A fast evaluation method of stitching interferometry error with relative angle

Abstract

This invention discloses a rapid evaluation method for splicing interferometry errors with determinable relative angles, comprising the following steps: dividing a specific mirror under test into sub-apertures, determining the number of sub-apertures and the measurement time for each sub-aperture; measuring the angle measurement error under the measurement environment based on the number of sub-apertures and the measurement time for each sub-aperture, using an interferometer and measurement platform to measure a reference plane mirror, and obtaining angle measurement error stability data corresponding to the number of sub-apertures and measurement time; calculating the cumulative sum distribution data of angle measurement errors based on the obtained angle measurement error stability data and determining the cumulative sum peak and valley values ​​of angle measurement errors; calculating the predicted peak and valley values ​​of the splicing interferometry surface shape error with determinable relative angles based on the obtained cumulative sum peak and valley values ​​of angle measurement errors, sub-aperture lengths, and overlap rates. This invention aims to rapidly and directly correlate angle measurement errors with relative angles to achieve evaluation of splicing interferometry surface shape errors.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement technology, specifically relating to a rapid evaluation method for splicing interferometry errors with a determinable relative angle. Background Technology

[0002] With the development of synchrotron radiation sources and free-electron laser devices, the requirements for the surface accuracy of X-ray curved mirrors are becoming increasingly stringent, reaching as high as 2 nm PV and 50 nrad RMS. Deterministic shaping processes such as elastic emission machining and ion beam polishing are commonly used to process X-ray mirrors, while high-precision surface shape measurement technology plays a crucial role in guiding the processing of X-ray curved mirrors. Existing measurement methods based on slope profilometers can only acquire one-dimensional profile data and cannot effectively guide deterministic shaping. Furthermore, the meridional length of X-ray mirrors is usually greater than the length of the area that an interferometer can measure in one pass, often requiring sub-aperture stitching along the meridional direction. Traditional stitching methods minimize the phase difference in a least-squares sense by optimizing the relative angles and piston displacements between sub-apertures. However, this method accumulates backlash errors and environmental disturbance errors during meridional stitching, thus failing to accurately obtain the low-frequency surface shape of the curved mirror. A relative angle-determinable stitching interferometry method achieves precise sub-aperture stitching by simultaneously measuring the relative angle changes between the measured surface and the reference plane. The basic principle of its splicing is to eliminate the relative angular deviation between sub-apertures in the meridional direction caused by splicing motion errors by directly measuring the relative angle between them. Regarding the relative angular deviation in the direction of the arc... and piston displacement deviation This can be obtained through optimization. Relative angle deviation. Angle measurement error, as one of the main sources of error, directly affects the measurement accuracy of relative angle determinable splicing interferometry. Reducing angle measurement error can greatly improve the measurement accuracy of relative angle determinable splicing interferometry. Existing angle measurement error evaluation methods have the following problems: (1) The evaluation index has a weak correlation with accuracy. Traditional angle measurement error evaluation indexes (such as peak-to-valley (PV), standard deviation (STD), and root mean square (RMS)) are not significantly correlated with the PV value of relative angle determinable splicing interferometry measurement surface shape error. (2) The simulation process is complex. Existing evaluation methods based on simulation models are inefficient and it is difficult to quickly quantify the impact of angle measurement error on the measurement accuracy of relative angle determinable splicing interferometry. (3) There is a lack of targeted optimization basis. Existing methods are difficult to reveal the quantitative relationship between angle measurement error and relative angle determinable splicing interferometry measurement error, and cannot guide the optimization of angle measurement error and the adjustment of splicing parameters. Therefore, how to quickly and directly correlate angular measurement errors with relative angles to achieve evaluation of spliced ​​interferometric surface shape errors has become a key technical problem that urgently needs to be solved. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a rapid evaluation method for splicing interferometry error with a definite relative angle, which addresses the above-mentioned problems in the prior art. The present invention aims to quickly and directly correlate angle measurement error with relative angle to realize the evaluation of splicing interferometry surface shape error, so as to guide the optimization of angle measurement error (AME) and the selection of splicing parameters.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0005] A rapid evaluation method for relative angle-determinable stitching interferometry errors includes the following steps: dividing a specific mirror under test into sub-apertures, determining the number of sub-apertures and the measurement time for each sub-aperture; measuring the angle measurement error under the measurement environment based on the number of sub-apertures and the measurement time for each sub-aperture, using an interferometer and measurement platform to measure a reference plane mirror, and obtaining angle measurement error stability data corresponding to the number of sub-apertures and measurement time; calculating the cumulative sum distribution data of angle measurement errors based on the obtained angle measurement error stability data, and determining the cumulative sum peak and valley values ​​of angle measurement errors; calculating the peak and valley values ​​of the predicted relative angle-determinable stitching interferometry surface shape error based on the obtained cumulative sum peak and valley values ​​of angle measurement errors, sub-aperture length, and overlap rate.

