A grazing incidence star stitching detection method for eliminating systematic errors

Abstract

The present invention discloses a grazing incidence star stitching detection method for eliminating systematic errors. The present invention uses a grazing incidence interference detection device to obtain sub-aperture compressed phase data of the surface of the component to be measured, and decompresses the sub-aperture phase data respectively to obtain sub-aperture decompressed phase data. Based on the phase values in the overlapping region of the sub-aperture decompressed phase data in two mutually perpendicular directions, the systematic astigmatism apertures PowerX and PowerY in the "direction x" and "direction y" are calculated. Then, the systematic astigmatism aperture and pose correction operations are subtracted from the sub-aperture decompressed phase data, and finally the full-aperture surface shape of the component to be measured is obtained by using a stitching fusion algorithm. The present invention realizes the elimination of the systematic astigmatism aperture in the grazing incidence interference measurement stitching process, reduces the requirement for the alignment accuracy of the grazing incidence interference measurement system, and greatly improves the accuracy of the grazing incidence interference measurement stitching result.

Description

Technical Field

[0001] The present invention relates to the technical field of optical measurement, and particularly relates to a grazing-incidence star-shaped stitching detection method for eliminating systematic errors. Background Art

[0002] With the development of the fields of optical precision measurement and semiconductors, the objects of optical detection have become diversified. Among them, the processing and detection requirements of large components such as large-aperture optical flats and large-aperture ceramic electrostatic chucks are increasing day by day. Such components have the characteristics of large area, large variation in surface flatness value, and partial non-specular reflection. This exceeds the measurement capability range of conventional interferometers for direct measurement, and the coordinate measuring machine detection method is difficult to meet the synchronous requirements of measurement accuracy and efficiency.

[0003] Compared with the direct measurement method of interferometers, the grazing-incidence measurement method not only expands the detection area of interferometers, but also improves the measurement ability of interferometers for rough surfaces. Compared with the coordinate measuring machine detection method widely used in the current industry, grazing-incidence interferometry has the advantages of non-contact, short detection time, high detection accuracy, large measurement range, good stability, and low detection cost.

[0004] Currently, the method of using the wavefront stitching result of interferometric measurement to evaluate the surface shape accuracy of large-aperture components has received increasing attention. However, as analyzed by Zhou You et al. in the literature "A Method for Correcting Systematic Errors in Sub-Aperture Stitching" (Laser & Optoelectronics Progress, Vol. 51, No. 5, 2014. Zhou You, Wang Qing, Liu Shijie), the wavefront stitching method of interferometric measurement will accumulate the systematic errors contained in the sub-aperture wavefront data. In particular, the quadratic low-order terms in the Zernike polynomials will follow the law of square amplification, forming an error amplification effect. This results in difficulty in obtaining a high-precision full-aperture surface shape result when using the wavefront stitching method to detect large-aperture components. Summary of the Invention

[0005] The purpose of the present invention is to provide a grazing-incidence star-shaped stitching detection method for eliminating systematic errors, which can improve the sub-aperture stitching accuracy, measure the surface shape of large-aperture components more accurately and efficiently, and is more suitable for the detection of large-aperture industrial products.

[0006] The technical solution for achieving the purpose of the present invention is: a grazing-incidence star-shaped stitching detection method for eliminating systematic errors, the steps are as follows:

[0007] Step 1: Use a grazing-incidence interferometer to measure the measured part to obtain its first sub-aperture compressed phase data, and then rotate the measured part by 90° for measurement to obtain the second sub-aperture compressed phase data.

[0008] Step 2: Perform phase decompression and size decompression on both the first sub-aperture phase data and the second sub-aperture phase data to correspondingly obtain the first sub-aperture decompressed phase data and the second sub-aperture decompressed phase data;

[0009] The decompression calculation formula is as follows:

[0010]

[0011] Among them, j represents the sub-aperture serial number, j = 1, 2. When j = 1, it represents the first sub-aperture, and when j = 2, it represents the second sub-aperture. W′ j is the compression phase data of the j-th sub-aperture; W j is the decompression phase data of the j-th sub-aperture; k is the grazing incidence compression coefficient; θ is the grazing incidence angle; (x 0 , y 0 ) is the coordinate of the compression phase data; (x, y) is the coordinate of the decompression phase data.

