A method and device for reconstructing lateral shearing interferometry wavefront

Abstract

The present invention discloses a lateral shearing interference wavefront reconstruction method and device, which relates to the field of optical measurement technology. The method uses an inaccurate shearing amount to perform wavefront reconstruction, thereby achieving high-precision wavefront reconstruction and solving the problem in the prior art that wavefront reconstruction depends on the calculation accuracy of the shearing amount. The method comprises: performing phase unwrapping on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device to obtain an initial phase, fitting the initial phase and the initial shearing amount through differential Zernike polynomials to obtain an initial wavefront to be measured after fitting; determining an initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase; determining multiple domain error values ​​corresponding to the initial error value based on a neighborhood optimization method, selecting the initial shearing amount or domain shearing amount corresponding to the minimum value to update the initial shearing amount; and when the updated error value corresponding to the updated shearing amount is less than a threshold value, determining the iterative wavefront to be measured determined by the updated shearing amount corresponding to the updated error value as the accurately reconstructed wavefront.

Description

Technical Field

[0001] The present invention relates to the field of optical measurement technology, and more particularly to a method and device for reconstructing a lateral shearing interference wavefront. Background Art

[0002] Lateral shearing interferometry is a wavefront interferometry measurement technique that does not require a reference mirror. It generates interference by superimposing the wavefront to be measured with its own laterally displaced sheared wavefront, and is used for surface shape and wavefront detection of optical components. Due to the characteristics of lateral shearing interferometry, the phase information extracted through the interference pattern is not the wavefront to be measured, but the differential wavefront in the shear direction of the wavefront to be measured. Therefore, the wavefront to be measured needs to be reconstructed from the differential wavefront. The methods of wavefront reconstruction can be mainly divided into pattern method and regional method. However, whether it is the pattern method or the regional method, the accuracy of wavefront reconstruction is affected by the shear amount, so the accuracy of the shear amount calculation is very critical.

[0003] Methods for calculating shear can be roughly divided into two categories. One is to directly calculate the shear using geometric formulas based on the structural parameters of the wavefront sensor (such as sensor spacing, optical path geometry, etc.). This method is easily affected by system assembly errors, resulting in inaccurate shear calculations. A calibration method for shear interference wavefront feature extraction based on a phase plate is proposed. This method introduces a rectangular groove with sharp edges on the phase plate and uses image processing technology to extract shear information from the shear wavefront. However, due to the limitations of the optical diffraction limit and the spatial filter, the edges of the extracted feature pattern will appear as slopes rather than ideal steep steps. A wavefront sensor shear calibration method based on a point source microscope is proposed. This method calculates the shear through the relationship between the lateral distance between the staggered point light sources and the grating diffraction order distribution. However, this method has high requirements for the collimation of the optical path, otherwise it will introduce systematic errors and affect the calibration accuracy of the shear.

[0004] Another type is to calculate directly from the interference pattern through image processing. One method introduces a defocused wavefront to improve the shear measurement accuracy in a transverse shearing interferometer, but its accuracy is related to the parameters of the optical system, such as focal length, magnification, and defocus, which all affect the shear measurement accuracy. Another method uses the Radon transform principle to obtain the mutation point of the integral curve to calculate the shear amount. This method requires the interference pattern to have clear edges and non-dark edge stripes, otherwise it is difficult to find the mutation point, affecting the accuracy of the shear calculation.

[0005] In summary, existing methods all achieve high-precision wavefront reconstruction by improving the calculation accuracy of the shear amount, which has high requirements on the optical path and is related to the optical system parameters. The present invention breaks through this limitation and uses imprecise shear amount to achieve high-precision wavefront reconstruction. Summary of the Invention

[0006] The embodiment of the present invention provides a lateral shearing interference wavefront reconstruction method and device, which uses an imprecise shear amount to perform wavefront reconstruction, thereby achieving high-precision wavefront reconstruction and solving the problem in the prior art that wavefront reconstruction depends on the accuracy of shear amount calculation.

[0007] An embodiment of the present invention provides a lateral shearing interferometry wavefront reconstruction method, comprising:

[0008] Phase unwrapping is performed on an initial lateral shearing interferogram obtained based on a lateral shearing interferometer to obtain an initial phase, and the initial phase and the initial shear amount are fitted using a differential Zernike polynomial to obtain an initial measured wavefront after fitting;

[0009] The initial wavefront to be measured and the initial shear amount generate a simulated lateral shearing interference pattern based on lateral shear interference, and the simulated lateral shearing interference pattern is phase unwrapped to obtain a simulated phase; based on the initial phase and the simulated phase, an initial error value corresponding to the initial shear amount is determined by an error function;

[0010] Based on the neighborhood optimization method, multiple neighborhood error values ​​corresponding to the initial error value are determined, and the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value is selected to update the initial shearing amount; when the updated error value corresponding to the updated shearing amount is less than a threshold, the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value is determined as the accurately reconstructed wavefront.