[0006] Optionally, when dividing a specific test mirror into sub-apertures, the process includes dividing the specific test mirror into sub-apertures based on the length of the specific test mirror and a given sub-aperture length and overlap rate parameter. The sub-aperture division adopts a uniform sub-aperture division method, and the overlap rate between adjacent sub-apertures is constant.

[0007] Optionally, when determining the number of sub-apertures and the measurement time for a single sub-aperture, the calculation function expression for the number of sub-apertures is:

[0008] ;

[0009] in, Number of sub-apertures For the length of a specific mirror being measured, For the sub-aperture length, This represents the overlap rate.

[0010] Optionally, the step of measuring the angle measurement error under the measurement environment based on the number of sub-apertures and the measurement time of a single sub-aperture, and using an interferometer and measurement platform to measure the reference plane mirror to obtain angle measurement error stability data corresponding to the number of sub-apertures and measurement time, includes:

[0011] S101: Measure the surface shape of the reference plane mirror using a wavefront interferometer;

[0012] S102: The surface shape of the reference plane mirror is measured by plane fitting using the least squares method;

[0013] S103: Extract the tilt term of the fitted plane as the tilt angle of the reference plane mirror shape;

[0014] S104: Jump to step S101 until continuous measurement is completed. Group, Given the number of sub-apertures, the measurement time and relative angle of each group can determine that the time for spliced ​​interferometry is the same for a single sub-aperture of a specific mirror under test, thus obtaining multiple sets of angle measurement error stability data corresponding to the number of sub-apertures and measurement time.

[0015] Optionally, when measuring the surface shape of the reference plane mirror using a wavefront interferometer in step S101, the measurement time for the surface shape of a single reference plane mirror is the same as the time required to determine a single sub-aperture of a specific pair of mirrors under test using relative angles, and is not less than 2 minutes; the number of consecutive measurements of the surface shape data of the reference plane mirror is consistent with the number of sub-apertures required to determine a specific pair of mirrors under test using relative angles.

[0016] Optionally, step S102, which involves measuring the surface shape of the reference plane mirror using the least squares method through plane fitting, includes: importing the surface shape data of the reference plane mirror into data processing software to extract the height data matrix.Z and the horizontal coordinate matrix X , Y ,in X , Y , Z The matrices are of the same size; from the height data matrix Z and the horizontal coordinate matrix X , Y Obtain the 3D point cloud dataset to be fitted. ,in For the first One point, For the first The three-dimensional coordinates of the points Let be the number of points in the 3D point cloud dataset; the least squares method is used for plane fitting, and its objective function is defined as the perpendicular distance from all data points to the fitting plane. Sum of squares :

[0017] ;

[0018] Among them, vertical distance The calculation is based on the plane equation The normal vector form is given by, where, x , y and z They are respectively xyz Directional coordinates For the plane parameters to be fitted, the sum of squares is obtained by solving... Minimize the plane parameters Thus, the optimal fitting plane is obtained.

