A robust support error separation method, electronic device and storage medium

Abstract

The application provides a robust support error separation method, an electronic device and a storage medium, and relates to the technical field of support error separation. The method comprises the following steps: processing a physical reference mark in a non-light aperture area of a to-be-detected optical element, and recording original coordinates of the physical reference mark in a coordinate system of the to-be-detected optical element; performing n times of interference measurement on the to-be-detected optical element; determining a 2D rotation matrix and a transverse translation vector corresponding to each measurement of the to-be-detected optical element; obtaining a preset measurement model; subtracting interference surface data M i of the i th measurement from interference surface data M true of the j th measurement; adopting a Zernike polynomial expansion W i , and combining M j to construct an over-determined equation set; and reversely obtaining support error; and the application can effectively separate the support error.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of support error separation, in particular to a robust support error separation method, an electronic device and a storage medium. BACKGROUND

[0002] In the manufacturing and testing process of high-precision optical systems at the nanometer or even sub-nanometer scale (such as high-end lenses, lithography lenses, etc.), "support error" is one of the core interference terms affecting the measurement accuracy; the support error specifically refers to the deformation error of an optical element caused by a support clamp (such as a bracket or clamp used to fix the element), which is directly related to factors such as clamping stress of the clamp and gravity of the element itself. In order to achieve the goal of ultra-precision measurement, it is necessary to accurately separate the support error from the original measurement data through "absolute testing" technology, which is a core technical requirement in the current high-precision optical detection field.

[0003] Currently, the "rotational testing method" is widely used as the mainstream technical solution for separating support error; the core model assumption of the rotational testing method is that "the optical element only undergoes ideal pure rotation without lateral translation during rotation", but in actual detection (especially for large-diameter optical elements such as concave mirrors and lenses with a diameter exceeding 200 mm), due to factors such as clamp positioning accuracy limitations and manual rotation operation deviations, the element will inevitably produce lateral translation (i.e. position offset in the direction perpendicular to the rotation axis). The contradiction between this actual lateral translation and the model "pure rotation" assumption makes it impossible for the method to provide sufficient geometric constraints for rotationally symmetric errors (such as spherical aberration, high-order spherical aberration, etc.) commonly found in optical systems, ultimately making it impossible to effectively separate such errors from the original data, directly affecting the reconstruction accuracy of the true surface topography; therefore, how to effectively separate the support error has become a technical problem to be solved. SUMMARY

[0004] In view of the above technical problems, the technical solution adopted by the present application is as follows:

[0005] According to a first aspect of the present application, a robust support error separation method is provided, the method comprising the following steps:

[0006] S100, a physical reference mark is processed in a non-pupil region of a to-be-detected optical element, and the original coordinates of the physical reference mark in the to-be-detected optical element coordinate system are recorded.

[0007] S200, the to-be-detected optical element is fixed on a support clamp, and n times of interference measurement are performed on the to-be-detected optical element; before each measurement, the optical element is manually rotated by a preset angle, and the interference surface data of the to-be-detected optical element and the pixel coordinate point set of the physical reference mark are synchronously collected each time.

[0008] S300, determining the 2D rotation matrix and the lateral translation vector corresponding to each measurement of the optical element to be detected with reference to the first measured pixel coordinate point set.

[0009] S400, obtaining a preset measurement model M k =W true (R k ,t k )+W supp ; wherein M k is the interference surface data of the kth measurement of the optical element to be detected; W true is the real surface topography of the optical element to be detected; (R k ,t k ) is the compound pose parameter of the kth measurement; R k and t k are the 2D rotation matrix and the lateral translation vector corresponding to the kth measurement of the optical element to be detected; W true (R k ,t k ) is the real surface of the optical element to be detected after transformation by (R k ,t k ); W supp is the support error; k = 1, 2, …, n.

[0010] S500, subtracting the interference surface data M i of the ith measurement from the interference surface data Mⱼ of the jth measurement to obtain M i -M j =W true (R i ,t i )-W true (R j ,t j ); i = 1, 2, …, n; j = 1, 2, …, n; i ≠ j.

[0011] S600, expanding W true using Zernike polynomials and constructing an overdetermined equation set in combination with M i -M j .

[0012] S700, solving the Zernike coefficients by the least square method to reconstruct W true , and substituting the reconstructed W true into the first measured pixel coordinate point set to obtain the support error W supp by back calculation.

[0013] According to another aspect of the present application, a non-transitory computer readable storage medium is also provided, the storage medium storing at least one instruction or at least one program, the at least one instruction or at least one program being loaded and executed by a processor to implement the robust support error separation method described above.

[0014] According to another aspect of the present application, an electronic device is also provided, comprising a processor and the non-transitory computer readable storage medium described above.

[0015] The present application has at least the following beneficial effects:

[0016] The robust support error separation method of the present application breaks through the assumption limitation of the traditional rotation test method "ideal pure rotation" by processing a physical reference mark in the non-light passing area of the optical element to be detected, accurately obtains the rotation matrix and the lateral translation vector, effectively captures the lateral translation in the measurement process, and provides complete geometric constraints for the rotationally symmetric error separation; redundant data is collected through multiple interference measurements, the measurement model is used to subtract and eliminate the fixed support error, and then the real surface is expanded by the front Zernike polynomial and an overdetermined equation set is constructed to solve the optimal solution, which not only realizes the synchronous separation of the rotationally symmetric error and the non-rotationally symmetric error, but also suppresses the measurement noise interference through the redundant constraints; the entire process does not need to strictly control the coaxiality of the element, is simple to operate and has high calculation efficiency, and finally the real surface topography of the element can be accurately reconstructed and the support error can be back calculated, the separation precision can reach the nanometer level, the robustness is strong, and the technical pain points of the traditional method, such as low separation precision and inability to process rotationally symmetric error, are effectively solved, and the support error can be effectively separated. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0018] Figure 1 A flowchart of the robust support error separation method provided for the embodiments of the present application is shown in the figure.

[0019] Figure 2 A schematic diagram of the relationship between the element reconstruction RMS error and the measurement noise level provided for the embodiments of the present application is shown in the figure.

[0020] Figure 3 A comparison diagram of the element reconstruction RMS error of the standard least squares method and the RANSAC method under different numbers of outliers provided for the embodiments of the present application is shown in the figure.

[0021] Figure 4A schematic diagram of the variation of the relative element reconstruction error with the support RMS ratio for embodiments of the present application;

[0022] Figure 5 A schematic diagram of the variation of the element reconstruction RMS error with the support instability level for embodiments of the present application;

[0023] Figure 6 A comparative schematic diagram of the real experimental support error separation results for embodiments of the present application. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative work fall within the protection scope of the present application.

