Large-aperture three-flat absolute testing method and system based on small-angle rotation

Abstract

The application discloses a kind of big aperture three flat crystal absolute inspection method and system based on small angle rotation.The method comprises the following steps: interference measurement is carried out by placing reference flat crystal TF and test flat crystal RF oppositely;Interference measurement is carried out between auxiliary flat crystal AF and RF by placing auxiliary flat crystal AF between TF and RF;Interference measurement is carried out between TF and AF after flipping AF;Interference measurement is carried out between TF and AF after rotating AF around Z axis by a small angle.Four groups of interference cavity data obtained by measurement are used to obtain high-precision absolute surface profile under small angle rotation condition by using the alternating iterative optimization model of pose parameter and surface profile distribution while stripping the influence of pose error.The application uses the measurement model of small angle rotation, effectively reduces the surface error introduced by flat crystal gravity deformation and support stress change, and uses the alternating iterative optimization model of pose parameter and surface profile distribution, effectively improves the pose error immunity of measurement operation;Overall operation is simple, efficient, and high in measurement precision.

Description

Technical Field

[0001] This invention belongs to the field of optical interferometry technology, specifically a method and system for absolute testing of large-aperture three-flat crystals based on small-angle rotation. Background Technology

[0002] With the widespread application of large-aperture planar optical components, the demand for absolute interferometric testing of large-aperture optical components is becoming increasingly urgent. In the classic three-plane mutual testing method, the one-dimensional profile of the three optical planes along the vertical direction can be quickly obtained through three relative measurements, but the full-aperture surface shape distribution cannot be obtained. To solve the problem of measuring the full-aperture absolute surface shape, current methods typically require an additional large-angle rotation of at least 90º or multiple rotation measurements covering 360º. Both of these methods require large-angle changes to the support posture of the optical plane, which easily introduces surface shape errors caused by the plane's own gravitational deformation and changes in support stress, thus reducing measurement accuracy. Furthermore, translation and rotation operations during the measurement process also introduce pose control errors, which further reduce measurement accuracy. Therefore, a high-precision absolute testing method that can overcome rotational deformation errors and pose control errors is urgently needed. Summary of the Invention

[0003] The purpose of this invention is to address the problems existing in the above-mentioned prior art methods by providing an absolute inspection method that overcomes rotational deformation error and pose control error, thereby achieving high-precision measurement of the full-aperture surface shape of large-diameter flat crystals.

[0004] The technical solution to achieve the objective of this invention is as follows: On the one hand, a method for absolute inspection of large-aperture three-flat crystals based on small-angle rotation is provided, the method comprising the following steps:

[0005] Step 1: Obtain interferometric measurement data for the reference flat, test flat, and auxiliary flat in four different relative orientations. The working surfaces of the reference flat, test flat, and auxiliary flat are denoted as working surface A, working surface B, and working surface C, respectively. The interferometric measurement data for the four different relative orientations are obtained through four measurements: interferometric measurement with working surface A and working surface B relative to each other; interferometric measurement with working surface C and working surface B relative to each other; interferometric measurement with working surface A and working surface C (rotated around the Y-axis) relative to each other; and interferometric measurement with working surface C rotated around the Z-axis by a preset small angle and then placed relative to working surface A after the flipped state. The horizontal direction along the flat surface is the X-axis, the vertical direction along the flat surface is the Y-axis, and the Z-axis is perpendicular to the flat surface and positive along the direction of reflected light.

[0006] Step 2: Construct an actual measurement model containing actual pose parameters, wherein the pose parameters are used to characterize the relative translation, actual rotation angle and actual rotation center position of the optical flat in each measurement state under the actual measurement state.

[0007] Step 3: Based on the actual measurement model, construct a system of parameterized linear equations consisting of the surface shape vector to be solved, the transformation matrix, and the measurement data vector composed of the four measurement data.

[0008] Step 4: Establish an alternating iterative optimization model for pose parameters and surface distribution. After setting the initial parameters, based on the parameterized linear equation system and the nonlinear solution process of pose parameters, alternate iteratively optimize and update the pose parameters and surface distribution until the convergence criteria are met.

[0009] Step 5: Update the parameterized linear equations based on the pose parameters obtained by iterative convergence, and solve for the absolute surface distribution of each flat crystal.

[0010] Furthermore, in step 1, the four measurements specifically include:

[0011] First measurement: Place the reference crystal flat TF and the test crystal flat RF opposite each other to form an interference cavity between working surface A and working surface B, and obtain the first interferometric measurement result. ;

[0012] Second measurement: Keeping the positions of TF and RF unchanged, place the auxiliary flat crystal AF between TF and RF to form an interference cavity between working surface C and working surface B, and obtain the second interferometric measurement result. ;

[0013] Third measurement: Flip AF around the Y-axis to form an interference cavity between working surface A and the flipped working surface C, and obtain the third interferometric measurement result. ;

[0014] Fourth measurement: Based on the state of the third measurement, keeping the working surface A unchanged, rotate AF clockwise around the Z-axis by a preset small angle. To obtain the fourth interferometric measurement result, an interference cavity is maintained between the rotated working surface C and the working surface A. ;in, Less than 15°.

