be tested, and extracting the centroid offset of the spot corresponding to each sub-aperture in the microlens array; obtaining a slope vector based on the centroid offset; reconstructing the Zernike reconstruction coefficient vector from the slope vector and using it as a low-order reference solution; constructing a multilayer perceptron residual compensation network; using the difference between the true Zernike coefficients and the low-order reference solution as the residual, and training the multilayer perceptron residual compensation network using the residual; inputting the slope vector into the trained multilayer perceptron residual compensation network to obtain predicted high-frequency residual coefficients; and linearly superimposing the low-order reference solution and the predicted high-frequency residual coefficients to obtain the full-band reconstructed wavefront coefficients, thereby completing the hybrid wavefront reconstruction. This invention improves the accuracy of full-band wavefront reconstruction.

Description

Technical Field

[0001] This invention relates to the field of adaptive optics technology, and in particular to a hybrid wavefront reconstruction method and system based on orthogonal matched pursuit and deep learning. Background Technology

[0002] Adaptive optics (AO) technology, by measuring and compensating for dynamic wavefront distortion in real time, has become a key support for fields such as high-resolution astronomical observation, laser transmission, and biomedical imaging. The Shack-Hartmann Wavefront Sensor (SHWFS) is widely used due to its simple structure and high light energy utilization. Its working principle involves segmenting and sampling the incident wavefront using a microlens array, obtaining local slope information of the wavefront by measuring the centroid shift of the light spot array on the focal plane, and then using a wavefront reconstruction algorithm to recover the full-aperture wavefront phase distribution.

[0003] Existing traditional wavefront reconstruction methods are mainly divided into region methods and mode methods. Mode methods reconstruct the wavefront by expanding the full-aperture wavefront phase into a linear combination of Zernike polynomials and solving for the mode coefficients of each order using the full-aperture slope data. However, limited by the number of sub-apertures in the microlens array, the slope-to-phase reconstruction matrix generally exhibits ill-conditioned characteristics. Furthermore, under strong atmospheric turbulence, spatial crosstalk between sub-apertures intensifies, disrupting the linear mapping relationship and leading to a significant decrease in reconstruction accuracy using traditional methods. To improve the accuracy of traditional reconstruction algorithms, existing improvement techniques are mainly divided into two categories: compressed sensing reconstruction and deep learning reconstruction, as detailed below: The first category is slope domain reconstruction technology based on compressed sensing. The core principle of this technology is to perform sparse reconstruction of the wavefront slope in the slope domain. The overall execution process consists of three cascaded operations: slope compression sampling, sparse reconstruction of the slope, and pattern-based phase reconstruction. The drawbacks of this technology are: the sparsity of the signal is highly dependent on the expansion effect of the slope signal on specific transform bases such as the Fourier basis; the reconstruction accuracy is constrained by both the sparse dictionary signal representation capability and the information loss from compressed sampling; and the conversion mapping relationship between the reconstructed slope and the wavefront phase needs to be calibrated separately, resulting in high process complexity and significant error accumulation.

[0004] The second category is data-driven wavefront reconstruction technology based on deep learning. This type of technology relies on network models such as convolutional neural networks (CNN) and multilayer perceptrons (MLP) to directly predict Zernike coefficients from SHWFS spot array images or slope vectors, and trains on a large dataset to fit the nonlinear mapping relationship between slope and phase. This type of purely data-driven model is a black box model and has two major technical shortcomings: first, the model has poor generalization ability, and the reconstruction performance drops sharply for turbulent conditions not covered by the training dataset; second, the model output results lack physical interpretability and cannot meet the high reliability requirements of adaptive optics systems.

[0005] Therefore, how to integrate the prior knowledge of physical models with the nonlinear fitting capabilities driven by data, and achieve high-precision and robust wavefront reconstruction across the entire frequency band while ensuring real-time reconstruction, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the technical defects of the existing deep learning reconstruction model, such as weak generalization ability, lack of physical interpretability, poor turbulence adaptability, and inability to take into account physical prior constraints, real-time reconstruction, high accuracy and high robustness of wavefront reconstruction across the entire turbulent frequency band.

[0007] Firstly, to address the aforementioned technical problems, this invention provides a hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning, comprising: S1. Obtain the image of the light spot array corresponding to the distorted wavefront to be tested, and extract the centroid offset of the light spot corresponding to each sub-aperture in the microlens array; obtain the slope vector based on the centroid offset of the light spot. S2. Select multiple Zernike aberration modes to be calibrated, and perturb each Zernike aberration mode; collect the wavefront slope of each Zernike aberration mode under the perturbation, and construct an interaction matrix; solve for the Zernike reconstruction coefficient vector based on the interaction matrix, the slope vector, and the preset sparsity; use the Zernike reconstruction coefficient vector as a low-order reference solution. S3. Construct a multilayer perceptron residual compensation network; use the difference between the true Zernike coefficients and the low-order benchmark solution as the first residual, and use the first residual to train the multilayer perceptron residual compensation network to obtain the optimal multilayer perceptron residual compensation network; input the slope vector into the optimal multilayer perceptron residual compensation network to obtain the predicted value of the high-frequency residual coefficients. S4. Linearly superimpose the low-order reference solution with the predicted high-frequency residual coefficients to obtain the full-band reconstructed wavefront coefficients; complete the hybrid wavefront reconstruction based on the full-band reconstructed wavefront coefficients.

