Synchronous Detection Method for Low and Medium Frequency Errors Based on Sub-Aperture Stitching and CGH Compensation

Abstract

The present invention relates to the field of surface shape detection, and particularly to a synchronous detection method for low and medium frequency errors based on sub-aperture stitching and CGH compensation. A full-aperture CGH compensator is designed, and the surface to be inspected of the aspheric-cylindrical element is subjected to full-aperture detection according to the full-aperture CGH compensator to obtain a full-aperture detection result; sub-aperture planning is carried out according to the surface shape of the surface to be inspected of the aspheric-cylindrical element, and a sub-aperture CGH compensator corresponding to each sub-aperture is designed, and sub-aperture stitching detection is carried out on the surface to be inspected of the aspheric-cylindrical element according to each sub-aperture CGH compensator to obtain a stitching detection result; wherein, a hierarchical smoothing optimization algorithm is used to perform phase smoothing processing on the overlapping area between two adjacent sub-apertures; the positions of each sub-aperture are calibrated by using the low-frequency information in the full-aperture detection result, and the displacement errors of each sub-aperture are corrected. The present invention can realize synchronous high-precision synchronous detection of low and medium frequency errors of aspheric-cylindrical elements.

Description

Technical Field

[0001] The present invention belongs to the technical field of surface shape detection, and particularly relates to a synchronous detection method for low and medium frequency errors based on sub-aperture stitching and CGH compensation. Background Art

[0002] In recent years, China has promoted the development of high-energy laser equipment in multiple application fields such as sea, land, air, and space, and various types of high-energy laser systems have been gradually developed and improved. High-energy laser systems have extremely high requirements for the accuracy and quality of beam shaping. Among them, the cylindrical system, as the core component of the beam shaping system, directly affects the transmission effect of the laser beam and the overall performance of the system.

[0003] Among various cylindrical systems, the reflective aspherical cylindrical system has significant advantages compared with the transmissive aspherical cylindrical system. First of all, the reflective aspherical cylindrical system does not rely on imported high-end optical materials such as quartz and has an independent and controllable material supply chain. Secondly, the reflective aspherical cylindrical system can withstand higher laser loads under high-energy laser conditions, ensuring the stability and durability of the system. In addition, the reflective aspherical cylindrical system performs better in terms of beam quality, can effectively reduce optical distortion and optimize the uniformity and distribution characteristics of the beam, so as to meet the requirements of precision applications.

[0004] High-precision cylindrical elements are the core of the cylindrical system, and the core challenges of corresponding high-energy laser aspherical cylindrical elements lie in the structural requirements of large aperture, high steepness, and asphericity. These characteristics increase the difficulty of manufacturing and detection. At present, there are technical bottlenecks in the manufacturing and control of the nano-scale medium frequency error in China. One of the important reasons is the lack of high-precision detection means for the medium frequency error.

[0005] As an effective optical detection technology, the computer-generated hologram (CGH) detection method can theoretically realize the detection of optical elements with arbitrary surface shapes. However, when applied to the detection of high-steepness aspherical cylindrical elements, several key problems still exist. When the surface of the aspherical cylindrical element is a convex cylinder, the effective area of the CGH full-aperture compensation detection is limited, and it is impossible to complete the detection in a one-time full-aperture compensation. It is necessary to cover the entire surface through stitching measurement; when the surface of the aspherical cylindrical element is a concave cylinder, due to the characteristics of large aperture, high steepness, and large deviation amount of the aspherical cylindrical element, it will lead to too high line frequency density of the CGH, increasing the manufacturing difficulty and measurement error. Moreover, the CGH compensation detection will introduce non-rotationally symmetric and complex two-dimensional projection distortion, which limits the detection accuracy and cannot provide accurate feedback on the processing link. Therefore, correcting the projection distortion is a necessary step to achieve high-precision detection.