[0015] Furthermore, the construction of the actual measurement model containing the actual pose parameters in step 2 specifically includes:

[0016] Let the surface shapes of working surfaces A, B, and C be respectively... , and ,in The coordinate position on the plane formed by the X-axis and Y-axis. , These are the coordinates on the X and Y axes, respectively; the first interferometric measurement result is recorded. Second interferometry results Third interferometry results Fourth interferometry results The corresponding surface distribution data are as follows: , , , ; by exist The area and exist The regions in the diagram serve as the reference positions for their respective surface shapes; Define pose parameters ,in express exist The amount of translation of the region relative to its reference position. , They are respectively exist The amount of translation of the region relative to its reference position along the X and Y axes; Indicates the flipped exist The amount of translation of the region relative to its reference position. They are the flipped versions exist The amount of translation of the region relative to its reference position along the X and Y axes; and They represent exist The region in the diagram, relative to its reference position, has its rotation center coordinates and actual rotation angle. , They are respectively exist The X and Y coordinates of the region in the figure relative to the rotation center of its reference position are both zero;

[0017] Establish a practical interferometry model that includes pose parameters:

[0018]

[0019] in,

[0020]

[0021] In the formula, , These are the coordinates after the x and y rotation transformations, respectively.

[0022] Furthermore, step 3, which involves constructing a system of parameterized linear equations, specifically includes:

[0023] Step 3-1, determine the pose parameters The determined set of common valid pixels For the three-sided shape involved in the four measurements , and Construct the corresponding sub-matrices respectively, and combine them to obtain the complete weight matrix. , represented as:

[0024]

[0025] In the formula, the block matrix Indicates the first In this measurement, the surface shape In pose parameters The interpolation weight matrix that maps the original coordinates to the measured coordinates under the influence of the interpolation weight matrix. , Its elements are the resampling weights of each valid pixel, with values ​​ranging from [0,1]. Represents a zero matrix of the corresponding size;

[0026] Step 3-2: Expand the discrete sampled values ​​of the surfaces to be solved on working surfaces A, B, and C into one-dimensional column vectors. , , And arrange them in order from beginning to end to form the surface vector to be solved. , represented as:

[0027]

[0028] Step 3-3: Record the results of the four measurements. , , , In the common valid pixel set The measurement data within are expanded into column vectors. , , and The data are arranged in a vector from beginning to end to form the measurement data. , represented as:

[0029]

[0030] Steps 3-4, based on the weight matrix 1. Surface vector to be solved and measurement data vector Establish a system of parameterized linear equations for the surface distribution:

[0031] .

[0032] Furthermore, the construction process of the block matrix in step 3-1 includes:

[0033] Step 3-1-1, define the submatrix construction operation: for the first... In this measurement, based on the surface shape and its transformation method, bilinear interpolation is used to calculate the weight values ​​of each coordinate point after the corresponding transformation of each surface shape, and a corresponding submatrix is ​​constructed; where, the submatrix... The row number is equal to the first row. The measurement results are in The number of elements within a shape is equal to the number of columns in the corresponding shape. The number of valid elements;

[0034] Step 3-1-2: Using the submatrix construction operation described above, the surface shape after the flip transformation is processed. and the surface shape after in-situ transformation Construct submatrices respectively and ;

[0035] Step 3-1-3: Using the submatrix construction operation described above, the surface shape after in-situ transformation is... and the surface shape after flipping transformation Construct submatrices respectively and ;

[0036] Step 3-1-4: Using the submatrix construction operation described above, the surface shape after the flipping transformation is processed. and the surface shape after in-situ transformation Construct submatrices respectively and ;

[0037] Step 3-1-5: Using the submatrix construction operation described above, the surface shape after the flip transformation is processed. and the surface shape after rotation transformation Construct submatrices respectively and .

[0038] Furthermore, step 4 establishes an alternating iterative optimization model for pose parameters and surface distribution, and performs alternating iterative optimization, specifically including:

[0039] Step 4-1: Set the initial values ​​of the pose parameters. ,in The nominal design value is the rotation angle.

[0040] Step 4-2, in the k-th iteration, the current pose parameters are... Substituting into the parametric linear equations, the current surface distribution solution is obtained. ;

[0041] Step 4-3, based on the current surface distribution solution We construct and solve a system of nonlinear difference residual equations for the pose parameters to obtain the updated pose parameters for the (k+1)th iteration. ;

[0042] Step 4-4: Determine whether the updated pose parameters meet the preset convergence conditions. If they do, terminate the iteration and output the final pose parameters. If they do not meet the conditions, let k = k+1 and return to step 4-2 to continue the iteration.

[0043] Furthermore, in step 4-3, the pose parameters for the (k+1)th iteration are solved. Specifically, it includes:

[0044] Step 4-3-1, based on the current pose parameters Determine the spatial constraint domain ;

[0045] Step 4-3-2, in the spatially constrained domain Internally, the flip-translation composite difference measured values ​​are constructed using actual measurement data. Compared with the measured value of rotational difference That is, for :

[0046]

[0047] Step 4-3-3, in the spatially constrained domain Inside, define the surface shape for the k-th iteration. and Calculation of the flip-translation composite difference of geometric parameters and rotational difference calculation values That is, for :

[0048]

[0049] In the formula, Both represent the surface shape distribution corresponding to the working surface C in the k-th iteration. Both represent the surface shape distribution corresponding to the working surface B in the k-th iteration;

[0050] Step 4-3-4, based on the principle that the measured difference value and the calculated difference value are equal, for the spatially constrained domain... A system of nonlinear equations is constructed for each discrete pixel within the array:

[0051]

[0052] In the formula, Let the system of residual equations for the k-th iteration be represented. Describes the spatial constraint domain of the k-th iteration. The flip-translation composite difference calculation value of all pixels within the range, Describes the spatial constraint domain of the k-th iteration. The rotation difference calculation value of all pixels within the range, Describes the spatial constraint domain of the k-th iteration. Measured values ​​of the flip-translation composite difference for all pixels within the array. Describes the spatial constraint domain of the k-th iteration. Measured rotational difference values ​​for all pixels within the area;

[0053] Step 4-3-5: Solve the nonlinear equations using a nonlinear least squares optimization algorithm to obtain the updated pose parameters. ;

[0054] Furthermore, the nonlinear least squares optimization algorithm is the Levenberg-Marquardt algorithm, also known as the LM algorithm.

