Large-aperture high-order convex aspherical surface shape detection method

Abstract

The application relates to the technical field of optical surface shape detection, and specifically provides a large-aperture high-order convex aspheric surface shape detection method, wherein aberration is reasonably distributed according to optical parameters of a high-order convex aspheric surface to be detected, low-order aberration and high-order aberration are respectively compensated through a Hindle-Shell compensator and a CGH compensator; a concave surface of the Hindle-Shell compensator is taken as a reference surface, wavelength modulation technology is used to change the wavelength of output laser light to realize phase shift of an interference signal, and aspheric wavefront reflected by the high-order convex aspheric surface to be detected and reference wavefront of the concave surface of the Hindle-Shell compensator form interference fringes; system errors introduced by wavelength change are eliminated, and the problem that wavelength modulation interference technology is applied to high-precision aspheric surface detection is solved. The application is not sensitive to machining and adjustment errors of the compensating element, the detection process is simple, the contrast of the interference fringes is high, and the detection precision is high.

Description

Technical Field

[0001] This invention relates to the field of optical surface shape detection technology, specifically providing a method for detecting the surface shape of a large-aperture, high-order convex aspherical surface. Background Technology

[0002] In optical systems, aspherical optical elements offer advantages such as expanded field of view, improved resolution, and reduced system complexity, leading to their increasing application in fields like astronomical optics. In recent years, a series of large-aperture astronomical telescopes designed and built abroad have seen a trend towards larger apertures and higher surface accuracy requirements for their secondary mirrors. For example, the E-ELT (European Extremely Large Telescope), built under the leadership of the European Southern Observatory, features a 4-meter secondary mirror and incorporates higher-order aspherical coefficients. Compared to second-order asphericals, higher-order asphericals offer greater design freedom, better correcting aberrations and improving the imaging quality of astronomical observations. However, high-precision inspection technology is a prerequisite and guarantee for high-precision manufacturing; currently, the inspection of large-aperture, higher-order convex asphericals remains a challenging problem in optical inspection.

[0003] Existing methods for detecting large-aperture convex aspherical surfaces all have certain drawbacks and problems. For aberration-free detection methods, the required Hindle sphere diameter is usually twice or even larger than the diameter of the inspected mirror. Current technology cannot guarantee the processing accuracy of the auxiliary spherical mirror. In addition, aberration-free detection can only detect quadratic surfaces and cannot detect higher-order convex aspherical surfaces. For methods that use lens compensators, a set of compensators with spherical aberration needs to be designed. The diameter of the compensator set is slightly larger than that of the convex higher-order aspherical surface. However, it is difficult to guarantee the processing accuracy of such a large-aperture lens compensator. For methods that use CGH compensators, due to the size limitations of existing micro-nano fabrication platforms, it is difficult to guarantee the processing accuracy of CGH with an aperture of 300mm or more.

[0004] Chinese patent application CN103335610A, published on October 2, 2013, entitled "Detection System for Large-Aperture Convex Higher-Order Aspherical Surfaces," discloses a method that uses a CGH combined with an auxiliary reflective sphere to achieve zero-position detection of the sub-aperture in the corresponding region of the large-aperture convex higher-order aspherical surface under test. Then, a sub-aperture stitching algorithm is used to obtain the full-aperture surface shape distribution information of the large-aperture convex higher-order aspherical surface under test. However, the sub-aperture stitching detection method has inherent drawbacks: insufficient precision of the stitching displacement mechanism, which introduces errors; complex stitching algorithm, requiring more sub-apertures for larger mirror diameters, leading to error accumulation, difficulty in error decoupling, and affecting the final detection accuracy.

[0005] Chinese patent application CN107796329A, published on March 13, 2018, entitled "A Device and Method for Detecting the Surface Shape of a Convex Aspherical Mirror," discloses a method that combines a CGH (Convex Aspherical Mirror) and an illumination lens. This method integrates the wavefront aberration compensation function of the CGH with the beam-convexity focusing function of the lens to detect large-aperture convex aspherical mirrors. However, in this method, the detection optical path is a non-common path system. Manufacturing and adjustment errors of the CGH and illumination lens, as well as environmental interference (air turbulence, vibration, etc.), can significantly affect the detection accuracy. Furthermore, the CGH and illumination lens respectively compensate for aberrations and converge light rays, with the CGH alone bearing the majority of the aberration compensation. This poses a significant challenge to the design and manufacturing accuracy of the CGH when detecting complex curved surfaces.