[0019] Optionally, when extracting the tilt term of the fitted plane as the tilt angle of the reference plane mirror shape in step S103, it includes directly taking the sum of squares. Minimize the plane parameters Planar parameters in The tilt angle of the reference plane mirror shape.

[0020] Optionally, the function expression for calculating the cumulative summation distribution data of the angle measurement error based on the obtained angle measurement error stability data is: ,in For the first The cumulative summation distribution data of the angle measurement errors. and For data sequence number, The maximum value is the number of sub-apertures. , The first of the obtained angle measurement error stability data Each angle measurement error data, The maximum value is .

[0021] Optionally, the function expression for calculating the cumulative summation peak-valley value of the angle measurement error is:

[0022] ;

[0023] in, This represents the cumulative sum of peak and valley values ​​of the angle measurement error. This is the cumulative summation distribution data for all angle measurement errors.

[0024] Optionally, the function expression for determining the peak and valley values ​​of the splicing interferometric surface shape error by calculating the predicted relative angle based on the cumulative summation peak and valley values ​​of the obtained angle measurement error, the sub-aperture length, and the overlap rate is as follows:

[0025] ;

[0026] in, To predict relative angles, the peak and valley values ​​of the splicing interferometric surface shape error can be determined. For the sub-aperture length, The overlap rate, This represents the cumulative summation of peak and valley values ​​for angle measurement errors.

[0027] Compared with the prior art, the present invention can mainly achieve the following beneficial effects: (1) The present invention, based on the cumulative-sum peak-to-valley (CS-PV) value of the angle measurement error (AME), proposes the CS-PV evaluation index by analyzing the angle measurement error mechanism, and solves the problem that the traditional angle measurement error evaluation index (PV, STD, RMS) and the PV value of the relative angle-determinable stitching interferometry (RADSI) surface shape error are not explicitly correlated. (2) The present invention, based on the cumulative-sum peak-to-valley value of the angle measurement error, solves the problem that the existing evaluation method based on simulation model is inefficient and difficult to quickly quantify the influence of AME on RADSI accuracy by establishing an explicit relationship model between AME and RADSI surface shape error. (3) The present invention provides a rapid evaluation method for relative angle determinable splicing interferometry errors based on the cumulative summation peak and valley values ​​of angle measurement errors. By establishing the relationship between splicing parameters, angle measurement errors, and RADSI surface shape measurement errors, this invention solves the problem that existing methods are unable to reveal the quantitative relationship between angle measurement errors and RADSI errors, and thus cannot guide the optimization of AME and the adjustment of splicing parameters. The present invention can establish an explicit relationship model between angle measurement errors and relative angle determinable splicing interferometry surface shape errors. Without complex simulations, it can directly and rapidly predict the relative angle determinable splicing interferometry surface shape errors through the cumulative summation peak and valley values ​​of angle measurement errors, thereby providing a quantitative basis for the optimization of angle measurement errors and the selection of splicing parameters. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0029] Figure 2 This is a flowchart illustrating the acquisition of angle measurement error stability data in an embodiment of the present invention.

[0030] Figure 3 This is a schematic diagram of the reference plane mirror shape in an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram of the least quadratic method fitting of the reference plane mirror in an embodiment of the present invention.

[0032] Figure 5 This is the angle measurement error measurement result in the embodiment of the present invention.

[0033] Figure 6This is the cumulative summation calculation result of the angle measurement error in the embodiments of the present invention.

[0034] Figure 7 This is a schematic diagram of the relative angle determinable splicing interferometric measurement platform structure in an embodiment of the present invention, wherein 1 is a reference plane mirror, 2 is a wavefront interferometer, 3 is the mirror to be measured, 4 is a two-dimensional electrically controlled translation stage, 5 is a main two-dimensional electrically controlled pitch and yaw stage, and 6 is a secondary two-dimensional electrically controlled pitch and yaw stage. Detailed Implementation

