Transverse shear interference wavefront reconstruction method and device

Abstract

The invention discloses a lateral shear interference wavefront reconstruction method and device, relates to the technical field of optical measurement, adopts inaccurate shear amount to perform wavefront reconstruction, realizes high-precision wavefront reconstruction, and solves the problem that wavefront reconstruction depends on shear amount calculation precision in the prior art. Comprising the following steps: performing phase unwrapping on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device to obtain an initial phase, and fitting the initial phase and an initial shearing amount through a differential Zernike polynomial to obtain a fitted initial wavefront to be measured; determining an initial error value corresponding to the initial shear amount through an error function based on the initial phase and the simulation phase; determining a plurality of domain error values corresponding to the initial error value based on a neighborhood optimization method, and selecting an initial shearing amount or a domain shearing amount corresponding to a minimum value to update the initial shearing amount; and when the updating error value corresponding to the updating shearing amount is smaller than the threshold value, determining the iteration wavefront to be measured determined by the updating shearing amount corresponding to the updating error value as the accurate reconstruction wavefront.

Description

Technical Field

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

[0002] Lateral shearing interferometry is a wavefront interferometry measurement technology that does not require a reference mirror. It generates interference by superimposing the wavefront to be measured with its own sheared wavefront that has undergone a lateral displacement. It 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, it is necessary to reconstruct the wavefront to be measured 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 amount of shear. Therefore, the accuracy of the calculation of the shear amount is very critical.

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

[0004] The other type is calculated directly from the interference pattern through image processing. One type introduces a defocused wavefront to improve the shear measurement accuracy in the lateral shearing interferometer, but its accuracy is related to the parameters of the optical system, such as focal length, magnification and defocus, which will affect the measurement accuracy of the shear; the other type uses the Radon transform principle to obtain the mutation point of the integral curve to calculate the shear. This method requires that the edge of the interference pattern is clear and the edge stripes cannot be dark stripes, otherwise it is difficult to find the mutation point, which affects the calculation accuracy of the shear.

[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 inaccurate 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 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.

[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 interference pattern obtained based on a lateral shearing interference device 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 wavefront to be measured after fitting;

[0009] The initial wavefront to be measured and the initial shear amount generate a simulated lateral shear interference pattern based on lateral shear interference, and the simulated lateral shear 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 domain error values ​​corresponding to the initial error value are determined, and the initial shearing amount or the domain 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] 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.

[0014] Preferably, the initial wavefront to be measured is expressed by the following formula:

[0015]

[0016] ΔW=ΔZa

[0017] ΔW x =ΔZ x a

[0018] ΔW y =ΔZ y a

[0019]

[0020] 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 Respectively represent N 2 ×1 column vector, ΔZ x and ΔZ y 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 The 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 lateral displacement of the initial wavefront W(x,y) along the y direction is s y The shear wavefront, Z j (x,y+s y ) indicates that the lateral displacement in the y direction is s y The Zernike polynomials of is the differential Zernike polynomial in the x direction, represents the differential Zernike polynomial in the y direction.

[0021] Preferably, determining the initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase specifically includes:

[0022] Based on the initial phase and the simulation phase, the x-direction error function, the y-direction error function and the total error function are obtained respectively by the following formulas, and the initial error value corresponding to the initial shearing 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 as follows:

[0023]

[0024] Among them, E x represents the x-direction error function, E yrepresents the error function in the y direction, 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 simulation unwrapped phase in the y direction.

[0025] Preferably, the determining of a plurality of domain error values ​​corresponding to the initial error value based on a 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:

[0026] According to the initial phase and the neighborhood shear amount of the initial shear amount, a first wavefront to be measured, a first lateral shear interference pattern, a first simulation phase and a neighborhood error value are obtained in sequence;

[0027] 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 shearing amount is updated with a neighborhood shearing amount or an initial shearing amount with a minimum value.