[0006] In addition, when the aspheric cylindrical element is subjected to full-aperture detection, it is restricted by the resolution of the interferometer, reducing the cycle resolution range, directly affecting the detection of intermediate-frequency errors, and further affecting the accurate analysis and control of the overall surface shape error. Summary of the Invention

[0007] In view of this, the present invention aims to provide a synchronous detection method for low and intermediate frequency errors based on sub-aperture stitching and CGH compensation to solve the technical problem that the prior art cannot simultaneously ensure the detection accuracy and detection efficiency of aspheric cylindrical elements.

[0008] To achieve the above object, the technical solution of the present invention is realized as follows:

[0009] A synchronous detection method for low and intermediate frequency errors based on sub-aperture stitching and CGH compensation includes the following steps:

[0010] S1: According to the surface shape of the surface to be inspected of the aspheric cylindrical element, a full-aperture CGH compensator for full-aperture compensation is designed by using the ray tracing method, and a detection optical path is built according to the full-aperture CGH compensator and the interferometer to perform full-aperture detection on the surface to be inspected of the aspheric cylindrical element to obtain a full-aperture detection result;

[0011] S2: Sub-aperture planning is performed according to the surface shape of the surface to be inspected of the aspheric cylindrical element, and a sub-aperture CGH compensator corresponding to each sub-aperture is designed. Each sub-aperture CGH compensator is placed in the detection optical path to replace the full-aperture CGH compensator to perform sub-aperture stitching detection on the surface to be inspected of the aspheric cylindrical element to obtain a stitching detection result. Among them, in the process of designing the sub-aperture CGH compensator corresponding to each sub-aperture, first, the initial phase function of the corresponding sub-aperture CGH compensator is calculated for each sub-aperture by using the ray tracing method, and then the phase smoothing process is performed on the overlapping region between two adjacent sub-apertures by using the hierarchical smoothing optimization algorithm;

[0012] S3: The full-aperture detection result and the stitching detection result are compared and analyzed, and the positions of each sub-aperture are calibrated by using the low-frequency information in the full-aperture detection result, and the displacement errors of each sub-aperture are corrected.

[0013] Further, the initial phase function of the sub-aperture CGH compensator is the complex optical field distribution when the wavefront propagates to the plane of the sub-aperture CGH compensator :

[0014] ;

[0015] Among them, , e represents the phase factor, i represents the complex number, represents the phase distribution function.

[0016] Further, in the process of designing different sub-aperture CGH compensators, the process of using the hierarchical smoothing optimization algorithm to perform phase smoothing on the overlapping region between two adjacent sub-apertures is as follows:

[0017] In the region with a sharp curvature change on the surface to be inspected of the aspheric cylindrical element, high-order polynomial interpolation is used to smoothly transition the phase difference, while in the region with a flat curvature change on the surface to be inspected of the aspheric cylindrical element, linear smoothing is used to smoothly transition the phase difference.

[0018] Further, the specific process of using high-order polynomial interpolation to smoothly transition the phase difference is as follows:

[0019] First, more than n + 1 sampling points are selected in the overlapping region, and the coordinates and phase values of each sampling point are recorded; where n represents the order.

[0020] Secondly, an interpolation polynomial is constructed ; where and represent the variables of two-dimensional interpolation, represents the coefficient solved by the least squares method, represents the two-dimensional interpolation polynomial function, which represents the predicted value of the phase difference at any point (x, y).

[0021] Further, the formula for linear smoothing is:

[0022] ;

[0023] where, where represents the phase distribution function after smoothing, w1 and w2 represent the weight coefficients, represents the phase distribution of the first sub-aperture region in the overlapping region, represents the phase distribution of the second sub-aperture region in the overlapping region.

[0024] Further, in the process of performing sub-aperture stitching detection on the surface to be inspected of the aspheric cylindrical element, first, an affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is constructed to map the coordinates of each detection point on the interferometer CCD to the corresponding position on the sub-aperture CGH compensator plane; secondly, a non-linear mapping relationship between the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator is constructed to convert the detection points on the sub-aperture CGH compensator plane to the corresponding positions on the surface to be inspected of the aspheric cylindrical element.