[0006] Furthermore, current interferometric testing of convex aspherical surfaces mostly employs mechanical phase-shifting interferometry, using the standard spherical mirror of the interferometer as the reference surface. The optical path between the standard spherical mirror and the mirror under test is a non-common optical path, placing high demands on the fabrication and alignment accuracy of the compensation components in this part. It is also susceptible to interference from environmental factors such as airflow and vibration, affecting the testing accuracy. Wavelength modulation interferometry is mostly applied to planar surface testing, and research on its application to the testing of complex aspherical surfaces is lacking. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides a method for detecting the surface shape of large-aperture high-order convex aspherical surfaces. It achieves full-aperture detection through hybrid compensation using a CGH compensator and a Hindle-Shell compensator, effectively reducing the propagation and accumulation of errors during surface shape detection. Based on wavelength modulation interferometry, using the concave surface of the Hindle-Shell compensator as the reference surface and a common optical path system for detection, the surface shape detection results are insensitive to processing and adjustment errors of the compensation elements. Through reasonable aberration allocation, the Hindle-Shell compensator and CGH compensator compensate for low-order and high-order aberrations respectively, greatly simplifying the design process, reducing the requirements for processing accuracy, and effectively improving the detection accuracy and efficiency of large-aperture convex aspherical optical elements. Furthermore, through a self-developed error calibration system, the influence of wavelength variations on the detection results is eliminated, solving the difficulty of applying wavelength modulation interferometry to the detection of complex aspherical surfaces, further improving the detection accuracy and efficiency of complex aspherical surfaces.

[0008] The method for detecting the surface shape of large-aperture high-order convex aspherical surfaces provided by this invention includes the following steps: S1: Based on the optical parameters of the high-order convex aspherical surface to be measured, select a spherical standard mirror that satisfies F#≤R#, where F#=f / D, R#=R / d, F# represents the F-number of the spherical standard mirror, R# represents the R-number of the high-order convex aspherical surface to be measured, f represents the focal length of the spherical standard mirror, D represents the aperture of the spherical standard mirror, R represents the vertex radius of curvature of the high-order convex aspherical surface to be measured, and d represents the aperture of the high-order convex aspherical surface to be measured; The Hindle-Shell compensator is designed based on the optical parameters of the high-order convex aspherical surface to be measured. The Hindle-Shell compensator is used to compensate for the low-order aberrations of the high-order convex aspherical surface to be measured caused by the quadratic surface. The CGH compensator is designed based on the remaining higher-order aberrations after compensation by the Hindle-Shell compensator. The CGH compensator compensates for the remaining higher-order aberrations and is divided into a main region, an alignment region, and a reference region. S2: Using a laser tracker, the wavelength modulation interferometer, spherical standard mirror, CGH compensator and the high-order convex aspherical surface to be tested are set in the detection optical path, and the concave surface of the Hindle-Shell compensator is used as the reference surface, and the detection optical path is a common optical path system. The wavelength modulation interferometer emits a plane wave, which is converted into a spherical wave by a spherical standard mirror. The positions of the wavelength modulation interferometer and the CGH compensator are adjusted so that the interference fringes in the alignment area are zero fringes, thus achieving alignment between the wavelength modulation interferometer and the CGH compensator. The wavelength modulation interferometer emits a plane wave, which is then emitted by the spherical standard mirror. The spherical wave then passes through the reference area and forms a mark line on the detection optical path. The position of the high-order convex aspherical surface to be measured is adjusted to the mark line to achieve the alignment of the CGH compensator with the high-order convex aspherical surface to be measured. Set the Hindle-Shell compensator between the CGH compensator and the high-order convex aspherical surface to be measured, and adjust the pose of the Hindle-Shell compensator until the interference fringes in the main region of the CGH compensator are zero. S3: Connect the wavelength meter to the light source of the wavelength modulation interferometer via optical fiber. Use a computer to control the wavelength modulation interferometer to change the wavelength of the output plane wave to achieve phase shift and generate interference fringes on the concave surface of the Hindle-Shell compensator. The interference fringes are formed by the interference of the aspherical wavefront reflected back from the higher-order convex aspherical surface under test with the reference wavefront of the concave surface of the Hindle-Shell compensator, with the concave surface of the Hindle-Shell compensator as the reference surface. At least 20 interference fringes and the corresponding wavelength data for each fringe are recorded by computer. The average of all interference fringes is used to obtain the detection result W, which is the surface shape detection result carrying systematic errors, and its expression is as follows: ; in, The surface shape detection results of the high-order convex aspherical surface to be tested are as follows. The systematic error introduced by the Hindle-Shell compensator due to machining accuracy and material uniformity. The systematic error introduced by the wavelength variation is represented by λ, which represents the wavelength. S4: Calculate the systematic error introduced by the Hindle-Shell compensator due to machining accuracy and material uniformity. The process is as follows: Remove the CGH compensator and place an auxiliary concave spherical mirror on the side of the Hindle-Shell compensator furthest from the wavelength modulation interferometer. Control the wavelength modulation interferometer to emit a plane wave. The plane wave is transformed into a spherical wavefront after passing through a spherical standard mirror. The spherical wavefront passes through the Hindle-Shell compensator and is reflected by the auxiliary concave spherical mirror along the original optical path. The reflected spherical wavefront interferes with the reference wavefront of the spherical standard mirror. The interference fringes obtained in the wavelength modulation interferometer represent the systematic errors introduced by the Hindle-Shell compensator due to manufacturing precision and material uniformity. ; Calculate the systematic error introduced by wavelength variation The process is as follows: Based on the wavelength data corresponding to each interference fringe recorded by the computer, the corresponding wavefront residual map is obtained. Each wavefront residual map is then processed to the same size as the corresponding interference fringe. The average of all wavefront residual maps is the systematic error introduced by the wavelength variation. ; The calculation formula for the test result of the high-order convex aspherical surface shape is as follows: .