[0035] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0036] like Figure 1 The rapid evaluation method for relative angle-determinable stitching interferometry (RADSI) measurement error in this embodiment includes the following steps: dividing a specific surface under test (SUT) into sub-apertures, determining the number of sub-apertures and the measurement time for each sub-aperture; measuring the angle measurement error (AME) under the measurement environment based on the number of sub-apertures and the measurement time for each sub-aperture, and measuring the reference plane mirror (RF) using an interferometer and measurement platform to obtain angle measurement error stability data corresponding to the number of sub-apertures and the measurement time; calculating the cumulative sum distribution data of the angle measurement error based on the obtained angle measurement error stability data, and determining the cumulative sum peak-to-valley (CS-PV) value of the angle measurement error; calculating the peak-to-valley value of the predicted relative angle-determinable stitching interferometry (RADSI) measurement surface shape error based on the obtained cumulative sum peak-to-valley value of the angle measurement error, the sub-aperture length, and the overlap rate. This embodiment, based on the relative angle determination of the peak and valley values ​​of the cumulative summation of angle measurement errors, proposes a rapid evaluation method for spliced ​​interferometric measurement errors. By analyzing the mechanism of angle measurement errors, it proposes the CS-PV evaluation index, which solves the problem of the non-obvious correlation between the traditional AME evaluation index (PV, STD, RMS) and the PV value of RADSI measurement surface shape error. This invention reveals the quantitative relationship between AME and RADSI error by establishing an explicit relationship model between AME and RADSI surface shape error, thus solving the problem of low efficiency and difficulty in quickly quantifying the impact of AME on RADSI accuracy of existing simulation model-based evaluation methods.

[0037] In this embodiment, when dividing a specific test mirror into sub-apertures, the sub-apertures are divided based on the length of the specific test mirror, using a given sub-aperture length and overlap rate parameter. As an optional implementation, this embodiment uses a uniform sub-aperture division method, where the overlap rate between adjacent sub-apertures is constant. For example, in this embodiment, the length of the specific test mirror is 300 mm, the sub-aperture length is 70 mm, and the overlap rate is 0.8.

[0038] In this embodiment, when determining the number of sub-apertures and the measurement time for a single sub-aperture, the calculation function expression for the number of sub-apertures is as follows:

[0039] ;

[0040] in, Number of sub-apertures For the length of a specific mirror being measured, For the sub-aperture length, The overlap rate is given above. Based on the parameter values, this embodiment specifically includes:

[0041] .

[0042] like Figure 2 As shown, in this 36th section, the angle measurement error under the measurement environment is measured based on the number of sub-apertures and the measurement time of a single sub-aperture. An interferometer and measurement platform are used to measure the reference plane mirror, and the stability data of the angle measurement error corresponding to the number of sub-apertures and the measurement time are obtained, including:

[0043] S101: The surface shape of the reference plane mirror was measured using a wavefront interferometer, and the results are as follows: Figure 3 As shown;

[0044] S102: The surface shape of the reference plane mirror is measured by plane fitting using the least squares method;

[0045] S103: Extract the tilt term of the fitted plane as the tilt angle of the reference plane mirror shape;

[0046] S104: Jump to step S101 until continuous measurement is completed. Group, Given the number of sub-apertures, the measurement time and relative angle of each group can determine that the time for spliced ​​interferometry is the same for a single sub-aperture of a specific mirror under test, thus obtaining multiple sets of angle measurement error stability data corresponding to the number of sub-apertures and measurement time.

[0047] In step S101 of this embodiment, when measuring the surface shape of the reference plane mirror using a wavefront interferometer, the measurement time for the surface shape of a single reference plane mirror is the same as the time required to determine a single sub-aperture of a specific pair of mirrors under test using relative angles, which is no less than 2 minutes; the number of consecutive surface shape data of the reference plane mirror is consistent with the number of sub-apertures required to determine a specific pair of mirrors under test using relative angles (17 in this embodiment).

