A wavefront restoration acceleration method based on dynamic restoration matrix

Abstract

The application provides a wave front recovery acceleration method based on a dynamic recovery matrix, which is suitable for solving wave front recovery coefficients by using a conjugate gradient and a variant thereof and accelerating wave front recovery by using a two-stage preprocessor. Compared with the wave front recovery by using the conjugate gradient variant algorithm without the preprocessor, the wave front recovery speed is improved by about 35% as a whole under the same recovery accuracy, and the multiplication operation amount of the wave front recovery is about 1 / 28 of that of the wave front recovery by using the SVD method. The application can effectively improve the wave front recovery and control real-time performance caused by the dynamic change of the recovery matrix due to the weighting of the slope or light intensity, expand the use range of the wave front sensor, and is expected to be used for high-precision and high-robustness wave front measurement in light-deficient scenes such as light intensity flickering.

Description

Technical Field

[0001] This invention belongs to the field of wavefront sensing technology, and particularly relates to a wavefront restoration acceleration method based on a dynamic restoration matrix. Background Technology

[0002] The Shak-Hartmann wavefront sensor (SH-WFS) is currently the most widely used wavefront sensor. It typically consists of a microlens and a CCD photoelectric sensor. It provides dynamic temporal-spatial distributions of beam phase and intensity with high temporal and spatial resolution, and is a wavefront testing instrument based on wavefront slope measurement. The Shak-Hartmann wavefront sensor has the following advantages: simple structure with no moving parts; and the ability to detect beacons of repetition rate pulses.

[0003] In practical applications, traditional wavefront reconstruction algorithms struggle to meet the accuracy requirements of scenarios such as atmospheric turbulence, noise, light intensity flicker within sub-apertures of Shaker-Hartmann wavefront sensors, and even light shortages. This necessitates weighting of light intensity and slope information, or sub-aperture removal, to achieve the required reconstruction accuracy and stable wavefront reconstruction. In 2013, Xue et al. proposed an intensity distribution-based control algorithm that increased the laser Strell ratio by 5% through intensity weighting. In 2016, Chen et al. increased the energy of the first-order diffraction ring from 41% to 64% through slope weighting. In 2020, Wei et al.'s experiments showed that for light-short scenarios, the sub-aperture removal method has relatively higher reconstruction accuracy compared to the slope zeroing method. These algorithms share the characteristic that they require resolving the inverse matrix of the reconstruction matrix. The SVD method is often used to calculate the generalized inverse of the restored matrix. However, the SVD method involves a large amount of computation, and the computational workload increases rapidly with the increase of the matrix dimension, which seriously affects the real-time performance of the system. This is also a factor that limits the widespread application of the photon aperture removal method. Therefore, it is urgent to find a method to accelerate the solution of wavefront restoration coefficients. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the issue of poor real-time performance of wavefront restoration using dynamic restoration matrix in scenarios where the sub-aperture of the Shaker-Hartmann wavefront sensor is lacking light or where slope and light intensity are weighted. A wavefront restoration acceleration method based on dynamic restoration matrix is ​​proposed, which can effectively improve the real-time performance of wavefront restoration under the same wavefront restoration accuracy.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a wavefront restoration acceleration method based on a dynamic restoration matrix. This method transforms the linear system to be solved into a linear system with the same solution but better spectral properties by constructing a two-stage preprocessor for the conjugate gradient or its variant, thereby accelerating the convergence speed of the iteration and improving the real-time performance of the solution. Taking the sub-aperture removal method as an application example, this method is specifically implemented through the following steps:

[0006] Step 1: Wavefront reconstruction based on the pattern method can be expressed by the linear equation G = Z. o A, where G is the slope data detected by the wavefront sensor, Z is the static restoration matrix, and A is the Zernike coefficient to be solved. To reduce computational complexity and improve restoration accuracy, the commonly used linear equation is: The generalized inverse of the static restored matrix is ​​used as the conjugate gradient or its variant as the first-stage preprocessing matrix.

[0007] Step 2: Construct the diagonal matrices W and Z that generate the dynamic restoration matrix. N =((WZ) o ) T (WZ o The matrix H is a dynamic restoration matrix. N M1 serves as the basis for optimizing the preprocessing matrix in the second stage. H is a cluster matrix with eigenvalues ​​between 0 and 1. The more concentrated the eigenvalue distribution, the faster the convergence speed of the preprocessing conjugate gradient squaring method. Therefore, the eigenvalue distribution in the condition number set of the H matrix can be modified.

[0008] Step 3: Reduce the condition number of the H matrix by improving the minimum eigenvalue of the H matrix, and estimate the minimum eigenvalue t and eigenvector V in a finite number of steps using the Krylov subspace method.

[0009] Step 4: T = Kt is the scaled eigenvalue, K is the scaling factor, and the second-stage preprocessing matrix can be expressed as M2 = M1 + M1 * V * (V T / T), with M2 as the preprocessing matrix for the final conjugate gradient flattening method.

[0010] Step 5: Solve for the wavefront Zernike mode coefficients using the preprocessed conjugate gradient or its variant.