[0009] Preferably, the wavelength modulation interferometer is an MST wavelength modulation interferometer.

[0010] Preferably, the diameter of the Hindle-Shell compensator is larger than the diameter of the high-order convex aspherical surface to be measured, and the diameter of the CGH compensator is less than 300 mm.

[0011] Preferably, in S4, the process of obtaining the wavefront residual map is as follows: The wavelength data corresponding to all interference fringes recorded by the computer are imported into the detection system simulated by ZEMAX, and the corresponding wavefront residual map is obtained through the wavelength data corresponding to each interference fringe.

[0012] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention employs wavelength modulation technology, using the concave surface of the Hindle-Shell compensator as the reference surface. The detection optical path is a common optical path system, and the detection light only passes through the compensation element once. The surface shape detection result is insensitive to the processing and adjustment errors of the compensation element. Since the detection light only passes through the compensation element once, light energy loss is reduced, and the contrast of interference fringes is improved. This allows for the detection of low-reflectivity mirror surfaces, expanding the interference detection range. Through reasonable aberration allocation, the Hindle-Shell compensator and the CGH compensator compensate for the low-order and high-order aberrations of high-order convex aspherical surfaces, respectively, reducing the design difficulty and processing accuracy requirements of the compensator and effectively improving the detection accuracy and efficiency of large-aperture convex aspherical optical elements. Furthermore, the hybrid compensation scheme of this invention can effectively reduce the size of the CGH compensator, avoiding the high requirements for the aperture size of the CGH compensator. A smaller-sized CGH compensator can be combined with the Hindle-Shell compensator to achieve full-aperture detection of large-aperture high-order convex aspherical surfaces, without the problems of central obstruction and sub-aperture stitching error accumulation.

[0013] This invention solves the problem of difficult alignment of multiple components in complex optical paths by using a laser tracker combined with multiple regions of a CGH compensator to adjust the position of optical components, thereby improving detection efficiency and accuracy. This invention effectively eliminates the systematic error introduced by wavelength variation in wavelength modulation interferometers, solves the difficulty of applying wavelength modulation interferometry to the detection of complex aspherical surfaces, and further improves the accuracy and efficiency of complex aspherical surface detection. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method for detecting the shape of large-aperture high-order convex aspherical surfaces according to an embodiment of the present invention; Figure 2 This is a system structure diagram of a large-aperture high-order convex aspherical surface shape detection system provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the optical path of a common optical path system provided according to an embodiment of the present invention; Figure 4 This is a transmission wavefront detection optical path diagram of the Hindle-Shell compensator provided according to an embodiment of the present invention; Figure 5 This is a system error diagram introduced by wavelength variation according to an embodiment of the present invention.