[0048] In this embodiment, step S102, measuring the surface shape of the reference plane mirror using the least squares method with plane fitting, includes: importing the surface shape data of the reference plane mirror into data processing software (such as Matlab) to extract the height data matrix. Z and the horizontal coordinate matrix X , Y ,in X , Y , Z The matrices are of the same size; from the height data matrix Z and the horizontal coordinate matrix X , Y Obtain the 3D point cloud dataset to be fitted. ,in For the first One point, For the first The three-dimensional coordinates of the points Let be the number of points in the 3D point cloud dataset; the least squares method is used for plane fitting, and its objective function is defined as the perpendicular distance from all data points to the fitting plane. Sum of squares :

[0049] ;

[0050] Among them, vertical distance The calculation is based on plane equations The normal vector form is given by, where, x , y and z They are respectively xyz Directional coordinates For the plane parameters to be fitted, the sum of squares is obtained by solving... Minimize the plane parameters Thus, the optimal fitting plane is obtained, specifically as follows: Figure 4 As shown.

[0051] Based on the obtained plane parameters It is possible to determine the direction along the meridian of a specific measured mirror ( The tilt angle, under normal circumstances, needs to be adjusted to a zero-fringe state for measurement when referring to the mirror surface shape. The tilt angle is... The value is on the order of rad, therefore the tilt angle can be approximated as equal to... Term coefficient (Unit: radians). Therefore, in step S103 of this embodiment, when extracting the tilt term of the fitted plane as the tilt angle of the reference plane mirror shape, it includes directly taking the sum of squares. Minimize the plane parameters Planar parameters in (Unit: radians) is the tilt angle of the mirror shape as a reference plane. In this embodiment, step S104 finally completes the continuous measurement. The angle measurement error data obtained by the group are as follows Figure 5 As shown, the time interval between each data point in the data is the same as the time required for RADSI measurement of a single sub-aperture of a specific mirror SUT, which is more than 2 minutes.

[0052] In this embodiment, the function expression for calculating the cumulative summation distribution data of the angle measurement error based on the obtained angle measurement error stability data is as follows: ,in For the first The cumulative summation distribution data of the angle measurement errors. and For data sequence number, The maximum value is the number of sub-apertures. , The first of the obtained angle measurement error stability data Each angle measurement error data, The maximum value is In this embodiment, the cumulative summation distribution data of the final calculated angle measurement error is as follows: Figure 6 As shown.

[0053] In this embodiment, the function expression for calculating the cumulative summation peak-valley value of the angle measurement error is:

[0054] ;

[0055] in, This represents the cumulative sum of peak and valley values ​​of the angle measurement error. The cumulative summation distribution data of all angle measurement errors is obtained in this embodiment. .

[0056] In this embodiment, the function expression for calculating the peak and valley values ​​of the splicing interferometric surface shape error based on the cumulative summation of the angle measurement error peak and valley values, the sub-aperture length, and the overlap rate is as follows:

[0057] ;

[0058] in, To predict relative angles, the peak and valley values ​​of the splicing interferometric surface shape error can be determined. For the sub-aperture length, The overlap rate, This represents the cumulative peak and valley values ​​of the angle measurement error. In the embodiment, the final predicted relative angle determines the peak and valley values ​​of the splicing interferometry surface shape error as follows:

[0059] .

[0060] Figure 7 The diagram shown is a structural schematic of the Relative Angle Determinable Interferometry (RADSI) measurement platform in this embodiment. (See attached diagram.) Figure 7 As can be seen, the relative angle in this embodiment determines that the RADSI (Rapid Interference Analysis) measurement platform consists of two two-dimensional pitch and tilt stages. The secondary two-dimensional electrically controlled pitch and tilt stage 6 is mounted on the primary two-dimensional electrically controlled pitch and tilt stage 5. The specific mirror under test 3 is placed on the primary two-dimensional electrically controlled pitch and tilt stage 5, and the reference plane mirror 1 is placed on the secondary two-dimensional electrically controlled pitch and tilt stage 6. The wavefront interferometer 2 is used to simultaneously measure the surface shape of the mirror under test 3 and the reference plane mirror 1. The two-dimensional electrically controlled translation stage 4 is used to translate the specific mirror under test 3, thereby measuring different sub-apertures. In this embodiment, the reference plane mirror 1 is an X-ray plane mirror. The specific mirror under test 3 can be a plane mirror or a curved mirror, especially suitable for curved mirrors (particularly one-dimensional cylindrical mirrors).