[0025] It should be noted that, based on the present disclosure, a person skilled in the art should appreciate that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, an apparatus can be implemented and / or a method can be practiced using any number of the aspects set forth herein. In addition, such an apparatus can be implemented and / or such a method can be practiced using other structure and / or functionality in addition to or other than one or more of the aspects set forth herein.

[0026] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative work fall within the protection scope of the present application. Figure 1 A flowchart of a robust support error separation method is shown in FIG. 1, and a robust support error separation method is introduced.

[0027] The robust support error separation method can include the following steps:

[0028] S100, a physical reference mark is processed in a non-pupil area of an optical element to be detected, and an original coordinate of the physical reference mark in a coordinate system of the optical element to be detected is recorded.

[0029] In the embodiment, a coordinate measuring machine (CMM) can be used to process the physical reference mark in the non-pupil area of the optical element to be detected. The CMM is a high-precision positioning and processing device in the optical field, and the positioning accuracy can reach microns, ensuring the accuracy of the mark position.

[0030] The non-aperture region of the optical element to be detected (i.e. the region where the edge of the element does not affect the propagation of light interference) is processed to avoid interference of the mark with subsequent interference measurement. 3-4 uniformly distributed "physical reference marks" are processed, preferably small concave points with a diameter of 0.5mm (the concave point structure is not easy to wear and is easy to identify in the interferometer image); the marks need to be uniformly distributed along the circumference of the element edge (such as 1 mark every 90°), to ensure that the rotation and translation of the element can be fully captured.

[0031] A "element coordinate system" (x-axis and y-axis along the radial direction of the element, z-axis perpendicular to the surface of the element) is established with the geometric center of the optical element as the origin; the three-dimensional coordinates of each mark in the coordinate system are accurately measured by CMM and recorded; for example, mark A (x=5mm, y=0mm, z=0mm), mark B (x=0mm, y=5mm, z=0mm), etc., as "reference anchor points" for subsequent pose comparison.

[0032] For example: taking a 200mm aperture concave lens as an example, 4 uniformly distributed concave point marks are processed on the edge non-aperture region of the lens by CMM, the center distance of the marks from the lens edge is 1mm, and the included angle between adjacent marks is 90°; record the coordinates of each mark relative to the center of the lens: mark 1 (6mm, 0mm, 0mm), mark 2 (0mm, 6mm, 0mm), mark 3 (-6mm, 0mm, 0mm), mark 4 (0mm, -6mm, 0mm).

[0033] This step processes uniformly distributed physical reference marks by high-precision equipment, providing stable and identifiable "anchor points" for subsequent pose estimation, solving the technical pain point that the traditional rotation test method cannot accurately capture the lateral translation of the element; at the same time, the original coordinates under the element coordinate system are recorded, ensuring the uniformity of the reference basis for pose calculation, avoiding the pose estimation error caused by the confusion of the reference, laying a foundation for the accurate solution of the subsequent compound pose parameters, and improving the stability of the entire error separation process.

[0034] S200, fixing the optical element to be detected on a support clamp, and performing n times of interference measurement on the optical element to be detected; before each measurement, manually rotating the optical element by a preset angle, and synchronously collecting the interference surface data of the optical element to be detected and the pixel coordinate point set of the physical reference mark.

[0035] In this embodiment, the optical element to be detected can be placed stably on the support clamp, and the contact area of the clamp is made of soft material (such as elastic rubber) to avoid scratching the surface of the element; the coaxiality does not need to be strictly controlled during fixing (the subsequent pose estimation can compensate for the translation), reducing the operation difficulty.

[0036] The Fizeau interferometer is used for measurement, the measurement accuracy of the interferometer is set to nanometer level (such as 0.1 nm), and the super-precision measurement requirement is matched; the number of measurements n is determined, and the value range of n is 5-8 times (both data redundancy and measurement efficiency are considered, too few times will be insufficient, and too many times will increase the calculation amount).

[0037] Before each measurement, the optical element is manually rotated by a preset angle (45° to 60°, too large angle is easy to cause the mark point to be out of the field of view of the interferometer, and too small angle is insufficient in data redundancy); after rotation, two groups of data are synchronously collected:

[0038] Interference surface data: pixel-level topographic data of the element surface captured by the interferometer, each pixel point corresponds to a topographic height value (unit: nm), forming a two-dimensional matrix;

[0039] Pixel coordinate point set of physical reference mark: 3-4 pixel coordinates of the physical reference mark in the interference image are extracted through the interference image recognition algorithm (such as the pixel coordinates of mark 1 in the kth measurement are (256, 320)), forming a point set P k .

[0040] For example, a 200 mm concave lens is fixed on a soft contact clamp, 6 times of measurement (n=6) are performed by using a 6-inch Fizeau interferometer, and the lens is manually rotated by 60° before each measurement; the interference surface data M1 (a two-dimensional matrix of 1024*1024 pixels, the height value range is-50 nm to 50 nm) is collected in the first measurement (k=1), and the pixel coordinate point set P1 of the four marks is extracted, that is, { (256, 320), (320, 384), (384, 320), (320, 256)}; the operation is repeated, and M2 to M6 and P2 to P6 are sequentially collected.

[0041] This step synchronously collects the interference surface data and the mark point coordinates through multiple rotation measurements, which provides multiple sets of comparison data for subsequent pose estimation and provides sufficient measurement samples for error separation; the manual rotation combined with the design of the soft clamp reduces the high-precision requirement for the operation equipment and improves the practicability of the method; the two groups of data collected synchronously have strong correlation, which avoids the time difference error caused by separate measurement of the pose and the interference data, ensures the space-time matching of the pose parameters and the interference data, and provides data guarantee for the accuracy of subsequent error separation.

[0042] S300, taking the pixel coordinate point set of the first measurement as a reference, determining the 2D rotation matrix and the horizontal translation vector corresponding to each measurement of the optical element to be detected.

[0043] Further, step S300 includes the following steps:

[0044] S310, for the pixel coordinate point set P k, and the target point set P k is the pixel coordinate set of the first physical reference mark measured (e.g., P1 = { (256, 320), (320, 384), (384, 320), (320, 256)}).

[0045] In this embodiment, the reference point set P1 is the pixel coordinate set of the first physical reference mark measured (e.g., P1 = { (256, 320), (320, 384), (384, 320), (320, 256)}). k is the pixel coordinate set of the kth measurement (e.g., P2 = { (260, 318), (322, 386), (382, 322), (318, 254)} when k = 2); ensure that the mark points of the two point sets are one-to-one corresponding (e.g., P k The first point in P1 corresponds to the first point in P1, which is the same physical reference mark).