[0055] Furthermore, the preset convergence condition mentioned in step 4-4 is:

[0056]

[0057] In the formula, The translation and center coordinate convergence threshold, The rotation angle convergence threshold, Let represent the residual equations for the (k+1)th iteration.

[0058] Furthermore, step 5 yields the absolute surface shape distribution of each flat crystal, specifically including:

[0059] Step 5-1: Substitute the pose parameters of the final converged output into the parameterized linear equation system, perform least squares calculation on the parameterized linear equation system, and obtain the optimal solution vector.

[0060] Step 5-2: Separate the one-dimensional column vectors corresponding to working surfaces A, B, and C from the optimal solution vector in sequence;

[0061] Step 5-3: Fill the separated one-dimensional column vectors into two-dimensional matrices according to the column priority or row priority rules of the original discrete sampling, and reconstruct the two-dimensional distribution of the absolute surface shape of the reference flat TF working surface A, the test flat RF working surface B, and the auxiliary flat AF working surface C, thus obtaining the absolute surface shape distribution of each flat.

[0062] On the other hand, a large-aperture three-plane crystal absolute inspection system based on small-angle rotation is provided to implement the large-aperture three-plane crystal absolute inspection method based on small-angle rotation. The system includes:

[0063] The first module is used to obtain the first interferometric measurement result obtained from the four measurements. Second interferometry results Third interferometry results and the results of the fourth interferometry ;

[0064] The second module is used to define pose parameters and construct an actual measurement model containing pose parameters, and to construct a parameterized linear equation system containing a weight matrix, a surface vector to be solved, and a measurement data vector based on the measurement model.

[0065] The third module is used to construct an alternating iterative optimization model for pose parameters and surface distribution. During the iteration process, the surface distribution vector and pose parameters are alternately optimized and updated until the pose parameters meet the preset convergence conditions.

[0066] The fourth module is used to solve the parameterized linear equations based on the converged pose parameters, and to inversely reconstruct the absolute surface distribution of the flat TF working surface A, flat RF working surface B, and flat AF working surface C.

[0067] On the other hand, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the large-aperture three-flat crystal absolute inspection method based on small-angle rotation.

[0068] Compared with the prior art, the significant advantages of this invention are:

[0069] (1) In the measurement process, the present invention only uses a small angle rotation of less than 15°, which can maintain the stability of the support posture of the flat crystal to the greatest extent and effectively reduce the surface shape error caused by the gravitational deformation of the flat crystal and the change of support stress.

[0070] (2) Innovatively, pose parameters are introduced and an alternating iterative optimization model of pose parameters and surface distribution is constructed. It can accurately solve the translation deviation, actual rotation angle and rotation center deviation in actual assembly and adjustment, and eliminate the influence of these pose control errors in surface solution, effectively improve the pose error immunity of measurement operation, and ensure the numerical stability of absolute surface restoration under small angle rotation conditions.

[0071] (3) The measurement process of this method is only one small-angle rotation measurement step more than the classic three-plane mutual inspection method. It is not only easy to operate and highly efficient, but also highly accurate. According to the simulation verification of the embodiment, the residual between the restored three-plane surface shape and the real surface shape is extremely small. The PV value of the restored residual of each working surface is better than 0.002 nm, and the RMS value can reach about 0.0001 nm, realizing the ultra-high precision inspection of the absolute surface shape of the full aperture of large-aperture flat crystal.

[0072] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the measurement process of the absolute testing method of the present invention in one embodiment.

[0074] Figure 2 This is a flowchart of the computational processing procedure of the present invention in one embodiment.

[0075] Figure 3 This is a schematic diagram of the actual surface shape of the working surface of each of the three optical planar elements obtained from simulation in one embodiment, wherein... Figure 3 In the diagram, (a) represents the true surface shape of A, with PV (peak-to-valley value) = 59.9787 nm and RMS (root mean square value) = 11.8178 nm. Figure 3 In the diagram, (b) represents the true surface shape of B, with PV = 36.6199 nm and RMS = 6.9179 nm. Figure 3 In the figure, (c) represents the true surface shape of C, with PV = 63.0009nm and RMS = 12.1170nm.

[0076] Figure 4 This is a schematic diagram of the surface shape of the working surfaces of three optical planar elements restored using the method of the present invention in one embodiment, wherein... Figure 4 In the diagram, (a) represents the restored surface shape of A, with PV = 59.9787 nm and RMS = 11.8178 nm. Figure 4 In the diagram, (b) represents the restored surface shape of B, with PV = 36.6205 nm and RMS = 6.9179 nm. Figure 4 In the figure, (c) represents the restored surface shape of C, with PV = 63.0014 nm and RMS = 12.1171 nm.