[0012] Step 3: Obtain the phase data of the overlapping area of the two sub-apertures according to the decompression phase data of the first sub-aperture and the decompression phase data of the second sub-aperture, and calculate the astigmatic aperture PowerX of the detection system in the x direction and the astigmatic aperture PowerY of the detection system in the y direction by using the above overlapping area phase data:

[0013] Express the decompression phase data of the j-th sub-aperture as a polynomial:

[0014] W j (x, y) = a 0 + a 1 x + a 2 y + a 3 x 2 + a 4 y 2

[0015] Express the two diameters on the inscribed circle in the overlapping area of the first sub-aperture and the second sub-aperture on the measured part as L x , L y , and make L x parallel to the "x direction", and L y parallel to the "y direction"; respectively express the phase data in the same areas as L x , L y in the decompression phase data of the first sub-aperture and the decompression phase data of the second sub-aperture in matrix form:

[0016]

[0017]

[0018] Among them, T represents matrix transpose; L 1x (x, y), L 2x (x, y) are the phase data in the first sub-aperture and the second sub-aperture that are the same as the diameter L xPhase data at the same position; L 1y (x, y), L 2y (x, y) are the phase data at the same position within the first sub-aperture and the second sub-aperture respectively with respect to the diameter L y Phase data at the same position.

[0019] Using the least squares method, calculate L 1x (x, y), L 2x (x, y) and L 1y (x, y), L 2y The phase fitting coefficients corresponding to (x, y) and where i represents the polynomial coefficient sequence number, i ∈ [0, 1, 2, 3, 4]; j represents the sub-aperture sequence number, j = 1, 2.

[0020] In the global coordinate system, for the first sub-aperture, the decompression direction is the "y direction", so the fitting coefficient simultaneously includes the warp Power(L x ) of the diameter of the measured part and the astigmatic aperture PowerX of the detection system; the fitting coefficient x contains the warp Power(L ) of the diameter of the measured part and part of the astigmatic aperture PowerY of the detection system. y The warp Power(L y ) of the diameter of the measured part and part of the astigmatic aperture PowerY of the detection system.

[0021] It is represented by a matrix as:

[0022]

[0023] where l is the length of the inscribed circle diameter after grazing incidence compression; D is the aperture of the grazing incidence interferometer.

[0024] In the global coordinate system, for the second sub-aperture, since the measured part rotates 90° during measurement and the decompression direction is the "x direction", the fitting coefficient contains the warp Power(L x ) of the diameter of the measured part and part of the astigmatic aperture PowerY of the detection system; the fitting coefficient x contains the warp Power(L ) of the diameter of the measured part and the astigmatic aperture PowerX of the detection system. y The warp Power(L y ) of the diameter of the measured part and the astigmatic aperture PowerX of the detection system.

[0025] It is represented by a matrix as:

[0026]

[0027] Combined with the least squares method, the phase data in the overlapping region of the two sub-apertures and the system astigmatism aperture are alternately iteratively optimized using the target convergence calculation formula to obtain PowerX and PowerY.

[0028] The target convergence calculation formula is:

[0029] max|PowerX (m+1) - PowerX (m) | < ε 1

[0030] max|PowerY (m+1) - PowerY (m) | < ε 2

[0031] In the formula, ε 1 , ε 2 are both the convergence thresholds for two adjacent iterations, and m represents the number of iterations.

[0032] Step 4: Based on PowerX and PowerY, calibrate the decompressed phase data of the j-th sub-aperture respectively, and correspondingly obtain the surface shape data of the j-th sub-aperture after eliminating the influence of the detection system.

[0033]

[0034] Step 5: Use the star stitching method to stitch the surface shape data of the two sub-apertures to obtain a new surface shape data of the sub-aperture:

[0035] Taking the detection coordinate system where the j-th sub-aperture is located as the reference coordinate system, the relative axial translation and tilt of the surface shape data of the (j + 1)-th sub-aperture in this coordinate system are expressed as:

[0036]

[0037] Establish the least squares objective function S, substitute the phase data in the overlapping region of the two sub-apertures, and solve for the pose adjustment coefficients Δa 0 , Δa 1 , Δa 2 :

[0038] S = ∑{ΔW real (x, y)} 2 = ∑{Δa 0 + Δa 1 ·x + Δa 2 ·y} 2 → min

[0039] Among them, ΔW real (x, y) represents the difference in the surface shape data between the j-th sub-aperture and the (j + 1)-th sub-aperture.