[0008] In one embodiment of the present invention, the formula for calculating the centroid offset of the light spot in step S1 is: ; ; in, This represents the offset along the x-axis. This represents the offset along the y-axis. and These represent the number of pixels in the x and y directions within a single detection window, respectively. Indicates the first The light intensity value of each pixel; and These represent the x-coordinate and y-coordinate of the corresponding pixel on the detector plane, respectively.

[0009] In one embodiment of the present invention, in step S2, multiple Zernike aberration modes to be calibrated are selected, and each Zernike aberration mode is perturbed; the wavefront slope of each Zernike aberration mode under the perturbation is collected, and the interaction matrix is ​​constructed as follows: Select the Zernike aberration mode to be calibrated; apply positive and negative perturbations to the Zernike aberration mode respectively to obtain the first wavefront; Optical propagation is performed on the first wavefront to obtain the corresponding perturbation light field; Measure the aperture slope of each sub-aperture after the perturbation light field passes through the Shaker-Hartmann wavefront sensor; concatenate all sub-aperture slopes under positive perturbation into a positive slope vector, and concatenate all sub-aperture slopes under negative perturbation into a negative slope vector; The response vector corresponding to the current Zernike aberration mode is calculated based on the positive slope vector, the negative slope vector, and the perturbation amplitude. Traverse all Zernikal aberration modes to be calibrated, and concatenate the response vectors corresponding to each mode column by column to obtain the interaction matrix.

[0010] In one embodiment of the present invention, the expression for the response vector is: ; in, This represents the response vector corresponding to the current Zernike aberration mode. Indicates the amplitude of the disturbance. This represents the positive slope vector. This represents the negative slope vector.

[0011] In one embodiment of the present invention, the step of solving the Zernike reconstruction coefficient vector based on the interaction matrix, the slope vector, and the preset sparsity in step S2 is as follows: S221. Define the initial support set and use the slope vector as the current residual; S222. Calculate the matching atoms based on the current residual and the interaction matrix; S223. Update the support set according to the matching atoms to obtain a new support set; S224. Select the columns corresponding to the new support set in the interaction matrix to form a submatrix; solve the current estimated coefficients based on the submatrix and the slope vector using least squares. S225. Update the residuals based on the current estimated coefficients, the submatrix, and the slope vector; use the updated residuals as the current residuals and update the iteration count. S226. Determine whether the current iteration number is greater than the preset sparsity; if so, use the current estimated coefficients as the Zernike reconstruction coefficient vector; otherwise, return to S222 and repeat until the current iteration number is greater than the preset sparsity.

[0012] In one embodiment of the present invention, the expression for the estimated coefficients is: ; in, Indicates the first The estimated coefficients of the next iteration. Represents the slope vector. Indicates the first The submatrix of the next iteration The symbol for transpose of a matrix.

[0013] In one embodiment of the present invention, in step S225, the residuals are updated based on the current estimated coefficients, the submatrix, and the slope vector; wherein the residual update expression is: ; in, Indicates the first The residual updated in the next iteration Represents the slope vector. Indicates the first The submatrix of the next iteration Indicates the first The estimated coefficients for the next iteration.

[0014] In one embodiment of the present invention, the theoretical covariance expression for each order of the Zernike coefficients in the Zernike reconstruction coefficient vector is as follows: ; in, Let represent the coefficient covariance of any two Zernike modes in the turbulent phase screen. Represents frequency characteristic factor, Represents the Kronecker symbol. Represents the gamma function; and Denotes the radial order of a Zernik polynomial; Indicates the entrance pupil diameter of the telescope. It represents the length of atmospheric coherence.

[0015] In one embodiment of the present invention, step S3, in which the multilayer perceptron residual compensation network is trained using the first residual to obtain the optimal multilayer perceptron residual compensation network, further includes constructing a loss function, and training the multilayer perceptron residual compensation network using the loss function and the first residual; wherein, the expression of the loss function is: ; in, Represents the loss function. This represents the total number of training samples. Indicates the first True Zernike coefficient residual labels for each sample Indicates the network's response to the first... Predicted high-frequency residual coefficients for each sample. express Regularization coefficient, This represents the weight parameters of a multilayer perceptron network.

[0016] Secondly, to solve the above-mentioned technical problems, the present invention provides a hybrid wavefront reconstruction system based on orthogonal matching pursuit and deep learning, used to implement the above-mentioned hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning, comprising: The acquisition and calculation module is used to acquire the image of the light spot array corresponding to the distorted wavefront under test, and extract the centroid offset of the light spot corresponding to each sub-aperture in the microlens array; and obtain the slope vector based on the centroid offset of the light spot. The calibration and reconstruction module is used to select multiple Zernike aberration modes to be calibrated and to perturb each Zernike aberration mode; to collect the wavefront slope of each Zernike aberration mode under the perturbation and to construct an interaction matrix; to solve for the Zernike reconstruction coefficient vector based on the interaction matrix, the slope vector and a preset sparsity; and to use the Zernike reconstruction coefficient vector as a low-order reference solution. The prediction module is used to construct a multilayer perceptron residual compensation network; the difference between the true Zernike coefficients and the low-order benchmark solution is used as the first residual, and the multilayer perceptron residual compensation network is trained using the first residual to obtain the optimal multilayer perceptron residual compensation network; the slope vector is input into the optimal multilayer perceptron residual compensation network to obtain the predicted value of the high-frequency residual coefficients. The output module is used to linearly superimpose the low-order reference solution with the predicted value of the high-frequency residual coefficients to output the full-band reconstructed wavefront coefficients; and to complete the hybrid wavefront reconstruction based on the full-band reconstructed wavefront coefficients.