[0077] Figure 5 This is a schematic diagram of the surface residuals of the working surfaces of the three optical planar elements restored using the method of the present invention in one embodiment, wherein... Figure 5 In the diagram, (a) represents the restoration error of A, with PV = 0.0013 nm and RMS = 0.0001 nm. Figure 5 In the diagram, (b) represents the restoration error of B, with PV = 0.0017 nm and RMS = 0.0001 nm. Figure 5 In the equation (c), C represents the recovery error, PV = 0.0014 nm, and RMS = 0.0001 nm. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0079] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0080] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0081] In one embodiment, combined Figure 1 A method for absolute inspection of large-aperture three-flat crystals based on small-angle rotation is provided, the method comprising the following steps:

[0082] Step 1: Obtain interferometric measurement data for the reference flat, test flat, and auxiliary flat in four different relative orientations. The working surfaces of the reference flat, test flat, and auxiliary flat are denoted as working surface A, working surface B, and working surface C, respectively. The interferometric measurement data for the four different relative orientations are obtained through four measurements: interferometric measurement with working surface A and working surface B relative to each other; interferometric measurement with working surface C and working surface B relative to each other; interferometric measurement with working surface A and working surface C (rotated around the Y-axis) relative to each other; and interferometric measurement with working surface C rotated around the Z-axis by a preset small angle and then placed relative to working surface A after the flipped state. The horizontal direction along the flat surface is the X-axis, the vertical direction along the flat surface is the Y-axis, and the Z-axis is perpendicular to the flat surface and positive along the direction of reflected light.

[0083] Step 2: Construct an actual measurement model containing actual pose parameters, wherein the pose parameters are used to characterize the relative translation, actual rotation angle and actual rotation center position of the optical flat in each measurement state under the actual measurement state.

[0084] Step 3: Based on the actual measurement model, construct a system of parameterized linear equations consisting of the surface shape vector to be solved, the transformation matrix, and the measurement data vector composed of the four measurement data.

[0085] Step 4: Establish an alternating iterative optimization model for pose parameters and surface distribution. After setting the initial parameters, based on the parameterized linear equation system and the nonlinear solution process of pose parameters, alternate iteratively optimize and update the pose parameters and surface distribution until the convergence criteria are met.

[0086] Step 5: Update the parameterized linear equations based on the pose parameters obtained by iterative convergence, and solve for the absolute surface distribution of each flat crystal.

[0087] Furthermore, in one embodiment, step 1, specifically includes the four measurements:

[0088] First measurement: Place the reference crystal flat TF and the test crystal flat RF opposite each other to form an interference cavity between working surface A and working surface B, and obtain the first interferometric measurement result. ;

[0089] Second measurement: Keeping the positions of TF and RF unchanged, place the auxiliary flat crystal AF between TF and RF to form an interference cavity between working surface C and working surface B, and obtain the second interferometric measurement result. ;

[0090] Third measurement: Flip AF around the Y-axis to form an interference cavity between working surface A and the flipped working surface C, and obtain the third interferometric measurement result. ;

[0091] Fourth measurement: Based on the state of the third measurement, keeping the working surface A unchanged, rotate AF clockwise around the Z-axis by a preset small angle. To obtain the fourth interferometric measurement result, an interference cavity is maintained between the rotated working surface C and the working surface A. ;in, Less than 15° (preferably, Take 10°).

[0092] Furthermore, in one embodiment, step 2, which involves constructing an actual measurement model containing actual pose parameters, specifically includes:

[0093] Let the surface shapes of working surfaces A, B, and C be respectively... , and ,in The coordinate position on the plane formed by the X-axis and Y-axis. , These are the coordinates on the X and Y axes, respectively; the first interferometric measurement result is recorded. Second interferometry results Third interferometry results Fourth interferometry results The corresponding surface distribution data are as follows: , , , ; by exist The area and exist The regions in the diagram serve as the reference positions for their respective surface shapes; Define pose parameters ,in express exist The amount of translation of the region relative to its reference position. , They are respectively exist The amount of translation of the region relative to its reference position along the X and Y axes; Indicates the flipped exist The amount of translation of the region relative to its reference position. They are the flipped versions exist The amount of translation of the region relative to its reference position along the X and Y axes; and They represent exist The region in the diagram, relative to its reference position, has its rotation center coordinates and actual rotation angle. , They are respectively exist The X and Y coordinates of the region in the figure relative to the rotation center of its reference position are both zero;

[0094] Establish a practical interferometry model that includes pose parameters:

[0095]

[0096] in,

[0097]

[0098] In the formula, , These are the coordinates after the x and y rotation transformations, respectively.

[0099] Furthermore, in one embodiment, step 3, constructing the parameterized linear equation system, specifically includes:

[0100] Step 3-1, determine the pose parameters The determined set of common valid pixels For the three-sided shape involved in the four measurements , and Construct the corresponding sub-matrices respectively, and combine them to obtain the complete weight matrix. , represented as:

[0101]

[0102] In the formula, the block matrix Indicates the first In this measurement, the surface shape In pose parameters The interpolation weight matrix that maps the original coordinates to the measured coordinates under the influence of the interpolation weight matrix. , Its elements are the resampling weights of each valid pixel, with values ​​ranging from [0,1]. Represents a zero matrix of the corresponding size;

[0103] Step 3-2: Expand the discrete sampled values ​​of the surfaces to be solved on working surfaces A, B, and C into one-dimensional column vectors. , , And arrange them in order from beginning to end to form the surface vector to be solved. , represented as:

[0104]

[0105] Step 3-3: Record the results of the four measurements. , , , In the common valid pixel set The measurement data within are expanded into column vectors. , , and The data are arranged in a vector from beginning to end to form the measurement data. , represented as:

[0106]

[0107] Steps 3-4, based on the weight matrix 1. Surface vector to be solved and measurement data vector Establish a system of parameterized linear equations for the surface distribution:

[0108] .

