A fast wavefront reconstruction method

Abstract

The application discloses a fast wavefront reconstruction method, which can be applied to Hartmann wavefront sensors and slope type wavefront sensors such as a shearing interferometer. When a wavefront is reconstructed by a region method or a spline method, initial slopes are down-sampled to form slope matrices of multiple scales, and then the wavefront is reconstructed from a large scale to a small scale. Except for the largest scale, the initial value of each scale is up-sampled from the previous scale. The method has simple and stable flow, is easy to implement, and can greatly reduce the iteration number and improve the numerical calculation stability compared with the existing method of directly reconstructing the original slope, so that the fast, stable and effective wavefront reconstruction is realized.

Description

Technical Field

[0001] This invention relates to a fast wavefront reconstruction method, and more particularly to a fast wavefront reconstruction method applicable to slope-type wavefront sensors such as Hartmann wavefront sensors and shear interferometers. Background Technology

[0002] Wavefront aberration measurement has wide applications in optical processing and manufacturing, laser systems, astronomical observation, and other fields. There are many principles and instruments for wavefront aberration measurement, among which slope-type wavefront sensors, such as Hartmann wavefront sensors and shearing interferometers, reconstruct the wavefront by sampling the slope of the wavefront aberration and have wide applications in related fields.

[0003] There are various methods for wavefront reconstruction of slope-type wavefront sensors, such as the region method, pattern method, spline method, and Fourier method. Among them, the region method and spline method are commonly used methods, which can reconstruct wavefront data with local characteristics and have high spatial resolution reconstruction accuracy. The region method creates a mesh model, establishes the relationship between the slope and the wavefront reconstruction points, obtains a least-squares constraint, and then solves this constraint through an iterative algorithm to obtain the reconstructed wavefront. As the complexity of the measured object increases, the resolution of wavefront reconstruction also increases accordingly, the number of slope sampling points increases, and the number of iterations required for convergence also increases. The computational cost of reconstructing a wavefront once is approximately the number of sampling points multiplied by the number of iterations. When both the number of sampling points and the number of iterations increase, the computational cost of reconstruction increases significantly. Therefore, a fast wavefront reconstruction algorithm is crucial for high-resolution slope-type wavefront sensors reconstructed using the region method. Summary of the Invention

[0004] This invention arose from the above background and invented a novel fast wavefront reconstruction method. This method uses a multi-scale approach, reconstructing sequentially from large scale to small scale. Since the reconstruction result of the large scale is used as the initial value when reconstructing at the small scale, the number of iterations can be effectively reduced, thereby improving the calculation speed and accuracy.

[0005] The technical problem to be solved by the present invention is to overcome the problem that the reconstruction speed is slow due to the large number of iterations when slope wavefront sensors reconstruct slope data using the region method or spline method in the prior art.

[0006] The technical solution adopted by this invention to solve its technical problem is: a fast wavefront reconstruction method, the steps of which are as follows:

[0007] Step 1) Obtain the slope matrix P with a resolution of L×M from the wavefront sensor. x and P y ;

[0008] Step 2) For P x and Py Perform downsampling on N layers to generate the slope matrix of N layers. and Where i = 1, 2, 3, ..., N, and the Nth layer is the layer with the largest scale;

[0009] Step 3) Using the default initial values, let i = N, and use wavefront restoration algorithm 1, from... and Reconstruction yields wavefront W N ;

[0010] Step 4) Update the value of i using i-1: i ← i-1;

[0011] Step 5) If i≥1, proceed to step 6); otherwise, jump to step 7.

[0012] Step 6) W i-1 Upsampling by Using the initial values, wavefront reconstruction algorithm 1 is used, by and Reconstruction yields wavefront W i (Jump to step 4);

[0013] Step 7) W 1 Upsampling by Using P as the initial value, wavefront reconstruction algorithm 2 is used. x and P y The wavefront W is obtained by reconstruction.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. The fast wavefront reconstruction method disclosed in this invention is suitable for high-resolution slope-type wavefront sensors that use iterative methods such as the region method or spline method to reconstruct the wavefront, and can effectively reduce the number of iterations and improve the reconstruction speed.