[0017] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: (1) The hybrid wavefront reconstruction method and system based on orthogonal matching pursuit and deep learning described in this invention decomposes wavefront reconstruction into two stages: a low-order coarse estimation driven by a physical model and a high-frequency residual refinement driven by data. On the one hand, based on the physical prior that the energy of turbulent wavefronts is mainly concentrated in low-order Zernike modes, the orthogonal matching pursuit algorithm is used to solve for the low-order wavefront coefficients, quickly restoring the main contour of the wavefront. On the other hand, a lightweight multilayer perceptron network is introduced to specifically fit and compensate for the high-frequency residual components lost by orthogonal matching pursuit due to the preset sparsity constraint. This two-stage architecture can overcome the inherent shortcomings of the pure orthogonal matching pursuit algorithm in truncating high-frequency wavefront information from the root, and significantly improve the reconstruction accuracy of the full-band wavefront under strong turbulent disturbance scenarios.

[0018] (2) Compared with the pure end-to-end deep learning scheme that directly establishes the mapping relationship between slope and complete wavefront coefficient, this invention only uses multilayer perceptron to learn residual components with amplitudes much lower than those of the complete wavefront, which greatly simplifies the difficulty of network fitting, reduces the need for large-scale labeled training data, effectively improves the model training convergence efficiency, and enhances the generalization and adaptation ability of the network under different turbulence intensities. Attached Figure Description

[0019] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0020] Figure 1 This is a flowchart of a hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning in a preferred embodiment of the present invention; Figure 2 This is a flowchart of the interaction matrix calibration process in a preferred embodiment of the present invention; Figure 3 This is a flowchart of the orthogonal matching pursuit algorithm in a preferred embodiment of the present invention; Figure 4 This is a diagram illustrating the overall architecture of a hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning in a preferred embodiment of the present invention. Figure 5 These are two-dimensional phase distribution diagrams and three-dimensional topographic diagrams of the atmospheric turbulence phase screen in a preferred embodiment of the present invention. Figure 6 This is a comparison diagram of the focal plane PSF before and after correction in a preferred embodiment of the present invention; Figure 7 This is a heatmap comparing the reconstruction results of Zernike coefficients of different orders in a preferred embodiment of the present invention. Figure 8 This is a 3D phase comparison diagram of wavefront reconstruction in a preferred embodiment of the present invention; Figure 9 This is a comparison chart of the Strell ratios of different reconstruction methods in a preferred embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0022] Example 1: Reference Figure 1 As shown, this invention provides a hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning, including but not limited to the following steps: S1. Obtain the image of the light spot array corresponding to the distorted wavefront to be tested, and extract the centroid offset of the light spot corresponding to each sub-aperture in the microlens array; obtain the slope vector based on the centroid offset of the light spot. S2. Select multiple Zernike aberration modes to be calibrated and perturb each Zernike aberration mode; collect the wavefront slope of each Zernike aberration mode under perturbation and construct the interaction matrix; solve the Zernike reconstruction coefficient vector based on the interaction matrix, slope vector and preset sparsity; use the Zernike reconstruction coefficient vector as the low-order benchmark solution. S3. Construct a multilayer perceptron residual compensation network; use the difference between the true Zernike coefficients and the low-order benchmark solution as the first residual, and use the first residual to train the multilayer perceptron residual compensation network to obtain the optimal multilayer perceptron residual compensation network; input the slope vector into the optimal multilayer perceptron residual compensation network to obtain the predicted value of the high-frequency residual coefficients. S4. Linearly superimpose the low-order reference solution with the predicted high-frequency residual coefficients to obtain the full-band reconstructed wavefront coefficients; based on the full-band reconstructed wavefront coefficients, complete the hybrid wavefront reconstruction.

[0023] This invention presents a hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning, which effectively solves the problems of high-frequency information loss due to sparsity limitations in pure compressed sensing algorithms, and poor generalization ability and weak physical interpretability of pure deep learning models. It achieves a wavefront reconstruction method that balances high accuracy and high real-time performance. This invention extracts the centroid offset of each sub-aperture spot and generates a slope vector, completely preserving the original measurement information of the wavefront gradient in the x and y directions, reducing measurement noise interference from the source. Simultaneously, it unifies the data output format, ensuring data compatibility for subsequent calibration and network input modules. Secondly, in step S2, perturbations are applied to each Zernike aberration mode and the corresponding slopes are collected to complete the interaction matrix calibration. Based on the physical prior that the energy of the atmospheric turbulent wavefront is concentrated in the low-order Zernike mode, the interaction matrix, the measured slope vector, and the low-order Zernike reconstruction coefficient vector with preset sparsity are combined as the low-order reference solution of the wavefront. On the one hand, the accurate calibration establishes a true physical mapping between the slope and the aberration coefficients, compensating for the coupling error caused by optical path assembly and transmission loss, and avoiding the physical meaningless pseudo-aberrations that are easily generated by the pure data-driven model. On the other hand, the sparse solution greatly reduces the computational dimension, enabling the rapid output of a stable and reliable wavefront main contour, while taking into account the low-latency real-time computing capability. At the same time, physical constraints are used to lock low-frequency dominant distortions such as tilt and defocus, suppressing the global reconstruction distortion problem from the root. Based on this, step S3 constructs a multilayer perceptron residual compensation network, using the difference between the true Zernike coefficients and the low-order benchmark solution as the network training residuals. This allows the network to learn only the high-frequency residual components whose energy is much lower than that of the complete wavefront coefficients. Compared to end-to-end deep learning models that directly fit the full-order coefficients, this greatly reduces the difficulty of network fitting and the dependence on large-scale labeled turbulence datasets. The lightweight network structure also ensures fast inference performance. This network is specifically designed to compensate for the high-frequency fine-scale turbulence distortions that are truncated and lost due to sparsity limitations in orthogonal matching pursuit. It specifically addresses the inherent defects of pure orthogonal matching pursuit algorithms, such as the lack of high-frequency information and the significant decrease in reconstruction accuracy in strong turbulence scenarios. Furthermore, since the low-order benchmark has fixed the overall trend of the wavefront, the network only adapts to high-frequency fluctuations under different operating conditions, effectively improving the model's generalization ability in various turbulence intensities. The phased training mode also avoids confusion between high- and low-order aberration features, reducing the risk of overfitting and underfitting. The final step, S4, linearly superimposes the low-order baseline solution output by the physical model with the high-frequency residual coefficients predicted by the network to obtain the full-band wavefront reconstruction coefficients. This combines the advantages of stable and reliable low-frequency reconstruction by the physical model and accurate restoration of high-frequency details by deep learning, fully covering all wavefront components from low to high order, and significantly improving the reconstruction accuracy of the full-band distorted wavefront under strong turbulence conditions. At the same time, the entire process adopts a modular and decoupled design. Adjustments to the optical path hardware only require recalibrating the interaction matrix, and changes in the turbulence scene only require fine-tuning the residual network, without changing the overall algorithm framework, which facilitates engineering implementation and modular iterative optimization.