[0040] Use S to take partial derivatives of Δa 0 、Δa 1 、Δa 2 respectively, and write them in the form of a matrix equation:

[0041]

[0042] Solve the matrix equation to obtain the unique solutions of Δa 0 、Δa 1 、Δa 2 and use the obtained pose adjustment coefficients to correct the surface shape data of the j-th sub-aperture.

[0043] And use the weighted average method to calculate the phase data of the overlapping region The calculation formula is as follows:

[0044]

[0045] In the formula, L j is the distance from the data point in the overlapping region of the j-th sub-aperture to the center of the sub-aperture, L j+1 is the distance from the data point in the overlapping region of the (j + 1)-th sub-aperture to the center of the sub-aperture, and R(θ) is the distance from the center of the sub-aperture passing through the data point in the overlapping region to the edge of the sub-aperture.

[0046] Step 6: Continue to rotate the measured part multiple times until the sub-aperture regions measured by the grazing incidence interferometer cover the entire surface of the measured part. Decompress the compressed phase data of the obtained sub-apertures and perform the operation of subtracting the system astigmatic aperture. Repeat Step 5 to perform stitching calculation on the surface shape data of all the above sub-apertures, that is, realize the grazing incidence star stitching detection of the full aperture.

[0047] The beneficial effects of the present invention are as follows: A grazing incidence star stitching detection method for eliminating systematic errors. Compared with the prior art, the present invention has a wider interference detection range, and at the same time solves the problems that the grazing incidence stitching measurement is affected by systematic errors and cannot achieve high-precision measurement of the surface shape of large-aperture components. The present invention uses the phase data of the overlapping region of the sub-apertures to calculate the system astigmatic aperture, realizing a grazing incidence measurement wavefront stitching method for eliminating the influence of the system astigmatic aperture, and has the advantages of improving the stitching detection accuracy, simple process, and fast calculation speed. Brief Description of the Drawings

[0048] The present invention will be further described below in conjunction with the drawings and embodiments.

[0049] Figure 1 is a principle flow chart of a grazing incidence star stitching detection method for eliminating systematic errors of the present invention.

[0050] Figure 2Schematic diagram of two mutually perpendicular sub-aperture detection regions for calculating the astigmatic aperture of the imaging system of the present invention.

[0051] Figure 3 In an embodiment, there are 4 sub-aperture phase diagrams for calculation, where Figure 3 (a) in it is the phase distribution obtained when the first sub-aperture is measured by grazing incidence, Figure 3 and (b) in it is the phase distribution obtained when the second sub-aperture is measured by grazing incidence, Figure 3 and (c) in it is the phase distribution obtained when the third sub-aperture is measured by grazing incidence, Figure 3 and (d) in it is the phase distribution obtained when the fourth sub-aperture is measured by grazing incidence.

[0052] Figure 4 In an embodiment, it is a schematic diagram of the stitching result distribution calculated by using the present method. Among them Figure 4 (a) in it is the two-dimensional phase distribution obtained by using the conventional stitching algorithm in an embodiment, Figure 4 and (b) in it is the three-dimensional phase distribution obtained by using the conventional stitching algorithm in an embodiment, Figure 4 and (c) in it is the two-dimensional phase distribution calculated by using the method of the present invention in an embodiment, Figure 4 and (d) in it is the three-dimensional phase distribution calculated by using the method of the present invention in an embodiment. Detailed implementation manners

[0053] In order to make the technical means, creative features, achieved purposes and effects realized by the present invention easy to understand, the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0054] In an embodiment, in combination with Figures 1 to 4 , a grazing incidence star stitching detection method for eliminating systematic errors is provided, which is characterized in that the method includes the following steps: Step 1: Measure the measured part by using a grazing incidence interferometer to obtain its first sub-aperture compressed phase data, and then rotate the measured part by 90° for measurement to obtain the second sub-aperture compressed phase data.