[0011] Preferably, the initial phase is as follows:

[0012]

[0013]

[0014] Among them, I1(x,y), I2(x,y), I3(x,y), I4(x,y) represent the light intensity of the four interference images. represents the extracted phase of point (x,y), φ (i,j) represents the corresponding unwrapped phase of the point (x, y), and k represents the fringe number of the interference fringe.

[0015] Preferably, the initial wavefront to be measured is expressed by the following formula:

[0016]

[0017]

[0018] ΔW=ΔZa

[0019] ΔW x =ΔZ x a

[0020] ΔW y =ΔZ y a

[0021]

[0022] Where W(x,y) represents the initial wavefront to be measured, a j represents the coefficient of the Zernike polynomial, J represents the number of terms of the Zernike polynomial used, and Z j (x,y) represents the normalized Zernike polynomial in the Cartesian coordinate system; represents the generalized inverse of ΔZ, ΔW x and ΔW y Represents N 2 ×1 column vector, ΔZ x and ΔZ y Indicates N 2 ×(J-1) matrix, s x represents the initial shear amount of x, s y represents the initial shear amount of y, W(x+s x ,y) indicates that the lateral displacement of the initial wavefront W(x,y) to be measured along the x direction is s x Shear wavefront, Z j (x+s x ,y) indicates that the lateral displacement in the x direction is s x The Zernike polynomial, W(x,y+s y ) indicates that the initial measured wavefront W(x,y) has a lateral displacement along the y direction of s y Shear wavefront, Z j (x,y+s y ) indicates that the lateral displacement in the y direction is s y The Zernike polynomials, is the differential Zernike polynomial in the x direction, represents the differential Zernike polynomial in the y direction.

[0023] Preferably, determining the initial error value corresponding to the initial shear amount through an error function based on the initial phase and the simulated phase specifically includes:

[0024] Based on the initial phase and the simulated phase, the x-direction error function, the y-direction error function, and the total error function are obtained by the following formulas, respectively. The initial error value corresponding to the initial shear amount is determined according to the total error function. The x-direction error function, the y-direction error function, and the total error function are shown as follows:

[0025]

[0026] Among them, E x represents the x-direction error function, E y represents the y-direction error function, E represents the total error function, ΔW x (x,y) is the initial unwrapping phase in the x direction, ΔW′ x (x,y) is the simulated unwrapped phase in the x direction, ΔW y (x,y) is the initial unwrapping phase in the y direction, ΔW′ y (x,y) is the simulated unwrapped phase in the y direction.

[0027] Preferably, the determining of a plurality of neighborhood error values ​​corresponding to the initial error value based on the neighborhood optimization method, and selecting the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount specifically includes:

[0028] According to the initial phase and the neighborhood shear amount of the initial shear amount, a first wavefront to be measured, a first lateral shearing interference pattern, a first simulated phase and a neighborhood error value are obtained in sequence;

[0029] According to the sizes of the plurality of neighborhood error values ​​and the initial error value, a neighborhood error value or an initial error value with a minimum value is selected, and the initial clipping amount is updated with the neighborhood clipping amount or the initial clipping amount with the minimum value.

[0030] Preferably, when the minimum value is less than a threshold value, determining the iterative measured wavefront determined based on the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value as the precise reconstructed wavefront specifically includes:

[0031] If a neighborhood error value or an initial error value with a minimum value is smaller than a set threshold, a neighborhood shearing amount or an initial shearing amount is determined based on the minimum value, and the iterative measured wavefront determined based on the neighborhood shearing amount or the initial shearing amount is determined as the accurately reconstructed wavefront.

[0032] An embodiment of the present invention provides a lateral shearing interferometry wavefront reconstruction device, comprising:

[0033] An obtaining unit is used to perform phase unwrapping on an initial lateral shearing interferogram obtained based on the lateral shearing interferometer to obtain an initial phase, and the initial phase and the initial shear amount are fitted by a differential Zernike polynomial to obtain an initial measured wavefront after fitting;

[0034] A first determining unit is configured to generate a simulated lateral shearing interferogram based on lateral shearing interference of the initial wavefront to be measured and the initial shearing amount, perform phase unwrapping on the simulated lateral shearing interferogram to obtain a simulated phase; and determine an initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase;

[0035] A second determining unit is configured to determine, based on a neighborhood optimization method, multiple neighborhood error values ​​corresponding to the initial error value, and select the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount; when the updated error value corresponding to the updated shearing amount is less than a threshold, determine the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value as the accurately reconstructed wavefront. An embodiment of the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes any one of the above-mentioned methods for reconstructing lateral shearing interference wavefronts.

[0036] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes any one of the above-mentioned lateral shearing interferometry wavefront reconstruction methods.

