A wavefront reconstruction method based on a regularized Boolean model

Abstract

The present invention provides a wavefront reconstruction method based on a regularized Boole model to solve the technical problem that in the traditional wavefront reconstruction model, during the reconstruction calculation, the high-frequency response decays greatly, resulting in large errors when the wavefront sensor measures high-frequency targets. A wavefront reconstruction method based on a regularized Boole model provided by the present invention includes the following steps: collecting dot matrix spot image data; calculating the spatial wavefront slope according to the dot matrix spot image data; constructing a Boole model and optimizing the Boole model to obtain a regularized Boole model wavefront phase frequency domain expression; performing an inverse discrete Fourier transform on the regularized Boole model wavefront phase frequency domain expression to calculate the spatial phase and obtain the wavefront reconstruction image of the target to be measured.

Description

Technical Field

[0001] The present invention relates to a wavefront reconstruction method, and in particular to a wavefront reconstruction method based on a regularized Boole model. Background Art

[0002] During the measurement process of a wavefront sensor, an image with wavefront information is reconstructed from the original wavefront image, and it is applied in fields such as atmospheric measurement, telescopic measurement, long-distance communication, and plasma measurement.

[0003] However, when the traditional wavefront reconstruction model performs reconstruction calculations, there is often a situation where the low-frequency response is relatively good and the high-frequency response decays greatly. This makes the wavefront sensor have a large error when measuring high-frequency targets, and thus also limits the application range of the wavefront sensor, which is a problem that is difficult to overcome. Summary of the Invention

[0004] The purpose of the present invention is to solve the technical problem that when the traditional wavefront reconstruction model performs reconstruction calculations, the large decay of the high-frequency response leads to a large error in the wavefront sensor when measuring high-frequency targets, and thus provides a wavefront reconstruction method based on a regularized Boole model.

[0005] In order to solve the above technical problems, the technical solution provided by the present invention is as follows:

[0006] A wavefront reconstruction method based on a regularized Boole model, characterized by comprising the following steps:

[0007] 1] Collect dot matrix spot image data;

[0008] 2] Calculate the spatial domain wavefront slope S x (x,y), S y (x,y);

[0009] 3] Construct a Boole model according to the spatial domain wavefront slope S x (x,y), S y (x,y), and optimize the Boole model to obtain the wavefront phase frequency domain expression of the regularized Boole model;

[0010] 3.1] Construct a Boole model, and the modeling expression of the relationship between the spatial domain wavefront slope of the Boole model and the spatial domain wavefront phase of the measurement point is:

[0011]

[0012] Among them, S x (x,y), S y (x,y) are respectively the spatial domain wavefront slopes in the x direction and y direction of the current sampling point, It represents the spatial wavefront phase of the point to be measured, h x and h y are the sampling intervals in the x - direction and y - direction respectively;

[0013] 3.2 Discretely Fourier - transform both ends of the modeling expression of the spatial domain obtained in step 3.1 to obtain the expression of the relationship between the wavefront slope in the frequency domain of the Boole model and the wavefront phase in the frequency domain of the point to be measured;

[0014] 3.3 Calculate the sum of squared errors for the expression of the relationship between the wavefront slope in the frequency domain of the Boole model and the wavefront phase in the frequency domain of the point to be measured obtained in step 3.2;

[0015] 3.4 Take the partial derivative of the sum of squared errors obtained in step 3.3 in the frequency domain, and obtain the wavefront phase expression in the frequency domain through the least - squares solution of the estimated value of the wavefront phase in the frequency domain;

[0016] 3.5 Introduce a regularization term into the wavefront phase expression in the frequency domain in step 3.4 to obtain the regularized wavefront phase expression in the frequency domain of the Boole model;

[0017] 3.6 Optimize the parameters of the regularized wavefront phase expression in the frequency domain of the Boole model obtained in step 3.5 to obtain the final regularized wavefront phase expression in the frequency domain of the Boole model;

[0018] 4 Perform an inverse discrete Fourier transform on the regularized wavefront phase expression in the frequency domain of the Boole model to calculate the spatial domain phase and obtain the wavefront reconstruction image of the target to be measured.