[0024] The hybrid wavefront reconstruction method described in this embodiment decomposes the wavefront reconstruction task into two stages: low-order mode physical coarse estimation and high-frequency residual data refinement, and finally achieves high-precision wavefront reconstruction across the entire frequency band through linear superposition.

[0025] Specifically, in step S1, an image of the corresponding light spot array of the distorted wavefront under test is acquired using a Shaker-Hartmann wavefront sensor, and the centroid offset of each sub-aperture is extracted using a weighted centroid method. In this embodiment, assuming the microlens array has M effective sub-apertures, a slope vector of 2M dimensions in both the x and y directions can be obtained. .

[0026] Furthermore, the mathematical expression for calculating the centroid offset of the light spot using the weighted centroid method is as follows: ; ; in, This represents the offset along the x-axis. This represents the offset along the y-axis. and These represent the number of pixels in the x and y directions within a single detection window, respectively. Indicates the first The light intensity value of each pixel. and These represent the x-coordinate and y-coordinate of the corresponding pixel on the detector plane, respectively.

[0027] Specifically, in step S2, the Orthogonal Matching Pursuit (OMP) algorithm is used to analyze the slope vector. The K most significant Zernike coefficients (i.e., the Zernike reconstructed coefficient vector) are reconstructed from the solution and used as the low-order benchmark solution. .in The sparsity is preset. This step utilizes the physical prior that atmospheric turbulent wavefront energy is concentrated in low-order models. The theoretical covariance expression for each order Zernike coefficient is as follows: ; in, Let represent the coefficient covariance of any two Zernike modes in the turbulent phase screen. Represents frequency characteristic factor, Represents the Kronecker symbol. Represents the gamma function; and Denotes the radial order of a Zernik polynomial; Indicates the entrance pupil diameter of the telescope. This represents the atmospheric coherence length. The formula shows that the main energy of wavefront distortion is concentrated in low-order modes, and the wavefront coefficient vector exhibits good sparsity under the Zernike basis.

[0028] Furthermore, this invention employs the OMP algorithm to achieve sparse wavefront reconstruction, and the mathematical model of this algorithm satisfies: ,in This is a pre-calibrated interaction matrix. This invention uses a push-pull method to calibrate the interaction matrix; the calibration process is as follows: Figure 2 As shown. The OMP algorithm iteratively selects the atom (i.e., the interaction matrix) most relevant to the current residual. The column vectors (corresponding to the responses of each Zernike mode) are used to gradually approximate the true coefficients by solving the least squares problem on the support set. The iterative reconstruction process is as follows: Figure 3 As shown.

[0029] Specifically, in step S2, based on the slope vector The Zernike reconstruction coefficient vector is obtained by solving for it, and this vector is used as the low-order baseline solution. The specific steps are as follows: S210. Select multiple Zernike aberration modes to be calibrated, and perturb each Zernike aberration mode; collect the wavefront slope of each Zernike aberration mode under perturbation, and construct the interaction matrix. The specific steps are as follows: S211. Select the Zernike aberration model to be calibrated; apply positive and negative perturbations to the Zernike aberration model respectively to obtain the first wavefront.

[0030] S212. Optical propagation is performed on the first wavefront to obtain the corresponding perturbation light field.

[0031] S213. Measure the aperture slope of each sub-aperture after the corresponding perturbation light field passes through the Shaker-Hartmann wavefront sensor; concatenate all sub-aperture slopes under positive perturbation into a positive slope vector, and concatenate all sub-aperture slopes under negative perturbation into a negative slope vector.

[0032] S214. Based on the positive slope vector, negative slope vector, and perturbation amplitude, calculate the response vector corresponding to the current Zernike aberration mode; where the expression for the response vector is: ; in, This represents the response vector corresponding to the current Zernike aberration mode. Indicates the amplitude of the disturbance. This represents the positive slope vector. This represents the negative slope vector. In this embodiment of the invention, the disturbance amplitude... The preferred value is 0.05 rad, that is, a positive disturbance is +0.05 rad and a negative disturbance is -0.05 rad.

