Virtual-real fusion method for multi-system structure optimization and surface error solving

Abstract

The virtual-real fusion method for multi-system structure optimization and surface error solving can improve the anti-vibration performance of sub-aperture stitching interferometry, avoid complex stitching algorithms, reduce system adjustment difficulty, and correct its return error. It includes: (1) determining the adjustment error with large control difficulty or greater influence on the wavefront of the image surface and its possible maximum value; (2) analysis of the influence of each adjustment error on the wavefront of the image surface; (3) analysis of the influence of each adjustment error on each Zernike coefficient, and determination of the calibration scheme of the adjustment error based on the influence size and independent or coupled condition; (4) optimization of the ideal virtual interferometer to obtain the virtual interferometer after adjustment error calibration, which has the same adjustment error as the actual interferometer system; (5) based on the virtual interferometer, the surface error is reconstructed by the synchronous reverse optimization reconstruction method to obtain the final measurement result.

Description

Technical Field

[0001] This invention relates to the field of photoelectric detection technology, and in particular to a virtual-real fusion method for optimizing the structure of multiple systems and solving surface errors. Background Technology

[0002] In the field of precision testing of large-aperture, small-F / # aspherical surfaces, the full-field interferometry method has always faced difficulties due to the design and manufacturing complexity of compensators, the resolution of interferometers, and the F / # of spherical lenses. Sub-aperture stitching interferometry, a solution proposed in the 1980s, divides the mirror under test into several sub-aperture regions within the measurement range of the large-F / # spherical lens of the interferometer, and measures them sequentially, thus circumventing the limitations of the full-field interferometry method. The measurement results from different sub-aperture regions are then stitched together to obtain the surface shape error distribution of the entire aperture. Depending on the shape of the sub-apertures, sub-aperture stitching interferometry can be divided into annular sub-aperture stitching interferometry and circular sub-aperture stitching interferometry. Annular sub-aperture stitching interferometry is designed for rotationally symmetric aspherical surfaces, where the sub-apertures are typically multiple concentric rings. The measurement uses a spherical lens to generate spherical waves with different radii of curvature to match the slopes of different rings on the measured surface, primarily expanding the longitudinal dynamic range of the interferometer. Zygo Corporation possesses commercially available instruments capable of performing circular subaperture stitched interferometry measurements. Circular subaperture stitched interferometry uses spherical waves of varying curvatures to match the local surface shape of the measured surface within different circular aperture ranges, significantly expanding the interferometer's lateral and longitudinal measurement range. It can detect planes, spheres, aspherical surfaces, and freeform surfaces, and has already been commercialized by QED Corporation. Therefore, circular subaperture stitched interferometry extends the interferometer's lateral and longitudinal dynamic range, enabling high-resolution detection of large-aperture, high-slope, and even off-axis aspherical surfaces without the use of a zero compensator.

[0003] However, the sub-aperture splicing interferometry method still has shortcomings in terms of vibration resistance, splicing algorithm, assembly and adjustment difficulty, and error correction.

[0004] First, the sub-aperture stitching interferometry method achieves full-aperture surface shape measurement by dividing the surface under test into multiple regions and measuring them sequentially. Since this method requires multiple measurements, the entire process is time-consuming, and environmental vibrations are unavoidable during this period, thus affecting measurement accuracy. Furthermore, the step-by-step measurement of sub-apertures typically relies on a motion control system to adjust the relative position of the surface under test or the interferometer, and the mechanical motion itself may induce additional vibration disturbances. Therefore, compared to full-field detection methods, the sub-aperture stitching interferometry method has relatively poor vibration resistance. It is necessary to explore ways to improve the vibration resistance of the sub-aperture stitching interferometry method.

[0005] Secondly, regardless of the specific sub-aperture stitching interferometry method used, the stitching algorithm that fuses different sub-aperture regions to obtain the full-aperture measurement result plays a crucial role. Currently, several landmark algorithms exist in the field of sub-aperture stitching, such as the Kwon-Thunen method, synchronous fitting method, discrete phase method, multi-aperture overlapping scanning technology, and sub-aperture stitching and positioning algorithms. However, all of them rely on complex mathematical calculations for positioning and phase inconsistency calibration between sub-apertures, which easily introduces positioning and calculation errors. Furthermore, vibration disturbances during the measurement process, as mentioned earlier, may introduce random and unknown positioning errors, further increasing the complexity and error of the algorithms. Therefore, there is a need to explore calibration-free data stitching algorithms.