[0037] An embodiment of the present invention provides a method and device for reconstructing a lateral shearing interference wavefront, the method comprising: performing phase unwrapping on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device to obtain an initial phase, fitting the initial phase and the initial shear amount through differential Zernike polynomials to obtain an initial measured wavefront after fitting; generating a simulated lateral shearing interference pattern based on lateral shearing interference using the initial measured wavefront and the initial shear amount, and performing phase unwrapping on the simulated lateral shearing interference pattern to obtain a simulated phase; determining an initial error value corresponding to the initial shear amount through an error function based on the initial phase and the simulated phase; determining multiple neighborhood error values ​​corresponding to the initial error value based on a neighborhood optimization method, and selecting the initial shear amount or neighborhood shear amount corresponding to the minimum value to update the initial shear amount; when the updated error value corresponding to the updated shear amount is less than a threshold value, determining the iterative measured wavefront determined by the updated shear amount corresponding to the updated error value as the accurately reconstructed wavefront. The method extracts the wrapped phase information by performing a four-step phase shift on the obtained shearing interferogram, unpacks the wrapped phase using a least squares phase unpacking algorithm based on DCT, then uses an inaccurate shearing amount to perform wavefront fitting based on the differential Zernike principle, and then regenerates a simulated transverse shearing interferogram using the transverse shearing interferometer principle. The simulated transverse shearing interferogram is preprocessed and unpacked to obtain a simulated phase. By determining an error function for the initial phase and the simulated phase and determining an initial error value corresponding to the initial shearing amount, an accurate reconstructed wavefront is ultimately obtained through iteration. The method adjusts the initial inaccurate initial shearing amount, uses the phase information extracted from the actual interferogram as the optimization target, and performs iterative optimization based on the error function. After iterative optimization, an accurate shearing amount and an accurate reconstructed wavefront are finally obtained, thereby achieving high-precision wavefront reconstruction. The method can obtain an accurate reconstructed wavefront even when the initial shearing amount is inaccurately calculated, greatly improving the practical applicability of the method, and is particularly useful when it is difficult to accurately determine the shearing amount under engineering conditions. Furthermore, the reconstruction result of the method provided by the embodiment of the present invention is consistent with the result obtained by the differential Zernike fitting, ensuring the precision and accuracy of the reconstructed wavefront. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 A schematic flow chart of a lateral shearing interferometry wavefront reconstruction method provided by an embodiment of the present invention;

[0040] Figure 2A Schematic diagram of four phase-shifted shearing interferometry in the x-direction provided by an embodiment of the present invention;

[0041] Figure 2B Schematic diagram of four phase-shifted shearing interferences in the y direction provided by an embodiment of the present invention;

[0042] Figure 3A The embodiment of the present invention provides Figure 2A The corresponding unwrapped phase diagram in the x-direction;

[0043] Figure 3B The embodiment of the present invention provides Figure 2B The corresponding unwrapped phase diagram in the y direction;

[0044] Figure 4A The initial shear amount provided by the embodiment of the present invention is Figure 3A 、 Figure 3B The unwrapped phase shown is a schematic diagram of the reconstructed wavefront obtained by differential Zernike fitting;

[0045] Figure 4B A schematic diagram of a wavefront to be measured provided by an embodiment of the present invention;

[0046] Figure 4C The embodiment of the present invention provides Figure 4A The reconstructed wavefront diagram shown is similar to Figure 4B Schematic diagram of the residual after the measured wavefront is reconstructed;

[0047] Figure 5A Schematic diagram of four simulated phase-shift shearing interferometers in the x-direction obtained based on lateral shearing interferometer according to an embodiment of the present invention;

[0048] Figure 5B Schematic diagram of four simulated phase-shift shearing interferometers in the y direction obtained based on lateral shearing interferometer according to an embodiment of the present invention;

[0049] Figure 6A The embodiment of the present invention provides Figure 5A Schematic diagram of the unwrapped phase in the x direction;

[0050] Figure 6B The embodiment of the present invention provides Figure 5B Schematic diagram of the unwrapped phase in the y direction;

[0051] Figure 7A Schematic diagram of wavefront reconstruction obtained based on the method provided in an embodiment of the present invention;

[0052] Figure 7B A schematic diagram of a wavefront to be measured provided by an embodiment of the present invention;

[0053] Figure 7C The embodiment of the present invention provides Figure 7A The reconstructed wavefront shown is the same as Figure 7B Schematic diagram of the residual after the measured wavefront is reconstructed;

[0054] Figure 8 A schematic structural diagram of a lateral shearing interferometer wavefront reconstruction device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0056] Terms involved in the embodiments of the present invention:

[0057] 1. Neighborhood Optimization is a widely used technique in optimization problems. Its basic idea is to gradually improve the optimization objective by searching for better solutions within the "neighborhood" of the current solution. A neighborhood is a set of solutions in the solution space that are close to the current solution based on some distance metric. For example, in a simple two-dimensional function optimization problem, assuming the solution is a point (x, y) on the plane, the neighborhood of this point can be defined as all points within a circle with a radius r centered at (x, y). This radius r determines the size of the neighborhood.