[0046] Initial transformation parameter assumption: first set an initial rotation angle θ0 (e.g., manually rotate a preset angle of 60°) and an initial translation vector (t x0 x0 = 0, t

[0047] Point set transformation and distance calculation: perform rotation and translation operations on each mark point in the target point set P k according to the initial transformation parameters to obtain the transformed point set P k '; calculate the Euclidean distance between each point in P k ' and the corresponding point in P1 (e.g., the distance d1 between the first point in P k ' and the first point in P1 is [(260cosθ0-260sinθ0+t x0 -256)²+(260sinθ0+260cosθ0+tᵧ0-320)²] 1 / 2 ], and sum them up to get the total distance D = Σd i (i = 1 ~ 4, corresponding to 4 mark points).

[0048] Iterative optimization: adjust the rotation angle θ and the translation vector (t x , tᵧ) by gradient descent method, repeat the "point set transformation → distance calculation" step, and each iteration makes the total distance D smaller; set the iteration termination condition (e.g., the iteration number reaches 100 times, or the difference between the two iterations D is less than 10 -6 pixels), at this time the obtained transformation parameters (θ_opt, t x _opt, tᵧ_opt) are the optimal transformation parameters that make the sum of distances between P k and the corresponding points in P0 minimum.

[0049] For example, taking the second measurement of the 200mm concave lens as an example, P1 is the first measurement of the 4 marker pixel coordinate set { (256, 320), (320, 384), (384, 320), (320, 256)} and P2 is the second measurement of the point set { (260, 318), (322, 386), (382, 322), (318, 254)}; the initial transformation parameters are set as θ0=60°, t x0 =0, tᵧ0=0, after 50 iterations, the total distance D decreases from the initial 12.3 pixels to 0.8 pixels, the iteration is terminated, and the optimal transformation parameters θ_opt=60.3°, t x _opt=0.12mm (corresponding to 3 pixels in the pixel coordinate, assuming that the pixel resolution of the interferometer image is 0.04mm / pixel), tᵧ_opt=0.08mm (corresponding to 2 pixels).

[0050] This step accurately finds the optimal transformation parameters that align the two sets of points through the iterative optimization characteristics of the ICP algorithm, solving the pose deviation problem caused by manual rotation; the ICP algorithm has fault tolerance for small position errors of the marker points, can effectively offset the slight noise interference when the marker points are recognized by the interferometer image, and ensures the reliability of the transformation parameters; at the same time, the one-to-one matching of the point sets avoids errors caused by confusion of different marker points, provides high-precision initial input for subsequent SVD solving of the rotation matrix and translation vector, and lays the foundation for accurate estimation of the compound pose parameters.

[0051] S320, a 2D rotation matrix R k and a horizontal translation vector t k are solved by SVD.

[0052] In this embodiment, the center coordinates of the reference point set P1 and the target point set P k , i.e. the mean coordinates, are calculated respectively; the two sets of points are respectively subtracted by the center coordinates of each set to obtain the decentered point sets, eliminating the influence of the overall translation of the point sets on the rotation solution; a 3x3 covariance matrix H is constructed.

[0053] The singular value decomposition of the covariance matrix H is performed to obtain H=UΣVᵀ (U and V are orthogonal matrices, and Σ is a diagonal matrix); a 2D rotation matrix R k =V×Uᵀ, if the determinant of R k is -1 (indicating mirror transformation, which does not conform to the actual rotation), the last column of V is adjusted to ensure that R k is a legal rotation matrix (determinant is 1); according to the center of the point set and the rotation matrix, a horizontal translation vector t k is calculated.

[0054] For example, continuing the example of S310, the center of P1 is C1 = (320, 320), and the center of P2 is C2 = (320.5, 319.5); after decentralization, the decentralized point set of P1 is P1'_1 = (-64, 0), P1'_2 = (0, 64), P1'_3 = (64, 0), P1'_4 = (0, -64); and the decentralized point set of P2 is P2'_1 = (-60.5, -1.5), P2'_2 = (1.5, 66.5), P2'_3 = (61.5, 2.5), P2'_4 = (-2.5, -65.5); after constructing the covariance matrix H and performing SVD decomposition, the rotation matrix R2 is [[cos60.3°, -sin60.3°], [sin60.3°, cos60.3°]] (corresponding to a rotation angle of 60.3°), and the translation vector t2 is (0.12mm, 0.08mm), which is consistent with the optimal transformation parameter of S310. P1'_1 is the coordinate point of the first physical fiducial marker in the pixel coordinate point set P1 of the first measurement after decentralization, P2'_1 is the coordinate point of the first physical fiducial marker in the pixel coordinate point set P2 of the second measurement after decentralization, and so on.

[0055] This step converts the optimal transformation parameter obtained by the ICP algorithm into a rigorous matrix solution through SVD decomposition, avoiding the approximation error of traditional geometric solving methods, ensuring that the solving accuracy of the 2D rotation matrix and the lateral translation vector reaches the micron level, and adapting to the pose requirements of ultra-precision measurement; the decentralization process eliminates the interference of the overall translation of the point set on the rotation solution, and the construction of the covariance matrix fully utilizes the position information of all the markers, improving the stability of the solution; the SVD algorithm itself has good numerical stability and can effectively deal with small noise in the marker coordinates, further ensuring the accuracy of the compound pose parameter and providing a reliable spatial transformation basis for subsequent error separation.

[0056] S400, obtaining a preset measurement model M k = W true (R k ,t k ) + W supp ; wherein M k is the interference surface data of the kth measurement of the optical element to be detected; W true is the true surface topography of the optical element to be detected; (R k ,t k ) is the compound pose parameter of the kth measurement; R k and t k are the 2D rotation matrix and the lateral translation vector corresponding to the kth measurement of the optical element to be detected, respectively; W true (R k ,t k) is the optical element to be tested via (R k ,t k The transformed real surface; W supp To support the error; k = 1, 2, ..., n.

[0057] In this embodiment, the establishment of the preset measurement model is based on the physical principle of interferometry—the surface data collected by the interferometer is a linear superposition of the "shape of the actual surface of the component after pose transformation" and the "support error." Therefore, the measurement model is established as follows: M k =W true (R) k ,t k )+W supp .