[0006] It is evident that the measurement accuracy of the sub-aperture stitching method is constrained by factors such as device structure, vibration resistance, and stitching algorithm, and the complexity of the assembly and adjustment process further exacerbates this problem. To address the mechanical errors introduced by multiple adjustment degrees of freedom, reduce the impact of environmental vibration, and improve the accuracy of the stitching algorithm, the assembly and adjustment process typically requires high-precision calibration of the system's pose relationship. However, this high-precision calibration places higher demands on equipment accuracy and the operator's technical skill level, significantly increasing the difficulty of assembly and adjustment. While the increased difficulty of assembly and adjustment mitigates the influence of errors from other factors to some extent, it also presents more challenges to the practical application and promotion of the system. Therefore, it is urgent to explore methods to reduce the difficulty of assembly and adjustment while maintaining or even improving the overall measurement accuracy.

[0007] Finally, most sub-aperture stitching interferometry methods are non-zero interferometric detection methods, which means that there is a backhaul error introduced by the measurement light not returning along the original path. However, most of the algorithms mentioned above do not handle the backhaul error, which requires the sub-aperture to be small enough, leading to an increase in the number of scans and a greater impact of stitching accumulation error and environmental factors; or the sub-aperture to be equipped with a variable compensator, increasing the system complexity. Therefore, in order to obtain high-precision aspherical surface shape error detection results, it is necessary to handle the backhaul error. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, the technical problem to be solved by this invention is to provide a virtual-real fusion method for optimizing the structure of multiple systems and solving surface errors. This method can improve the vibration resistance of the sub-aperture splicing interferometry, avoid complex splicing algorithms, reduce the difficulty of system assembly and adjustment, and correct its back-pass error.

[0009] The technical solution of this invention is: a virtual-real fusion method for multi-system structure optimization and surface error solving, which includes the following steps:

[0010] (1) Determine the types of assembly and adjustment errors that need to be considered in subsequent steps. Based on the structure of the interferometric system and the specific operation in the assembly and adjustment process, determine the assembly and adjustment errors that are difficult to control or have a significant impact on the image wavefront and their possible maximum values.

[0011] (2) Analysis of the impact of various assembly and adjustment errors on the image wavefront, through simulation analysis step (1).

[0012] The effect of the assembly and adjustment error obtained in the experiment on the wavefront of the image plane of the interferometric system;

[0013] (3) Based on the influence relationship obtained in step (2), determine the subsequent calibration scheme, analyze the influence of each assembly and adjustment error on each Zernike coefficient, and determine the calibration scheme of the assembly and adjustment error based on the magnitude of the influence and the independence or coupling situation. The scheme includes the order of calibration of each assembly and adjustment error and the Zernike coefficient that should be monitored during the calibration of each assembly and adjustment error.

[0014] (4) Set the optimization objective in the ideal virtual interferometer to the image wavefront W of the N sub-apertures obtained by actual interferometry. n The optimization variable is the assembly and adjustment error of each component;

[0015] Based on the assembly and adjustment error calibration scheme determined in step (3), the ideal virtual interferometer is optimized to obtain the virtual interferometer after assembly and adjustment error calibration, which has the same assembly and adjustment error as the actual interferometer system.

[0016] (5) Based on the virtual interferometer obtained in step (4), the surface error is reconstructed by the synchronous reverse optimization reconstruction method to obtain the final measurement result.

[0017] This invention can suppress the backlash error caused by partial compensation in the sub-aperture stitching interferometry, handle situations where the structural parameters and assembly / adjustment errors of multiple sub-aperture measurement systems are different, reduce the impact of assembly / adjustment errors on measurement errors in sub-aperture scanning measurement, improve the overall vibration resistance of sub-aperture stitching measurement, reduce the assembly / adjustment difficulty of the system, and avoid the positioning and calculation errors introduced by complex sub-aperture stitching algorithms. Attached Figure Description

[0018] Figure 1 This is a flowchart of a virtual-real fusion method for multi-system structure optimization and surface error solving according to the present invention.

[0019] Figure 2 This is a diagram of the sub-aperture splicing interference system used in a specific embodiment of the present invention.

[0020] Figure 3 It is the true value of the surface shape error of the measured surface used in a specific embodiment of the present invention.

[0021] Figure 4This is the sub-aperture layout used in a specific embodiment of the present invention.