[0061] In summary, this embodiment of the method, by analyzing the mechanism of angle measurement error, proposes an evaluation index based on the cumulative summation of peak and valley values. This addresses the problem of the lack of explicit correlation between the peak and valley values ​​of traditional angle measurement error evaluation indices (PV, STD, RMS) and RADSI measurement surface shape errors. By establishing an explicit relationship model between angle measurement error and RADSI (relative angle determinable splicing interferometry) surface shape error, it reveals the quantitative relationship between angle measurement error and RADSI error, solving the problems of low efficiency and difficulty in quickly quantifying the impact of angle measurement error on RADSI accuracy in existing simulation-based evaluation methods. This embodiment of the method can improve the accuracy and flexibility of interferometer instrument transfer function measurement, and is particularly suitable for the calibration and testing of wavefront interferometers. Compared with traditional methods, this embodiment of the method not only avoids the difficulties of processing millimeter, sub-millimeter, or even nanometer amplitude ITF sinusoidal phase plates using traditional processing methods, but also provides more accurate measurement results based on the definition of the instrument transfer function, possessing significant theoretical value and application prospects. This invention presents a rapid evaluation method for relative angle-determinable stitched interferometry errors based on the cumulative summation peak-valley values ​​of angle measurement errors. By analyzing the mechanism of angle measurement errors, it proposes an evaluation index based on the cumulative summation peak-valley values. This addresses the problem of the lack of explicit correlation between the peak-valley values ​​of traditional angle measurement error evaluation indices (PV, STD, RMS) and the relative angle-determinable stitched interferometry surface shape errors. This invention reveals the quantitative relationship between angle measurement errors and relative angle-determinable stitched interferometry surface shape errors by establishing an explicit relationship model. This solves the problems of low efficiency and difficulty in quickly quantifying the impact of angle measurement errors on the accuracy of relative angle-determinable stitched interferometry using existing simulation-based evaluation methods. This invention can establish an explicit relationship model between angle measurement errors and relative angle-determinable stitched interferometry surface shape errors without complex simulations. It directly predicts the relative angle-determinable stitched interferometry surface shape errors through the cumulative summation peak-valley values ​​of angle measurement errors, thus providing a quantitative basis for angle measurement error optimization and stitching parameter selection.

[0062] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A rapid evaluation method for splicing interferometry errors with relatively identifiable angles, characterized in that, The process includes the following steps: dividing the specific mirror under test into sub-apertures, determining the number of sub-apertures and the measurement time for each sub-aperture; measuring the angle measurement error under the measurement environment based on the number of sub-apertures and the measurement time for each sub-aperture, using an interferometer and measurement platform to measure the reference plane mirror, and obtaining angle measurement error stability data corresponding to the number of sub-apertures and the measurement time; calculating the cumulative summation distribution data of the angle measurement error based on the obtained angle measurement error stability data, and determining the cumulative summation peak and valley values ​​of the angle measurement error. The peak and valley values ​​of the splicing interferometric measurement surface shape error can be determined by calculating the predicted relative angle based on the cumulative summation peak and valley values ​​of the obtained angle measurement error, the sub-aperture length, and the overlap rate; the functional expression for calculating the cumulative summation distribution data of the angle measurement error based on the obtained angle measurement error stability data is as follows: ,in For the first The cumulative summation distribution data of the angle measurement errors. and For data sequence number, The maximum value is the number of sub-apertures. , The first of the obtained angle measurement error stability data Each angle measurement error data, The maximum value is The function expression for calculating the cumulative summation peak and valley values ​​of the angle measurement error is as follows: ； in, This is the cumulative sum of peak and valley values ​​of the angle measurement error. The cumulative summation distribution data of all angle measurement errors; the functional expression for determining the peak and valley values ​​of the splicing interferometric surface shape error by calculating the predicted relative angle based on the obtained cumulative summation peak and valley values ​​of angle measurement errors, sub-aperture length, and overlap rate is as follows: ； in, To predict relative angles, the peak and valley values ​​of the splicing interferometric surface shape error can be determined. For the sub-aperture length, The overlap rate, This represents the cumulative summation of peak and valley values ​​for angle measurement errors.