[0019] Furthermore, step 3.2 is specifically as follows:

[0020] Discretely Fourier - transform both ends of the modeling expression of the relationship between the spatial wavefront slope of the Boole model and the spatial wavefront phase of the point to be measured to obtain the expression of the relationship between the wavefront slope in the frequency domain and the wavefront phase in the frequency domain of the point to be measured:

[0021]

[0022] where, are the wavefront slopes in the frequency domain in the x - direction and y - direction respectively, is the wavefront phase in the frequency domain of the point to be measured; are the averaging operators in the x - direction and y - direction, are the differential operators in the x - direction and y - direction;

[0023] where, The expressions of are respectively:

[0024]

[0025]

[0026]

[0027]

[0028] where k x , k y ranges from [-π / (h x ), π / (h x ) - 2π / (Nh x ),] where N is the number of sampling points and i is the imaginary unit.

[0029] Furthermore, step 3.3] is specifically as follows:

[0030] Find the sum of squared errors of the expression of the relationship between the frequency-domain wavefront slope and the frequency-domain wavefront phase at the point to be measured

[0031]

[0032] where is the estimated value of the wavefront phase in the frequency domain.

[0033] Furthermore, step 3.4] is specifically as follows:

[0034] Take the partial derivative in the frequency domain of the expression of the sum of squared errors obtained in step 3.3] Through the least-squares solution of the estimated value of the wavefront phase in the frequency domain, the frequency-domain expression of the wavefront phase is obtained as:

[0035]

[0036] where ω x = k x h x = 2πf x , ω y = k y h y = 2πf y , where f x , f y is the spatially normalized frequency, with a value range of (-0.5, 0.5).

[0037] Furthermore, step 3.5] is specifically as follows:

[0038] Introduce a regularization term into the frequency-domain expression of the wavefront phase in step 3.4]. The denominator regularization term spatial-domain expression ε r1 and the numerator regularization term spatial-domain expression ε r2 are respectively:

[0039]

[0040]

[0041] Among them, λ and γ are the coefficients of the regularization terms; is the estimated value of the spatial domain wavefront phase;

[0042] According to the denominator regularization term spatial domain expression ε r1 and the numerator regularization term spatial domain expression ε r2 , the denominator regularization term frequency domain expression ε reg1 and the numerator regularization term frequency domain expression ε reg2 are respectively obtained:

[0043]

[0044] Among them, the differential operator of the regularization term in the x direction the differential operator of the regularization term in the y direction

[0045] According to the denominator regularization term frequency domain expression ε reg1 and the numerator regularization term frequency domain expression ε reg2 , the preliminary regularized boolean model wavefront phase frequency domain expression is obtained:

[0046]

[0047] Among them, represents conjugate, represents conjugate.

[0048] Furthermore, step 3.5] also includes:

[0049] Substitute the expression of obtained in step 3.2], and expression into the preliminary regularized boolean model wavefront phase frequency domain expression; introduce the system modulation function

[0050] Let h x =h y =1, and the regularized boolean model wavefront phase frequency domain expression is obtained:

[0051]

[0052] Furthermore, in step 3.6], the optimized parameters are the coefficients λ and γ of the regularization terms.

[0053] Further, in step 1], the acquisition of the dot matrix spot image data is specifically as follows:

[0054] 1.1] Acquire the dot matrix spot image;

[0055] 1.2] Preprocess the acquired dot matrix spot image to remove noise interference.

[0056] Further, in step 1], a Shack-Hartmann wavefront sensor is used to acquire the spot matrix image.

[0057] The beneficial effects of the present invention compared with the prior art are as follows:

[0058] 1. The wavefront reconstruction method based on the regularized Boole model provided by the present invention constructs a regularized Boole model compared with the traditional method, optimizes the frequency response characteristics, shows good performance in the high-frequency response characteristics, and further improves the measurement accuracy of the wavefront sensor, realizing accurate wavefront reconstruction calculation.

[0059] 2. The wavefront reconstruction method based on the regularized Boole model provided by the present invention completes all wavefront reconstruction calculations in the frequency domain. Its algorithm structure is simple, the amount of calculation is small, and it can be efficiently parallelized, improving the operation speed of the system.

[0060] 3. The wavefront reconstruction method based on the regularized Boole model provided by the present invention simultaneously introduces regularization terms to the numerator and denominator of the wavefront phase frequency domain calculation expression, which can further optimize the frequency response characteristics.