[0028] 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 accurate reconstruction wavefront specifically includes:

[0029] If a neighborhood error value or an 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.

[0030] An embodiment of the present invention provides a lateral shearing interferometry wavefront reconstruction device, comprising:

[0031] An obtaining unit is used to perform phase unwrapping on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device to obtain an initial phase, wherein the initial phase and the initial shearing amount are fitted by a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;

[0032] A first determining unit is used for generating a simulated lateral shearing interference pattern based on lateral shearing interference for the initial wavefront to be measured and the initial shearing amount, performing phase unwrapping on the simulated lateral shearing interference pattern to obtain a simulated phase; and determining an initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase;

[0033] The second determination unit is used to determine multiple domain error values ​​corresponding to the initial error value based on a neighborhood optimization method, and select the initial shearing amount or the domain 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 value, the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value is determined as the accurately reconstructed wavefront. An embodiment of the present invention provides an embodiment of the present invention provides a computer device, 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 any one of the above-mentioned lateral shearing interference wavefront reconstruction methods.

[0034] 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 interference wavefront reconstruction methods.

[0035] The 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 domain error values ​​corresponding to the initial error value based on a neighborhood optimization method, and selecting the initial shear amount or the domain 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 four-step phase shift on the obtained shearing interference pattern, unpacks the wrapped phase using the least squares phase unpacking algorithm based on DCT, then uses the inaccurate shearing amount to perform wavefront fitting according to the differential Zernike principle, and then uses the transverse shearing interference principle to regenerate the simulated transverse shearing interference pattern of the initial wavefront to be measured after fitting, and pre-processes and unpacks the simulated transverse shearing interference pattern to obtain the simulated phase. By determining the error function for the initial phase and the simulated phase and determining the initial error value corresponding to the initial shearing amount, the accurate reconstructed wavefront is finally obtained through iteration. The method adjusts the initial inaccurate initial shearing amount, takes the phase information extracted from the actual interference pattern as the optimization target, performs iterative optimization based on the error function, and finally obtains the accurate shearing amount and the accurate reconstructed wavefront after iterative optimization, thereby realizing high-precision wavefront reconstruction; the method can obtain an accurate reconstructed wavefront when the initial shearing amount is inaccurately calculated, which greatly improves the practical applicability of the method, and is very useful when it is difficult to accurately determine the shearing amount under engineering conditions. Further, 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

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0037] Figure 1 A schematic flow chart of a lateral shearing interferometry wavefront reconstruction method provided by an embodiment of the present invention;

[0038] Figure 2A A schematic diagram of four phase-shifted shearing interferences in the x-direction provided by an embodiment of the present invention;

[0039] Figure 2B A schematic diagram of four phase-shifted shearing interferences in the y direction provided by an embodiment of the present invention;

[0040] Figure 3A The embodiment of the present invention provides Figure 2A The corresponding unwrapped phase diagram in the x direction;

[0041] Figure 3B The embodiment of the present invention provides Figure 2B The corresponding unwrapped phase diagram in the y direction;

[0042] 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;

[0043] Figure 4B A schematic diagram of a wavefront to be measured provided by an embodiment of the present invention;

[0044] Figure 4C The embodiment of the present invention provides Figure 4A The schematic diagram of the reconstructed wavefront shown is similar to Figure 4B The residual diagram after the measured wavefront is reconstructed is shown;

[0045] Figure 5A Schematic diagram of four simulated phase-shift shearing interferences in the x-direction obtained based on lateral shearing interference provided by an embodiment of the present invention;

[0046] Figure 5B Schematic diagram of four simulated phase-shift shearing interferences in the y direction obtained based on lateral shearing interference provided by an embodiment of the present invention;

[0047] Fig. 6A The embodiment of the present invention provides Figure 5A Schematic diagram of the unwrapped phase in the x direction;

[0048] Figure 6B The embodiment of the present invention provides Figure 5B Schematic diagram of the unwrapped phase in the y direction;