[0011] Furthermore, the process of Krylov estimating the minimum eigenvalue described in step 3 is as follows:

[0012] Step 3.1: Determine the first-stage preprocessing matrix M1 and the non-zero random vector X0, and then perform a normalization operation on the non-zero random vector X0: X = X0 / ||X0||2.

[0013] Step 3.2: The process of solving for the eigenvectors is as follows:

[0014]

[0015] Where i is the number of iterations and α is the iteration step size.

[0016] Step 3.3: Repeat step 3.2 to solve for the minimum eigenvalue, eigenvector, and minimum eigenvalue t = V. THV.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] This invention accelerates the convergence speed through a two-stage preprocessing method, which can further improve the speed of solving mode coefficients by the photon aperture removal method. While taking into account the tolerance of wavefront sensor pair spot loss, it provides an effective solution for high-precision, high-frame-rate wavefront restoration in cases of uneven near-field light intensity distribution and light intensity flicker of beacon light, thus broadening the applicability of the photon aperture removal method. Attached Figure Description

[0019] Figure 1 This is a flowchart of the preprocessing iteration process for the aperture removal method of this invention.

[0020] Figure 2 The diagram shows the distortion wavefront data acquisition device in the embodiment, where 1 is a parallel light source generating device, 2 is a linear polarizer, 3 is a reflector, 4 is a beam splitter, 5 is a spatial light modulator (SLM), 6 and 8 are a 4-f system composed of the first and second lenses, 7 is an aperture, 9 is a microlens array, and 10 is a CCD camera.

[0021] Figure 3 This is a graph showing the ratio of the condition number of the M2 matrix in the second stage of sample processing to the condition number of the M1 matrix in the first stage of preprocessing, as illustrated in the example.

[0022] Figure 4 The results of solving the mode coefficient multiplication computation for 1000 test samples in the example are shown below, using the SVD method, the conjugate gradient squaring method, and the preprocessed conjugate gradient squaring method. Figure 4 (a) is a comparison of the computational complexity of solving mode coefficient multiplication using the SVD method, the conjugate gradient squaring method, and the preprocessed conjugate gradient squaring method. Figure 4 (b) is a graph showing the ratio of the computational cost of the SVD method to the computational cost of the preprocessing conjugate gradient squaring method. Figure 4 (c) is a comparison of the computational complexity of solving mode coefficient multiplication using the conjugate gradient squaring method and the preprocessed conjugate gradient squaring method. Figure 4 The graph in (d) shows the ratio of the computational cost of conjugate gradient squaring multiplication to the computational cost of preprocessing conjugate gradient squaring multiplication. Detailed Implementation

[0023] To make the objectives and technical solutions of this invention clearer and more intuitive, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0024] In the embodiments, the data acquisition device system is as follows: Figure 2As shown, 1 is a parallel light source generating device, 2 is a linear polarizer, 3 is a reflector, 4 is a beam splitter, 5 is a spatial light modulator (SLM), 6 and 8 are a 4-f system composed of the first and second lenses, 7 is an aperture, 9 is a microlens array, and 10 is a CCD camera. The main parameters in this embodiment are as follows: wavelength 635nm, number of sub-apertures 16×16, sub-aperture size 400μm, microlens focal length 42.3mm, and pixel size 6.4μm×6.4μm.

[0025] like Figure 1 As shown, the specific steps of the wavefront restoration acceleration method based on the dynamic restoration matrix include:

[0026] Step 1: Generate the first 35 random incident wavefronts using the Kolmogorov turbulence model and calculate the wavefront reconstruction matrix Z. O The first-stage preprocessing matrix M1 is used to perform a 20% random photon depletion process on the acquired incident wavefront, generating the corresponding photon depletion sub-aperture removal diagonal matrix W and Z. N .

[0027] Step 2: Calculate matrix H and find its minimum eigenvalue and eigenvector.

[0028] Furthermore, in step 2, the calculation of the minimum eigenvalue and eigenvector of matrix H uses the Krylov method with an iteration step size α of 1.1, a fixed number of iterations i = 15, and a scaling factor K of 3. Figure 3 This is a ratio diagram of the condition numbers of the first-stage preprocessing matrix M1 and the second-stage preprocessing matrix M2, which is calculated using the minimum eigenvalues ​​and eigenvectors of matrix H. The degree to which the condition numbers of matrix M2 are concentrated compared to those of matrix M1 is related to the number of iterations required to estimate the minimum eigenvalues ​​and eigenvectors of matrix H.

[0029] Step 3: Calculate the second-stage preprocessing matrix M2 using the estimated minimum eigenvalues ​​and eigenvectors. In a real system, the eigenvalues ​​and eigenvectors can be accurately obtained, and the calculated second-stage preprocessing matrix M2 can be used multiple times.

[0030] Step 4: Select the conjugate gradient variant, conjugate gradient flattening method, as the target algorithm for acceleration, and solve the wavefront Zernike coefficients by preprocessing the conjugate gradient flattening method.