[0015] The reference numerals in the figures include: 1. Wavelength meter; 2. Wavelength modulation interferometer; 3. Interferometer adjustment mechanism; 4. Spherical standard mirror; 5. CGH compensator; 6. CGH compensator adjustment mechanism; 7. Hindle-Shell compensator; 8. High-order convex aspherical surface to be measured; 9. High-order convex aspherical surface to be measured adjustment mechanism; 10. Auxiliary concave spherical reflector; 11. Detailed Implementation

[0016] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the 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 merely illustrative of the invention and do not constitute a limitation thereof.

[0018] like Figure 1 As shown in the figure, this invention proposes a method for detecting the surface shape of a large-aperture, high-order convex aspherical surface, which specifically includes the following steps: S1: First, the spherical standard mirror 4, CGH compensator 5, and Hindle-Shell compensator 7 need to be designed and the detection optical path needs to be built using computer software. The specific design process uses conventional and general techniques, mainly relying on computer software for implementation. The basic optical path is built in the software, as follows: like Figure 2 As shown, the following components are sequentially arranged along the detection optical path of the system: wavelength modulation interferometer 2, spherical standard mirror 4, CGH compensator 5 (computational hologram), Hindle-Shell compensator 7, and the high-order convex aspherical surface to be measured 9. This detection optical path constitutes a common optical path system to reduce the impact of processing and adjustment errors of CGH compensator 5 and Hindle-Shell compensator 7 on the surface shape detection results. Furthermore, the above components are respectively fixed on the interferometer adjustment mechanism 3, CGH compensator adjustment mechanism 6, Hindle-Shell compensator adjustment mechanism 8, and high-order convex aspherical surface to be measured adjustment mechanism 10, and the positions of each component in the system are adjusted by the corresponding adjustment mechanisms.

[0019] Based on the function and characteristics of each component, the specific design is as follows: Wavelength modulation interferometer 2 is used to emit plane waves during the detection process. Wavelength modulation interferometer 2 is an MST wavelength modulation interferometer, which modulates the phase shift by changing the wavelength. Different wavelengths of light propagate at different speeds in the material, leading to changes in the phase difference. By analyzing the changes in the position of the interference fringes caused by this wavelength modulation, the surface shape information of the convex aspherical mirror can be obtained. Its principle can be expressed by the following formula: ; Where L represents the length of the interference cavity, and the wavelength modulation interferometer 2 can arbitrarily adjust the length L of the interference cavity. Indicates phase difference, This indicates the detection wavelength of wavelength modulation interferometer 2. This indicates the wavelength difference.

[0020] Phase difference The phase difference is proportional to the cavity length L. In other words, the choice of cavity length L directly affects the phase difference. The magnitude of the phase difference. As L increases, the phase difference... The phase difference will also increase accordingly; when L decreases, the phase difference... It will also decrease.

[0021] In addition, a computer is connected to the front end of the wavelength modulation interferometer 2 for processing the interference patterns during the detection process and for designing the optical parameters of the compensator and components. The light source of the wavelength modulation interferometer 2 is also connected to a wavelength meter 1 via optical fiber, which is used to measure the wavelength of the plane wave emitted by the wavelength modulation interferometer 2.

[0022] The spherical standard mirror 4 is used during the detection process to converge and modulate the plane wave emitted by the wavelength modulation interferometer 2 into a spherical wavefront. The parameters of the spherical standard mirror 4 need to be determined based on the optical parameters of the higher-order convex aspherical surface 9 to be measured. The surface shape parameters of the higher-order convex aspherical surface 9 to be measured are input into the computer software to solve for the initial structure of the compensation optical path. The parameters of the spherical standard mirror 4 are determined based on the optical parameters of the higher-order convex aspherical surface 9 to be measured. The spherical standard mirror 4 must satisfy the following: F#≤R#; Where F# = f / D, R# = R / d, F# represents the F-number of the spherical standard mirror 4, R# represents the R-number of the higher-order convex aspherical surface 9 to be measured, f represents the focal length of the spherical standard mirror 4, D represents the aperture of the spherical standard mirror 4, R represents the vertex radius of curvature of the higher-order convex aspherical surface 9 to be measured, and d represents the aperture of the higher-order convex aspherical surface 9 to be measured.