[0109] Preferably, in some embodiments, the construction process of the block matrix in step 3-1 includes:

[0110] Step 3-1-1, define the submatrix construction operation: for the first... For each measurement, based on the surface shape involved and its transformation method (including but not limited to in-situ, flipped, or rotated), the weight value of each coordinate point of each surface shape after the corresponding transformation is calculated using bilinear interpolation, and a corresponding submatrix is ​​constructed; where, the submatrix... The row number is equal to the first row. The measurement results are in The number of elements within a shape is equal to the number of columns in the corresponding shape. The number of valid elements;

[0111] Step 3-1-2: Using the submatrix construction operation described above, the surface shape after the flip transformation is processed. and the surface shape after in-situ transformation Construct submatrices respectively and ;

[0112] Step 3-1-3: Using the submatrix construction operation described above, the surface shape after in-situ transformation is... and the surface shape after flipping transformation Construct submatrices respectively and ;

[0113] Step 3-1-4: Using the submatrix construction operation described above, the surface shape after the flipping transformation is processed. and the surface shape after in-situ transformation Construct submatrices respectively and ;

[0114] Step 3-1-5: Using the submatrix construction operation described above, the surface shape after the flip transformation is processed. and the surface shape after rotation transformation Construct submatrices respectively and .

[0115] Furthermore, in one embodiment, step 4 involves establishing an alternating iterative optimization model for pose parameters and surface distribution, and then iteratively optimizing it, specifically including:

[0116] Step 4-1: Set the initial values ​​of the pose parameters. ,in The nominal design value is the rotation angle.

[0117] Step 4-2, in the k-th iteration, the current pose parameters are... Substituting into the parametric linear equations, the current surface distribution solution is obtained. ;

[0118] Step 4-3, based on the current surface distribution solution We construct and solve a system of nonlinear difference residual equations for the pose parameters to obtain the updated pose parameters for the (k+1)th iteration. ;

[0119] Step 4-4: Determine whether the updated pose parameters meet the preset convergence conditions. If they do, terminate the iteration and output the final pose parameters. If they do not meet the conditions, let k = k+1 and return to step 4-2 to continue the iteration.

[0120] Preferably, in some embodiments, the pose parameters for the (k+1)th iteration are solved in step 4-3. Specifically, it includes:

[0121] Step 4-3-1, based on the current pose parameters Determine the spatial constraint domain ;

[0122] Step 4-3-2, in the spatially constrained domain Internally, the flip-translation composite difference measured values ​​are constructed using actual measurement data. Compared with the measured value of rotational difference That is, for :

[0123]

[0124] Step 4-3-3, in the spatially constrained domain Inside, define the surface shape for the k-th iteration. and Calculation of the flip-translation composite difference of geometric parameters and rotational difference calculation values That is, for :

[0125]

[0126] In the formula, Both represent the surface shape distribution corresponding to the working surface C in the k-th iteration. Both represent the surface shape distribution corresponding to the working surface B in the k-th iteration;

[0127] Step 4-3-4, based on the principle that the measured difference value and the calculated difference value are equal, for the spatially constrained domain... A system of nonlinear equations is constructed for each discrete pixel within the array:

[0128]

[0129] In the formula, Let the system of residual equations for the k-th iteration be represented. Describes the spatial constraint domain of the k-th iteration. The flip-translation composite difference calculation value of all pixels within the range, Describes the spatial constraint domain of the k-th iteration. The rotation difference calculation value of all pixels within the range, Describes the spatial constraint domain of the k-th iteration. Measured values ​​of the flip-translation composite difference for all pixels within the array. Describes the spatial constraint domain of the k-th iteration. Measured rotational difference values ​​for all pixels within the area; From 2 Composed of several equations for The number of pixels in;

[0130] Step 4-3-5: Solve the nonlinear equations using a nonlinear least squares optimization algorithm to obtain the updated pose parameters. ;

[0131] Preferably, in some embodiments, the nonlinear least squares optimization algorithm employs, but is not limited to, the Levenburg-Marquardt algorithm, i.e., the LM algorithm.

[0132] Preferably, in some embodiments, the preset convergence condition in step 4-4 is:

[0133]

[0134] In the formula, The translation and center coordinate convergence threshold, The rotation angle convergence threshold, Let represent the residual equations for the (k+1)th iteration.

[0135] Furthermore, in one embodiment, step 5, which involves determining the absolute surface shape distribution of each flat crystal, specifically includes:

[0136] Step 5-1: Substitute the pose parameters from the final converged output into the parameterized linear equation system, perform least squares calculation on the parameterized linear equation system, and obtain the optimal solution vector (surface distribution). );

[0137] Step 5-2: Separate the one-dimensional column vectors corresponding to working surfaces A, B, and C from the optimal solution vector in sequence;

[0138] Step 5-3: Fill the separated one-dimensional column vectors into two-dimensional matrices according to the column priority or row priority rules of the original discrete sampling, and reconstruct the two-dimensional distribution of the absolute surface shape of the reference flat TF working surface A, the test flat RF working surface B, and the auxiliary flat AF working surface C, thus obtaining the absolute surface shape distribution of each flat.

[0139] In one embodiment, a large-aperture three-plane crystal absolute inspection system based on small-angle rotation is provided for implementing the large-aperture three-plane crystal absolute inspection method based on small-angle rotation. The system includes:

[0140] The first module is used to obtain the first interferometric measurement result obtained from the four measurements. Second interferometry results Third interferometry results and the results of the fourth interferometry ;

[0141] The second module is used to define pose parameters and construct an actual measurement model containing pose parameters, and to construct a parameterized linear equation system containing a weight matrix, a surface vector to be solved, and a measurement data vector based on the measurement model.