[0058] M k The interferometric surface data from the k-th measurement (i.e., the two-dimensional matrix acquired in S200, containing superimposed information of the actual surface and support errors); W true The actual surface morphology of the component (fixed and unchanging, independent of the number of measurements, and the target quantity to be reconstructed); (R) k ,t k ) represents the composite pose parameters of the k-th measurement (the 2D rotation matrix and lateral translation vector obtained by S300); W true (R) k ,t k ) is the true surface (R) k ,t k The transformed form (through W) true Perform R for each pixel coordinate k Rotation, t k The translation yields the result, which is related to M. k Spatial alignment); W supp The support error (the component deformation caused by the weight of the fixture and the clamping stress is fixed and unchanging, and is independent of the number of measurements; it is the target quantity to be separated).

[0059] For example, in the third measurement of a 200mm concave lens, M3 is the superimposed data including the actual surface and support errors, R3=60.1°, t3=(0.1mm, 0.09mm) are the pose parameters solved by S300, and W... true (R3,t3) represents the shape of a real concave surface after a 60.1° rotation and a (0.1mm, 0.09mm) translation. W supp The 0.8nm RMS deformation error is caused by the fixture; the three factors satisfy M3=W. true (R3,t3)+W supp .

[0060] This step quantifies the composition of the interferometric data through a clear measurement model, clearly defining the physical meaning and correlation of each parameter, providing a solid theoretical basis for subsequent error separation; in the model, "W" supp The core assumption of "constant and unchanging" is a key prerequisite for achieving "subtracting the support error from the two measurement data," while "W" true The "posture transformation" setting adapts to the rotation and translation of components in actual measurement, solving the problem of the disconnect between traditional models and actual operation, and providing logical support for high-precision error separation.

[0061] S500, the interference surface data M of the i-th measurement i Subtracting the interferometric surface data Mⱼ from the j-th measurement, we obtain M. i -M j =W true (R) i ,t i -W true (R) j ,t j ); i = 1, 2, ..., n; j = 1, 2, ..., n; i is not equal to j.

[0062] In this embodiment, the interference surface data M1 to M from n measurements n In the M array, select all pairs of data that satisfy "i ≠ j" (M i Mⱼ), forming multiple sets of data pairs (e.g., when n=6, C(6,2)=15 sets of data pairs can be formed).

[0063] Model substitution and subtraction: Substitute each group (M) i Substituting Mⱼ into the measurement model of S400, we get: M i =W true (R) i ,t i )+W supp M j =W true (R) j ,t j )+W supp Subtracting the two equations, since W supp Keeping it constant, we can directly eliminate it, resulting in: M i -M j =W true (R) i ,t i -W true (R) j ,t j ).

[0064] Perform the above operation on all data pairs to obtain multiple sets containing only W. trueand the equation of the corresponding pose parameters, the left side of the equation is the known "data difference" (which can be calculated by M i and Mⱼ directly), and the right side is the "shape difference" containing only the unknown W true .

[0065] For example, select M1 and M3 of a 200mm concave lens to form a data pair, substitute into the model to obtain: M1 = W true (R1, t1) + W supp , M3 = W true (R3, t3) + W supp ; after subtracting the two equations, W supp is eliminated to obtain M1-M3 = W true (R1, t1) - W true (R3, t3), wherein the left side M1-M3 can be calculated directly by two-dimensional matrix subtraction, and the right side contains only one unknown W true .

[0066] This step uses the characteristic of "W supp fixed and unchanged" to directly eliminate the support error by simple data subtraction, and converts the complex problem containing double unknowns (W true and W supp ) into a simple problem containing only a single unknown (W true ), greatly reducing the difficulty of solving; at the same time, multiple sets of equations formed by multiple sets of data pairs provide sufficient constraint conditions for subsequent construction of over-determined equation sets, avoiding the ambiguity of solving caused by a single data pair, and improving the accuracy and stability of W true reconstruction, which clears the obstacles for accurate separation of the final support error.

[0067] S600, expand W true using Zernike polynomials, and construct an over-determined equation set in combination with M i -M j .

[0068] Further, the Zernike polynomials are the first 36 Zernike polynomials, and the first 36 Zernike polynomials include a spherical aberration term, a defocus term, and a high-order spherical aberration term for characterizing the rotationally symmetric error; by expanding W t ᵣᵤ e using the first 36 Zernike polynomials, the rotationally symmetric error and the non-rotationally symmetric error of the optical element to be detected are separated at the same time.

[0069] In this embodiment, the Zernike polynomial is a standard tool for representing surface topography in the field of optics, and the first 36 terms cover low-order aberrations (such as defocus and spherical aberration) and high-order aberrations (such as high-order spherical aberration), which can accurately fit the surface of an optical element and avoid calculation redundancy caused by too many terms. The expansion formula is: W true (x, y) = a1Z1(x, y) + a2Z2(x, y) + … + a 36 Z 36 (x, y), where (x, y) is the element surface coordinate, Z1~Z 36 are preset basis functions (known), and a1~a 36 are Zernike coefficients to be solved (unknown).

[0070] Substitute the equation to build the equation set: Substitute the expansion formula of W true into S500 to get each set of “M i -M j ” equations. Since W true (R k , t k ) is the shape after pose transformation, (x, y) in the expansion formula needs to be rotated by R k and translated by t k before being substituted into the equation. Finally, each equation is converted into a linear equation about a1~a 36 . Taking 1024x1024 pixels as an example, 15 sets of (i, j) data pairs will generate 15x1024x1024≈1572 million equations, while the unknown number is 36 Zernike coefficients. At this time, the number of equations (tens of millions) is much larger than the unknown number (36), forming an over-determined equation set.

[0071] Implementation of the expansion of W true : The real surface topography W true of the optical element is represented as a linear combination of the first 36 Zernike polynomials, and the expansion formula is W true (ρ, θ) = a1Z1(ρ, θ) + a2Z2(ρ, θ) + … + a 36 Z 36 (ρ, θ), where (ρ, θ) is the polar coordinate of the element surface (ρ is the normalized radius and θ is the polar angle), Z1~Z 36 are the first 36 Zernike basis functions (such as Z4=2ρ²-1, corresponding to the defocus term; Z 10 =6ρ 4 -6ρ 2 +1, corresponding to the spherical aberration term), and a1~a 36 are the Zernike coefficients to be solved, and the coefficient size reflects the strength of the corresponding aberration (error).