[0025] Further, the process of constructing the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is as follows: Feature points are arranged on the surface to be inspected of the aspheric cylindrical element, and the affine transformation parameters between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system are solved according to the feature points. and , based on the affine transformation parameters and the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is constructed;

[0026] ;

[0027] ;

[0028] wherein, represents the correction coefficient for correcting the scale difference between the two coordinate systems, represents the abscissa of the detection point on the interferometer CCD, represents the ordinate of the detection point on the interferometer CCD, represents the abscissa of the reference point selected in the interferometer CCD coordinate system, represents the ordinate of the reference point selected in the interferometer CCD coordinate system, represents the angle of the reference point in the polar coordinate system, represents the relative rotation angle between the interferometer CCD and the sub-aperture CGH compensator, represents the abscissa of the corresponding reference point in the sub-aperture CGH compensator coordinate system, represents the ordinate of the corresponding reference point in the sub-aperture CGH compensator coordinate system.

[0029] Further, the process of constructing the non-linear mapping relationship between the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator is as follows: The intersection point between a certain normal ray of the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator is calculated, and the non-linear mapping relationship between the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator is constructed;

[0030] wherein, the intersection point coordinates are:

[0031] ;

[0032] ;

[0033] ;

[0034] wherein, represents the working distance of the detection optical path, Represents the coordinate value of the detection point on the surface to be inspected of the aspheric cylindrical element in the x direction. Represents the coordinate value of the detection point on the surface to be inspected of the aspheric cylindrical element in the y direction. Represents the coordinate value of the detection point on the surface to be inspected of the aspheric cylindrical element in the z direction. Represents the surface shape error of the surface to be inspected of the aspheric cylindrical element. Represents the aperture size of the surface to be inspected of the aspheric cylindrical element. Represents the angle between the plane normal of the sub-aperture CGH compensator and the optical axis.

[0035] Furthermore, during the process of performing sub-aperture stitching detection on the surface to be inspected of the aspheric cylindrical element, a weighted average algorithm is used to optimize the stitching traces during sub-aperture stitching. The optimization formula is as follows:

[0036] ;

[0037] Wherein, O1 and O2 are the center points of two adjacent sub-apertures respectively, P is a point within the overlapping area of the two sub-apertures. Is the phase value of point P. And Correspond to the detection results of the two sub-apertures at point P respectively. X P 、 、 Correspond to the vectors represented by point P, point O1, and point O2 respectively.

[0038] Furthermore, during the process of calibrating the positions of each sub-aperture and correcting the displacement errors of each sub-aperture by using the low-frequency information in the full-aperture detection results, first, based on the full-aperture detection results, the overall surface shape low-frequency error distribution E(x, y) of the surface to be inspected is obtained, and the stitching detection result e i (x, y) is subjected to low-pass filtering to extract the low-frequency error component L i (x, y). Secondly, a least squares objective function i Is constructed through the low-frequency error component L , and the position offset amounts (Δx i , Δy i ) of each sub-aperture are iteratively optimized and solved to achieve the position calibration of each sub-aperture; then, an overlapping area phase difference evaluation function ; wherein, Represents the phase distribution in the overlapping area of the i-th sub-aperture region, Represents the phase distribution in the overlapping area of the j-th sub-aperture region. A small adjustment amount δx and δy are introduced and the phase difference evaluation function Minimization is performed to determine the final position correction amount of each sub-aperture, and each sub-aperture performs position correction according to its respective final position correction amount; among them, the minimization formula is: , represents the small position adjustment amount in the x direction, represents the small position adjustment amount in the y direction.

[0039] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0040] 1. The present invention divides the aspheric cylindrical element into sub-apertures, designs multiple different sub-aperture CGH compensators for hybrid splicing detection, and solves the problems of limited detection range and low accuracy in the traditional CGH full-aperture compensation.