[0022] Figure 5 It is the surface shape error of the measured surface obtained according to a specific embodiment of the present invention.

[0023] Wherein: 1-light source, 2-linear polarizer, 3-λ / 2 waveplate, 4-collimating lens, 5-polarizing beam splitter, 6-first λ / 4 waveplate, 7-reference mirror, 8-second λ / 4 waveplate, 9-compensation mirror, 10-polarizing grating, 11-third λ / 4 waveplate, 12-mirror under test, 13-fourth λ / 4 waveplate, 14-lens, 15-polarizing camera. Detailed Implementation

[0024] like Figure 1 As shown, this virtual-real fusion method for multi-system structure optimization and surface error solving includes the following steps:

[0025] (1) Determine the types of assembly and adjustment errors that need to be considered in subsequent steps. Based on the structure of the interferometric system and the specific operation in the assembly and adjustment process, determine the assembly and adjustment errors that are difficult to control or have a significant impact on the image wavefront and their possible maximum values.

[0026] (2) Analysis of the impact of various assembly and adjustment errors on the image wavefront, through simulation analysis step (1).

[0027] The effect of the assembly and adjustment error obtained in the experiment on the wavefront of the image plane of the interferometric system;

[0028] (3) Based on the influence relationship obtained in step (2), determine the subsequent calibration scheme, analyze the influence of each assembly and adjustment error on each Zernike coefficient, and determine the calibration scheme of the assembly and adjustment error based on the magnitude of the influence and the independence or coupling situation. The scheme includes the order of calibration of each assembly and adjustment error and the Zernike coefficient that should be monitored during the calibration of each assembly and adjustment error.

[0029] (4) Set the optimization objective in the ideal virtual interferometer to the image wavefront W of the N sub-apertures obtained by actual interferometry. n The optimization variable is the assembly and adjustment error of each component;

[0030] Based on the assembly and adjustment error calibration scheme determined in step (3), the ideal virtual interferometer is optimized to obtain the virtual interferometer after assembly and adjustment error calibration, which has the same assembly and adjustment error as the actual interferometer system.

[0031] (5) Based on the virtual interferometer obtained in step (4), the surface error is reconstructed by the synchronous reverse optimization reconstruction method to obtain the final measurement result.

[0032] This invention can suppress the backlash error caused by partial compensation in the sub-aperture stitching interferometry, handle situations where the structural parameters and assembly / adjustment errors of multiple sub-aperture measurement systems are different, reduce the impact of assembly / adjustment errors on measurement errors in sub-aperture scanning measurement, improve the overall vibration resistance of sub-aperture stitching measurement, reduce the assembly / adjustment difficulty of the system, and avoid the positioning and calculation errors introduced by complex sub-aperture stitching algorithms.

[0033] Preferably, in step (3), two interferometric system models with completely identical structures are established in the ray tracing program according to the structural parameters of the interferometric system; then, the assembly and adjustment errors obtained in step (1) are added to one of them in sequence to obtain a virtual interferometer with assembly and adjustment errors, while the other remains in an ideal state and is defined as an ideal virtual interferometer; the image wavefronts of the two systems are obtained and analyzed to obtain the influence of the assembly and adjustment errors on the image wavefront.

[0034] Preferably, steps (1)-(3) are carried out before the actual measurement, and steps (4)-(5) are carried out after the actual interferometric measurement obtains the image plane wavefront W of N sub-apertures. n Then proceed, n = 1, 2, ... N.

[0035] Preferably, in step (1), the maximum value is an estimate of the visual error during the optical path assembly process. Some systems may use computer-aided assembly, in which case the maximum value here can be the error caused by computer-aided assembly.

[0036] Preferably, in step (2), the difference between the wavefront Zernike coefficients of the actual interferometer and the ideal virtual interferometer is calculated to obtain ΔZ. i To model the effect of errors on the image wavefront, where i still represents the number of Zernike polynomial terms; each error is independently added to the virtual interferometer to obtain the Zernike coefficients of each component assembly error on the image wavefront of each sub-aperture when the measured sphere does not contain surface shape errors. It should be noted that in step (2), the Zernike polynomial is not necessarily used to characterize the effect, that is, the effect of modeling errors is not necessarily represented by Zernike coefficients.