[0072] Synchronous separation of two kinds of errors: Substitute the expansion into the "M i -M j =W true (R i ,t i )-W true (R j ,t j )" equation, since the rotationally symmetric error terms (such as Z4, Z 10 ) are unchanged after rotation transformation, and the non-rotationally symmetric error terms (such as Z2, Z7) change with the angle after rotation transformation, the over-determined equation group is constructed by multiple (i, j) pairs, and the a1~a 36 , the coefficients corresponding to the rotationally symmetric terms (such as a4, a 10 ) directly represent the size of the rotationally symmetric error, and the coefficients corresponding to the non-rotationally symmetric terms (such as a2, a7) directly represent the size of the non-rotationally symmetric error, thereby realizing the synchronous separation of the two kinds of errors.

[0073] For example, for a 200mm concave lens, in the expansion of W true , a4=0.3nm (corresponding to defocus term error), a 10 =0.25nm (corresponding to spherical aberration term error), and a 22 =0.1nm (corresponding to high-order spherical aberration term error), these coefficients correspond to the rotationally symmetric error; a2=0.15nm (corresponding to x-direction tilt error), a7=0.08nm (corresponding to coma term error), these coefficients correspond to the non-rotationally symmetric error; by solving 36 coefficients, both the rotationally symmetric error such as spherical aberration, high-order spherical aberration which cannot be separated by traditional methods, and the non-rotationally symmetric error such as tilt, coma are obtained, and comprehensive error separation is realized.

[0074] In this step, the rotationally symmetric error and the non-rotationally symmetric error related terms of the surface of the optical element are accurately covered, the core defect that the traditional rotation test method can only separate the non-rotationally symmetric error and cannot separate the rotationally symmetric error is solved; the orthogonality of the Zernike polynomials ensures that the coefficient solving of different error terms does not interfere with each other, and the accuracy of the separation result is high; the selection of the first 36 terms ensures the comprehensiveness of the error representation while avoiding the calculation redundancy and overfitting problem caused by too many terms, and the separation accuracy and calculation efficiency are considered; the synchronous separation of the two kinds of errors does not need to increase the measurement steps, simplifies the operation process, makes the interferometric measurement data more comprehensively and accurately reflect the real surface quality of the element, and meets the demand of nanoscale ultra-precision optical detection.

[0075] S700, the Zernike coefficients are solved by the least square method to reconstruct W true , and the reconstructed W trueSubstitute the first measured pixel coordinate point set, and back-propagation to get the support error W supp .

[0076] In this embodiment, the least square method is used to solve the over-determined equation set constructed by S600. The core of the least square method is to find a set of a1~a 36 , so that the "residual sum of squares" of all equations is minimized (i.e. the overall fitting effect is optimal); the over-determined equation set is arranged into a matrix form Ax=b (A is the coefficient matrix, known; x is the vector composed of a1~a 36 , unknown; b is the data difference vector, known), and the optimal solution of a1~a T is obtained by matrix operation x=(A -1 A) T b (A T is the transpose of A, (A T A) -1 is the inverse matrix). 36

[0077] Reconstruct W true : Substitute the solved Zernike coefficients a1~a 36 into the expansion formula to obtain the complete expression of W true (x, y), that is, to reconstruct the real surface topography of the element.

[0078] Back-propagation of W supp : Since the pose parameters of the first measurement (k=1) are (R1=unit matrix, t1=zero vector), the measurement model is simplified as M1=W true +W supp ; Substitute the reconstructed W true into the formula to back-propagate to obtain W supp =M1-W true .

[0079] For example, for the over-determined equation set of a 200mm concave lens, 36 Zernike coefficients (such as a1=0.2nm, a2=0.15nm…a 36 =0.03nm) are obtained by solving the least square method, and the real surface W true (RMS value is 3.2nm) is reconstructed by substituting the expansion formula; Substitute W true into the first measurement data M1 to back-propagate to obtain the support error W supp (RMS value is 0.8nm), that is, the element deformation error caused by the fixture is accurately separated.

[0080] This step efficiently solves the over-determined equation set by the least square method, ensures the optimal solution of the Zernike coefficient, and further realizes the high-precision reconstruction of the real surface W true ; W supp ​, avoids complex pose transformation calculation, and reduces error transmission risk; and the separated W supp The method has high precision, effectively eliminates the interference of support error on the measurement result, makes the interference measurement data truly reflect the real surface topography of the element, meets the demand of nanoscale ultra-precision measurement, is simple in method flow and strong in operability, and is suitable for practical application in an industrial scene.

[0081] In an exemplary embodiment, the least square solution in the above embodiment is based on the premise that W supp The support state is constant in all measurements, but in practice, the change of the support state will introduce "abnormal data". In order to solve this problem, before step S600, the method further includes the following steps:

[0082] S510, constructing a temporary model by randomly extracting two groups of data from the interference surface data of n measurements.

[0083] Further, step S510 includes the following steps:

[0084] S511, extracting a pair of measurement data M p and M q as samples; p=1, 2,..., n; q=1, 2,..., n; and p is not equal to q.

[0085] In this embodiment, random extraction is performed from the interference surface data of n measurements, without deliberate screening, so as to ensure randomness of the extraction (in line with the core logic of the RANSAC framework, to avoid subjective error).

[0086] The random extraction of the minimum sample pair not only ensures the efficiency of model construction (one pair of data can meet the constraint), but also avoids subjective error caused by initial data screening; the selection of the minimum sample pair is in line with the RANSAC core idea of "constructing an effective model with the least data", and provides a simple and reliable initial reference for subsequent outlier discrimination, and meets the demand of rapid data processing in an industrial scene.

[0087] S512, determining the temporary real surface W p corresponding to M p and the lateral translation vector t p , the 2D rotation matrix R q corresponding to M q and the lateral translation vector t q , and the preset measurement model, to determine the temporary real surface W p corresponding to M q and M true （pq） , the temporary support error W p corresponding to M supp （p） and Mq Corresponding temporary support error W supp （q） And determine the support reference level S （pq） .

[0088] In this embodiment, the sample pair (M p , M q ) is substituted into the preset measurement model M=W true (R,t)+W supp , to obtain: M p =W true (R p ,t p )+W supp (p) ; M q =W true (R q ,t q )+W supp (q) .

[0089] Solve the temporary real surface W true (pq) : subtract the two equations to eliminate W supp (the support error is fixed, but it is not assumed to be uniform in the temporary model, and only the relative relationship is solved through data pairs), to obtain M p -M q =W true (R p ,t p )-W true (R q ,t q ); W true is expanded by using the first 36 Zernike polynomials, a temporary overdetermined equation set (only based on the sample pair) is constructed, and the temporary real surface W true (pq) is solved by using the least square method.

