Low-intermediate frequency error synchronous detection method based on sub-aperture splicing and CGH compensation

Abstract

The invention relates to the field of surface shape detection, in particular to a low-intermediate frequency error synchronous detection method based on sub-aperture splicing and CGH compensation, and the method comprises the steps: designing a full-aperture CGH compensator, carrying out the full-aperture detection of a to-be-detected surface of an aspheric cylindrical surface element according to the full-aperture CGH compensator, and obtaining a full-aperture detection result; sub-aperture planning is carried out according to the surface shape of the to-be-detected surface of the aspheric cylindrical surface element, a sub-aperture CGH compensator corresponding to each sub-aperture is designed, sub-aperture splicing detection is carried out on the to-be-detected surface of the aspheric cylindrical surface element according to each sub-aperture CGH compensator, and a splicing detection result is obtained; wherein phase smoothing processing is carried out on an overlapping region between two adjacent sub-apertures by adopting a layered smoothing optimization algorithm; and calibrating the position of each sub-aperture and correcting the displacement error of each sub-aperture by using low-frequency information in a full-aperture detection result. According to the invention, synchronous high-precision synchronous detection of low-intermediate frequency errors of the aspheric cylindrical surface element can be realized.

Description

Technical Field

[0001] The invention belongs to the technical field of surface shape detection, and in particular relates to a low intermediate frequency error synchronous detection method based on sub-aperture splicing and CGH compensation. Background Art

[0002] In recent years, my country 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 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 all types of cylindrical systems, reflective aspheric cylindrical systems have significant advantages over transmissive aspheric cylindrical systems. First, reflective aspheric cylindrical systems do not rely on imported high-end optical materials such as quartz and have an independent and controllable material supply chain. Secondly, reflective aspheric cylindrical systems can withstand higher laser loads under high-energy laser conditions to ensure the stability and durability of the system. In addition, reflective aspheric cylindrical systems perform better in terms of beam quality, can effectively reduce optical distortion and optimize the uniformity and distribution characteristics of the beam, thereby meeting the needs of precision applications.

[0004] High-precision cylindrical elements are the core of cylindrical systems, and the core challenges of high-energy laser aspheric cylindrical elements are large aperture, high steepness and aspheric structural requirements. These characteristics increase the difficulty of manufacturing and testing. At present, there are technical bottlenecks in the nano-scale manufacturing and control of intermediate frequency errors in China. One of the important reasons is the lack of high-precision detection methods for intermediate frequency errors.

[0005] As an effective optical detection technology, the computer-generated holography (CGH) detection method can theoretically realize the detection of optical components of arbitrary surface shapes. However, when it is applied to the detection of high-steepness non-spherical cylindrical components, it still faces several key problems. When the surface of the non-spherical cylindrical component is a convex cylinder, the effective area of ​​the CGH full-aperture compensation detection is limited, and the detection cannot be completed in a one-time full-aperture compensation. The entire surface must be covered by splicing measurement; when the surface of the non-spherical cylindrical component is a concave cylinder, due to the large aperture, high steepness and large deviation characteristics of the non-spherical cylindrical component, the line frequency density of the CGH will be too high, increasing the difficulty of production and measurement errors. In addition, CGH compensation detection will introduce non-rotational symmetry and complex two-dimensional projection distortion, which will limit 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, full-aperture detection of non-spherical cylindrical components is limited by the resolution of the interferometer, which reduces the period resolution range and directly affects the detection of intermediate frequency errors, thereby affecting the accurate analysis and control of the overall surface error. Summary of the invention

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

[0008] To achieve the above object, the technical solution created by the present invention is implemented as follows: A low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation comprises the following steps: 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.

[0009] Furthermore, 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.

[0010] Furthermore, when designing CGH compensators with different sub-apertures, the process of using a hierarchical smoothing optimization algorithm to perform phase smoothing on the overlapping region between two adjacent sub-apertures 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.

[0011] Furthermore, 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).

[0012] Furthermore, the formula for linear smoothing is: ; Among them, among them, 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.