2. The rapid evaluation method for splicing interferometry error that can be determined by relative angles according to claim 1, characterized in that, When dividing a specific test mirror into sub-apertures, the process includes dividing the specific test mirror into sub-apertures based on the given sub-aperture length and overlap rate parameter according to the length of the specific test mirror. The sub-aperture division adopts a uniform sub-aperture division method, and the overlap rate between adjacent sub-apertures is constant.

3. The rapid evaluation method for splicing interferometry error that can be determined by relative angles according to claim 2, characterized in that, The function expression for calculating the number of sub-apertures and the measurement time for a single sub-aperture is as follows: ； in, Number of sub-apertures For the length of a specific mirror being measured, For the sub-aperture length, This represents the overlap rate.

4. The rapid evaluation method for splicing interferometry error that can be determined by relative angles according to claim 1, characterized in that, The step involves measuring the angle measurement error under the measurement environment based on the number of sub-apertures and the measurement time for a single sub-aperture. This is achieved by using an interferometer and a measurement platform to measure the reference plane mirror and obtaining angle measurement error stability data corresponding to the number of sub-apertures and measurement time. S101: Use a wavefront interferometer to measure the surface shape of the reference plane mirror; S102: The surface shape of the reference plane mirror is measured by plane fitting using the least squares method; S103: Extract the tilt term of the fitted plane as the tilt angle of the reference plane mirror shape; S104: Jump to step S101 until continuous measurement is completed. Group, Given the number of sub-apertures, the measurement time and relative angle of each group can determine that the time for spliced ​​interferometry is the same for a single sub-aperture of a specific mirror under test, thus obtaining multiple sets of angle measurement error stability data corresponding to the number of sub-apertures and measurement time.

5. The rapid evaluation method for splicing interferometry error that can be determined by relative angles according to claim 4, characterized in that, When measuring the surface shape of a reference plane mirror using a wavefront interferometer in step S101, the measurement time for the surface shape of a single reference plane mirror is the same as the time required to determine a single sub-aperture of a specific pair of mirrors under test using relative angles, and is no less than 2 minutes; the number of consecutive measurements of the surface shape data of the reference plane mirror is consistent with the number of sub-apertures required to determine a specific pair of mirrors under test using relative angles.

6. The rapid evaluation method for splicing interferometry error that can be determined by relative angles according to claim 4, characterized in that, Step S102, which involves measuring the surface shape of the reference plane mirror using the least squares method with plane fitting, includes: importing the surface shape data of the reference plane mirror into data processing software to extract the height data matrix. Z and the horizontal coordinate matrix X , Y ,in X , Y , Z The matrices are of the same size; from the height data matrix Z and the horizontal coordinate matrix X , Y Obtain the 3D point cloud dataset to be fitted. ,in For the first One point, For the first The three-dimensional coordinates of the points Let be the number of points in the 3D point cloud dataset; the least squares method is used for plane fitting, and its objective function is defined as the perpendicular distance from all data points to the fitting plane. Sum of squares : ； Among them, vertical distance The calculation is based on plane equations The normal vector form is given by, where, x , y and z They are respectively xyz Directional coordinates For the plane parameters to be fitted, the sum of squares is obtained by solving... Minimize the plane parameters Thus, the optimal fitting plane is obtained.

7. The rapid evaluation method for splicing interferometry error that can be determined by relative angles according to claim 6, characterized in that, When extracting the tilt term of the fitted plane as the tilt angle of the reference plane mirror shape in step S103, this includes directly taking the sum of squares. Minimize the plane parameters Planar parameters in The tilt angle of the reference plane mirror shape.

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