[0090] Back-propagate the temporary support error: substitute W true (pq) into the measurement models of M p and M q , respectively, to back-propagate to obtain: W supp (p) =M p -W true (pq) (R p , t p ); W supp (q) =M q -W true (pq) (R q , tq ).

[0091] Calculate the support reference level S (pq) Calculate W respectively supp (p) and W supp (q) The RMS value (root mean square, a core indicator for measuring the magnitude of error) is used as the average of the two values ​​as a supporting reference level, i.e., S. (pq) =[RMS(W supp (p) )+RMS(W supp (q) )] / 2.

[0092] For example, continuing with the sample pair (M1, M5) from S511, R1=0°, t1=(0,0), R5=240.1°, t5=(0.11mm,0.07mm); substituting these values ​​into the measurement model and subtracting them, the temporary true surface W is obtained. true (15) ; by reverse deduction, W is obtained supp (1) RMS = 0.78nm, W supp (5) RMS = 0.82nm; Supporting reference level S (15) =(0.78+0.82) / 2=0.8nm.

[0093] By eliminating support errors through subtraction of sample pairs, the core error separation process is followed to ensure consistency between the temporary model and the final model. The support reference level is calculated based on the mean of the support errors of two samples, avoiding the bias caused by a single data point and providing a stable benchmark for subsequent residual calculation. The construction of the temporary model only requires a pair of data, which is computationally intensive and efficient, and can quickly provide a basis for outlier identification, thus improving the overall algorithm's running speed.

[0094] S520, calculate the reconstruction residuals of the remaining data and the temporary model.

[0095] Furthermore, step S520 includes the following steps:

[0096] S521, W true （pq） Substitute any of the other measured interferometric surface data MQ into the inverse solution to obtain the temporary support error W corresponding to MQ. supp （MQ） .

[0097] In this embodiment, the remaining measured interferometric surface data MQ refers to the sample pair (M) p M q All interference surface data outside of the specified area; temporary real surface Wtrue (pq) The measurement model of MQ is MQ = W true (R Q ,t Q )+W supp (MQ) , and W true (pq) has been determined, R Q and t Q are known pose parameters solved by S300, so the temporary support error W supp (MQ) is obtained by back calculation: W true (R Q ,t Q ).

[0098] For example, the sample pair is (M1, M5), and the remaining data is M2, M3, M4, and M6; W true (15) is substituted into the measurement model of M2, R2 = 60.3°, t2 = (0.12mm, 0.08mm), and the back calculation obtains W supp (M2) RMS = 0.81nm; similarly, the back calculation obtains W supp (M3) = 0.79nm, W supp (M4) = 2.1nm, and W supp (M6) = 0.83nm.

[0099] S522, the RMS value of W supp （MQ） is determined, and the reconstruction residual ΔS （pq） of S MQ .

[0100] In this embodiment, the reconstruction residual ΔS MQ is the absolute difference between the RMS value of the temporary support error W supp (MQ) corresponding to MQ and the support reference level S (pq) , that is, ΔS MQ = |RMS(W supp (MQ) )-S (pq) |.

[0101] Since the support error W supp is fixed and does not change, the W supp (MQ) of reliable data should be close to S (pq) , and the smaller the residual is, the better the data consistency is; otherwise, it is an outlier.

[0102] The data reliability is converted into a calculable numerical index by the consistency of the residual quantization data and the temporary model, avoiding the deviation of subjective judgment; the calculation logic of the residual is simple and intuitive, and the calculation efficiency is high, which can quickly distinguish the advantages and disadvantages of the data, provide a clear quantitative standard for subsequent outlier elimination, and solve the problem that the traditional algorithm cannot objectively identify outliers.

[0103] S530, the interference surface data with a reconstructed residual greater than a preset threshold is determined as an outlier and is eliminated, and the remaining interference surface data is marked as an inlier.

[0104] Further, the preset threshold value is in the range of 0.1 nm to 1.0 nm; according to the adjustment of the measurement accuracy requirement, a smaller value is taken for ultra-precision measurement, such as τ = 0.5 nm.

[0105] The preset threshold value is used to realize the automatic elimination of outliers, which is simple and efficient, and avoids the subjectivity and tediousness of manual screening; after eliminating the outliers, the remaining inlier data has higher consistency, which can effectively reduce the interference of abnormal data on subsequent solving, improve the precision of final support error separation, and solve the core defect that the traditional algorithm is sensitive to outliers.

[0106] S540, determining the final support error based on the interference surface data marked as inliers.

[0107] Further, step S540 includes the following steps:

[0108] S541, iteratively traversing all minimum sample pairs (M p , M q ) in the interference surface data of n measurements, and repeatedly performing the construction of a temporary model based on each minimum sample pair.

[0109] In this embodiment, all possible minimum sample pairs (M p , M q ) in n measurement data are traversed, and the total number of sample pairs is the combination number C(n, 2) (n is the number of measurements).

[0110] For each group of sample pairs, the complete process of S512 (constructing a temporary model), S520 (calculating a residual), and S530 (marking inliers / outliers) is repeatedly performed to obtain the inlier set corresponding to each group of sample pairs.

[0111] The iterative traversal of all sample pairs avoids the contingency of single sampling (such as the inlier judgment deviation caused by the fact that a certain group of sample pairs contains outliers), and ensures the comprehensiveness and reliability of inlier screening; through cross-validation of multiple sample pairs, the truly reliable data can be more objectively identified, providing sufficient basis for the selection of the optimal inlier set, and improving the robustness of the algorithm.

[0112] S542, calculate the reconstruction residual of the remaining interference surface data and the temporary model, and determine the inliers and outliers to select the inlier subset with the most inliers.

[0113] For example, for 15 groups of sample pairs, the number of inliers in each group is counted (e.g., sample pair (M1, M5) corresponds to 5 inliers, sample pair (M2, M3) corresponds to 4 inliers, etc.).

[0114] Select the inlier set with the most inliers as the final inlier subset M inlier If there are multiple groups of sample pairs with the same number of inliers, select the group with the smallest inlier residual sum (to further ensure the quality of the inliers).

[0115] Selecting the inlier set with the most inliers is essentially selecting the "model that is most supported by the majority of data", which is in line with the core idea of the RANSAC framework; having the most inliers means that the data consistency is optimal and can maximize the exclusion of outliers; if there are multiple groups of inliers with the same number of inliers, further filtering is performed based on the residual sum to ensure the quality of the final inlier set, providing an optimal data basis for high-precision solving.

[0116] S543, based on the inlier subset and its corresponding 2D rotation matrix and lateral translation vector, re-execute steps S600 to S700 to construct a global least squares system and solve it to obtain the final real surface topography and support error of the optical element to be detected after robust optimization.