[0016] 2. In the implementation of the fast wavefront reconstruction method disclosed in this invention, the large-scale calculation results can be discarded after being used as the initial values ​​for the next small-scale layer, making it suitable for hardware pipeline processing. Attached Figure Description

[0017] Figure 1 This is a flowchart of a fast wavefront reconstruction method according to the present invention;

[0018] Figure 2 The slope matrix P, which is 128×128, obtained during the implementation of this invention. x and P y ;

[0019] Figure 3For P x and P y The slope matrix of the first layer obtained after downsampling and and The resolution is 64×64;

[0020] Figure 4 To and The slope matrix of the second layer obtained after downsampling and and The resolution is 32×32;

[0021] Figure 5 To and The slope matrix of the third layer obtained after downsampling and and The resolution is 16×16;

[0022] Figure 6 To and The slope matrix of the 4th layer obtained after downsampling and and The resolution is 16×16;

[0023] Figure 7 For the regional method using the Fried model, by and Reconstruction yields wavefront W i , where i = 1, 2, 3, 4;

[0024] Figure 8 To make W 1 Upsampling and with As initial values, the region method of the Southwell model is used, with P as the initial value. x and P y The wavefront W is obtained by reconstruction. Detailed Implementation

[0025] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0026] This implementation scheme uses a Hartmann wavefront detector with a microprism array structure and describes a fast wavefront reconstruction method, the operation process of which is as follows: Figure 1 As shown, the specific steps are as follows:

[0027] 1) This implementation scheme obtains a slope matrix P with a resolution of 128×128 from the imaging element of the Hartmann wavefront detector. x and P y ,like Figure 2 As shown, L = 128, M = 128;

[0028] 2) For P x and P y Perform downsampling at 4 layers to generate a slope matrix at 4 layers. and Where i = 1, 2, 3, 4, the 4th layer is the layer with the largest scale, i.e., N = 4, and the slope matrix is ​​from the 1st layer to the 4th layer. and Each as Figures 3 to 6 As shown;

[0029] 3) Using the default initial values ​​(all 0s), let i = 4, and use the region method of the Fried model, from... and Reconstruction yields wavefront W 4 ,like Figure 7 As shown;

[0030] 4) Update the value of i using i-1: i ← i-1;

[0031] 5) If i≥1, proceed to step 6); otherwise, jump to step 7.

[0032] 6) W i-1 Upsampling by As initial values, the region method of the Fried model is used, by and Reconstruction yields wavefront W i (Jump to step 4) to reconstruct the obtained W 1 W 2 W 3 like Figure 7 As shown;

[0033] 7) W 1 Upsampling by As initial values, the region method of the Southwell model is used, with P as the initial value. x and P y The wavefront W is obtained through reconstruction. And W Figure 8 As shown.

[0034] Using Southwell's algorithm directly, through P x and P y Wavefront reconstruction was performed, with iterative relative accuracy down to 1×10⁻⁶. -7 The process terminates at a certain point, requiring 450 iterations. In this implementation, the fourth layer has 1 iteration, the third layer has 1 iteration, the second layer has 1 iteration, and the first layer has 38 iterations. W is used. 1 Interpolated Using the initial values, Southwell was then used for reconstruction, resulting in 281 iterations. It is evident that this invention significantly reduces the number of iterations required, accelerates the iteration process, and improves the speed of wavefront reconstruction.

[0035] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fast wavefront reconstruction method, characterized in that: The steps of this method are as follows: Step 1) Obtain the slope matrix P with a resolution of L×M from the wavefront sensor. x and P y ; Step 2) For P x and P y Perform downsampling on N layers to generate the slope matrix of N layers. and Where i = 1, 2, 3, ..., N, and the Nth layer is the layer with the largest scale; Step 3) Using the default initial values, let i = N, and use wavefront restoration algorithm 1, from... and Reconstruction yields wavefront W N ; Step 4) Update the value of i using i-1; Step 5) If i≥1, proceed to step 6); otherwise, jump to step 7. Step 6) W i-1 Upsampling by Using the initial values, wavefront reconstruction algorithm 1 is used, by and Reconstruction yields wavefront W i (Jump to step 4); Step 7) W 1 Upsampling by Using P as the initial value, wavefront reconstruction algorithm 2 is used. x and P y The wavefront W is obtained by reconstruction.

2. The fast wavefront reconstruction method according to claim 1, characterized in that: Wavefront restoration algorithm 1 and wavefront restoration algorithm 2 are independent of each other; they can be consistent or inconsistent.

3. The fast wavefront reconstruction method according to claim 1, characterized in that: In step 2), when downsampling, for locations with missing data, the average value of adjacent locations is used instead.

4. The fast wavefront reconstruction method according to claim 1, characterized in that: In step 4), when performing upsampling, if data extrapolation is required, use boundary value substitution, linear extrapolation of boundary values, or the mean of boundary values.

5. The fast wavefront reconstruction method according to claim 1, characterized in that: Wavefront restoration algorithm 1 adopts the region method of the Fried model.

6. The fast wavefront reconstruction method according to claim 5, characterized in that: Wavefront restoration algorithm 2 adopts the region method of the Southwell model.

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