[0061] 4. The wavefront reconstruction method based on the regularized Boole model provided by the present invention uses a Shack-Hartmann wavefront sensor for the wavefront sensor. It has the advantages of high light energy utilization rate, fast detection speed, and stable performance, further improving the accuracy of wavefront image restoration. Description of the Drawings

[0062] Figure 1 It is a flowchart of a wavefront reconstruction method based on the regularized Boole model of the present invention;

[0063] Figure 2 It is a schematic diagram of the Boole spatial domain wavefront reconstruction model in the embodiment of the present invention;

[0064] Figure 3 It is a three-dimensional schematic diagram of the frequency response characteristics of the regularized Boole model in the embodiment of the present invention;

[0065] Figure 4 It is a comparison diagram of the frequency response characteristics in the x-axis direction of the regularized Boole model and the traditional model curve in the embodiment of the present invention. Detailed Embodiments

[0066] To make the advantages and features of the present invention clearer, the following further elaborates on the present invention in conjunction with the accompanying drawings and specific embodiments.

[0067] As Figure 1 shown, a wavefront reconstruction method based on a regularized Boole model specifically includes the following steps:

[0068] 1】Collect lattice spot image data;

[0069] 1.1】Use a Shack - Hartmann wavefront sensor with high - speed, high - precision, and large target surface to collect lattice spot image data; in this embodiment, an independently developed Shack - Hartmann wavefront sensor is used to collect image data, with a target surface size of 2592 * 2048 pixels and a micro - lens array resolution of 128 * 128. Its advantages of high light energy utilization rate, fast detection speed, and stable performance further improve the accuracy of wavefront image restoration.

[0070] 1.2】Pre - process the collected lattice spot image to remove noise interference.

[0071] 2】Calculate the spatial wavefront slope S x (x,y), S y (x,y);

[0072] Calculate the spatial wavefront slope S x (x,y), S y (x,y) according to the area of the wavefront to be reconstructed in the lattice spot image data;

[0073] In this embodiment, the selected calculation area is a rectangular area. In other embodiments, when the calculation area is an irregular shape, the irregular shape can be extended to a rectangle for selection.

[0074] 3】Construct a Boole model based on the spatial wavefront slope S x (x,y), S y (x,y) and optimize the Boole model to obtain the wavefront phase frequency - domain expression of the regularized Boole model;

[0075] 3.1】Construct a Boole model. As Figure 2 shown, the modeling expression of the relationship between the spatial wavefront slope of the Boole model and the spatial wavefront phase of the point to be measured is:

[0076]

[0077] Among them, S x (x,y) is the spatial wavefront slope in the x - direction of the current sampling point, and S y (x,y) is the spatial wavefront slope in the y - direction of the current sampling point. is the wavefront phase in the airspace of the point to be measured, h x is the sampling interval in the x direction, h y is the sampling interval in the y direction;

[0078] 3.2】Taking the discrete Fourier transform of both sides of formula (1) gives

[0079]

[0080] where is the wavefront slope in the frequency domain in the x direction, is the wavefront slope in the frequency domain in the y direction, is the wavefront phase in the frequency domain of the point to be measured; is the average operator in the x and y directions, is the differential operator in the x and y directions;

[0081] where The expressions of are respectively:

[0082]

[0083]

[0084]

[0085]

[0086] where k x , k y The value range is [-π / (h x ), π / (h x ) - 2π / (Nh x )], N is the number of sampling points, and i is the imaginary unit;

[0087] 3.3】Finding the sum of squared errors of formula (2) Its expression is

[0088]

[0089] where is the frequency domain estimated value of the wavefront phase;

[0090] 3.4】Taking the partial derivative of formula (3) in the frequency domain Through the least squares solution of the frequency domain estimated value of the wavefront phase, the frequency domain expression of the wavefront phase is obtained as:

[0091]

[0092] In the formula, ω x = kx h x = 2πf x , ω y = k y h y = 2πf y , where f x , f y is the spatial normalized frequency, with a value range of (-0.5, 0.5).