[0041] 2. The present invention uses a hierarchical smoothing optimization algorithm to perform phase smoothing processing on the overlapping regions between sub-apertures, effectively solving the subsequent phase mismatch problem.

[0042] 3. The present invention uses a weighted average algorithm to optimize the splicing traces during sub-aperture splicing, further improving the detection accuracy.

[0043] 4. The present invention solves its distortion mapping function through ray tracing, and uses the mirror feature points to achieve high-precision alignment between the distortion correction result and the mirror, completing high-precision correction of projection distortion.

[0044] 5. Utilize the low-frequency information in the full-aperture detection result to accurately calibrate the positions between sub-apertures, correct displacement errors, better align and splice each sub-aperture, ensure the detection accuracy of the hybrid compensation in the present invention, and effectively improve the spatial period resolution range, break through the resolution limit of the interferometer, and achieve synchronous detection with low and medium frequency error nanometer accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0046] Figure 1 is a schematic flow chart of a low and medium frequency error synchronous detection method based on sub-aperture splicing and CGH compensation according to an embodiment of the present invention;

[0047] Figure 2 is a schematic structural diagram of a detection optical path built according to an embodiment of the present invention;

[0048] Figure 3 is a schematic sub-aperture planning diagram according to an embodiment of the present invention;

[0049] Figure 4 It is a schematic diagram of hierarchical smoothing optimization of the overlapping area of sub-apertures according to the embodiments of the present invention

[0050] Figure 5 It is a schematic diagram of splicing trace optimization during sub-aperture splicing according to the embodiments of the present invention

[0051] Figure 6 It is a schematic diagram of low-frequency error correction according to the embodiments of the present invention

[0052] Explanation of reference numerals: full-aperture CGH compensator 1, interferometer 2, aspheric cylindrical element 3 Detailed implementation manners

[0053] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation to the present invention

[0054] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other

[0055] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "plurality" is two or more

[0056] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations

[0057] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0058] As Figure 1 shown, the low-medium frequency error synchronous detection method based on sub-aperture stitching and CGH compensation provided by the embodiment of the present invention includes the following steps:

[0059] S1: According to the surface shape of the surface to be inspected of the aspheric cylindrical element, a full-aperture CGH compensator for full-aperture compensation is designed by means of ray tracing, and a detection optical path is built according to the full-aperture CGH compensator and the interferometer to perform full-aperture detection on the surface to be inspected of the aspheric cylindrical element, and a full-aperture detection result is obtained.

[0060] The design of the full-aperture CGH compensator belongs to the prior art, so it will not be elaborated here.

[0061] The built detection optical path is as Figure 2 shown. The full-aperture CGH compensator 1 is arranged between the interferometer 2 and the aspheric cylindrical element 3. The surface to be inspected of the aspheric cylindrical element 3 can be a concave cylindrical or convex cylindrical surface.

[0062] S2: Sub-aperture planning is carried out according to the surface shape of the surface to be inspected of the aspheric cylindrical element, and a sub-aperture CGH compensator corresponding to each sub-aperture is designed, and each sub-aperture CGH compensator is placed in the detection optical path to replace the full-aperture CGH compensator, and sub-aperture stitching detection is carried out on the surface to be inspected of the aspheric cylindrical element, and a stitching detection result is obtained.

[0063] The present invention carries out sub-aperture planning on the surface to be inspected of the aspheric cylindrical element based on the principle of sub-aperture planning covering the full aperture according to the surface shape of the surface to be inspected of the aspheric cylindrical element, and it is necessary to ensure that the overlapping area between two adjacent sub-apertures is greater than 1 / 4 of the sub-aperture area. The sub-aperture planning result is as Figure 3 shown.

[0064] For each sub-aperture, a corresponding sub-aperture CGH compensator is designed. When designing the sub-aperture CGH compensator, in order to solve the problem of phase step caused by regional differences in the surface parameters of the aspheric cylindrical element during subsequent sub-aperture stitching, the present invention adopts a hierarchical smoothing optimization algorithm to perform phase smoothing processing on the overlapping area between two adjacent sub-apertures to avoid the problem of phase mismatch during subsequent sub-aperture stitching.