[0055] Furthermore, in one embodiment, the phase data directly measured by the grazing incidence interferometer in Step 1 is the phase data compressed by grazing incidence and cannot be directly used to represent the surface shape error of the measured part.

[0056] Step 2: Perform phase decompression and size decompression on both the first sub-aperture phase data and the second sub-aperture phase data to correspondingly obtain the first sub-aperture decompressed phase data and the second sub-aperture decompressed phase data;

[0057] The decompression calculation formula is:

[0058]

[0059] Among them, j represents the sub-aperture serial number, where j = 1, 2. When j = 1, it represents the first sub-aperture, and when j = 2, it represents the second sub-aperture. W′ j is the compressed phase data of the j-th sub-aperture; W j is the decompressed phase data of the j-th sub-aperture; k is the grazing-incidence compression coefficient; θ is the magnitude of the grazing-incidence angle; (x 0 , y 0 ) are the coordinates of the compressed phase data; (x, y) are the coordinates of the decompressed phase data.

[0060] Furthermore, in one of the embodiments, since the size decompression only decompresses the data in the y direction in step two, the systematic errors included in the sub-aperture decompressed phase data are differently changed in the x and y directions, forming systematic astigmatic apertures PowerX and PowerY.

[0061] Furthermore, in one of the embodiments, the target convergence calculation formula in step three is:

[0062] max|PowerY (m+1) - PowerX (m) | < ε 1

[0063] max|PowerY (m+1) - PowerY (m) | < ε 2

[0064] In the formula, ε 1 , ε 2 are both the convergence thresholds for two adjacent iterations, and m represents the number of iterations.

[0065] Step three: According to the decompressed phase data of the first sub-aperture and the decompressed phase data of the second sub-aperture, obtain the phase data of the overlapping region of the two sub-apertures, and calculate the astigmatic aperture PowerX of the detection system in the x direction and the astigmatic aperture PowerY of the detection system in the y direction by using the above-mentioned overlapping region phase data:

[0066] Express the decompressed phase data of the j-th sub-aperture as a polynomial:

[0067] W j (x, y) = a 0 + a 1 x + a 2 y + a 3 x 2 + a 4 y 2

[0068] The two diameters on the inscribed circle in the overlapping area of ​​the first sub-aperture and the second sub-aperture on the measured object are represented as L x , L y , let L x Parallel to the "x direction", L y parallel to the "y direction"; respectively, the first sub-aperture decompressed phase data and the second sub-aperture decompressed phase data with L x , L y The phase data of the same area is expressed in matrix form:

[0069]

[0070]

[0071] Where T represents matrix transpose; L 11 (x,y),L 2x (x, y) are the first sub-aperture, the second sub-aperture and the diameter L respectively. x Phase data at the same position; L 1y (x,y),L 2y (x, y) are the first sub-aperture, the second sub-aperture and the diameter L respectively. y Phase data at the same position.

[0072] Using the least squares method, we can calculate L 1x (x,y),L 2x (x,y) and L 1y (x,y),L 2y Phase fitting coefficient corresponding to (x,y) and Wherein, i represents the polynomial coefficient number, i∈[0,1,2,3,4]; j represents the subaperture number, j=1,2.

[0073] In the global coordinate system, for the first subaperture, the decompression direction is the "y direction", so the fitting coefficient It also includes the DUT L x Diameter warpage Power(L x ) and detection system astigmatism aperture PowerX; fitting coefficient Includes the DUT L y Diameter warpage Power(L y ) and part of the detection system astigmatism aperture PowerY.

[0074] It can be expressed as a matrix:

[0075]

[0076] where, l is the length of the inner circle diameter after grazing incidence compression; D is the aperture of the grazing incidence interferometer;

[0077] In the global coordinate system, for the second sub-aperture, since the measured part rotates 90° during measurement and the decompression direction is the "x direction", the fitting coefficient includes the warpage Power(L x of the diameter of the measured part and the astigmatic aperture PowerY of part of the detection system; the fitting coefficient x includes the warpage Power(L of the diameter of the measured part and the astigmatic aperture PowerX of the detection system. y y )

[0078] It is represented by a matrix as:

[0079]

[0080] Combined with the least squares method, the phase data of the overlapping region of the two sub-apertures and the astigmatic aperture of the system are alternately iteratively optimized using the target convergence calculation formula to obtain PowerX and PowerY.