[0117] In this embodiment, only the final inlier subset M inlier and its corresponding 2D rotation matrix R k , lateral translation vector t k are retained (the data and pose parameters corresponding to the outliers are excluded).

[0118] Repeat the core process: re-execute the complete process of S600 (Zernike polynomial expansion + construction of overdetermined equation set) and S700 (least squares method solving + back-propagation of support error) based on inlier data; obtain the final real surface topography and support error after robust optimization.

[0119] For example, the final inlier set is {M1, M2, M3, M5, M6}, and the corresponding pose parameters are (R1, t1), (R2, t2), (R3, t3), (R5, t5), (R6, t6); based on these data, an overdetermined equation set is constructed to solve 36 Zernike coefficients, and the final real surface topography (RMS = 3.1 nm) is reconstructed; substituting M1 back-propagates to obtain the final support error (RMS = 0.79 nm), which is significantly more accurate than the result without excluding outliers (RMS = 1.2 nm).

[0120] In this embodiment, the optimal inner point set is re-solved, which completely eliminates the interference of outliers, and solves the problem of low separation accuracy caused by abnormal data in traditional algorithms; the inner point data has high consistency, the constructed overdetermined equation set is more reliable, the Zernike coefficient solved by the least square method is more accurate, and the final real surface topography and support error have stronger robustness and accuracy; the whole process does not need to add additional measurement steps, only the precision is improved by data optimization, which takes into account the practicability and efficiency, and meets the needs of nanoscale ultra-precision measurement.

[0121] In an exemplary embodiment, simulation experiments are carried out using the method in the above embodiment, and the results are shown in Figures 2 to 6 As shown in Figure 2 With the continuous increase of measurement noise level (up to 50% of the real surface RMS value), the fitting error of the separation algorithm increases obviously, but still remains below 0.5 nm, which shows that the algorithm has strong robustness to random noise.

[0122] As shown in Figure 3 With the increase of the number of outliers, the fitting error obtained by the conventional least square method is increasing, but the fitting error obtained by the random sampling consensus method proposed in this patent is always maintained at a low level (below 0.1 nm) and is obviously different from the conventional least square method, which has strong robustness to outliers.

[0123] As shown in Figure 4 The separation ability of the algorithm for different ratios of support error to real surface RMS can be seen from Figure 4 When the support error RMS is 4 times the surface RMS, the separation error of the algorithm is the largest, but the separation error of the algorithm still remains at a low level (0.01 nm), so the algorithm can support high-precision real surface support error separation.

[0124] As shown in Figure 5 The robustness of the algorithm to small perturbations, when the support error has a small change, the fitting error of the real surface can still be controlled at a low level (0.1 nm), which shows that the algorithm has strong robustness to data stability.

[0125] Figure 6Fig. 6 is a diagram showing the support error separation results in a real experiment, wherein sub-figures (a), (b), (c) are the support surface types corresponding to the separation results of the "rotation-translation" method, the "composite pose" method of the present application and the "rotation" method respectively, sub-figures (d), (e) are the difference diagrams of the support error separation results of the "rotation-translation" method and the "composite pose" method, and the difference diagram of the support error separation results of the "rotation-translation" method and the "rotation" method; by taking the rotation-translation method as a reference benchmark, it can be obtained from the comparison of sub-figures (d), (e) that the support surface type obtained by the "composite pose" method of the present application is highly consistent with the support surface type obtained by the rotation-translation method, and has a great improvement compared with the traditional rotation method.

[0126] Sub-figures (f), (g), (h) are the real surface types corresponding to the separation results of the "rotation-translation" method, the "composite pose" method of the present application and the "rotation" method respectively, sub-figures (i), (j) are the difference diagrams of the real surface type separation results of the "rotation-translation" method and the "composite pose" method, and the difference diagram of the real surface type separation results of the "rotation-translation" method and the "rotation" method; by taking the rotation-translation method as a reference benchmark, it can be obtained from the comparison of sub-figures (i), (j) that the support surface type obtained by the "composite pose" method of the present application is highly consistent with the real surface type obtained by the rotation-translation method, and has a great improvement compared with the traditional rotation method.

[0127] In addition, although the various steps of the methods in the present disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in this specific order, or that all of the steps shown must be performed to achieve the desired results. Additionally or alternatively, certain steps can be omitted, multiple steps can be combined into one step, and / or one step can be divided into multiple steps, etc.

[0128] The embodiments of the present application also provide a non-transitory computer readable storage medium, which can be arranged in an electronic device to save at least one instruction or at least one program related to a method in the method embodiments, and the at least one instruction or the at least one program is loaded and executed by the processor to implement the method provided by the above-mentioned embodiments.

[0129] The program product can employ any combination of one or more computer-readable media. The computer-readable media can be a computer-readable storage medium or a computer-readable signal medium. The computer-readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include the following: an electrical connection having one or more wires, a portable disc, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0130] The computer-readable signal medium can include a computer-readable storage medium that is propagated as a carrier wave. The computer-readable signal medium can further be any computer-readable medium that is not a storage medium. The computer-readable signal medium can be a computer-readable storage medium that is a propagated signal.

[0131] The program code embodied on the computer-readable media can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0132] The program code can be executed by one or more programmable processors, which can be implemented as one or more microprocessors, microcontrollers, microcomputers, digital signal processors, central processing units, state machines, logic circuitries, and / or any devices that can execute program instructions. The program code can include one or more computer-readable instructions that are executable by one or more processors. The computer-readable instructions can include instructions for performing the operations and / or methods disclosed herein.

[0133] Embodiments of the present disclosure also provide an electronic device including a processor and the aforementioned non-transitory computer-readable storage medium.

[0134] The electronic device is merely an example, and should not bring any limitation to the functions and usage scope of the embodiments of the present disclosure.

[0135] The electronic device is in the form of a general purpose computing device. Components of the electronic device can include, but are not limited to, the at least one processor, the at least one memory, a bus that connects the different system components including the memory and the processor.

[0136] The memory stores program codes which can be executed by the processor, so that the processor performs steps in various embodiments described in the specification.

[0137] The memory can include a readable medium in the form of volatile memory, such as random access memory (RAM) and / or cache memory, and can further include read only memory (ROM).

[0138] The memory can also include program / utility programs having a set of (at least one) program modules, such as an operating system, one or more application programs, other programs / modules, and program data, each or a combination thereof can include an implementation of a network environment.

[0139] The bus can be one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor or a local bus using any of a variety of bus architectures.