[0058] Figure 1 A schematic flow chart of a lateral shearing interferometer wavefront reconstruction method provided by an embodiment of the present invention is shown below. Figures 1 to 7C Taking the example of FIG. 1 as an example, the lateral shearing interference wavefront reconstruction method provided by the embodiment of the present invention is described in detail. Figure 1 As shown, the method mainly includes the following steps:

[0059] Step 101: performing phase unwrapping on an initial lateral shearing interferogram obtained by a lateral shearing interferometer to obtain an initial phase. The initial phase and the initial shear amount are fitted using a differential Zernike polynomial to obtain a fitted initial wavefront to be measured.

[0060] Step 102: Generate a simulated transverse shearing interferogram based on transverse shearing interference using the initial wavefront to be measured and the initial shearing amount, perform phase unwrapping on the simulated transverse shearing interferogram to obtain a simulated phase; and determine an initial error value corresponding to the initial shearing amount using an error function based on the initial phase and the simulated phase.

[0061] Step 103: Determine multiple neighborhood error values ​​corresponding to the initial error value based on the neighborhood optimization method, select the initial shearing amount or neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount; when the minimum value is less than a threshold value, determine the iterative measured wavefront determined based on the initial shearing amount or neighborhood shearing amount corresponding to the minimum value as the accurately reconstructed wavefront.

[0062] In step 101, it is necessary to obtain an initial lateral shearing interference pattern based on a lateral shearing interference device. Specifically, when the wavefront with the measured surface information passes through the shearer, a sheared wavefront that is laterally translated with the original wavefront is obtained. The two interfere with each other in the overlapping area. The interference wavefront passes through the imaging lens and enters a focal plane imaging system, thereby obtaining four synchronous phase-shifted interference images at the same time, as shown in the following example. Figure 2A The four phase-shifted shear interferences in the x-direction are shown. Figure 2B The four phase-shifted shearing interferograms in the y direction are shown. For each point (x, y) in the region, the four interferograms can be expressed by the following formulas:

[0063]

[0064]

[0065]

[0066]

[0067] Using the four interferograms with different phase shifts mentioned above, the phase of point (x, y) can be calculated using the following formula:

[0068]

[0069] Among them, I1(x,y), I2(x,y), I3(x,y) and I4(x,y) represent the light intensity of the interference field, a(x,y) represents the DC light intensity component of the interference pattern, and b(x,y) represents the AC modulation term. Represents the differential wrapped phase of the point (x,y).

[0070] Furthermore, according to formula (2), an inverse tangent operation is performed when extracting the phase. The extracted wrapped phase is between (-π, π), and discontinuous jumps appear in the extracted phase distribution. Such jumps do not reflect the true phase information. This discontinuous phase information needs to be spliced ​​and expanded into a continuous phase to obtain phase information that contains the true surface shape of the optical element.

[0071] The embodiment of the present invention provides a method for implementing the above-mentioned phase unwrapping using a DCT-based least squares method, specifically:

[0072] If the wrapped phase extracted in this embodiment is within an m×n discrete rectangular area, the wrapped phase can be expressed as Among them, i=0,1,…,m-1; j=0,1,…,n-1. And φ (i,j) is the corresponding unwrapped phase. The relationship between the wrapped phase and the unwrapped phase can be expressed by the following formula:

[0073]

[0074] Wherein, k represents the fringe number of the interference fringe, i = 0, 1, ..., m-1; j = 0, 1, ..., n-1.

[0075] Furthermore, we define the wrapping operator as W r , then the wrapping operator can be expressed by the following formula:

[0076]

[0077] The difference in the x direction can be calculated according to the following formula The difference in the y direction

[0078]

[0079] Furthermore, by combining equations (5) and (6), we obtain the equation system V:

[0080]

[0081] By transforming the normal equation of formula (7), we can obtain the discretized Poisson equation in the discrete region as follows:

[0082] φ (i+1,j) -2φ (i,j) +φ (i-1,j) +φ (i,j+1) -2φ (i,j) +φ (i,j-1) =

[0083] ρ (i,j) (8)

[0084] In formula (8),

[0085] According to the obtained unwrapped phase φ (i,j) The discrete cosine transform spectrum of And perform inverse discrete cosine transform to get:

[0086]

[0087] in, p=0, ω1(p)=1, 1≤o≤m-1, q=0, ω1(q)=1, 1≤q≤n-1.

[0088] Furthermore, first (i,j) Perform discrete cosine transform to get Then, φ is solved by inverse discrete cosine transform. (i,j) :

[0089] Simplify equation (9) and solve it accurately according to the following formula:

[0090]

[0091] Unwrapped phase and differential wavefront ΔW in the x and y directions x and ΔW y The relationship between them is as follows:

[0092]

[0093] Where, is the spatial angular frequency, λ is the wavefront of the light wave to be measured, ΔW x and ΔW y is the differential wavefront of the wavefront to be measured, φ x (x,y) and φ y (x,y) The differential phase of the wavefront to be measured.