[0081] The target convergence calculation formula is:

[0082] max|PowerX (m+1) - PowerX (m) | < ε 1

[0083] max|PowerY (m+1) - PowerY (m) | < ε 2

[0084] In the formula, ε 1 , ε 2 are both the convergence thresholds for adjacent two iterations, and m represents the number of iterations.

[0085] Step 4: Based on PowerX and PowerY, calibrate the decompressed phase data of the j-th sub-aperture respectively, and correspondingly obtain the surface shape data of the j-th sub-aperture after eliminating the influence of the detection system

[0086]

[0087] Step 5: Use the star stitching method to stitch the surface shape data of the two sub-apertures to obtain a new surface shape data of the sub-aperture:

[0088] Taking the detection coordinate system where the j-th sub-aperture is located as the reference coordinate system, the relative axial translation and tilt of the surface shape data of the (j + 1)-th sub-aperture in this coordinate system are expressed as:​

[0089]

[0090] Establish the least - square objective function S, substitute the phase data in the overlapping region of two sub - apertures, and solve for the pose adjustment coefficients Δa 0 、Δa 1 、Δa 2 :

[0091] S = ∑{ΔW real (x, y)} 2 = ∑{Δa 0 + Δa 1 ·x + Δa 2 ·y} 2 → min

[0092] where, ΔW real (x, y) represents the difference in the surface shape data between the j - th sub - aperture and the (j + 1) - th sub - aperture;

[0093] Take the partial derivatives of S with respect to Δa 0 、Δa 1 、Δa 2 respectively, and write it in the form of a matrix equation:

[0094]

[0095] Solve the matrix equation to obtain the unique solutions of Δa 0 、Δa 1 、Δa 2 and use the obtained pose adjustment coefficients to correct the surface shape data of the j - th sub - aperture;

[0096] And calculate the phase data in the overlapping region using the weighted average method The calculation formula is as follows:

[0097]

[0098] In the formula, L j is the distance from the data point in the overlapping region of the j - th sub - aperture to the center of the sub - aperture, L j+1 is the distance from the data point in the overlapping region of the (j + 1) - th sub - aperture to the center of the sub - aperture, and R(θ) is the distance from the center of the sub - aperture passing through the data point in the overlapping region to the edge of the sub - aperture.

[0099] Furthermore, in one of the embodiments, any two sub - apertures in the star - shaped stitching method described in step five have an overlapping region. In theory, the phase values obtained from two measurements of the same region are equal, but due to processes such as mechanical movement and rotational adjustment of the component under test, there will be differences between the two measurement results.

[0100] Step 6: Continuously rotate the DUT multiple times until the sub-aperture region measured by the grazing incidence interferometer covers the entire surface of the DUT. Decompress the obtained sub-aperture compressed phase data and perform the operation of subtracting the system astigmatic aperture. Repeat Step 5 to perform stitching calculation on all the above sub-aperture surface shape data, that is, realize the grazing incidence star stitching detection of the full aperture.

[0101] Embodiment 1

[0102] In this embodiment, a dynamic 150 interferometer is used as the measuring device, with a grazing incidence angle of 83° and a maximum measuring aperture of 800 mm. The steps of the grazing incidence star stitching detection method for eliminating system errors are as follows:

[0103] Step 1: Perform sub-aperture measurement on a ceramic electrostatic chuck with an aperture of 576 mm according to the pre-planned path to obtain 4 sub-aperture compressed phase data as Figure 3 shown. The size of these compressed phase data is 2048×2048 pixels.

[0104] Step 2: Perform phase decompression and coordinate decompression operations on the j-th sub-aperture compressed phase data respectively. The relationship between the sub-aperture compressed phase data and the sub-aperture decompressed phase data is expressed as:

[0105]

[0106] where j represents the sub-aperture serial number, W′ j is the j-th sub-aperture compressed phase data; W j is the j-th sub-aperture decompressed phase data; k is the grazing incidence compression coefficient; θ is the size of the grazing incidence angle; (x 0 , y 0 ) is the coordinate of the compressed phase data; (x, y) is the coordinate of the decompressed phase data.