[0037] Preferably, in step (3), only the axial offset of the measured surface has a significant impact on the defocusing of each sub-aperture; the axial offset of the measured surface has a significant impact on the tilting of the off-axis sub-aperture; the eccentricity of the measured surface has a significant impact on the tilting of each sub-aperture; and the various assembly and adjustment errors of the polarization grating have a significant impact on the tilting of each sub-aperture. This refers to the situation in a specific embodiment.

[0038] Preferably, in step (3), the following assembly and adjustment error calibration scheme is formulated for the interference optical path (this refers to the situation in a specific embodiment):

[0039] The defocusing term of each sub-aperture is set as the optimization target, and the axial position of the measured surface is adjusted.

[0040] Optimize the optical path structure obtained in step (1); based on the optical path structure obtained in step (1), set the tilt term of each sub-aperture.

[0041] As the optimization target, the eccentricity and tilt of the measured surface, and the adjustment errors of each component of the polarization grating are addressed.

[0042] Optimize the poor performance.

[0043] Preferably, in step (4), the Zernike polynomial is used to characterize the image wavefront, and the optimization objective in the ideal virtual interferometer is to optimize the image wavefront W. n The Zernike coefficients Z obtained after fitting ni In step (4), the Zernike polynomial is not necessarily used for characterization. There are other methods to represent the image wavefront. The Zernike coefficients are used in this specific embodiment.

[0044] Preferably, in step (5), the surface shape error of the measured surface is characterized using Zernike polynomials. However, in step (5), the surface shape error of the measured surface is not necessarily characterized using Zernike polynomials. This refers to the use of Zernike coefficients in a specific embodiment.

[0045] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0046] Building such Figure 2 The sub-aperture stitched interferometry system shown measures the surface shape error of the mirror under test. It includes a light source 1, a linear polarizer 2, a λ / 2 waveplate 3, a collimating lens 4, a polarizing beam splitter 5, a first λ / 4 waveplate 6, a reference mirror 7, a second λ / 4 waveplate 8, a compensating mirror 9, a polarizing grating 10, a third λ / 4 waveplate 11, the mirror under test 12, a fourth λ / 4 waveplate 13, a lens 14, and a polarizing camera 15. The true value of the surface shape error of the mirror under test is shown below. Figure 3 As shown. The sub-aperture layout is as follows. Figure 4 As shown. After collecting sub-aperture data, the proposed method of this invention is used to perform multi-system structure optimization and surface error solving, with the following steps:

[0047] 1. Determine assembly and adjustment errors: Identify the types of assembly and adjustment errors that need to be considered in subsequent steps.

[0048] Based on the structure of the interferometric system and the specific operations during the assembly and adjustment process, determine the assembly and adjustment errors that are difficult to control or have a significant impact on the image wavefront, and their maximum possible values.

[0049] Most components in the optical path are located in the plane wave path, which is easy to assemble and adjust and has little impact on the image wavefront. Therefore, the analysis focuses on the components in the spherical wave path. In the experiment, the polarization grating and the third λ / 4 waveplate are mounted in the sleeve by a retainer. Therefore, the assembly and adjustment errors of the two are considered together. The effects of the eccentricity and tilt of the measured surface on the interferogram will compensate for each other. In other words, their effects on the image wavefront are similar and will be optimized simultaneously in the subsequent assembly and adjustment error calibration process. Therefore, only the eccentricity error is considered here.

[0050] Based on the optical path structure and assembly process observed in the experiment, the assembly and adjustment errors of the components in the optical path and their possible maximum values ​​are shown in Table 1. The maximum values ​​are all estimated values ​​of visual errors during the optical path assembly and adjustment process.

[0051] Table 1. Assembly and adjustment errors of each component and their maximum possible values.

[0052]

[0053] 2. Analysis of the impact of various assembly and adjustment errors on the image wavefront: The impact of the assembly and adjustment errors obtained in step 1 on the image wavefront of the interferometric system is analyzed through simulation.

[0054] Based on the structural parameters of the interferometric system, two identical interferometric system models are established in the ray tracing program. Then, the assembly and adjustment errors obtained in step 1 are sequentially added to one of them to obtain a virtual interferometer with assembly and adjustment errors, while the other remains in an ideal state, defined as an ideal virtual interferometer. The image wavefronts of the two systems are acquired and analyzed to determine the influence of the assembly and adjustment errors on the image wavefront.

[0055] To quantify the analysis and standardize optimization criteria, the embodiment uses Zernike polynomials to characterize the image wavefront. Specifically, the aforementioned analysis process involves fitting the image wavefronts of the two systems to obtain the Zernike coefficients under the influence of assembly / adjustment errors and under ideal conditions. Subtracting these two values ​​yields the impact of assembly / adjustment errors on the image wavefront, which is quantified in the form of Zernike coefficients.