[0065] The process of designing the sub-aperture CGH compensator is as follows:

[0066] First, for each sub-aperture, the initial phase function of the corresponding sub-aperture CGH compensator is calculated by means of ray tracing.

[0067] The initial phase function of the sub-aperture CGH compensator is the complex optical field distribution when the wavefront propagates to the plane of the sub-aperture CGH compensator. :

[0068] ;

[0069] Among them, , e represents the phase factor, i represents the complex number, represents the phase distribution function.

[0070] Then, the hierarchical smoothing optimization algorithm is used to perform phase smoothing on the overlapping region between two adjacent sub-apertures.

[0071] The principle of using the hierarchical smoothing optimization algorithm to perform phase smoothing on the overlapping region between sub-apertures is based on the curvature change of different regions of the surface to be inspected of the aspheric cylindrical element, and the interpolation order is flexibly selected to achieve high-precision phase smoothing of the overlapping region, as Figure 4 shown. Specifically, in the region with a drastic curvature change of the surface to be inspected of the aspheric cylindrical element, high-order polynomial interpolation is used to smooth the phase difference, while in the region with a flat curvature change of the surface to be inspected of the aspheric cylindrical element, linear smoothing is used to reduce the computational complexity.

[0072] The specific process of using high-order polynomial interpolation to smooth the phase difference is as follows:

[0073] First, more than n + 1 sampling points are selected in the overlapping region, and the coordinates and phase values of each sampling point are recorded; among them, n represents the order;

[0074] Secondly, an interpolation polynomial is constructed; among them, and represent the variables of two-dimensional interpolation, represents the coefficient solved by the least squares method, represents the two-dimensional interpolation polynomial function, representing the predicted value of the phase difference at any point (x, y).

[0075] The formula used for linear smoothing to smooth the phase difference is:

[0076] ;

[0077] Among them, represents the phase distribution function after smoothing, w1 and w2 represent the weight coefficients, w1 and w2 are determined according to the distance ratio of the sampling point to the center of each sub-aperture, represents the phase distribution of the first sub-aperture region in the overlapping region, represents the phase distribution of the second sub-aperture region in the overlapping region.

[0078] The hierarchical smoothing optimization algorithm can adapt to the topography of different regions of the surface to be inspected of aspheric cylindrical elements, ensure calculation accuracy and efficiency, and reduce the problem of error accumulation.

[0079] Due to the different curvatures of points on the surface to be inspected of aspheric cylindrical elements and the influence of interferometer errors, projection distortion will occur during the sub-aperture stitching inspection of aspheric cylindrical elements. To correct the projection distortion, first, an affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is constructed to map the coordinates of each detection point on the interferometer CCD to the corresponding position on the sub-aperture CGH compensator plane; second, a non-linear mapping relationship between the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator is constructed to convert the detection points on the sub-aperture CGH compensator plane to the corresponding positions on the surface to be inspected of the aspheric cylindrical element. This step-by-step transformation from the interferometer CCD to the sub-aperture CGH compensator and then to the inspection surface realizes high-precision correction of the projection distortion.

[0080] By calculating the relationship between the CGH compensator and the surface to be inspected of the aspheric cylindrical element, solving the two-dimensional non-linear mapping relationship (Mirror-CGH) between the surface to be inspected of the aspheric cylindrical element and the CGH compensator, arranging feature points on the surface to be inspected of the aspheric cylindrical element, solving the affine transformation parameters (CCD-CGH) between the interferometer CCD coordinate system and the CGH compensator coordinate system based on the feature points, and constructing a two-dimensional projection distortion mapping function of the detection result and the surface to be inspected of the aspheric cylindrical element based on the two-dimensional non-linear mapping relationship and the affine transformation parameters, the projection distortion is corrected.