[0023] In existing technologies, the CGH compensator 5 typically compensates for most aberrations on its own, which poses significant challenges to the design and manufacturing accuracy of the CGH compensator 5 when inspecting complex curved surfaces. To address this issue, this invention combines the CGH compensator 5 with the Hindle-Shell compensator 7 to jointly compensate for aberrations.

[0024] The Hindle-Shell compensator 7 is used to compensate for aberrations, i.e., low-order aberrations, caused by the quadratic surface of the high-order convex aspherical surface 9 under test. Its lens center thickness and the radii of curvature of its front and rear surfaces are calculated using the first definition of conic sections, based on the radius of curvature, aperture, and conic constant of the high-order convex aspherical surface 9 under test. The specific design process of the Hindle-Shell compensator 7 can be performed using specialized software. Based on the radius of curvature, aperture, and conic constant of the high-order convex aspherical surface 9 under test, the lens radius of curvature and the front-rear spacing of the Hindle-Shell compensator 7 are calculated using the first definition of conic sections. The side of the Hindle-Shell compensator 7 closest to the wavelength modulation interferometer 2 is convex, and the side furthest from the wavelength modulation interferometer 2 is concave. During the testing process, the concave surface of the wavelength modulation interferometer 2 is used as the reference surface, and the wavefront of this concave surface is used as the reference wavefront.

[0025] The CGH compensator 5 is mainly used to compensate for residual higher-order aberrations. Based on the residual higher-order aberrations compensated by the Hindle-Shell compensator 7, a hologram is generated by computer. The compensation region of the CGH compensator 5 is designed by dividing the hologram into regions. The compensation region of the CGH compensator 5 is mainly divided into the following three regions: 1. Main region: This region is responsible for compensating the remaining higher-order aberrations of the high-order convex aspherical surface 9 to be measured, so as to achieve high-precision null detection.

[0026] 2. Alignment Area: This area reflects the alignment between the wavelength modulation interferometer 2 and the CGH compensator 5. By controlling the positions of the interferometer adjustment mechanism 3 and the CGH compensator adjustment mechanism 6, the wavelength modulation interferometer 2 and the CGH compensator 5 are moved. The purpose is to observe that the interference pattern in the alignment area is zero fringes, thus confirming that the two are correctly aligned.

[0027] 3. Reference Area: This area is used for alignment between the CGH compensator 5 and the high-order convex aspherical surface 9 to be measured. By setting a marker line in the reference area, light passes through the reference area and projects the marker line onto one side of the high-order convex aspherical surface 9 to be measured. By adjusting the lateral and vertical axis positions of the high-order convex aspherical surface 9 to be measured, the high-order convex aspherical surface 9 to be measured is ensured to be in the correct position, achieving alignment with the CGH compensator 5. Since this embodiment of the invention combines the CGH compensator 5 and the Hindle-Shell compensator to compensate for higher-order aberrations and lower-order aberrations respectively, the aperture of the Hindle-Shell compensator 7 is larger than only slightly larger than the aperture of the high-order convex aspherical surface 9 to be measured, ensuring that the aperture of the CGH compensator 5 is less than 300mm. This solves the problem that the accuracy of existing surface shape detection is limited by the machining accuracy of the large-diameter CGH compensator 5. In addition, this invention adopts a common optical path system, which further reduces the sensitivity of the surface shape detection results to the machining accuracy of the CGH compensator 5 and the Hindle-Shell compensator 7. Furthermore, this invention combines the CGH compensator 5 and the Hindle-Shell compensator to achieve full-aperture detection of large-diameter, high-order convex aspherical surfaces, eliminating the problems of central obstruction and sub-aperture splicing error accumulation during detection.