[0056] By subtracting the Zernik coefficients of the image plane of the actual interferometer from those of the ideal virtual interferometer, we can obtain ΔZ. iTo model the effect of errors on the image wavefront, where i still represents the Zernike polynomial term number, each error in Table 1 is independently added to the virtual interferometer. The effects of assembly and adjustment errors of each component on the Zernike coefficients of each sub-aperture image wavefront are shown in Table 2, assuming the measured sphere has no surface shape errors. Since the same assembly and adjustment error has different effects on the central and off-axis sub-apertures, and the changes introduced by the same Zernike coefficient on the image wavefront of different off-axis apertures are not entirely equal but of the same magnitude, for simplicity, Table 2 lists the magnitude changes of the Zernike coefficients of the image wavefronts of the central and off-axis apertures caused by assembly and adjustment errors, without listing specific numerical values. The magnitudes are expressed as ΔZ for the central and off-axis apertures. i and off-axis △Z i It is indicated that, in addition, the ratios of the Zernike coefficients 5-36 on the image wavefront to those listed in the table are generally less than 1 / 10, and therefore are not listed.

[0057] Table 2. The influence of component assembly and adjustment errors on the Zernike coefficient of the image wavefront and its magnitude (λ).

[0058]

[0059] Note: In the table, "-" indicates that the impact of the assembly error on the coefficient of the Zernike term is 1 / 10 compared to other terms.

[0060] the following

[0061] 3. Determining the calibration scheme for assembly and adjustment errors: Based on the influence relationship obtained in step 2, determine the subsequent calibration scheme.

[0062] The impact of various assembly and adjustment errors on Zernike coefficients is analyzed, and a calibration scheme for these errors is determined based on the magnitude of the impact and whether they are independent or coupled. This scheme includes, but is not limited to, the order of calibration for each assembly and adjustment error, and the Zernike coefficients to be monitored during the calibration of each error.

[0063] From Table 2, we can obtain:

[0064] ①Analysis of the last two columns of defocus terms shows that only the axial offset of the measured surface has a significant impact on the defocus terms of each sub-aperture.

[0065] ② Further analysis of the axial offset of the measured surface reveals that the axial offset of the measured surface also has a significant impact on the tilt term of the axle aperture.

[0066] ③ Analysis of the eccentricity of the measured surface shows that it only has a significant impact on the tilt term of each sub-aperture;

[0067] ④ Analysis of the assembly and adjustment errors of the first four rows of polarization gratings shows that they only significantly affect the tilt term of the off-axis aperture.

[0068] Based on the above conclusions, the following calibration scheme for the assembly and adjustment error of this interference optical path is formulated:

[0069] ① Set the defocus term of each sub-aperture as the optimization target to optimize the axial position of the measured surface;

[0070] ②Based on the optical path structure obtained in step 1, the tilt of each sub-aperture is set as the optimization target to optimize the eccentricity and tilt of the measured surface and the assembly and adjustment errors of the polarization grating.

[0071] 4. Assembly and adjustment error calibration: Based on the calibration scheme determined in step 3, the assembly and adjustment error is calibrated by reverse optimization in the ray tracing program.

[0072] The optimization objective in the ideal virtual interferometer is set as the image wavefront W of the N sub-apertures obtained from the actual interferometry. n The optimization variable is the assembly and adjustment error of each component. Based on the assembly and adjustment error calibration scheme determined in step 3, the ideal virtual interferometer is optimized to obtain a virtual interferometer with calibrated assembly and adjustment errors, that is, a virtual interferometer with the same assembly and adjustment errors as the actual interferometric system.

[0073] As mentioned earlier, to quantify the analysis and unify the optimization criteria, the embodiment uses Zernike polynomials to characterize the image plane wavefront. Therefore, the optimization objective in the ideal virtual interferometer in the embodiment is the image plane wavefront W. n The Zernike coefficients Z obtained after fitting ni .

[0074] 5. Surface shape error reconstruction: Based on the virtual interferometer obtained in step 4, the surface shape error is reconstructed through a synchronous inverse optimization reconstruction method to obtain the final measurement result.