[0094] The embodiment of the present invention uses the least square method based on DCT to implement phase unwrapping, wherein: Figure 2A The unwrapped phases of the four phase-shifted shearing interferograms in the x-direction are shown as Figure 3A As shown, Figure 2B The unwrapped phase of the four phase-shifted shear interference images in the y direction is shown as Figure 3B shown.

[0095] In practical applications, Radon transform is used to calculate the projection of a certain graphic matrix in a specified direction θ, which can also be regarded as the line integral of the graphic matrix in the specified direction θ. The Radon transform of an image along a specified direction can be expressed as:

[0096]

[0097] Among them, R θ represents the line integral of the interference pattern in the specified direction θ, x′ and y′ are two perpendicular directions of the rectangular coordinate system established along the direction θ, and I represents the light intensity of the interference pattern.

[0098] Select different projection directions for the interference pattern (generally 0° to 180°), calculate the line integrals of the interference pattern in different directions, and obtain the projection results of the Radon transform. In an embodiment of the present invention, since the lateral shearing interference pattern has a maximum spot area in the shearing direction and a minimum spot area in the direction perpendicular to it, the difference in width between the maximum spot area and the minimum spot area is the size of the shearing amount. Analyze the Radon transform results, for areas outside the spot area, it is a dark area with a small grayscale value. In this area, the Radon transform value increases linearly and changes slowly. However, when entering the spot area, the transform value increases very quickly, and there will be a mutation at the edge of the spot. By finding the position of the mutation point, the width of the spot area in the specified projection direction can be calculated (taking the lateral shearing interference pattern in the x direction as an example, generally the 0° projection direction corresponds to the maximum spot area, and the 90° projection direction corresponds to the minimum spot area), thereby obtaining the initial shear amount s in the x direction. x Similarly, the initial shear amount s in the y direction can be obtained y .

[0099] Furthermore, based on the initial phase and initial shear amount determined above, Zernike polynomials are used for fitting. In practical applications, the wavefront to be measured W(x, y) can be expressed by a series of fringe Zernike polynomials as follows:

[0100]

[0101] Where J represents the number of terms in the Zernike polynomial, Z j (x,y) represents the normalized Zernike polynomial in the Cartesian coordinate system, a j are the coefficients of the Zernike polynomial.

[0102] Furthermore, the differential wavefronts in the x and y directions generated by the two wavefronts in the overlapping area are expressed as:

[0103]

[0104] Among them, (s x ,s y ) are the initial shear amounts in the x and y directions, W(x+s x ,y) is the lateral displacement of the wavefront W(x,y) to be measured along the x direction, which is s x Shear wavefront, Zj (x+s x ,y) is the lateral displacement in the x direction, s x The Zernike polynomial, W(x,y+s y ) is the lateral displacement of the wavefront W(x,y) to be measured along the y direction, which is s y Shear wavefront, Z j (x,y+s y ) is the lateral displacement in the y direction, s y The Zernike polynomials, a j represents the coefficients of the Zernike polynomials, is the differential Zernike polynomial in the x direction, is the differential Zernike polynomial in the y direction.

[0105] The above relationship can be expressed as a vector:

[0106]

[0107] ΔW=ΔZa (18)

[0108] Where ΔW x and ΔW y N 2 ×1 column vector, ΔZ x and ΔZ y Yes N 2 ×(J-1) matrix,

[0109] The coefficient a of the wavefront expression to be measured is solved by the least squares method, which can be expressed as:

[0110]

[0111] Where, represents the generalized inverse of ΔZ, It is given by:

[0112]

[0113] Furthermore, the initial wavefront to be measured W(x, y) can be obtained by fitting the Zernike coefficients, which is expressed by formula (14). Figure 4A The initial shear amount provided by the embodiment of the present invention is Figure 3A 、 Figure 3B The unwrapped phase is shown as a schematic diagram of the reconstructed wavefront obtained by differential Zernike fitting. Figure 4B A schematic diagram of a wavefront to be measured provided by an embodiment of the present invention, Figure 4C for Figure 4A The reconstructed wavefront diagram shown is similar to Figure 4B FIG. 1 is a schematic diagram of the residual after the measured wavefront is reconstructed, wherein the PV (Peak to Valley) of the residual is 1.3268λ and the RMS (Root-Mean–Square) is 0.3254λ.

[0114] It should be noted that PV represents the difference between the maximum value (highest point) and the minimum value (lowest point) of the surface shape W(x, y) of the optical element, that is:

[0115] PV=W max -W min (twenty one)

[0116] Among them, W max and W min They represent the maximum and minimum values ​​of the face shape W(x,y), respectively. x and y are the serial numbers of the valid rows and columns of the face shape, respectively.

[0117] RMS represents the root mean square value of the surface error, and its calculation formula is as follows:

[0118]

[0119] Wherein, W(x, y) is the surface shape of the optical element, x and y are the serial numbers of the rows and columns of the surface shape, respectively, and N is the number of valid elements in the surface shape.