[0142] The third module is used to construct an alternating iterative optimization model for pose parameters and surface distribution. During the iteration process, the surface distribution vector and pose parameters are alternately optimized and updated until the pose parameters meet the preset convergence conditions.

[0143] The fourth module is used to solve the parameterized linear equations based on the converged pose parameters, and to inversely reconstruct the absolute surface distribution of the flat TF working surface A, flat RF working surface B, and flat AF working surface C.

[0144] Specific limitations regarding the large-aperture three-panel crystal absolute testing system based on small-angle rotation can be found in the limitations of the large-aperture three-panel crystal absolute testing method based on small-angle rotation mentioned above, and will not be repeated here. Each module in the aforementioned large-aperture three-panel crystal absolute testing system based on small-angle rotation can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independent of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0145] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the large-aperture three-flat crystal absolute inspection method based on small-angle rotation:

[0146] Step 1: Obtain interferometric measurement data for the reference flat, test flat, and auxiliary flat in four different relative orientations. The working surfaces of the reference flat, test flat, and auxiliary flat are denoted as working surface A, working surface B, and working surface C, respectively. The interferometric measurement data for the four different relative orientations are obtained through four measurements: interferometric measurement with working surface A and working surface B relative to each other; interferometric measurement with working surface C and working surface B relative to each other; interferometric measurement with working surface A and working surface C (rotated around the Y-axis) relative to each other; and interferometric measurement with working surface C rotated around the Z-axis by a preset small angle after being rotated in the rotated state and then placed relative to working surface A. The horizontal direction along the flat surface is the X-axis, the vertical direction along the flat surface is the Y-axis, and the Z-axis is perpendicular to the flat surface and positive along the direction of reflected light.

[0147] Step 2: Construct an actual measurement model containing actual pose parameters, wherein the pose parameters are used to characterize the relative translation, actual rotation angle and actual rotation center position of the optical flat in each measurement state under the actual measurement state.

[0148] Step 3: Based on the actual measurement model, construct a system of parameterized linear equations consisting of the surface shape vector to be solved, the transformation matrix, and the measurement data vector composed of the four measurement data.

[0149] Step 4: Establish an alternating iterative optimization model for pose parameters and surface distribution. After setting the initial parameters, based on the parameterized linear equation system and the nonlinear solution process of pose parameters, alternate iteratively optimize and update the pose parameters and surface distribution until the convergence criteria are met.

[0150] Step 5: Update the parameterized linear equations based on the pose parameters obtained by iterative convergence, and solve for the absolute surface distribution of each flat crystal.

[0151] For specific limitations on each step, please refer to the limitations on the absolute inspection method for large-diameter three-flat crystals based on small-angle rotation mentioned above, which will not be repeated here.

[0152] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being executed by a processor to implement the steps of the large-aperture three-flat crystal absolute inspection method based on small-angle rotation:

[0153] Step 1: Obtain interferometric measurement data for the reference flat, test flat, and auxiliary flat in four different relative orientations. The working surfaces of the reference flat, test flat, and auxiliary flat are denoted as working surface A, working surface B, and working surface C, respectively. The interferometric measurement data for the four different relative orientations are obtained through four measurements: interferometric measurement with working surface A and working surface B relative to each other; interferometric measurement with working surface C and working surface B relative to each other; interferometric measurement with working surface A and working surface C (rotated around the Y-axis) relative to each other; and interferometric measurement with working surface C rotated around the Z-axis by a preset small angle after being rotated in the rotated state and then placed relative to working surface A. The horizontal direction along the flat surface is the X-axis, the vertical direction along the flat surface is the Y-axis, and the Z-axis is perpendicular to the flat surface and positive along the direction of reflected light.

[0154] Step 2: Construct an actual measurement model containing actual pose parameters, wherein the pose parameters are used to characterize the relative translation, actual rotation angle and actual rotation center position of the optical flat in each measurement state under the actual measurement state.

[0155] Step 3: Based on the actual measurement model, construct a system of parameterized linear equations consisting of the surface shape vector to be solved, the transformation matrix, and the measurement data vector composed of the four measurement data.

[0156] Step 4: Establish an alternating iterative optimization model for pose parameters and surface distribution. After setting the initial parameters, based on the parameterized linear equation system and the nonlinear solution process of pose parameters, alternate iteratively optimize and update the pose parameters and surface distribution until the convergence criteria are met.

[0157] Step 5: Update the parameterized linear equations based on the pose parameters obtained by iterative convergence, and solve for the absolute surface distribution of each flat crystal.

[0158] For specific limitations on each step, please refer to the limitations on the absolute inspection method for large-diameter three-flat crystals based on small-angle rotation mentioned above, which will not be repeated here.

[0159] As a specific example, in one embodiment, the invention will be further verified and described with reference to the accompanying drawings.

[0160] The flowchart of the computational processing of this invention is as follows: Figure 2As shown, the three-plane real surface shape in the embodiment is as follows: Figure 3 As shown, the three planar surfaces restored using this invention are as follows: Figure 4 As shown, the residuals between the restored surface shape and the true surface shape are as follows: Figure 5 As shown, the residuals of the three plane shapes restored by the present invention are very small. The residuals PV and RMS of the restored plane A are 0.0013nm and 0.0001nm, respectively; the residuals PV and RMS of the restored plane B are 0.0017nm and 0.0001nm, respectively; and the residuals PV and RMS of the restored plane C are 0.0014nm and 0.0001nm, respectively.