[0028] After the initial design of Hindle-Shell compensator 7 and CGH compensator 5 is completed, error sensitivity analysis is required. Once the design accuracy meets the requirements, tolerance allocation is performed. Hindle-Shell compensator 7 compensates for low-order aberrations caused by the quadratic surface of the measured high-order convex aspherical surface 9, while CGH compensator 5 compensates for the remaining high-order aberrations. After the parameters of Hindle-Shell compensator 7 and CGH compensator 5 are confirmed to be correct, they can be manufactured. After manufacturing, optical recalculation of the physical object is required to confirm that the parameters of the manufactured Hindle-Shell compensator 7 and CGH compensator 5 are within the manufacturing error range. The above design, manufacturing, and testing processes are all existing technologies and are no different from conventional compensator design processes. After the design of each component is completed, the detection optical path is constructed.

[0029] S2: Adjust the positions of each component in the detection optical path to achieve alignment of the wavelength modulation interferometer 2, CGH compensator 5, Hindle-Shell compensator 7, and the high-order convex aspherical surface 9 to be measured: Using a laser tracker, the wavelength modulation interferometer 2, the spherical standard mirror 4, the CGH compensator 5, and the high-order convex aspherical surface 9 to be measured are placed in the detection optical path and adjusted to the same height.

[0030] Using the alignment area of ​​CGH compensator 5, the wavelength modulation interferometer 2 and CGH compensator 5 are aligned. Specifically, the wavelength modulation interferometer 2 is controlled to emit a plane wave, which is converted into a spherical wave by the spherical standard mirror. The positions of the wavelength modulation interferometer 2 and CGH compensator 5 are adjusted by the interferometer adjustment mechanism 3 and the CGH compensator adjustment mechanism 6 so that the interference pattern of the alignment area is zero fringes, thus realizing the alignment of the wavelength modulation interferometer 2 and CGH compensator 5.

[0031] Using the reference area of ​​CGH compensator 5, CGH compensator 5 and the high-order convex aspherical surface 9 to be measured are aligned. Specifically, while keeping the positions of wavelength modulation interferometer 2 and CGH compensator 5 unchanged, light is projected through the reference area onto one side of the high-order convex aspherical surface 9 to be measured to form a marking line. The lateral and vertical axis positions of the high-order convex aspherical surface 9 to be measured are adjusted by the high-order convex aspherical surface adjustment mechanism 10 so that the high-order convex aspherical surface 9 to be measured is located at the marking line position, thereby achieving the alignment of CGH compensator 5 and the high-order convex aspherical surface 9 to be measured.

[0032] A Hindle-Shell compensator 7 is placed between the CGH compensator 5 and the high-order convex aspherical surface 9 to be measured. The position and orientation of the Hindle-Shell compensator 7 are adjusted by the Hindle-Shell compensator adjustment mechanism 8 until the interference pattern in the main region is zero fringes. At this point, the adjustment of all optical elements in the detection optical path is complete. The detection optical path now constitutes a common optical path system, as shown below. Figure 3 The light path emitted by the wavelength modulation interferometer 2 and incident on the high-order convex aspherical surface 9 to be measured coincides with the light path after the light is reflected by the high-order convex aspherical surface 9 to be measured.

[0033] S3: Connect wavelength meter 1 to the light source of wavelength modulation interferometer 2 via optical fiber. Control the light source to change its wavelength, creating a phase shift and generating interference fringes on the reference surface. These interference fringes are formed by the interference of the aspherical wavefront reflected from the high-order convex aspherical surface 9 (the surface to be measured) with the reference wavefront of the concave surface of the Hindle-Shell compensator 7, using the concave surface of the Hindle-Shell compensator 7 as the reference surface. Record 20 interference fringes and the wavelength data of each fringe at the same moment using a computer. Average the 20 interference fringes to obtain the detection result W, where W is the surface shape detection result carrying systematic errors, expressed as: .

[0034] in, The surface shape detection results are for the high-order convex aspherical surface 9 to be tested. The systematic error introduced by the Hindle-Shell compensator 7 due to machining accuracy and material uniformity. The systematic error introduced by the wavelength variation is represented by λ, where λ represents the wavelength. Furthermore, since the detection accuracy of wavelength meter 1 can reach the picometer level, the wavefront aberration introduced by wavelength meter 1 is less than λ / 100, and the error is negligible.