[0107] Step 3: Based on the position information of the sub-aperture phase in the global coordinate system, obtain the coordinate information of the inscribed circle region of the overlapping part of the sub-apertures. Further, obtain the coordinate information of the diameters L x 、L y of the inscribed circle in the "direction x" and "direction y". Using the least squares method, calculate the phase fitting coefficients of the diameters L x 、L y in the two sub-apertures respectively. According to the system error separation relation formula, continuously iterate and optimize the calculation to obtain the system astigmatic aperture numbers PowerX and PowerY in the two directions included in each sub-aperture phase data.

[0108] Step 4: Based on the system astigmatic aperture numbers PowerX and PowerY calculated in Step 3, correct the system astigmatic aperture for each sub-aperture phase.

[0109] Step Five: According to the phase difference in the overlapping area of sub-apertures, use the least squares method to calibrate the translation and tilt poses of each sub-aperture, and finally use the weighted fusion stitching algorithm to restore the full-aperture surface phase data.

[0110] By using a dynamic 150 interferometer to measure the stitching and calculate the full-aperture phase distribution by grazing incidence, the phase distributions obtained without correcting the system astigmatism aperture are as Figure 4 (a) and Figure 4 (b) shown, and the phase distributions obtained after correcting the system astigmatism aperture are as Figure 4 (c) and Figure 4 (d) shown. Compared with the traditional stitching method, the method of the present invention can not only increase the measurement range, but also effectively reduce the "edge effect" of the stitching result, making the stitching boundary transition more smoothly and improving the accuracy of the stitching result. It can be seen that the method of the present invention can effectively eliminate the influence caused by system errors in the stitching measurement process for the case where the grazing incidence detection system is not well calibrated, and can achieve high-precision stitching and restoration of the full-aperture surface shape.