[0161] In summary, the absolute verification method proposed in this invention adds only one small-angle rotation measurement to the classic three-plane mutual verification method, without changing the pose of the large-aperture optical flat, thus effectively reducing gravity deformation error and support stress error. Furthermore, to address influencing factors such as position control errors during actual measurement, this method introduces pose parameters. By constructing an alternating iterative optimization model of pose parameters and surface shape distribution, it effectively improves the measurement operation's immunity to pose errors, ultimately achieving high-precision restoration of the large-aperture surface shape.

[0162] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A method for absolute inspection of large-aperture three-flat crystals based on small-angle rotation, characterized in that, The method includes the following steps: Step 1: Obtain interferometric measurement data for the reference flat, test flat, and auxiliary flat in four different relative orientations. The working surfaces of the reference flat, test flat, and auxiliary flat are denoted as working surface A, working surface B, and working surface C, respectively. The interferometric measurement data for the four different relative orientations are obtained through four measurements: interferometric measurement with working surface A and working surface B relative to each other; interferometric measurement with working surface C and working surface B relative to each other; interferometric measurement with working surface A and working surface C (rotated around the Y-axis) relative to each other; and interferometric measurement with working surface C rotated around the Z-axis by a preset small angle and then placed relative to working surface A after the flipped state. The horizontal direction along the flat surface is the X-axis, the vertical direction along the flat surface is the Y-axis, and the Z-axis is perpendicular to the flat surface and positive along the direction of reflected light. Step 2: Construct an actual measurement model containing actual pose parameters, wherein the pose parameters are used to characterize the relative translation, actual rotation angle and actual rotation center position of the optical flat in each measurement state under the actual measurement state. Step 3: Based on the actual measurement model, construct a system of parameterized linear equations consisting of the surface shape vector to be solved, the transformation matrix, and the measurement data vector composed of the four measurement data. Step 4: Establish an alternating iterative optimization model for pose parameters and surface distribution. After setting the initial parameters, based on the parameterized linear equation system and the nonlinear solution process of pose parameters, alternate iteratively optimize and update the pose parameters and surface distribution until the convergence criteria are met. Step 5: Update the parameterized linear equations based on the pose parameters obtained by iterative convergence, and solve for the absolute surface distribution of each flat crystal.

2. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 1, characterized in that, Step 1 includes four measurements: First measurement: Place the reference crystal flat TF and the test crystal flat RF opposite each other to form an interference cavity between working surface A and working surface B, and obtain the first interferometric measurement result. ; Second measurement: Keeping the positions of TF and RF unchanged, place the auxiliary flat crystal AF between TF and RF to form an interference cavity between working surface C and working surface B, and obtain the second interferometric measurement result. ; Third measurement: Flip AF around the Y-axis to form an interference cavity between working surface A and the flipped working surface C, and obtain the third interferometric measurement result. ; Fourth measurement: Based on the state of the third measurement, keeping the working surface A unchanged, rotate AF clockwise around the Z-axis by a preset small angle. To obtain the fourth interferometric measurement result, an interference cavity is maintained between the rotated working surface C and the working surface A. ;in, Less than 15°.

3. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 2, characterized in that, Step 2, which involves constructing an actual measurement model containing actual pose parameters, specifically includes: Let the surface shapes of working surfaces A, B, and C be respectively... , and ,in The coordinate position on the plane formed by the X-axis and Y-axis. , These are the coordinates on the X and Y axes, respectively; the first interferometric measurement result is recorded. Second interferometry results Third interferometry results Fourth interferometry results The corresponding surface distribution data are as follows: , , , ; by exist The area and exist The regions in the diagram serve as the reference positions for their respective surface shapes; Define pose parameters ,in express exist The amount of translation of the region relative to its reference position. , They are respectively exist The amount of translation of the region relative to its reference position along the X and Y axes; Indicates the flipped exist The amount of translation of the region relative to its reference position. They are the flipped versions exist The amount of translation of the region relative to its reference position along the X and Y axes; and They represent exist The region in the diagram, relative to its reference position, has its rotation center coordinates and actual rotation angle. , They are respectively exist The X and Y coordinates of the region in the figure relative to the rotation center of its reference position are both zero; Establish a practical interferometry model that includes pose parameters: ； in, ； In the formula, , These are the coordinates after the x and y rotation transformations, respectively.

4. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 3, characterized in that, Step 3 involves constructing a system of parameterized linear equations, specifically including: Step 3-1, determine the pose parameters The determined set of common valid pixels For the three-sided shape involved in the four measurements , and Construct the corresponding sub-matrices respectively, and combine them to obtain the complete weight matrix. , represented as: ； In the formula, the block matrix Indicates the first In this measurement, the surface shape In pose parameters The interpolation weight matrix that maps the original coordinates to the measured coordinates under the influence of the interpolation weight matrix. , Its elements are the resampling weights of each valid pixel, with values ​​ranging from [0,1]. Represents a zero matrix of the corresponding size; Step 3-2: Expand the discrete sampled values ​​of the surfaces to be solved on working surfaces A, B, and C into one-dimensional column vectors. , , And arrange them in order from beginning to end to form the surface vector to be solved. , represented as: ； Step 3-3: Record the results of the four measurements. , , , In the common valid pixel set The measurement data within are expanded into column vectors. , , and The data are arranged in a vector from beginning to end to form the measurement data. , represented as: ； Steps 3-4, based on the weight matrix 1. Surface vector to be solved and measurement data vector Establish a system of parameterized linear equations for the surface distribution: 。 5. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 4, characterized in that, The construction process of the block matrix in step 3-1 includes: Step 3-1-1, define the submatrix construction operation: for the first... In this measurement, based on the surface shape and its transformation method, bilinear interpolation is used to calculate the weight values ​​of each coordinate point after the corresponding transformation of each surface shape, and a corresponding submatrix is ​​constructed; where, the submatrix... The row number is equal to the first row. The measurement results are in The number of elements within a shape is equal to the number of columns in the corresponding shape. The number of valid elements; Step 3-1-2: Using the submatrix construction operation described above, the surface shape after the flip transformation is processed. and the surface shape after in-situ transformation Construct submatrices respectively and ; Step 3-1-3: Using the submatrix construction operation described above, the surface shape after in-situ transformation is... and the surface shape after flipping transformation Construct submatrices respectively and ; Step 3-1-4: Using the submatrix construction operation described above, the surface shape after the flipping transformation is processed. and the surface shape after in-situ transformation Construct submatrices respectively and ; Step 3-1-5: Using the submatrix construction operation described above, the surface shape after the flip transformation is processed. and the surface shape after rotation transformation Construct submatrices respectively and .

6. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 4, characterized in that, Step 4 involves establishing an alternating iterative optimization model for pose parameters and surface distribution, and then iteratively optimizing it. Specifically, this includes: Step 4-1: Set the initial values ​​of the pose parameters. ,in The nominal design value is the rotation angle. Step 4-2, in the k-th iteration, the current pose parameters are... Substituting into the parametric linear equations, the current surface distribution solution is obtained. ; Step 4-3, based on the current surface distribution solution We construct and solve a system of nonlinear difference residual equations for the pose parameters to obtain the updated pose parameters for the (k+1)th iteration. ; Step 4-4: Determine whether the updated pose parameters meet the preset convergence conditions. If they do, terminate the iteration and output the final pose parameters. If they do not meet the conditions, let k = k+1 and return to step 4-2 to continue the iteration.

7. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 6, characterized in that, In step 4-3, the pose parameters for the (k+1)th iteration are solved. Specifically, it includes: Step 4-3-1, based on the current pose parameters Determine the spatial constraint domain ; Step 4-3-2, in the spatially constrained domain Internally, the flip-translation composite difference measured values ​​are constructed using actual measurement data. Compared with the measured value of rotational difference That is, for : ； Step 4-3-3, in the spatially constrained domain Inside, define the surface shape for the k-th iteration. and Calculation of the flip-translation composite difference of geometric parameters and rotational difference calculation values That is, for : ； In the formula, Both represent the surface shape distribution corresponding to the working surface C in the k-th iteration. Both represent the surface shape distribution corresponding to the working surface B in the k-th iteration; Step 4-3-4, based on the principle that the measured difference value and the calculated difference value are equal, for the spatially constrained domain... A system of nonlinear equations is constructed for each discrete pixel within the array: ； In the formula, Let the system of residual equations for the k-th iteration be represented. Describes the spatial constraint domain of the k-th iteration. The flip-translation composite difference calculation value of all pixels within the range, Describes the spatial constraint domain of the k-th iteration. The rotation difference calculation value of all pixels within the range, Describes the spatial constraint domain of the k-th iteration. Measured values ​​of the flip-translation composite difference for all pixels within the array. Describes the spatial constraint domain of the k-th iteration. Measured rotational difference values ​​for all pixels within the area; Step 4-3-5: Solve the nonlinear equations using a nonlinear least squares optimization algorithm to obtain the updated pose parameters. ; The preset convergence condition mentioned in step 4-4 is: ； In the formula, The translation and center coordinate convergence threshold, The rotation angle convergence threshold, Let represent the residual equations for the (k+1)th iteration.

8. The absolute inspection method for large-aperture three-flat crystals based on small-angle rotation according to claim 4, characterized in that, Step 5 involves solving for the absolute surface shape distribution of each flat crystal, specifically including: Step 5-1: Substitute the pose parameters of the final converged output into the parameterized linear equation system, perform least squares calculation on the parameterized linear equation system, and obtain the optimal solution vector. Step 5-2: Separate the one-dimensional column vectors corresponding to working surfaces A, B, and C from the optimal solution vector in sequence; Step 5-3: Fill the separated one-dimensional column vectors into two-dimensional matrices according to the column priority or row priority rules of the original discrete sampling, and reconstruct the two-dimensional distribution of the full-aperture absolute surface shape of the test flat TF working surface A, the reference flat RF working surface B, and the auxiliary flat AF working surface C, thus obtaining the absolute surface shape distribution of each flat.

9. A large-aperture three-flat crystal absolute inspection system based on small-angle rotation, used to implement the method described in any one of claims 1 to 8, characterized in that, The system includes: The first module is used to obtain the first interferometric measurement result obtained from the four measurements. Second interferometry results Third interferometry results and the results of the fourth interferometry ; The second module is used to define pose parameters and construct an actual measurement model containing pose parameters, and to construct a parameterized linear equation system containing a weight matrix, a surface vector to be solved, and a measurement data vector based on the measurement model. The third module is used to construct an alternating iterative optimization model for pose parameters and surface distribution. During the iteration process, the surface distribution vector and pose parameters are alternately optimized and updated until the pose parameters meet the preset convergence conditions. The fourth module is used to solve the parameterized linear equations based on the converged pose parameters, and to inversely reconstruct the absolute surface distribution of the flat TF working surface A, flat RF working surface B, and flat AF working surface C.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 8.

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