[0049] Fig. 7A A schematic diagram of wavefront reconstruction obtained based on the method provided in an embodiment of the present invention;

[0050] Figure 7B A schematic diagram of a wavefront to be measured provided by an embodiment of the present invention;

[0051] Figure 7C The embodiment of the present invention provides Fig. 7A The reconstructed wavefront image shown is similar to Figure 7B The residual diagram after the measured wavefront is reconstructed is shown;

[0052] Figure 8 A schematic structural diagram of a lateral shearing interferometer wavefront reconstruction device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0054] Terms involved in the embodiments of the present invention:

[0055] 1. Neighborhood Optimization Method is a technique widely used in optimization problems. Its basic idea is to gradually improve the optimization target by searching for better solutions in the "neighborhood" of the current solution. The so-called neighborhood refers to a set of solutions that are close to the current solution in the solution space under a certain distance metric. For example, in a simple two-dimensional function optimization problem, assuming that the solution is a point (x, y) on the plane, then the neighborhood of this point can be defined as all points within a circle with a radius of r and a center of (x, y). This radius r determines the size of the neighborhood.

[0056] Figure 1 A schematic flow chart of a lateral shearing interferometry wavefront reconstruction method provided by an embodiment of the present invention is as follows: Figure 1 to Figure 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:

[0057] Step 101, performing phase unwrapping on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device to obtain an initial phase, and fitting the initial phase and the initial shearing amount by using a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;

[0058] Step 102, the initial wavefront to be measured and the initial shear amount generate a simulated lateral shear interference pattern based on lateral shear interference, and the simulated lateral shear 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;

[0059] Step 103, based on the neighborhood optimization method, determine multiple domain error values ​​corresponding to the initial error value, select the initial shearing amount or the domain shearing amount corresponding to the minimum value to update the initial shearing amount; when the minimum value is less than a threshold value, the iterative measured wavefront determined based on the initial shearing amount or the domain shearing amount corresponding to the minimum value is determined as the accurately reconstructed wavefront.

[0060] In step 101, it is necessary to obtain three lateral shearing interference patterns based on the lateral shearing interference device. Specifically, when the wavefront with the measured surface information passes through the shearer, a shearing wavefront that is laterally translated from 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. Specifically, Figure 2A The four phase-shifted shear interferences in the x-direction are shown Figure 2B The four phase-shifted shearing interference patterns in the y direction are shown. For each point (x, y) in the region, the four interference patterns can be expressed by the following formulas:

[0061]

[0062] Using the above four interference patterns with different phase shifts, the phase of point (x, y) can be calculated by the following formula:

[0063]

[0064] 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, b(x,y) represents the AC modulation term, Represents the differential wrapped phase of the point (x,y).

[0065] Furthermore, according to formula (2), an inverse tangent operation is performed when extracting the phase, and the extracted wrapped phase is between (-π, π), and discontinuous jumps appear in the extracted phase distribution. This jump does not reflect the real phase information, and it is necessary to splice and expand this discontinuous phase information into a continuous phase to obtain the phase information containing the real surface shape of the optical element.

[0066] The embodiment of the present invention provides a method for implementing the above phase unwrapping using a least square method based on DCT, specifically:

[0067] If the wrapped phase extracted in this embodiment is within an m×n discrete rectangular region, 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 unwrapping phase. The relationship between the wrapping phase and the unwrapping phase can be expressed by the following formula:

[0068]

[0069] Wherein, k represents the fringe number of the interference fringe, i = 0, 1, ..., m-1; j = 0, 1, ..., n-1.