[0111] The above shows and describes 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 by the above embodiments. The above embodiments and the descriptions in the specification only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. A grazing incidence star stitching method for eliminating systematic errors, characterized in that, it comprises the following steps: Step 1: Measure the measured part using a grazing incidence interferometer to obtain its first sub-aperture compressed phase data, and then rotate the measured part by 90° for measurement to obtain the second sub-aperture compressed phase data; Step 2: Perform phase decompression and size decompression on both the first sub-aperture phase data and the second sub-aperture phase data to correspondingly obtain the first sub-aperture decompressed phase data and the second sub-aperture decompressed phase data; The decompression calculation formula is: Among them, j represents the sub-aperture serial number, j = 1, 2. When j = 1, it represents the first sub-aperture, and when j = 2, it represents the second sub-aperture. W' j is the compressed phase data of the j-th sub-aperture; W j is the decompressed phase data of the j-th sub-aperture; k is the grazing incidence compression coefficient; θ is the grazing incidence angle; (x 0 , y 0 ) is the coordinate of the compressed phase data; (x, y) is the coordinate of the decompressed phase data; Step 3: According to the first sub-aperture decompressed phase data and the second sub-aperture decompressed phase data, obtain the overlapping region phase data of the two sub-apertures, and use the above overlapping region phase data to calculate the astigmatic aperture PowerX of the detection system in the x direction and the astigmatic aperture PowerY of the detection system in the y direction: Express the decompressed phase data of the j-th sub-aperture as a polynomial: W j (x,y) = a 0 +a 1 x + a 2 y + a 3 x 2 +a 4 y 2 Express two diameters on the inscribed circle within the overlapping region of the first sub-aperture and the second sub-aperture on the device under test as L x and L y . Let L x be parallel to the "x direction", and L y be parallel to the "y direction". Represent in matrix form the phase data of the same regions in the first sub-aperture decompressed phase data and the second sub-aperture decompressed phase data that correspond to L x and L y respectively: where T represents matrix transpose; L 1x L(x,y), L 2x L(x,y) are the phase data at the same position within the first sub-aperture and the second sub-aperture respectively with respect to the diameter L x ; L 1y L(x,y), L 2y L(x,y) are the phase data at the same position within the first sub-aperture and the second sub-aperture respectively with respect to the diameter L y ; Using the least squares method, calculate L respectively 1x (x, y), L 2x (x, y) and L 1y (x, y), L 2y (x, y) corresponding phase fitting coefficients and where i represents the polynomial coefficient serial number, i ∈ [0, 1, 2, 3, 4]; j represents the sub-aperture serial number, j = 1, 2; In the global coordinate system, for the first sub-aperture, the direction of decompression is the "y direction", so the fitting coefficient simultaneously includes the warpage Power(L x of the diameter of the measured part x ) and the astigmatic aperture PowerX of the detection system; the fitting coefficient includes the warpage Power(L y of the diameter of the measured part y ) and part of the astigmatic aperture PowerY of the detection system; Express it in matrix form as: where, l is the length of the inscribed circle diameter after grazing incidence compression; D is the aperture of the grazing incidence interferometer; In the global coordinate system, for the second sub-aperture, since the measured part rotates by 90° during measurement and the decompression direction is the "x direction", the fitting coefficient includes the warpage Power(L x of the diameter of the measured part x ) and the astigmatic aperture PowerY of the partial detection system; the fitting coefficient includes the warpage Power(L y of the diameter of the measured part y ) and the astigmatic aperture PowerX of the detection system; Express it in matrix form as: Combined with the least squares method, use the target convergence calculation formula to alternately iterate and optimize the overlapping region phase data of the two sub-apertures and the system astigmatic aperture to obtain PowerX and PowerY; Step 4: Based on PowerX and PowerY, calibrate the decompressed phase data of the j-th sub-aperture respectively, and correspondingly obtain the surface shape data of the j-th sub-aperture after eliminating the influence of the detection system Step 5: Use the star stitching method to stitch the surface shape data of the two sub-apertures to obtain a new sub-aperture surface shape data: Taking the detection coordinate system where the j-th sub-aperture is located as the reference coordinate system, the relative axial translation and tilt of the (j + 1)-th sub-aperture surface shape data in this coordinate system are expressed as: Establish the least - squares objective function \(S\), substitute the phase data in the overlapping region of the two sub - apertures, and solve for the pose adjustment coefficients \(\Delta a\) 0 , \(\Delta a\) 1 , \(\Delta a\) 2 : S = ∑{ΔW real (x, y)} 2 = ∑{Δa 0 + Δa 1 · x + Δa 2 · y} 2 → min where, ΔW real (x, y) represents the difference in surface shape data between the j-th sub-aperture and the (j + 1)-th sub-aperture; Take the partial derivatives of Δa with respect to S respectively 0 、Δa 1 、Δa 2 and write them in the form of a matrix equation: Solve the matrix equation to obtain Δa 0 , Δa 1 , Δa 2 The unique solution, and use the obtained pose adjustment coefficient to correct the surface shape data of the j-th sub-aperture; And the weighted average method is used to calculate the phase data of the overlapping region The calculation formula is as follows: where L j is the distance from the data point in the overlapping region of the j-th sub-aperture to the center of the sub-aperture, and L j+1 is the distance from the data point in the overlapping region of the (j + 1)-th sub-aperture to the center of the sub-aperture, and R(θ) is the distance from the center of the sub-aperture passing through the data point in the overlapping region to the edge of the sub-aperture; Step 6: Continue to rotate the measured part multiple times until the sub-aperture area measured by the grazing incidence interferometer covers the entire surface of the measured part. Perform decompression and system astigmatic aperture deduction operations on the obtained sub-aperture compressed phase data, and repeat Step 5 to perform stitching calculations on all the above sub-aperture surface shape data, that is, realize the grazing incidence star stitching detection of the full aperture.

2. A grazing incidence star stitching detection method for eliminating systematic errors according to claim 1, characterized in that, in Step 3, the target convergence calculation formula is: max|PowerX (m+1) -PowerX (m) |<ε 1 max|PowerY (m+1) -PowerY (m) |<ε 2 where ε 1 , ε 2 are both the convergence thresholds for two adjacent iterations, and m represents the number of iterations.

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