[0093] 3.5】To optimize its frequency response characteristics, a regularization term is introduced into the wavefront phase frequency domain expression, that is, into formula (4). In this example, regularization terms are introduced into both the numerator and the denominator;

[0094] Among them, the spatial domain expression ε of the denominator regularization term r1 and the spatial domain expression ε of the numerator regularization term r2 are respectively:

[0095]

[0096]

[0097] Among them, λ and γ are the coefficients of the regularization term; represents the estimated value of the spatial domain wavefront phase;

[0098] According to the spatial domain expression ε of the denominator regularization term r1 and the spatial domain expression ε of the numerator regularization term r2 , the frequency domain expressions ε of the denominator regularization term reg1 and the frequency domain expression ε of the numerator regularization term reg2 are respectively obtained as follows:

[0099]

[0100] Among them, the differential operator of the regularization term in the x direction the differential operator of the regularization term in the y direction

[0101] According to the frequency domain expression ε of the denominator regularization term reg1 and the frequency domain expression ε of the numerator regularization term reg2 , the preliminary regularized boole model wavefront phase frequency domain expression is obtained:

[0102]

[0103] Among them, represents the conjugate of represents the conjugate of

[0104] 3.6】The The expression, and in step 3.5 Substitute the expression into formula (5), that is, substitute the preliminary regularized boolean model wavefront phase frequency domain expression; introduce the system modulation function

[0105] Meanwhile, considering the modulation effect of the microlens array, let h x = h y = 1, and obtain the regularized boolean model wavefront phase frequency domain calculation expression:

[0106]

[0107] 3.7] Optimize the coefficients λ, γ of the regularization term, that is, optimize the frequency response characteristics of the regularized boolean model, and obtain the final regularized boolean model wavefront phase frequency domain calculation expression.

[0108] In this embodiment, the selected coefficients of the regularization term are λ = 16, γ = 13, and its spatial frequency response characteristics are as Figure 3 , Figure 4 shown, Figure 3 is the three-dimensional schematic diagram of the regularized boolean model frequency response characteristics, Figure 4 is the comparison of the regularized boolean model frequency response characteristics in the x-axis direction and the frequency response characteristics of the other three traditional models. It can be seen that after adding the regularization term, the frequency response characteristics of the system are significantly improved. Compared with other models, the frequency response characteristics of this model are closer to the unit frequency response characteristics in the entire frequency band range, and the frequency response characteristics of the model are better.

[0109] 4] Use IDFT to calculate the wavefront phase in the spatial domain Obtain the wavefront reconstruction image of the target to be measured.

[0110] Perform the inverse discrete Fourier transform (IDFT) on the regularized boolean model wavefront phase frequency domain expression to calculate the wavefront phase in the spatial domain Obtain the wavefront reconstruction image of the target to be measured.

[0111] In this embodiment, the selected calculation region is a rectangular region, and the fast algorithm IFFT is used to calculate the wavefront phase in the spatial domain The above is only used to illustrate the technical solution of the present invention, rather than to limit it. For those of ordinary skill in the art, the specific technical solutions recorded in the above embodiments can be modified, or some of the technical features can be equivalently replaced, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions protected by the present invention.

Claims

1. A wavefront reconstruction method based on a regularized Boolean model, characterized in that, Including the following steps:

1. Collect the dot matrix spot image data; 2】Calculate the spatial domain wavefront slope S based on the dot matrix spot image data x (x,y), S y (x,y); 3】According to the spatial domain wavefront slope S x (x, y), S y (x, y) to construct a Boolean model, and optimize the Boolean model to obtain the wavefront phase frequency domain expression of the regularized Boolean model; 3.

1. Construct a Boolean model. The modeling expression of the relationship between the spatial wavefront slope of the Boolean model and the spatial wavefront phase of the point to be measured is: Among them, S x (x,y) and S y (x,y) are the spatial wavefront slopes in the x-direction and y-direction of the current sampling point respectively, represents the spatial wavefront phase of the point to be measured, h x and h y are the sampling intervals in the x-direction and y-direction respectively; 3.

2. Perform discrete Fourier transform on both ends of the modeling expression of the spatial domain obtained in step 3.1 to obtain the expression of the relationship between the wavefront slope in the frequency domain of the Boolean model and the wavefront phase in the frequency domain of the point to be measured; 3.

3. Calculate the sum of squared errors for the expression of the relationship between the wavefront slope in the frequency domain of the Boolean model and the wavefront phase in the frequency domain of the point to be measured obtained in step 3.2; 【3.4】Take the partial derivative of the sum of squared errors obtained in step 【3.3】 in the frequency domain, and obtain the frequency-domain expression of the wavefront phase through the least squares solution of the estimated value of the wavefront phase in the frequency domain ; obtain the frequency-domain expression of the wavefront phase 3.