[0070] Furthermore, we define the wrapping operator as W r , then the wrapping operator can be expressed by the following formula:

[0071]

[0072] The difference in the x direction can be calculated according to the following formula The difference in the y direction

[0073]

[0074] Furthermore, by combining equations (5) and (6), we obtain the equation system V:

[0075]

[0076] By transforming the normal equation of formula (7), we can obtain the discretized Poisson equation in the discrete region as follows:

[0077] φ (i+1,j) –2φ (i，) +φ (i-1,j) +φ (i，j+1) -2φ (i，j) +φ (i，j-1) =

[0078] ρ(i,j) (8)

[0079] In formula (8),

[0080] According to the obtained unwrapping phase φ (i,j) The discrete cosine transform spectrum of And perform inverse discrete cosine transform to get:

[0081]

[0082] in,

[0083] Furthermore, we first (i,j) Perform discrete cosine transform to get Then, φ is solved by inverse discrete cosine transform (i,j) :

[0084] Simplify equation (9) and solve it accurately according to the following formula:

[0085]

[0086] Unwrapped phase and differential wavefront ΔW in x and y directions x and ΔW y The relationship between them is as follows:

[0087]

[0088] In the formula, 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.

[0089] 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.

[0090] 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:

[0091]

[0092] Among them, R θ represents the line integral of the interference pattern in the specified direction θ, x′ and y′ are two directions perpendicular to each other in the rectangular coordinate system established along the direction θ, and I represents the light intensity of the interference pattern.

[0093] 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 the embodiment of the present invention, since the lateral shearing interference pattern has the largest spot area in the shearing direction and the smallest spot area in the direction perpendicular to it, the difference between the width of the largest spot area and the smallest spot area is the size of the shearing amount. Analyze the Radon transform results, for the area outside the spot area, it is a dark area with a small grayscale value. The Radon transform value in this area grows linearly and changes slowly, and when entering the spot area, the transform value grows 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 largest spot area, and the 90° projection direction corresponds to the smallest 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 .

[0094] Furthermore, based on the initial phase and initial shear amount determined above, the wavefront to be measured W(x, y) can be represented by a series of fringe Zernike polynomials as follows:

[0095]

[0096] 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.

[0097] Furthermore, the differential wavefronts in the x and y directions generated by the two wavefronts in the overlapping area are expressed as:

[0098]

[0099] 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, s x The shear wavefront, Z j (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, s y The shear wavefront, Z j (x,y+sy ) is the lateral displacement in the y direction, s y The Zernike polynomials of 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.

[0100] The above relationship can be expressed as a vector:

[0101]

[0102] ΔW=ΔZa (18)

[0103] Where, ΔW x and ΔW y N 2 ×1 column vector, ΔZ x and ΔZ y YesN 2 ×(J-1) matrix,

[0104] The coefficient a of the wavefront expression to be measured is solved by the least squares method, which can be expressed as:

[0105]

[0106] In the formula, represents the generalized inverse of ΔZ, Given by:

[0107]

[0108] Furthermore, the initial wavefront W(x, y) to be measured 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 schematic diagram of the reconstructed wavefront shown is similar to Figure 4B The residual schematic diagram after the measured wavefront is reconstructed is shown, wherein the PV (Peak to Valley) of the residual is 1.3268λ, and the RMS (Root-Mean–Square) is 0.3254λ.

[0109] 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:

[0110] PV=W max -W min (twenty one)

[0111] Among them, W max and W min They represent the maximum and minimum values ​​of the face shape W(x,y), respectively, and x and y are the serial numbers of the valid rows and columns of the face shape, respectively.

[0112] RMS represents the root mean square value of the surface error, and its calculation formula is as follows:

[0113]

[0114] 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.

[0115] 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 generate a simulated lateral shearing interference pattern based on lateral shearing interference, and the simulated lateral shearing interference pattern is further phase unwrapped to obtain the placement phase. Here, the phase unwrapping of the simulated lateral shearing interference pattern can refer to step 101, which will not be repeated here. In an embodiment of the present invention, Figure 5A Four simulated phase-shift shearing interferometry diagrams in the x-direction based on lateral shearing interferometry are provided. Figure 5B Four schematic diagrams of simulated phase-shift shearing interference in the y direction obtained based on lateral shearing interference are provided. Fig. 6A Provides Figure 5A The corresponding unwrapped phase diagram in the x direction, Figure 6B Provides Figure 5B Corresponding unwrapped phase diagram in the y direction.