[0013] Furthermore, in the process of performing sub-aperture stitching detection on the surface to be inspected of the non-spherical cylindrical element, first, an 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, a 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.

[0014] Furthermore, 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: characteristic points are arranged on the surface to be tested 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 characteristic 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.

[0015] Furthermore, 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.

[0016] Furthermore, in the process of performing sub-aperture splicing inspection on the surface to be inspected of the non-spherical cylindrical element, a 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.

[0017] Furthermore, 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 region in the overlapping area, introduces small adjustment values ​​δx and δy 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.

[0018] Compared with the prior art, the invention can achieve the following beneficial effects: 1. The present invention divides the non-spherical cylindrical element into sub-apertures and designs multiple different sub-aperture CGH compensators for mixed splicing detection, thereby solving the problems of limited detection range and low accuracy in traditional CGH full-aperture compensation.

[0019] 2. The present invention uses a hierarchical smoothing optimization algorithm to perform phase smoothing on the overlapping areas between sub-apertures, effectively solving the subsequent phase mismatch problem.

[0020] 3. The present invention uses a weighted average algorithm to optimize the splicing traces during sub-aperture splicing to further improve the detection accuracy.

[0021] 4. The present invention solves the distortion mapping function by ray tracing, realizes high-precision alignment between the distortion correction result and the mirror surface with the help of mirror feature points, and completes high-precision correction of projection distortion.

[0022] 5. Utilize the low-frequency information in the full-aperture detection results to accurately calibrate the positions between the sub-apertures, correct the displacement error, better align and splice the sub-apertures, ensure the detection accuracy of the hybrid compensation in the present invention, and effectively improve the spatial period resolution range, breaking through the resolution limitation of the interferometer, and realizing the synchronous detection of low intermediate frequency errors with nanometer precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings: Figure 1 It is a flow chart of a low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation according to an embodiment of the invention; Figure 2 It is a schematic diagram of the structure of the detection optical path constructed according to the embodiment of the invention; Figure 3 is a schematic diagram of sub-aperture planning according to an embodiment of the invention; Figure 4 is a schematic diagram of hierarchical smoothing optimization of the sub-aperture overlap region according to an embodiment of the invention; Figure 5 is a schematic diagram of optimizing the splicing traces during sub-aperture splicing according to an embodiment of the invention; Figure 6 2 is a schematic diagram of low-frequency error correction according to an embodiment of the present invention.

[0024] Explanation of the reference numerals: full-aperture CGH compensator 1, interferometer 2, aspherical cylindrical element 3. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0026] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0027] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are 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 therefore cannot be understood as a limitation on 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 number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0028] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0029] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0030] like Figure 1 As shown, the low intermediate frequency error synchronization detection method based on sub-aperture splicing and CGH compensation provided by the embodiment of the present invention includes the following steps: S1: According to the shape of the surface to be inspected of the aspherical 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 surface to be inspected of the aspherical cylindrical component to obtain a full-aperture detection result.

[0031] The design of the full-aperture CGH compensator belongs to the prior art and will not be described in detail here.

[0032] The detection optical path constructed is as follows Figure 2 As shown, the full-aperture CGH compensator 1 is arranged between the interferometer 2 and the non-spherical cylindrical element 3, and the surface to be inspected of the non-spherical cylindrical element 3 can be a concave cylindrical surface or a convex cylindrical surface.

[0033] S2: Perform sub-aperture planning according to the surface shape of the to-be-tested surface of the aspherical cylindrical element, and design a sub-aperture CGH compensator corresponding to each sub-aperture, and 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 aspherical cylindrical element, and obtain the splicing detection result.

[0034] According to the surface shape of the non-spherical cylindrical element to be inspected, the present invention performs sub-aperture planning on the non-spherical cylindrical element to be inspected based on the sub-aperture planning principle of full-aperture coverage. 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 follows: Figure 3 shown.

[0035] 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 surface parameters of non-spherical cylindrical elements when the sub-apertures are subsequently spliced, the present invention uses a hierarchical smoothing optimization algorithm to perform phase smoothing on the overlapping area between two adjacent sub-apertures, so as to avoid the problem of phase mismatch when the sub-apertures are subsequently spliced.