[0120] In step 102, after the initial wavefront to be measured is determined according to the above steps, the initial wavefront to be measured and the initial shear amount can be used to generate a simulated transverse shearing interference pattern based on transverse shearing interference, and the simulated transverse shearing interference pattern is further phase unwrapped to obtain the placement phase. Here, the phase unwrapping of the simulated transverse shearing interference pattern can refer to step 101 and will not be repeated here. In the embodiment of the present invention, Figure 5A Provides four simulated phase-shift shearing interferometry diagrams in the x-direction based on lateral shearing interferometry. Figure 5B Schematic diagrams of four simulated phase-shift shearing interferences in the y direction obtained based on lateral shearing interference are provided. Figure 6A Provided with Figure 5A The corresponding unwrapped phase diagram in the x-direction, Figure 6B Provided with Figure 5B Schematic diagram of the corresponding unwrapped phase in the y direction.

[0121] Furthermore, based on the initial phase and the simulated phase determined in step 101, an initial error function can be constructed by the following formula, specifically:

[0122] The error functions in the x- and y-directions are shown below:

[0123]

[0124] Furthermore, based on the above-mentioned error functions in the x-direction and y-direction, the total error function can be obtained as follows:

[0125]

[0126] Among them, E x represents the x-direction error function, E y represents the y-direction error function, E represents the total error function, ΔW x (x, y) is the initial unwrapping phase in the x direction, ΔW′ x (x, y) is the simulated unwrapped phase in the x direction, ΔW y (x, y) is the initial unwrapping phase in the y direction, ΔW′ y (x, y) is the simulated unwrapped phase in the y direction.

[0127] In step 103, the initial error value corresponding to the initial shearing amount can be determined according to the above 102. Furthermore, based on the neighborhood optimization method, multiple neighborhood shearing amounts corresponding to the initial shearing amount can be determined, and the neighborhood error value corresponding to each neighborhood shearing amount can also be determined. The minimum value is selected from the multiple neighborhood error values ​​and the initial error value, and the initial shearing amount is updated with the neighborhood shearing amount or the initial shearing amount corresponding to the minimum value. During multiple iterations, if the determined minimum value is less than the threshold, the iterative measured wavefront determined based on the neighborhood shearing amount or the initial shearing amount corresponding to the minimum value can be determined as the final desired precise reconstructed wavefront.

[0128] For example:

[0129] Step 103-1, according to the initial shearing amount (s x , s y ) Determine the initial error value corresponding to the initial shear amount.

[0130] Step 103-2: If the multiple neighborhood shearing amounts of the initial shearing amount are determined to be (s x -1,s y -1)、(s x , s y -1)、(s x +1,s y -1)、(s x -1,s y )、(s x +1,s y )、(s x -1,s y +1)、(s x ,s y +1)、(s x +1,s y+1), each neighborhood shearing amount is brought into the initial shearing amount of step 101, and the neighborhood error value corresponding to each neighborhood shearing amount can be determined based on steps 101 and 102;

[0131] In step 103-3, the initial error values ​​and the neighborhood error values ​​corresponding to the initial clipping amount and the neighborhood clipping amount are compared, and the initial clipping amount or the neighborhood clipping amount corresponding to the minimum value is selected to update the initial clipping amount to obtain an updated clipping amount; steps 103-1 to 103-3 are repeated once to obtain an updated clipping amount.

[0132] Step 103-4, when the updated error value corresponding to the updated shearing amount obtained after the update is the minimum value of the updated error values ​​obtained after multiple updates, the updated error value with the minimum value is compared with the threshold value. If the updated error value with the minimum value is smaller than the threshold value, the iterative wavelength to be measured determined according to the updated error value with the minimum value can be determined as the accurately reconstructed wavefront; correspondingly, if the updated error value with the minimum value is not smaller than the threshold value, in order to prevent the local optimal solution, the neighborhood is jumped out, and the initial shearing amount in step 101 is assigned a random value within the set area, and then the above steps 103-1 to 103-3 are re-executed to obtain the updated shearing amount. If the updated error value corresponding to the updated shearing amount is the minimum update error value and is smaller than the threshold value at the same time, the iterative wavelength to be measured determined by the minimum update error value is determined as the accurately reconstructed wavefront.

[0133] Figure 7A Provides wavefront reconstruction images, Figure 7B Provides the wavefront diagram to be measured, Figure 7C The provided diagram shows the residuals after the reconstruction of the reconstructed wavefront image and the measured wavefront. The PV of the residual is 4.9979×10 -10 λ,RMS is 1.0757×10 -10 λ.