[0033] S215. Traverse all Zernike aberration modes to be calibrated, and concatenate the response vectors corresponding to each mode column by column to obtain the interaction matrix. .

[0034] In the above steps, steps S212 to S213 are the data verification stage.

[0035] S220. Based on the interaction matrix, slope vector, and preset sparsity, solve for the Zernike reconstruction coefficient vector. The specific steps are as follows: S221. Define the initial support set and use the slope vector as the current residual. Specifically, the initial support set... empty set Number of iterations The initial value is 1, and the initial residual is... .

[0036] S222. Calculate the matching atoms based on the current residual and interaction matrix; where the expression for the matching atom is: ; in, Indicates the first Matching atoms in the next iteration Indicates the first The residual of the next iteration; Representing the interaction matrix The Column vector.

[0037] S223. Update the support set based on the matching atoms to obtain a new support set; the mathematical expression for updating the support set is: ; in, Indicates the first The support set updated in the next iteration. Indicates the first The support set updated in the next iteration. The union symbol represents the set of sets.

[0038] S224. Select the columns corresponding to the new support set in the interaction matrix to form a submatrix; based on the submatrix and the slope vector, use least squares to solve for the current estimated coefficients; where the expression for the estimated coefficients is: ; in, Indicates the first The estimated coefficients of the next iteration. Represents the slope vector. Indicates the first The submatrix of the next iteration The transpose symbol for a matrix. This represents the Zernike reconstruction coefficient vector.

[0039] S225. Update the residuals based on the current estimated coefficients, submatrices, and slope vector; use the updated residuals as the current residuals, and update the iteration count (i.e., ...). The residual update expression is: ; in, Indicates the first The residual updated in the next iteration Indicates the first The submatrix of the next iteration Indicates the first The estimated coefficients for the next iteration.

[0040] S226. Determine whether the current iteration number is greater than the preset sparsity, i.e. If yes, then the current estimated coefficients are used as the Zernike reconstruction coefficient vector; otherwise, return to step S222 and repeat until the current iteration number is greater than the preset sparsity. It should be noted that the output Zernike reconstruction coefficient vector is only available on the support set. The corresponding dimension has a non-zero coefficient.

[0041] Furthermore, preset sparsity The range of values ​​is determined by the physical prior that the wavefront energy is concentrated in low-order modes. In this embodiment of the invention, a preset sparsity is used. Preferably, the value is 35, which indicates that the OMP algorithm selects 35 of the most significant Zernike patterns to reconstruct the main wavefront contour, and discards all other patterns besides the aforementioned 35 significant patterns. Furthermore, in this embodiment of the invention, steps S222 to S225 belong to the iterative solution stage.

[0042] Specifically, in step S3, a lightweight multilayer perceptron (MLP) residual compensation network is constructed, and the slope vector is... As input, the output is the predicted value of the high-frequency residual coefficients that the OMP algorithm failed to recover. This network is specifically designed to learn the complex nonlinear mapping from slope features to high-order Zernike coefficient residuals.

[0043] Furthermore, the residual compensation network of the multilayer perceptron comprises an input layer, four hidden layers, and an output layer. The input layer has a dimension of 512, corresponding one-to-one with the slope vectors acquired by the 16×16 sub-apertures in the x and y directions. The neurons in the four hidden layers have dimensions of 512, 256, 128, and 64 respectively. The output layer has a dimension of 60, corresponding to the residual components of the 60th-order Zernike reconstruction coefficient vector. All hidden layers employ the ReLU activation function to introduce nonlinear mapping, while the output layer uses a linear activation function to suit the residual regression solution task.

[0044] Furthermore, during the training phase of the multilayer perceptron residual compensation network, the residuals reconstructed using the orthogonal matching pursuit algorithm are used as supervision labels. Specifically, the first residual is defined as the true Zernike coefficient. Reconstruct the coefficient vector with Zernike (i.e., the low-order benchmark solution) The difference .

[0045] Furthermore, the process of training the multilayer perceptron residual compensation network using the first residual to obtain the optimal multilayer perceptron residual compensation network also includes constructing a loss function and training the multilayer perceptron residual compensation network using the loss function and the first residual. In addition, this embodiment also employs the Adam optimizer to perform parameter updates and introduces an early stopping mechanism to avoid model overfitting at the training process level.

[0046] Furthermore, in this embodiment of the invention, mean squared error (MSE) loss is selected and combined with an L2 regularization term to form the total loss, thereby constraining the network weights and suppressing overfitting. The expression for the total loss function is: ; in, Represents the loss function. This represents the total number of training samples. Indicates the first True Zernike coefficient residual labels for each sample Indicates the network's response to the first... Predicted high-frequency residual coefficients for each sample. express Regularization coefficient, This represents the weight parameters of a multilayer perceptron network.

[0047] The complete training process of the multilayer perceptron residual compensation network is described in detail below with reference to an exemplary embodiment: For example, a physical model (Von Kármán power spectrum) is used to generate full-band slope data including high-frequency aliasing errors as network input; the actual Zernike coefficients are used as input. With OMP reconstruction value The difference (i.e., the residual) The residual coefficients are used as supervisory labels for network training, rather than complete wavefront coefficients; a bottleneck network consisting of multiple fully connected hidden layers is adopted, and its output layer dimension matches the total order of the Zernike coefficients to be compensated, directly outputting the predicted residual coefficient values; the total number of network parameters is controlled in the hundreds of thousands to ensure millisecond-level inference latency; the mean squared error (MSE) loss function plus L2 regularization term is used to make the network focus on the larger high-order aberration components that the OMP algorithm failed to compensate for.