[0036] The process of designing a sub-aperture CGH compensator is: Firstly, the initial phase function of the corresponding sub-aperture CGH compensator is calculated for each sub-aperture by ray tracing.

[0037] 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.

[0038] Then, a hierarchical smoothing optimization algorithm is used to perform phase smoothing on the overlapping region between two adjacent sub-apertures.

[0039] The principle of using the hierarchical smoothing optimization algorithm to smooth the phase of the overlapping area between each sub-aperture is based on the curvature change of different areas of the test surface of the non-spherical cylindrical element, and flexibly selects the interpolation order to achieve high-precision phase smoothing in the overlapping area, such as Figure 4 Specifically, 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 reduce the computational complexity.

[0040] 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).

[0041] The formula used to smooth out the transition phase difference using linear smoothing is: ; in, represents the phase distribution function after smoothing, w1 and w2 represent weight coefficients, and w1 and w2 are determined according to the distance ratio from the sampling point to the center of each sub-aperture. 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.

[0042] The hierarchical smoothing optimization algorithm can adapt to the morphology of different areas of the surface to be inspected of the non-spherical cylindrical component, while ensuring the calculation accuracy and efficiency and reducing the error accumulation problem.

[0043] Due to the different curvatures of each point on the test surface of the non-spherical cylindrical element and the influence of the interferometer error, projection distortion will occur during the sub-aperture stitching test of the non-spherical cylindrical element. In order to correct the projection distortion, 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 test surface 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 test surface of the non-spherical cylindrical element. This step-by-step conversion from the interferometer CCD to the sub-aperture CGH compensator and then to the test surface realizes high-precision correction of projection distortion.

[0044] By calculating the relationship between the CGH compensator and the surface to be tested of the aspheric cylindrical element, the two-dimensional nonlinear mapping relationship (Mirror-CGH) between the surface to be tested of the aspheric cylindrical element and the CGH compensator is solved, and feature points are arranged on the surface to be tested of the aspheric cylindrical element. According to the feature points, the affine transformation parameters (CCD-CGH) between the interferometer CCD coordinate system and the CGH compensator coordinate system are solved. Based on the two-dimensional nonlinear mapping relationship and the affine transformation parameters, a two-dimensional projection distortion mapping function between the detection result and the surface to be tested of the aspheric cylindrical element is constructed to correct the projection distortion.

[0045] 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.

[0046] 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.

[0047] In the process of sub-aperture splicing detection 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 to further improve the detection accuracy. Figure 5 As shown, 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.

[0048] 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 between each sub-aperture, and correct the displacement error between each sub-aperture.

[0049] 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 ei(x, y) are low-pass filtered to extract the low-frequency error component Li(x, y). Secondly, the least squares objective function is constructed through the low-frequency error component Li(x, y) , and iteratively optimize and solve the position offset (Δxi, Δyi) of each sub-aperture to realize the position calibration of each sub-aperture; then, establish 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 region in the overlapping area, introduces small adjustment values ​​δx and δy 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. and Correct the position of each sub-aperture, such as Figure 6 shown.

[0050] By using the low-frequency information in the full-aperture detection results, the positions between the sub-apertures are accurately calibrated, the displacement error is corrected, and the sub-apertures are better aligned and spliced, ensuring the detection accuracy of the hybrid compensation in the present invention, and effectively improving the spatial period resolution range, breaking through the limitations of the interferometer, and realizing nano-precision synchronous detection of low-medium frequency errors. Taking a 300mm-diameter non-spherical cylindrical element as an example, the CGH full-aperture compensation detection is limited by the 1k×1k resolution of the interferometer, and the minimum resolvable value of the spatial period frequency band is about 0.3mm. Using CGH sub-aperture splicing compensation detection, taking the sub-aperture area of ​​100mm as an example, the measured spatial period frequency band resolvable range is less than 0.1mm.

[0051] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0052] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in 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 region in the overlapping area, introduces small adjustment values ​​δx and δy 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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