[0134] An embodiment of the present invention provides a method for reconstructing a lateral shearing interferometer wavefront. The method extracts wrapped phase information by performing a four-step phase shift on the obtained shearing interferogram. The wrapped phase is unwrapped using a least-squares phase unwrapping algorithm based on a DCT. An inaccurate shear amount is then used to perform wavefront fitting based on the differential Zernike principle. The fitted initial measured wavefront is then regenerated into a simulated lateral shearing interferogram using the lateral shearing interferometer principle. The simulated lateral shearing interferogram is then preprocessed and unwrapped to obtain a simulated phase. An error function is determined for the initial phase and the simulated phase, and an initial error value corresponding to the initial shear amount is determined. An accurate reconstructed wavefront is ultimately obtained through iteration. The method adjusts the initial inaccurate initial shear amount, uses the phase information extracted from the actual interferogram as the optimization target, and performs iterative optimization based on the error function. After iterative optimization, an accurate shear amount and an accurate reconstructed wavefront are ultimately obtained, thereby achieving high-precision wavefront reconstruction. The method can obtain an accurate reconstructed wavefront even when the initial shear amount is inaccurately calculated, greatly improving the practical applicability of the method. It is particularly useful when it is difficult to accurately determine the shear amount under engineering conditions. Furthermore, the reconstruction result of the method provided in the embodiment of the present invention is consistent with the result obtained by differential Zernike fitting, ensuring the precision and accuracy of the reconstructed wavefront.

[0135] Based on the same inventive concept, an embodiment of the present invention provides a lateral shearing interference wavefront reconstruction device. Since the principle and method of solving the technical problem of the device are similar, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0136] like Figure 8 As shown, the apparatus includes an obtaining unit 801 , a first determining unit 802 and a second determining unit 803 .

[0137] An obtaining unit 801 is configured to perform phase unwrapping on an initial transverse shearing interferogram obtained based on a transverse shearing interferometer to obtain an initial phase, and to fit the initial phase and the initial shear amount using a differential Zernike polynomial to obtain a fitted initial wavefront to be measured;

[0138] A first determining unit 802 is configured to generate a simulated transverse shearing interferogram based on the transverse shearing interference of the initial wavefront to be measured and the initial shearing amount, perform phase unwrapping on the simulated transverse shearing interferogram to obtain a simulated phase; and determine an initial error value corresponding to the initial shearing amount using an error function based on the initial phase and the simulated phase;

[0139] The second determination unit 803 is used to determine multiple neighborhood error values ​​corresponding to the initial error value based on the neighborhood optimization method, and select the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount; when the updated error value corresponding to the updated shearing amount is less than the threshold, the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value is determined as the accurately reconstructed wavefront.

[0140] It should be understood that the units included in the above-mentioned lateral shearing interferometer wavefront reconstruction device are merely logical divisions based on the functions implemented by the device. In actual applications, the above-mentioned units can be superimposed or split. Furthermore, the functions implemented by the lateral shearing interferometer wavefront reconstruction device provided in this embodiment correspond one-to-one with the lateral shearing interferometer wavefront reconstruction method provided in the above-mentioned embodiment. The more detailed processing flow implemented by this device has been described in detail in the above-mentioned method embodiment 1 and will not be described in detail here.

[0141] Another embodiment of the present invention also provides a computer device, which includes: a processor and a memory; the memory is used to store computer program code, and the computer program code includes computer instructions; when the processor executes the computer instructions, the electronic device executes each step of the lateral shearing interference wavefront reconstruction method in the method flow shown in the above method embodiment.

[0142] Another embodiment of the present invention also provides a computer-readable storage medium, which stores computer instructions. When the computer instructions are executed on a computer device, the computer device executes each step of the lateral shearing interference wavefront reconstruction method in the method flow shown in the above method embodiment.

[0143] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0144] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A lateral shearing interferometry wavefront reconstruction method, characterized in that: include: Phase unwrapping is performed on an initial lateral shearing interferogram obtained based on a lateral shearing interferometer to obtain an initial phase, and the initial phase and the initial shear amount are fitted using a differential Zernike polynomial to obtain an initial measured wavefront after fitting; The initial wavefront to be measured and the initial shear amount generate a simulated lateral shearing interference pattern based on lateral shear interference, and the simulated lateral shearing interference pattern is phase unwrapped to obtain a simulated phase; based on the initial phase and the simulated phase, an initial error value corresponding to the initial shear amount is determined by an error function; Determine multiple neighborhood error values ​​corresponding to the initial error value based on a neighborhood optimization method, select the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount; when the updated error value corresponding to the updated shearing amount is less than a threshold, determine the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value as the accurately reconstructed wavefront; The determining of the initial error value corresponding to the initial shear amount by using an error function based on the initial phase and the simulated phase specifically includes: Based on the initial phase and the simulated phase, the x-direction error function, the y-direction error function, and the total error function are obtained by the following formulas, respectively. The initial error value corresponding to the initial shear amount is determined according to the total error function. The x-direction error function, the y-direction error function, and the total error function are shown as follows: Among them, E x represents the x-direction error function, E y represents the y-direction error function, E represents the total error function, ΔW x (x,y) is the initial unwrapping phase in the x direction, ΔW′ x (x,y) is the simulated unwrapped phase in the x direction, ΔW y (x,y) is the initial unwrapping phase in the y direction, ΔW′ y (x,y) is the simulated unwrapped phase in the y direction, n x Indicates the number of points involved in the calculation in the x direction, n y Indicates the number of points involved in the calculation in the y direction.