5. Introduce a regularization term into the wavefront phase frequency domain expression in step 3.4 to obtain the regularized wavefront phase frequency domain expression of the Boolean model; 3.

6. Optimize the parameters of the regularized wavefront phase frequency domain expression of the Boolean model obtained in step 3.5 to obtain the final regularized wavefront phase frequency domain expression of the Boolean model; 4] Perform an inverse discrete Fourier transform on the regularized Boolean model wavefront phase frequency domain expression to calculate the spatial domain phase. Obtain the wavefront reconstruction image of the target to be measured.

2. The wavefront reconstruction method based on a regularized Boolean model according to claim 1, characterized in that: Step 3.2 is specifically: perform discrete Fourier transform on both ends of the modeling expression of the relationship between the spatial wavefront slope of the Boolean model and the spatial wavefront phase of the point to be measured to obtain the expression of the relationship between the wavefront slope in the frequency domain and the wavefront phase in the frequency domain of the point to be measured: wherein, are the frequency-domain wavefront slopes in the x-direction and y-direction respectively, is the frequency-domain wavefront phase of the point to be measured; are the averaging operators in the x-direction and y-direction, are the differential operators in the x-direction and y-direction; Among them, The expressions of are respectively: where k x , k y ranges from [-π / (h x ), π / (h x ) - 2π / (Nh x ), N is the number of sampling points, and i is the imaginary unit.

3. The wavefront reconstruction method based on a regularized Boolean model according to claim 2, characterized in that: Step 3.3】Specifically: calculate the sum of squared errors of the expression of the relationship between the frequency-domain wavefront slope and the frequency-domain wavefront phase at the point to be measured Among them, is the estimated value of the wavefront phase in the frequency domain.

4. The wavefront reconstruction method based on a regularized Boolean model according to claim 3, characterized in that: Step 3.4】Specifically: Take the partial derivative of the expression of the sum of squared errors obtained in Step 3.3】 in the frequency domain Through the least squares solution of the wavefront phase frequency domain estimated value obtain the wavefront phase frequency domain expression as: where ω x = k x h x = 2πf x , ω y = k y h y = 2πf y , where f x , f y is the spatial normalization frequency, with a value range of (-0.5, 0.5).

5. The wavefront reconstruction method based on a regularized Boolean model according to claim 4, characterized in that: Step 3.5】Specifically: introduce a regularization term into the wavefront phase frequency domain expression in Step 3.4】, and the spatial domain expressions ε r1 of the denominator regularization term and the spatial domain expression ε r2 of the numerator regularization term are respectively: where λ and γ are the coefficients of the regularization terms; is the estimated value of the airspace wavefront phase; According to the denominator regularization term spatial domain expression ε r1 and the numerator regularization term spatial domain expression ε r2 , the denominator regularization term frequency domain expression ε reg1 and the numerator regularization term frequency domain expression ε reg2 are obtained respectively as follows: Among them, the differential operator of the regularization term in the x direction The differential operator of the regularization term in the y direction According to the denominator regularization term frequency domain expression ε reg1 and the numerator regularization term frequency domain expression ε reg2 , the preliminary regularized boole model wavefront phase frequency domain expression is obtained: Among them, denotes the conjugate of denotes the conjugate of 6. A wavefront reconstruction method based on a regularized Boolean model according to claim 5, characterized in that: Step 3.5 also includes: substituting the expression obtained in Step 3.2], , and expressions into the preliminary regularized boolean model wavefront phase frequency domain expression; introducing the system modulation function Let h x = h y = 1, and the regularized boolean model wavefront phase frequency domain expression is obtained:

7. A wavefront reconstruction method based on a regularized Boolean model according to claim 6, characterized in that: In step 3.6, the optimized parameters are the coefficients λ and γ of the regularization term.

8. A wavefront reconstruction method based on a regularized Boolean model according to any one of claims 1-7, characterized in that: In step 1, collecting the dot matrix spot image data specifically includes: 1.

1. Collect the dot matrix spot image; 1.

2. Preprocess the collected dot matrix spot image to remove noise interference.

9. A wavefront reconstruction method based on a regularized Boolean model according to claim 8, characterized in that: In step 1, a Shack-Hartmann wavefront sensor is used to collect the spot matrix image.

Images