[0116] Further, according to the initial phase and the simulated phase determined in step 101, an initial error function can be constructed by the following formula, specifically:

[0117] The error functions in the x- and y-directions are shown below:

[0118]

[0119] Furthermore, according to the above-mentioned error functions in the x-direction and the y-direction, the total error function can be obtained, which is as follows:

[0120]

[0121] Among them, E x represents the x-direction error function, E y represents the error function in the y direction, 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 simulation unwrapped phase in the y direction.

[0122] 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 field 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 field shearing amount or the initial shearing amount corresponding to the minimum value. During multiple iterations, if the determined minimum value is less than a threshold value, the iterative measured wavefront determined according to the field shearing amount or the initial shearing amount corresponding to the minimum value can be determined as the final desired precise reconstructed wavefront.

[0123] For example:

[0124] Step 103-1, according to the initial shearing amount (s x ,s y ) determines the initial error value corresponding to the initial shear amount.

[0125] 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 domain shearing amount can be determined based on steps 101 and 102;

[0126] Step 103-3, compare the initial error value and the neighborhood error value corresponding to the initial clipping amount and the neighborhood clipping amount, select the initial clipping amount or the neighborhood clipping amount corresponding to the minimum value to update the initial clipping amount, and obtain the updated clipping amount; repeat steps 103-1 to 103-3 once to obtain an updated clipping amount.

[0127] 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; accordingly, 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 a random value of the initial shearing amount in step 101 is assigned 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 less 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.

[0128] Fig. 7A Provides wavefront reconstruction images, Figure 7B Provides the wavefront image to be measured. Figure 7C The residual diagram after reconstruction of the reconstructed wavefront image and the measured wavefront is provided; the PV of the residual is 4.9979×10 -10 λ, RMS is 1.0757×10 -10 λ.

[0129] The embodiment of the present invention provides a lateral shearing interference wavefront reconstruction method, which performs four-step phase shift on the obtained shearing interference pattern to extract the wrapped phase information, unwraps the wrapped phase using the least squares phase unwrapping algorithm based on DCT, then uses the inaccurate shearing amount to perform wavefront fitting according to the differential Zernike principle, and then uses the lateral shearing interference principle to regenerate the simulated lateral shearing interference pattern of the initial wavefront to be measured after fitting, and pre-processes and unwraps the simulated lateral shearing interference pattern to obtain the simulated phase. By determining the error function for the initial phase and the simulated phase and determining the initial error value corresponding to the initial shearing amount, the accurate reconstructed wavefront is finally obtained through iteration. The method adjusts the initial inaccurate initial shearing amount, takes the phase information extracted from the actual interference pattern as the optimization target, performs iterative optimization based on the error function, and finally obtains the accurate shearing amount and the accurate reconstructed wavefront after iterative optimization, thereby realizing high-precision wavefront reconstruction; the method can obtain an accurate reconstructed wavefront when the initial shearing amount is inaccurately calculated, which greatly improves the practical applicability of the method, and is very useful when it is difficult to accurately determine the shearing 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, thereby ensuring the precision and accuracy of the reconstructed wavefront.

[0130] 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.

[0131] like Figure 8 As shown, the device includes an obtaining unit 801, a first determining unit 802 and a second determining unit 803.

[0132] The obtaining unit 801 is used to perform phase unwrapping on the initial lateral shearing interference pattern obtained based on the lateral shearing interference device 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 wavefront to be measured after fitting;

[0133] A first determining unit 802 is used for generating a simulated lateral shearing interference pattern based on the lateral shearing interference of the initial wavefront to be measured and the initial shearing amount, performing phase unwrapping on the simulated lateral shearing interference pattern to obtain a simulated phase; and determining an initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase;

[0134] The second determination unit 803 is used to determine multiple domain error values ​​corresponding to the initial error value based on the neighborhood optimization method, and select the initial shearing amount or the domain 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 value, the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value is determined as the accurately reconstructed wavefront.