2. The method according to claim 1, wherein The initial phase is as follows: Among them, I1(x,y), I2(x,y), I3(x,y), I4(x,y) represent the light intensity of the four interference images. represents the extracted phase of point (x,y), φ (i,j) represents the corresponding unwrapped phase of the point (x, y), k represents the fringe number of the interference fringe, and arctan represents the inverse tangent function.

3. The method according to claim 1, wherein The initial wavefront to be measured is expressed by the following formula: ΔW=ΔZa ΔW x =ΔZ x a ΔW y =ΔZ y a Where W(x,y) represents the initial wavefront to be measured, a j represents the coefficient of the Zernike polynomial, J represents the number of terms of the Zernike polynomial used, and Z j (x,y) represents the normalized Zernike polynomial in the Cartesian coordinate system; represents the generalized inverse of ΔZ, ΔW x and ΔW y Represents N 2 ×1 column vector, ΔZ x and ΔZ y Indicates N 2 ×(J-1) matrix, s x represents the initial shear amount of x, s y represents the initial shear amount of y, W(x+s x ,y) indicates that the lateral displacement of the initial wavefront W(x,y) to be measured along the x direction is s x Shear wavefront, Z j (x+s x ,y) indicates that the lateral displacement in the x direction is s x The Zernike polynomial, W(x,y+s y ) indicates that the initial measured wavefront W(x,y) has a lateral displacement along the y direction of s y Shear wavefront, Z j (x,y+s y ) indicates that the lateral displacement in the y direction is s y The Zernike polynomials, is the differential Zernike polynomial in the x direction, represents the differential Zernike polynomial in the y direction, ΔW represents the vector composed of the differential wavefront data in two orthogonal directions, ΔZ represents the matrix composed of the components of the differential Zernike polynomials in the x and y directions, which is the basis function matrix for wavefront reconstruction, and a represents the weighting coefficient vector when the original wavefront is expanded into Zernike polynomials.

4. The method according to claim 1, wherein The determining of a plurality of neighborhood error values ​​corresponding to the initial error value based on the neighborhood optimization method, and selecting the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount specifically includes: According to the initial phase and the neighborhood shear amount of the initial shear amount, a first wavefront to be measured, a first lateral shearing interference pattern, a first simulated phase and a neighborhood error value are obtained in sequence; According to the sizes of the plurality of neighborhood error values ​​and the initial error value, a neighborhood error value or an initial error value with a minimum value is selected, and the initial clipping amount is updated with the neighborhood clipping amount or the initial clipping amount with the minimum value.

5. The method according to claim 1, wherein When the minimum value is less than a threshold, determining the iterative measured wavefront determined based on the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value as the precise reconstructed wavefront specifically includes: If a neighborhood error value or initial error value with a minimum value is less than a set threshold, a neighborhood shearing amount or an initial shearing amount is determined based on the minimum value, and the iterative measured wavefront determined based on the neighborhood shearing amount or the initial shearing amount is determined as the accurately reconstructed wavefront.

6. A lateral shearing interferometry wavefront reconstruction device, characterized in that: include: An obtaining unit is used to perform phase unwrapping on an initial lateral shearing interferogram obtained based on the lateral shearing interferometer to obtain an initial phase, and the initial phase and the initial shear amount are fitted by a differential Zernike polynomial to obtain an initial measured wavefront after fitting; A first determining unit is configured to generate a simulated lateral shearing interferogram based on lateral shearing interference of the initial wavefront to be measured and the initial shearing amount, perform phase unwrapping on the simulated lateral shearing interferogram to obtain a simulated phase; and determine an initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase; A second determining unit is configured to determine a plurality of neighborhood error values ​​corresponding to the initial error value based on a neighborhood optimization method, select the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value to update the initial shearing amount; and when the updated error value corresponding to the updated shearing amount is less than a threshold, determine the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value as the accurately reconstructed wavefront; The first determining unit is specifically configured to: Based on the initial phase and the simulated phase, the x-direction error function, the y-direction error function, and the total error function are obtained by the following formulas, respectively. The initial error value corresponding to the initial shear amount is determined according to the total error function. The x-direction error function, the y-direction error function, and the total error function are shown as follows: Among them, E x represents the x-direction error function, E y represents the y-direction error function, E represents the total error function, ΔW x (x,y) is the initial unwrapping phase in the x direction, ΔW′ x (x,y) is the simulated unwrapped phase in the x direction, ΔW y (x,y) is the initial unwrapping phase in the y direction, ΔW′ y (x,y) is the simulated unwrapped phase in the y direction, n x Indicates the number of points involved in the calculation in the x direction, n y Indicates the number of points involved in the calculation in the y direction.

7. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the lateral shearing interference wavefront reconstruction method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that A computer program is stored, and when the computer program is executed by a processor, the processor is caused to perform the lateral shearing interference wavefront reconstruction method according to any one of claims 1 to 5.

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