[0075] Similarly, to quantify the analysis and unify the optimization standards, this paper also uses Zernike polynomials to characterize the surface shape error of the measured surface. The obtained surface shape error of the measured surface is as follows: Figure 5 As shown. It can be seen that it is related to... Figure 3 The true values ​​of the surface shape errors shown are consistent, and the difference in PV is only 0.0889λ, while the difference in RMS is only 0.0027λ.

[0076] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A virtual-real fusion method for multi-system structure optimization and surface error solving, characterized in that: It includes the following steps: (1) Determine the types of assembly and adjustment errors that need to be considered in subsequent steps. Based on the structure of the interferometric system and the specific operation in the assembly and adjustment process, determine the assembly and adjustment errors that are difficult to control or have a significant impact on the image wavefront and their possible maximum values. (2) Analysis of the influence of each assembly and adjustment error on the image wavefront: The influence of the assembly and adjustment error obtained in step (1) on the image wavefront of the interferometric system is analyzed by simulation. (3) Based on the influence relationship obtained in step (2), determine the subsequent calibration scheme, analyze the influence of each assembly and adjustment error on each Zernike coefficient, and determine the calibration scheme of the assembly and adjustment error based on the magnitude of the influence and the independence or coupling situation. The scheme includes the order of calibration of each assembly and adjustment error and the Zernike coefficient that should be monitored during the calibration of each assembly and adjustment error. (4) Set the optimization objective in the ideal virtual interferometer to the image wavefront W of the N sub-apertures obtained by actual interferometry. n The optimization variable is the assembly and adjustment error of each component; according to the assembly and adjustment error calibration scheme determined in step (3), the ideal virtual interferometer is optimized to obtain the virtual interferometer after assembly and adjustment error calibration, which has the same assembly and adjustment error as the actual interferometer system; (5) Based on the virtual interferometer obtained in step (4), the surface error is reconstructed by the synchronous reverse optimization reconstruction method to obtain the final measurement result.

2. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 1, characterized in that: In step (3), based on the structural parameters of the interferometric system, two interferometric system models with completely identical structures are established in the ray tracing program; then, the assembly and adjustment errors obtained in step (1) are added to one of them in sequence to obtain a virtual interferometer with assembly and adjustment errors, while the other remains in an ideal state and is defined as an ideal virtual interferometer; the image wavefronts of the two systems are obtained and analyzed to obtain the influence of assembly and adjustment errors on the image wavefront.

3. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 1, characterized in that: Steps (1)-(3) are carried out before the actual measurement, and steps (4)-(5) are carried out after the image wavefronts of N sub-apertures are obtained by the actual interferometric measurement. W n Then proceed, n = 1, 2, ... N.

4. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 3, characterized in that: In step (1), the maximum value is the estimated value of visual error during the optical path assembly process.

5. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 4, characterized in that: In step (2), the difference between the wavefront Zernike coefficients of the actual interferometer and the ideal virtual interferometer is calculated to obtain ΔZ. i To model the effect of errors on the image plane wavefront, where i still represents the Zernike polynomial term number; each error is added independently to the virtual interferometer in turn to obtain the Zernike coefficients of each component assembly error on the image plane wavefront of each sub-aperture when the measured sphere does not contain surface shape errors.

6. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 5, characterized in that: In step (3), only the axial offset of the measured surface has a significant impact on the defocusing term of each sub-aperture; the axial offset of the measured surface has a significant impact on the tilting term of the off-axis sub-aperture; the eccentricity of the measured surface has a significant impact on the tilting term of each sub-aperture; and the various assembly and adjustment errors of the polarization grating have a significant impact on the tilting term of each sub-aperture.

7. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 6, characterized in that: In step (3), the following assembly and adjustment error calibration scheme is formulated for the interference optical path: The defocusing term of each sub-aperture is set as the optimization target, and the axial position of the measured surface is adjusted. Optimize the optical path structure obtained in step (1); based on the optical path structure obtained in step (1), set the tilt term of each sub-aperture. As the optimization target, the eccentricity and tilt of the measured surface, and the adjustment errors of each component of the polarization grating are addressed. Optimize the poor performance.

8. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 7, characterized in that: In step (4), the Zernike polynomial is used to characterize the image wavefront, and the optimization objective in the ideal virtual interferometer is to optimize the image wavefront W. n The Zernike coefficients Z obtained after fitting ni .

9. The virtual-real fusion method for multi-system structure optimization and surface error solving according to claim 8, characterized in that: In step (5), the surface shape error of the measured surface is characterized by Zernike polynomials.

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