[0048] Specifically, in step S4, the low-order benchmark solution obtained in step S2 is... The predicted high-frequency residual coefficients obtained in step S3 Linear superposition is performed to obtain the final full-band reconstructed wavefront coefficients. Among them, the full-band reconstructed wavefront coefficients The expression is: .

[0049] The above linear superposition utilizes the orthogonality of Zernike polynomials. The OMP algorithm determines the dominant coefficients of the low-order modes using the least squares method, while the MLP supplements the residual correction of the high-order modes on the same basis. The two are mathematically independent and functionally complementary.

[0050] This invention employs the physical prior that wavefront distortion energy is concentrated in low-order aberrations (i.e., the Zernike coefficient covariance theory derived by Noll). The orthogonal matching pursuit algorithm can accurately capture all low-order aberration components and output a wavefront reference solution with clear physical interpretability. A lightweight multilayer perceptron residual compensation network is used to adaptively compensate for high-frequency residuals in a data-driven manner, compensating for the loss of high-frequency wavefront information caused by the pre-defined sparsity constraint of the orthogonal matching pursuit algorithm. The reference solution and the compensated residuals are linearly superimposed within the same set of Zernike orthogonal polynomials. The two types of components are independent of each other and complementary, ultimately achieving high-precision wavefront distortion reconstruction across the entire waveband.

[0051] Furthermore, to verify the effectiveness of the hybrid wavefront reconstruction method described in this embodiment of the invention, an optical path experimental platform was built to conduct comparative verification tests. The specific experimental setup and test content are as follows: Specifically, refer to Figure 4As shown, the experiment includes an offline training phase and an online prediction phase: the offline training phase is used to pre-optimize the parameters and converge the model of the multilayer perceptron residual compensation network; the online prediction phase is used for real-time computation on the measured data, outputting predicted values ​​of high-frequency residual coefficients. The hardware implementing these two modes includes a data input unit, an OMP solving unit, a residual construction unit, a residual learning unit, a test input unit, a residual prediction unit, a system fusion unit, and a reconstruction output unit. The data input unit, OMP solving unit, residual construction unit, and residual learning unit cooperate to execute the entire offline training task of the multilayer perceptron residual compensation network; the test input unit, OMP solving unit, residual prediction unit, system fusion unit, and reconstruction output unit cooperate to achieve the online real-time prediction function, and during online computation, the measured slope vector is used... The sample to be tested is input into the OMP solving unit and the residual prediction unit. The main experimental procedure is as follows: First, the image of the light spot array corresponding to the distorted wavefront to be tested is acquired through the Shaker-Hartmann wavefront sensor, and the slope vector is extracted using the weighted centering method. Secondly, the orthogonal matching pursuit algorithm is used to analyze the slope vector. The low-order Zernike coefficient benchmark solution is reconstructed. ( Figure 4 (represented by OMP coefficients in Chinese); then, the slope vector... Inputting a pre-trained lightweight multilayer perceptron residual compensation network, the predicted values ​​of high-frequency residual coefficients are obtained. ( Figure 4 (represented by predicted residuals); finally, the low-order benchmark solution... Predicted values ​​of high-frequency residual coefficients Linear superposition is performed to obtain the final full-band reconstructed wavefront coefficients. .

[0052] Furthermore, the simulation parameters of the Shaker-Hartmann wavefront sensor are shown in Table 1, thereby generating the distorted wavefront data to be reconstructed.

[0053] Table 1:

[0054] Furthermore, in this experiment, an end-to-end virtual optical experimental platform was constructed based on the Hcipy optical simulation library. The dataset generated a full-band atmospheric turbulence phase screen with a spatial resolution of 128×128 based on the Von Kármán power spectrum model, producing a total of 100,000 independent wavefront samples. Each sample contains a 512-dimensional slope vector. 60-dimensional OMP benchmark solution And 60-dimensional high-frequency residual coefficient prediction values The dataset is divided into training, validation, and test sets in a 7:2:1 ratio. A typical atmospheric turbulence phase screen generated by Von Kármán's power spectrum is shown below. Figure 5 As shown. Figure 5 The left image is a two-dimensional phase distribution map; the right image is the corresponding three-dimensional topography map.

[0055] Furthermore, the wavefront reconstruction effects and performance of different reconstruction methods on the test set are compared, for example... Figure 6 and Figure 7 As shown. Figure 6 The far-field point spread function (PSF) in the pure open-loop state is compared with the PSF obtained after correction using the pure OMP algorithm, the pure MLP algorithm, and the method described in this invention. It can be seen that the PSF obtained by the method of this invention has the most concentrated spot size, the highest center brightness, and effectively suppressed sidelobe energy, thus most closely resembling the ideal Airy disk morphology.

[0056] Furthermore, Figure 7 This graph compares the reconstruction results of Zernike coefficients of different orders using different reconstruction methods. The horizontal axis represents the Zernike mode order, and each row corresponds to the reconstruction result of different methods. The rows marked "Hybrid" represent the reconstruction results of the hybrid wavefront reconstruction method proposed in this embodiment. (Refer to...) Figure 7 As shown, in the low-to-mid-order region (orders 1-35), both the OMP algorithm and the method described in this invention can fit the true value well; in the high-order region (orders 35-60), the pure OMP algorithm is limited by the preset sparsity, and the predicted coefficient values ​​decay rapidly and approach zero, completely losing the ability to recover high-frequency details, while the prediction results of the method described in this invention closely fit the true value curve across the entire frequency band, demonstrating good residual compensation capability.