[0081] The process of constructing the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is as follows: arranging feature points on the surface to be inspected of the aspheric cylindrical element, and solving the affine transformation parameters between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system and , based on the affine transformation parameters and constructing the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system;

[0082] ;

[0083] ;

[0084] where represents the correction coefficient for correcting the scale difference between the two coordinate systems, represents the abscissa of the detection point on the interferometer CCD, represents the ordinate of the detection point on the interferometer CCD, represents the abscissa of the reference point selected in the interferometer CCD coordinate system, represents the ordinate of the reference point selected in the interferometer CCD coordinate system, represents the angle of the reference point in the polar coordinate system, represents the relative rotation angle between the interferometer CCD and the sub-aperture CGH compensator, represents the abscissa of the corresponding reference point in the sub-aperture CGH compensator coordinate system, represents the ordinate of the corresponding reference point in the sub-aperture CGH compensator coordinate system.

[0085] The process of constructing the non-linear mapping relationship between the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator is as follows: calculate the intersection point between a certain normal ray of the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator, and construct the non-linear mapping relationship between the surface to be inspected of the aspheric cylindrical element and the sub-aperture CGH compensator;

[0086] Among them, the intersection point coordinates are:

[0087] ;

[0088] ;

[0089] ;

[0090] Among them, represents the working distance of the detection optical path, represents the coordinate value of the detection point on the surface to be inspected of the aspheric cylindrical element in the x direction, represents the coordinate value of the detection point on the surface to be inspected of the aspheric cylindrical element in the y direction, represents the coordinate value of the detection point on the surface to be inspected of the aspheric cylindrical element in the z direction, represents the surface shape error of the surface to be inspected of the aspheric cylindrical element, represents the aperture size of the surface to be inspected of the aspheric cylindrical element, represents the angle between the plane normal of the sub-aperture CGH compensator and the optical axis.

[0091] During the sub-aperture stitching detection of the surface to be inspected of the aspheric cylindrical element, the weighted average algorithm is used to optimize the stitching traces during sub-aperture stitching to further improve the detection accuracy. As Figure 5 shown, the formula for optimization is as follows:

[0092] ;

[0093] Wherein, O1 and O2 are respectively the center points of two adjacent sub-apertures, and P is a point within the overlapping area of the two sub-apertures. is the phase value of point P. and respectively correspond to the detection results of the two sub-apertures at point P. X P 、 、 respectively correspond to the vectors represented by point P, point O1, and point O2.

[0094] S3: Compare and analyze the full-aperture detection result with the stitching detection result, and use the low-frequency information in the full-aperture detection result to calibrate the positions between the sub-apertures and correct the displacement errors between the sub-apertures.

[0095] In the process of using the low-frequency information in the full-aperture detection result to calibrate the positions of the sub-apertures and correct the displacement errors of the sub-apertures, first, based on the full-aperture detection result, obtain the overall surface shape low-frequency error distribution E(x, y) of the surface to be inspected, and perform low-pass filtering on the stitching detection result ei(x, y) to extract the low-frequency error component Li(x, y). Secondly, construct a least-squares objective function , and iteratively optimize and solve the position offset (Δxi, Δyi) of each sub-aperture to achieve the position calibration of each sub-aperture; then, establish an overlapping area phase difference evaluation function ; wherein, represents the phase distribution of the i-th sub-aperture area in the overlapping area, represents the phase distribution of the j-th sub-aperture area in the overlapping area. Introduce small adjustment amounts δx and δy and minimize the phase difference evaluation function to determine the final position correction amount of each sub-aperture, and each sub-aperture corrects its position according to its respective final position correction amount; wherein, the minimization formula is: , represents the small position adjustment amount in the x direction, represents the small position adjustment amount in the y direction. According to and correct the positions of the sub-apertures, as shown in Figure 6 .