[0135] It should be understood that the units included in the above-mentioned lateral shearing interference wavefront reconstruction device are only logical divisions based on the functions implemented by the device. In practical applications, the above-mentioned units can be superimposed or split. In addition, the functions implemented by the lateral shearing interference wavefront reconstruction device provided in this embodiment correspond one-to-one to the lateral shearing interference wavefront reconstruction method provided in the above-mentioned embodiment. The more detailed processing flow implemented by the device has been described in detail in the above-mentioned method embodiment 1 and will not be described in detail here.

[0136] 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.

[0137] Another embodiment of the present invention further 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.

[0138] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other 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.

[0139] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A lateral shearing interferometry wavefront reconstruction method, characterized in that: include: Phase unwrapping is performed on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device 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 wavefront to be measured after fitting; The initial wavefront to be measured and the initial shear amount generate a simulated lateral shear interference pattern based on lateral shear interference, and the simulated lateral shear 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; Based on the neighborhood optimization method, multiple domain error values ​​corresponding to the initial error value are determined, and the initial shearing amount or the domain 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.

2. The method according to claim 1, characterized in that 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), and k represents the fringe number of the interference fringe.

3. The method according to claim 1, characterized in that 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 Respectively represent N 2 ×1 column vector, ΔZ x and ΔZ y 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) along the x direction is s x The 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 lateral displacement of the initial wavefront W(x, y) along the y direction is s y The shear wavefront, Z j (x,y+s y ) indicates that the lateral displacement in the y direction is s y The Zernike polynomials of is the differential Zernike polynomial in the x direction, represents the differential Zernike polynomial in the y direction.

4. The method according to claim 1, characterized in that The determining the initial error value corresponding to the initial shearing amount through an error function based on the initial phase and the simulated phase specifically includes: Based on the initial phase and the simulation phase, the x-direction error function, the y-direction error function and the total error function are obtained respectively by the following formulas, and the initial error value corresponding to the initial shearing 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 as follows: Among them, E x represents the x-direction error function, E y represents the error function in the y direction, 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.

5. The method according to claim 1, characterized in that The method of determining a plurality of domain error values ​​corresponding to the initial error value based on a 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 shear interference pattern, a first simulation 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 shearing amount is updated with a neighborhood shearing amount or an initial shearing amount with a minimum value.

6. The method according to claim 1, characterized in that 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 accurate reconstruction wavefront, specifically includes: If a neighborhood error value or an 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.

7. A lateral shearing interferometer wavefront reconstruction device, characterized in that: include: An obtaining unit is used to perform phase unwrapping on an initial lateral shearing interference pattern obtained based on a lateral shearing interference device to obtain an initial phase, wherein the initial phase and the initial shearing amount are fitted by a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting; A first determining unit is used for generating a simulated lateral shearing interference pattern based on the lateral shearing interference of the initial wavefront to be measured and the initial shearing amount, and performing phase unwrapping on the simulated lateral shearing interference pattern to obtain a simulated phase; Determine an initial error value corresponding to the initial shear amount through an error function based on the initial phase and the simulated phase; The second determination unit is used to determine multiple domain error values ​​corresponding to the initial error value based on the neighborhood optimization method, and select the initial shearing amount or the domain 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 value, the iterative measured wavefront determined by the updated shearing amount corresponding to the updated error value is determined as the accurately reconstructed wavefront.

8. A computer device, characterized in that: The computer device includes 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 the lateral shearing interference wavefront reconstruction method as described in any one of claims 1-6.

9. 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 executes the lateral shearing interference wavefront reconstruction method as described in any one of claims 1-6.

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