[0031] Furthermore, the solution process for the preprocessing conjugate gradient flattening method in step 4 is as follows:

[0032]

[0033] Where b and A are the results of correcting the slope vector and the restored matrix, ρ, and α is an intermediate variable, β and α are the search step size, u and p are the search direction, M2 is the second-stage preprocessing matrix, r is the update error, and x0 is a random initial vector. Here, x0 uses the zero vector. In the experiment, the solution result of the previous iteration can be selected as the initial vector for the next iteration.

[0034] Step 5: Compare the computational complexity of SVD, the preprocessed conjugate gradient squaring method, and the conjugate gradient squaring method. Here, the number of multiplication operations for each algorithm is used as the evaluation criterion. The total number of multiplication operations for the preprocessed conjugate gradient squaring method is:

[0035] CM pcgs =MN + (4K + 1)N 2 +7KN-2N+3K-2,

[0036] The computational complexity of multiplication using the conjugate gradient square method is:

[0037] CM cgs =MN + (2K + 1)N 2 +7KN-2N+3K-2,

[0038] The computational complexity of SVD multiplication based on one-sided Jacobian is:

[0039] CM svd =(N 2 +7N+3)K+2N 2 +NM

[0040] Where M is the row dimension of the wavefront reconstruction matrix, N is the column dimension of the wavefront reconstruction matrix, and K is the number of iterations of the algorithm. Figure 4 The results of solving the mode coefficient multiplication operation for 1000 test samples in the example are shown below, using the SVD method, the conjugate gradient square method, and the preprocessed conjugate gradient square method. Figure 4 (a) shows a comparison of the computational complexity of solving mode coefficient multiplications using the SVD method, the conjugate gradient squaring method, and the preprocessed conjugate gradient squaring method. The conjugate gradient squaring method has an advantage over the SVD method in solving mode coefficients using the photon aperture removal method. Figure 4 (b) shows the ratio of the computational cost of the SVD method to that of the preprocessing conjugate gradient squared multiplication method. The computational cost of the SVD method is approximately 28 times that of the preprocessing conjugate gradient squared multiplication method. Figure 4 The diagram compares the computational complexity of solving mode coefficient multiplication using the conjugate gradient squaring method and the preprocessed conjugate gradient squaring method (c). The preprocessed conjugate gradient squaring method shows a significant improvement in overall wavefront recovery speed compared to the conjugate gradient squaring method. Figure 4 As shown in (d), the wavefront recovery speed of the preprocessed conjugate gradient squaring method is improved by about 35% compared with that of the conjugate gradient squaring method.

[0041] In summary, this invention can further improve the solution speed of wavefront reconstruction mode coefficients through a two-stage preprocessing method, broaden the applicability of the photon-depleted aperture removal method, and provide an effective method for high-precision, high-bandwidth wavefront measurement of dynamic reconstruction matrices.

[0042] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any transformations or substitutions that can be conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of the present invention.

Claims

1. A dynamic restoration matrix based wavefront restoration acceleration method, characterized by: The method is realized by the following steps: Step 1: Linear equation representation of wavefront reconstruction based on modal method is G = Z O A, where G is the slope data detected by wavefront sensor, Z O is the static reconstruction matrix, and A is the Zernike mode coefficient; in order to reduce the calculation complexity and improve the reconstruction accuracy, the linear equation is The generalized inverse of the static reconstruction matrix is taken as the first stage preconditioning matrix of the conjugate gradient or its variant, that is Step 2: Constructing a diagonal matrix W, Z which generates a dynamic recovery matrix w = ((WZ o ) T (WZ o )) is a dynamic recovery matrix, and the matrix h = Z N M1 is the optimization basis of the second stage preconditioning matrix, and the eigenvalue matrix of H is a cluster diagonal matrix between 0 and 1. The more concentrated the eigenvalue distribution is, the faster the convergence speed of the preconditioned conjugate gradient or its variant is. Therefore, the first stage preconditioning matrix M1 is further optimized by modifying the condition number of the eigenvalue distribution of the H matrix. Step 3: reduce the condition number of the H matrix by improving the minimum eigenvalue of the H matrix, and estimate the minimum eigenvalue t and the eigenvector V by a finite step through the Krylov subspace method; Step 4: T = Kt is the scaled eigenvalue, K is the scale factor, the second stage preconditioning matrix is represented as M2 = M1 + M1*V*(V T / T), M2 is used as the preconditioning matrix of the final conjugate gradient or its variants; Step 5: solve the wavefront Zernike mode coefficient A by using the final preconditioning matrix M2 of the conjugate gradient or its variant.

2. The wavefront restoration acceleration method based on dynamic restoration matrix according to claim 1, characterized in that: The process of estimating the minimum eigenvalue t by the Krylov subspace method in step 3 is as follows: Step 3.1: determine the first-stage preconditioning matrix M1 and a non-zero random vector X0, and then normalize the non-zero random vector X0: X = X0 / ||X0||2; The solving process of the eigenvector is as follows: Wherein, i is the iteration number, and a is the iteration step. Step 3.3: Repeating step 3.2 can solve the minimum eigenvalue eigenvector and minimum eigenvalue t = V T HV.

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