[0140] The electronic device can also communicate with one or more external devices, such as a keyboard or a pointing device, through an I / O interface. The electronic device can also communicate with one or more devices that enable a user to interact with the electronic device, and / or with any devices (e.g., a router, a modem, etc.) that enable the electronic device to communicate with one or more other computing devices. Such communication can occur via an I / O interface. Also, the electronic device can communicate with one or more networks (such as a local area network (LAN), a wide area network (WAN), and / or the public network, such as the Internet) through a network adapter. The network adapter communicates with the other modules of the electronic device via the bus. It should be appreciated that other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0141] Those skilled in the art can clearly understand the example embodiments described herein through the above description of the example embodiments, and the example embodiments described herein can be implemented by software or by software in combination with necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash disk, a mobile hard disk, or the like) or on a network, and includes a number of instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to perform the methods according to the embodiments of the present disclosure.

[0142] Embodiments of the present disclosure also provide a computer program product comprising program code for causing an electronic device to perform the steps of the methods according to the various example embodiments of the present disclosure described above in the specification when the program product is run on the electronic device.

[0143] Although some specific embodiments of the present disclosure have been described in detail by way of examples, those skilled in the art should understand that the above examples are only for illustration, and are not intended to limit the scope of the present disclosure. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of the present disclosure.

Claims

1. A robust support error separation method, characterized in that, The method includes the following steps: S100, Process physical reference marks in the non-light-transmitting aperture area of ​​the optical element to be tested, and record the original coordinates of the physical reference marks in the coordinate system of the optical element to be tested itself; S200, the optical element to be tested is fixed on the support fixture, and n interferometric measurements are performed on the optical element to be tested; before each measurement, the optical element is manually rotated by a preset angle, and the interference surface data and the pixel coordinate point set of the physical reference mark of the optical element to be tested are collected simultaneously during each measurement; S300, using the pixel coordinate point set of the first measurement as a reference, determines the 2D rotation matrix and lateral translation vector corresponding to each measurement of the optical element to be detected; S400, Obtain the preset measurement model M k =W true (R) k ,t k )+W supp Among them, M k W represents the interference surface data from the k-th measurement of the optical element under test. true The actual surface morphology of the optical element to be tested; (R) k ,t k R represents the composite pose parameters of the k-th measurement. k and t k These are the 2D rotation matrix and lateral translation vector corresponding to the k-th measurement of the optical element under test, respectively; W true (R) k ,t k ) is the optical element to be tested via (R k ,t k The transformed real surface; W supp To support the error; k = 1, 2, ..., n; S500, the interference surface data M of the i-th measurement i Subtracting the interferometric surface data Mⱼ from the j-th measurement, we obtain M. i -M j =W true (R) i ,t i -W true (R) j ,t j ); i = 1, 2, ..., n; j = 1, 2, ..., n; i is not equal to j; S600 uses Zernike polynomial expansion W true and combined with M i -M j Construct an overdetermined system of equations; S700, reconstructing W by solving the Zernike coefficients using the least squares method. true And will reconstruct W true Substituting the pixel coordinates from the initial measurement, the support error W is calculated. supp .

2. The robust support error separation method according to claim 1, characterized in that, Step S300 includes the following steps: S310, for the pixel coordinate point set P of the k-th measurement. k Using the initial set of pixel coordinates P1 as a reference, the ICP algorithm is used to search for P... k The transformation parameter that minimizes the sum of distances between each physical reference mark in P1 and its corresponding physical reference mark in P1 after rotation and translation; S320, using SVD to solve for the 2D rotation matrix R corresponding to the transformation parameters. k and the lateral translation vector t k .

3. The robust support error separation method according to claim 1, characterized in that, The Zernike polynomials are the first 36 Zernike polynomials, and these first 36 Zernike polynomials include spherical aberration terms, defocus terms, and higher-order spherical aberration terms characterizing rotational symmetry errors; W is expanded using the first 36 Zernike polynomials. true At the same time, it separates the rotational symmetry error and the non-rotational symmetry error of the optical element under test.

4. The robust support error separation method according to claim 1, characterized in that, Prior to step S600, the method further includes the following steps: S510, randomly select two sets of data from the interferometric surface data of n measurements to construct a temporary model; S520, calculate the reconstruction residuals of the remaining data and the temporary model; S530, identify and remove interferometric surface data whose reconstruction residuals are greater than a preset threshold as outliers, and mark the remaining interferometric surface data as inliers; S540, based on the interference surface data marked as interior points, determines the final support error.

5. The robust support error separation method according to claim 4, characterized in that, Step S510 includes the following steps: S511, extract a pair of measurement data M from the interferometric surface data of n measurements. p and M q As a sample; p = 1, 2, ..., n; q = 1, 2, ..., n; p ≠ q; S512, according to M p The corresponding 2D rotation matrix R p and the lateral translation vector t p M q The corresponding 2D rotation matrix R q and the lateral translation vector t q And a preset measurement model to determine M p and M q The corresponding temporary real surface W true （pq） M p The corresponding temporary support error W supp （p） With M q The corresponding temporary support error W supp （q） And determine the supporting reference level S （pq） .

6. The robust support error separation method according to claim 5, characterized in that, Step S520 includes the following steps: S521, W true （pq） Substitute any interferometric surface data MQ from the other measurements, and solve for the temporary support error W corresponding to MQ. supp （MQ） ; S522, confirm W supp （MQ） RMS value and S （pq） Reconstruction residual ΔS MQ .

7. The robust support error separation method according to claim 6, characterized in that, Step S540 includes the following steps: S541, iterate through all the smallest sample pairs (M) in the interferometric surface data from n measurements. p M q ), repeatedly execute the process of building a temporary model based on each minimum sample pair; S542, calculate the reconstruction residuals between the remaining interference surface data and the temporary model, and distinguish between in-point and out-point operations, and filter out the subset of in-points with the largest number of in-points; S543, based on the subset of interior points and their corresponding 2D rotation matrix and lateral translation vector, repeat steps S600 to S700 to construct and solve the global least squares system to obtain the final real surface morphology and support error of the optical element under test after robustness optimization.

8. The robust support error separation method according to claim 6, characterized in that, The preset threshold value ranges from 0.1nm to 1.0nm.

9. A non-transitory computer-readable storage medium, wherein the storage medium stores at least one instruction or at least one program segment, characterized in that, The at least one instruction or the at least one program segment is loaded and executed by the processor to implement the robust support error separation method as described in any one of claims 1-8.

10. An electronic device, characterized in that, Includes a processor and the non-transitory computer-readable storage medium as described in claim 9.

Images