[0057] To further illustrate the wavefront reconstruction effects of different methods, the Zernike coefficients predicted by different methods were reconstructed into three-dimensional wavefront phase maps for comparison, such as... Figure 8 As shown. Figure 8 3D phase diagrams of the original wavefront, wavefront reconstructed by the OMP algorithm, wavefront reconstructed by the MLP algorithm, and wavefront reconstructed by the method of this invention are presented for typical samples. Furthermore, to comprehensively and quantitatively evaluate the actual correction performance of the method of this invention, this experiment uses the system focal plane Strehl ratio (SR) as the evaluation index, and statistically analyzes the Strehl ratio improvement corresponding to different reconstruction algorithms. The comparison results are as follows: Figure 9 As shown, the method proposed in this invention improves the Strell ratio by 112.5% ​​compared to the pure OMP method.

[0058] This invention proposes a hybrid wavefront reconstruction method based on orthogonal matching pursuit (ORP) and deep learning. Its underlying logic involves decomposing the wavefront reconstruction task into two stages: a low-order coarse estimation driven by a physical model and a high-frequency refinement driven by data. The ORP algorithm captures the main contour of the wavefront based on the physical prior that wavefront energy is concentrated in low-order modes. A lightweight multilayer perceptron network specifically learns and compensates for the high-frequency residual components lost due to sparsity limitations in ORP. This overcomes the inherent defect of pure ORP, which completely truncates high-frequency information due to preset sparsity, thus significantly improving the accuracy of full-band wavefront reconstruction under strong turbulence. Furthermore, compared to pure end-to-end deep learning models that require learning a complex mapping from slope to complete wavefront coefficients, the multilayer perceptron network in this invention only needs to learn residual components with energy much smaller than the complete wavefront coefficients. This greatly reduces the learning difficulty of the network and its dependence on training data, thereby improving the network model's generalization ability and training efficiency under different turbulent environments.

[0059] Furthermore, the embodiments of the present invention employ a lightweight multilayer perceptron network with only 440,000 parameters and a single-frame inference latency of 1.2ms, which meets the bandwidth requirements of kilohertz-level real-time closed-loop control in adaptive optics systems. Moreover, the first-level orthogonal matching tracking algorithm is based on a clear physical model, ensuring the interpretability of low-order aberration reconstruction results and solving the reliability problem caused by the black-box characteristics of pure data-driven models.

[0060] Example 2: Based on the same inventive concept, this embodiment provides a hybrid wavefront reconstruction system based on orthogonal matching pursuit and deep learning. The principle of solving the problem is similar to that of the hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning provided in Embodiment 1, and the repeated parts will not be described again.

[0061] This embodiment provides a hybrid wavefront reconstruction system based on orthogonal matching pursuit and deep learning, used to implement the hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning described in Embodiment 1, including: The acquisition and calculation module is used to acquire the image of the spot array corresponding to the distorted wavefront under test, and extract the spot centroid offset corresponding to each sub-aperture in the microlens array; based on the spot centroid offset, the slope vector is obtained. The calibration and reconstruction module is used to select multiple Zernike aberration modes to be calibrated and perturb each Zernike aberration mode; collect the wavefront slope of each Zernike aberration mode under perturbation and construct the interaction matrix; solve the Zernike reconstruction coefficient vector based on the interaction matrix, slope vector and preset sparsity; and use the Zernike reconstruction coefficient vector as a low-order reference solution. The prediction module is used to construct a multilayer perceptron residual compensation network. The difference between the true Zernike coefficients and the low-order benchmark solution is used as the first residual. The multilayer perceptron residual compensation network is trained using the first residual to obtain the optimal multilayer perceptron residual compensation network. The slope vector is input into the optimal multilayer perceptron residual compensation network to obtain the predicted values ​​of high-frequency residual coefficients. The output module is used to linearly superimpose the low-order reference solution with the predicted high-frequency residual coefficients to output the full-band reconstructed wavefront coefficients; and to complete the hybrid wavefront reconstruction based on the full-band reconstructed wavefront coefficients.

[0062] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0063] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0064] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0065] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0066] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning, characterized in that, include: S1. Obtain the image of the light spot array corresponding to the distorted wavefront to be tested, and extract the centroid offset of the light spot corresponding to each sub-aperture in the microlens array. Based on the centroid offset of the light spot, the slope vector is obtained; S2. Select multiple Zernike aberration modes to be calibrated, and perturb each Zernike aberration mode; collect the wavefront slope of each Zernike aberration mode under the perturbation, and construct an interaction matrix; solve for the Zernike reconstruction coefficient vector based on the interaction matrix, the slope vector, and the preset sparsity; use the Zernike reconstruction coefficient vector as a low-order reference solution. S3. Construct a multilayer perceptron residual compensation network; use the difference between the true Zernike coefficients and the low-order benchmark solution as the first residual, and use the first residual to train the multilayer perceptron residual compensation network to obtain the optimal multilayer perceptron residual compensation network; input the slope vector into the optimal multilayer perceptron residual compensation network to obtain the predicted value of the high-frequency residual coefficients. S4. Linearly superimpose the low-order reference solution with the predicted high-frequency residual coefficients to obtain the full-band reconstructed wavefront coefficients; complete the hybrid wavefront reconstruction based on the full-band reconstructed wavefront coefficients.

2. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 1, characterized in that, In step S1, the formula for calculating the centroid offset of the light spot is: ； ； in, This represents the offset along the x-axis. This represents the offset along the y-axis. and These represent the number of pixels in the x and y directions within a single detection window, respectively. Indicates the first The light intensity value of each pixel; and These represent the x-coordinate and y-coordinate of the corresponding pixel on the detector plane, respectively.

3. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 1, characterized in that, In step S2, multiple Zernike aberration modes to be calibrated are selected, and each Zernike aberration mode is perturbed; the wavefront slope of each Zernike aberration mode under the perturbation is collected, and the interaction matrix is ​​constructed as follows: Select the Zernike aberration mode to be calibrated; apply positive and negative perturbations to the Zernike aberration mode respectively to obtain the first wavefront; Optical propagation is performed on the first wavefront to obtain the corresponding perturbation light field; Measure the aperture slope of each sub-aperture after the perturbation light field passes through the Shaker-Hartmann wavefront sensor; concatenate all sub-aperture slopes under positive perturbation into a positive slope vector, and concatenate all sub-aperture slopes under negative perturbation into a negative slope vector; The response vector corresponding to the current Zernike aberration mode is calculated based on the positive slope vector, the negative slope vector, and the perturbation amplitude. Traverse all Zernikal aberration modes to be calibrated, and concatenate the response vectors corresponding to each mode column by column to obtain the interaction matrix.

4. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 3, characterized in that, The expression for the response vector is: ; in, This represents the response vector corresponding to the current Zernike aberration mode. Indicates the amplitude of the disturbance. This represents the positive slope vector. This represents the negative slope vector.

5. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 1, characterized in that, In step S2, the step of solving the Zernike reconstruction coefficient vector based on the interaction matrix, the slope vector, and the preset sparsity is as follows: S221. Define the initial support set and use the slope vector as the current residual; S222. Calculate the matching atoms based on the current residual and the interaction matrix; S223. Update the support set according to the matching atoms to obtain a new support set; S224. Select the columns corresponding to the new support set in the interaction matrix to form a submatrix; solve the current estimated coefficients based on the submatrix and the slope vector using least squares. S225. Update the residuals based on the current estimated coefficients, the submatrix, and the slope vector; use the updated residuals as the current residuals and update the iteration count. S226. Determine whether the current iteration number is greater than the preset sparsity; if so, use the current estimated coefficients as the Zernike reconstruction coefficient vector; otherwise, return to S222 and repeat until the current iteration number is greater than the preset sparsity.

6. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 5, characterized in that, The expression for the estimated coefficients is: ； in, Indicates the first The estimated coefficients of the next iteration. Represents the slope vector. Indicates the first The submatrix of the next iteration The symbol for transpose of a matrix.

7. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 5, characterized in that, In step S225, the residuals are updated based on the current estimated coefficients, the submatrix, and the slope vector; wherein the residual update expression is: ； in, Indicates the first The residual updated in the next iteration Represents the slope vector. Indicates the first The submatrix of the next iteration Indicates the first The estimated coefficients for the next iteration.

8. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 1, characterized in that, The theoretical covariance expression for each order of the Zernike coefficients in the Zernike reconstruction coefficient vector is as follows: ； in, Let represent the coefficient covariance of any two Zernike modes in the turbulent phase screen. Represents frequency characteristic factor, Represents the Kronecker symbol. Represents the gamma function; and Denotes the radial order of a Zernik polynomial; Indicates the entrance pupil diameter of the telescope. It represents the length of atmospheric coherence.

9. The hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning according to claim 1, characterized in that, In step S3, the process of training the multilayer perceptron residual compensation network using the first residual to obtain the optimal multilayer perceptron residual compensation network further includes constructing a loss function and training the multilayer perceptron residual compensation network using the loss function and the first residual; wherein, the expression of the loss function is: ； in, Represents the loss function. This represents the total number of training samples. Indicates the first True Zernike coefficient residual labels for each sample Indicates the network's response to the first... Predicted high-frequency residual coefficients for each sample. express Regularization coefficient, This represents the weight parameters of a multilayer perceptron network.

10. A hybrid wavefront reconstruction system based on orthogonal matching pursuit and deep learning, used to implement the hybrid wavefront reconstruction method based on orthogonal matching pursuit and deep learning as described in any one of claims 1 to 9, characterized in that, include: The acquisition and calculation module is used to acquire the image of the spot array corresponding to the distorted wavefront under test, and extract the centroid offset of the spot corresponding to each sub-aperture in the microlens array. Based on the centroid offset of the light spot, the slope vector is obtained; The calibration and reconstruction module is used to select multiple Zernike aberration modes to be calibrated and to perturb each Zernike aberration mode; to collect the wavefront slope of each Zernike aberration mode under the perturbation and to construct an interaction matrix; to solve for the Zernike reconstruction coefficient vector based on the interaction matrix, the slope vector and a preset sparsity; and to use the Zernike reconstruction coefficient vector as a low-order reference solution. The prediction module is used to construct a multilayer perceptron residual compensation network; the difference between the true Zernike coefficients and the low-order benchmark solution is used as the first residual, and the multilayer perceptron residual compensation network is trained using the first residual to obtain the optimal multilayer perceptron residual compensation network; the slope vector is input into the optimal multilayer perceptron residual compensation network to obtain the predicted value of the high-frequency residual coefficients. The output module is used to linearly superimpose the low-order reference solution with the predicted value of the high-frequency residual coefficients to output the full-band reconstructed wavefront coefficients; and to complete the hybrid wavefront reconstruction based on the full-band reconstructed wavefront coefficients.

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