[0096] Using the low-frequency information in the full-aperture detection results, accurately calibrate the positions between each sub-aperture, correct the displacement error, better align and splice each sub-aperture, ensure the detection accuracy of the hybrid compensation in the present invention, effectively improve the spatial period resolution range, break through the limitations of the interferometer, and realize the synchronous detection of low- and medium-frequency error with nanometer accuracy. Taking a 300-mm-aperture aspheric cylindrical element as an example, under the resolution limit of 1k×1k of the interferometer for the CGH full-aperture compensation detection, the minimum resolvable value of the spatial period frequency band is about 0.3 mm. While using the CGH sub-aperture stitching compensation detection, taking the 100-mm sub-aperture area as an example, the resolvable range of the measured spatial period frequency band is less than 0.1 mm.

[0097] It should be understood that various forms of the processes shown above can be used, steps can be reordered, added or deleted. For example, the steps recited in the disclosure of the present invention can be executed in parallel, sequentially or in a different order, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and no limitation is made herein.

[0098] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation, characterized in that: The steps include: S1: According to the surface shape of the to-be-tested surface of the non-spherical cylindrical component, a full-aperture CGH compensator for full-aperture compensation is designed by ray tracing, and a detection optical path is built based on the full-aperture CGH compensator and the interferometer to perform full-aperture detection on the to-be-tested surface of the non-spherical cylindrical component to obtain a full-aperture detection result; S2: Perform sub-aperture planning according to the surface shape of the to-be-tested surface of the non-spherical cylindrical element, design a sub-aperture CGH compensator corresponding to each sub-aperture, place each sub-aperture CGH compensator in the detection optical path to replace the full-aperture CGH compensator, perform sub-aperture splicing detection on the to-be-tested surface of the non-spherical cylindrical element, and obtain a splicing detection result; wherein, in the process of designing the sub-aperture CGH compensator corresponding to each sub-aperture, firstly, calculate the initial phase function of the corresponding sub-aperture CGH compensator for each sub-aperture by using a ray tracing method, and then use a hierarchical smoothing optimization algorithm to perform phase smoothing processing on the overlapping area between two adjacent sub-apertures; S3: Compare and analyze the full-aperture detection result with the splicing detection result, use the low-frequency information in the full-aperture detection result to calibrate the position of each sub-aperture, and correct the displacement error of each sub-aperture.

2. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 1 is characterized in that: The initial phase function of the sub-aperture CGH compensator is the complex light field distribution when the wavefront propagates to the sub-aperture CGH compensator plane. : ； in, , e represents the phase factor, i represents the complex number, represents the phase distribution function.

3. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 1 is characterized in that: When designing CGH compensators with different sub-apertures, the process of phase smoothing the overlapping area between two adjacent sub-apertures using a hierarchical smoothing optimization algorithm is as follows: In the area where the curvature of the test surface of the non-spherical cylindrical element changes dramatically, a high-order polynomial interpolation process is used to smooth the transition phase difference, while in the area where the curvature of the test surface of the non-spherical cylindrical element changes flatly, a linear smoothing process is used to smooth the transition phase difference.

4. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 3 is characterized in that: The specific process of using high-order polynomial interpolation to smooth the transition phase difference is: First, more than n+1 sampling points are selected in the overlapping area, and the coordinates and phase values ​​of each sampling point are recorded; where n represents the order; Second, construct the interpolation polynomial ;in, and Variables representing two-dimensional interpolation, represents the coefficients of least square method, Represents a two-dimensional interpolating polynomial function, representing the predicted value of the phase difference at any point (x, y).

5. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 3 is characterized in that: The formula for linear smoothing is: ； in, represents the phase distribution function after smoothing, w1 and w2 represent weight coefficients, represents the phase distribution of the first sub-aperture region in the overlapping area, Represents the phase distribution of the second sub-aperture region in the overlapping area.

6. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 3 is characterized in that: In the process of sub-aperture stitching detection of the surface to be inspected of the non-spherical cylindrical element, firstly, the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is constructed, and the coordinates of each detection point on the interferometer CCD are mapped to the corresponding position on the sub-aperture CGH compensator plane; secondly, the nonlinear mapping relationship between the surface to be inspected of the non-spherical cylindrical element and the sub-aperture CGH compensator is constructed, and the detection points on the sub-aperture CGH compensator plane are converted to the corresponding positions on the surface to be inspected of the non-spherical cylindrical element.

7. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 6, characterized in that: The process of constructing the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system is as follows: feature points are arranged on the test surface of the non-spherical cylindrical element, and the affine transformation parameters between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system are solved according to the feature points. and , based on the affine transformation parameters and Construct the affine transformation relationship between the interferometer CCD coordinate system and the sub-aperture CGH compensator coordinate system; ； ； in, represents the correction factor to correct the scale difference between the two coordinate systems, represents the horizontal coordinate of the detection point on the interferometer CCD, represents the ordinate of the detection point on the interferometer CCD, represents the horizontal coordinate of the reference point selected in the interferometer CCD coordinate system, represents the ordinate of the reference point selected in the interferometer CCD coordinate system, Represents the angle of the reference point in the polar coordinate system, represents the relative rotation angle between the interferometer CCD and the subaperture CGH compensator, represents the abscissa of the corresponding reference point in the subaperture CGH compensator coordinate system, Represents the ordinate of the corresponding reference point in the sub-aperture CGH compensator coordinate system.

8. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 6, characterized in that: The process of constructing the nonlinear mapping relationship between the surface to be inspected of the non-spherical cylindrical element and the sub-aperture CGH compensator is as follows: calculating the intersection point between a normal ray of the surface to be inspected of the non-spherical cylindrical element and the sub-aperture CGH compensator, and constructing the nonlinear mapping relationship between the surface to be inspected of the non-spherical cylindrical element and the sub-aperture CGH compensator; The intersection coordinates for: ； ； ； in, Indicates the working distance of the detection light path. It represents the coordinate value of the detection point on the surface to be detected of the non-spherical cylindrical element in the x direction, It represents the coordinate value of the detection point on the surface to be detected of the non-spherical cylindrical element in the y direction, It represents the coordinate value of the detection point on the surface to be detected of the non-spherical cylindrical element in the z direction, Indicates the surface error of the non-spherical cylindrical element to be tested. Indicates the aperture size of the surface to be inspected of the non-spherical cylindrical element, represents the angle between the plane normal of the subaperture CGH compensator and the optical axis.

9. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 1, characterized in that: In the process of sub-aperture splicing inspection of the surface to be inspected of the non-spherical cylindrical element, the weighted average algorithm is used to optimize the splicing traces during sub-aperture splicing. The optimization formula is as follows: ； Among them, O1 and O2 are the center points of two adjacent sub-apertures, and P is a point in the overlapping area of ​​the two sub-apertures. is the phase value of point P, and They correspond to the detection results of the two sub-apertures at point P, X P , , They correspond to the vectors represented by point P, point O1, and point O2 respectively.

10. The low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to claim 1, characterized in that: In the process of using the low-frequency information in the full-aperture detection results to calibrate the position of each sub-aperture and correct the displacement error of each sub-aperture, firstly, the overall low-frequency error distribution E(x, y) of the surface to be tested is obtained based on the full-aperture detection results, and the splicing detection results e i (x, y) is low-pass filtered to extract the low-frequency error component L i (x, y), and secondly, through the low-frequency error component L i (x,y) constructs the least squares objective function , and iteratively optimize the position offset of each sub-aperture (Δx i ,Δy i ) realizes the position calibration of each sub-aperture; then, establishes the phase difference evaluation function of the overlapping area ;in, represents the phase distribution of the i-th sub-aperture region in the overlapping area, represents the phase distribution of the jth sub-aperture area in the overlapping area, introduces small position adjustments δx and δy in the x- and y-directions, and evaluates the phase difference function Minimization processing is performed to determine the final position correction amount of each sub-aperture, and each sub-aperture is corrected according to its final position correction amount; wherein the minimization formula is: , represents a small position adjustment in the x direction, Indicates a small position adjustment in the y direction.

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