[0035] S4: Eliminate systematic errors and improve the surface shape detection accuracy of the high-order convex aspherical surface 9 to be measured: First, eliminate the systematic errors introduced by the Hindle-Shell compensator 7 due to machining accuracy and material uniformity. The specific process is as follows: like Figure 4 As shown, the CGH compensator 5 in the detection optical path is removed. An auxiliary concave spherical mirror 11 is placed on the side of the Hindle-Shell compensator 7 away from the wavelength modulation interferometer 2. The wavelength modulation interferometer 2 is controlled to emit a plane wave. The plane wave becomes a spherical wavefront after passing through the spherical standard mirror 4. After passing through the Hindle-Shell compensator 7, the spherical wavefront is reflected by the auxiliary concave spherical mirror 11 along the original optical path. The reflected spherical wavefront interferes with the reference wavefront of the spherical standard mirror 4. The interference fringes obtained in the wavelength modulation interferometer 2 are the systematic error of the Hindle-Shell compensator 7. .

[0036] Then, systematic errors introduced by wavelength changes are eliminated. The specific process is as follows: The wavelength data corresponding to all interference fringes recorded by the computer are imported into the ZEMAX simulation detection system. A corresponding wavefront residual image is obtained using the wavelength data for each interference fringe. Image processing is used to make the size of the wavefront residual image the same as the size of the corresponding interference fringe. This process is repeated for all 20 wavelength data sets. Finally, the average of the 20 wavefront residual images is calculated, and the result represents the systematic error introduced by the wavelength variation. .

[0037] Finally, the surface shape detection result W carrying systematic errors is subtracted from the systematic errors introduced by the Hindle-Shell compensator 7 due to machining accuracy and material uniformity. and systematic errors introduced by wavelength variation The high-precision detection results of the nine-sided high-order convex aspherical surface to be tested are as follows: .

[0038] Furthermore, the embodiments of the present invention are not limited to the surface shape detection of large-aperture high-order convex aspherical surfaces, but are also applicable to the detection of convex aspherical reflectors of various curved surface types.

[0039] like Figure 5As shown, this invention has been verified in practical applications. A detection system for a high-order convex aspherical mirror with an effective aperture D = 860 mm, a quadratic surface constant K = -2.53, containing 6th, 8th, 10th, and 12th order terms, and a vertex radius of curvature R = 2570.4 was designed using the method of this invention. Zero-position detection of the large-aperture high-order convex aspherical mirror was achieved using a hybrid compensation method of CGH compensator 5 and Hindle-Shell compensator 7. The influence of each error source on the wavefront was obtained through sensitivity analysis. After error calibration, systematic errors were removed from the detection results. The analysis results show that the detection accuracy of the method described in this invention can reach 5 nm RMS, meeting the requirements for high-precision surface shape detection.

[0040] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0041] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for detecting the surface shape of a large-diameter, high-order convex aspherical surface, characterized in that, Includes the following steps: S1: Based on the optical parameters of the high-order convex aspherical surface to be measured, select a spherical standard mirror that satisfies F#≤R#, where F#=f / D, R#=R / d, F# represents the F-number of the spherical standard mirror, R# represents the R-number of the high-order convex aspherical surface to be measured, f represents the focal length of the spherical standard mirror, D represents the aperture of the spherical standard mirror, R represents the vertex radius of curvature of the high-order convex aspherical surface to be measured, and d represents the aperture of the high-order convex aspherical surface to be measured; Based on the optical parameters of the high-order convex aspherical surface to be measured, a Hindle-Shell compensator is designed. The Hindle-Shell compensator is used to compensate for the low-order aberrations of the high-order convex aspherical surface to be measured caused by the quadratic surface. Based on the remaining higher-order aberrations compensated by the Hindle-Shell compensator, a CGH compensator is designed to compensate for the remaining higher-order aberrations, and the CGH compensator is divided into a main region, an alignment region, and a reference region. S2: Using a laser tracker, a wavelength modulation interferometer, a spherical standard mirror, a CGH compensator, and the high-order convex aspherical surface to be tested are set in the detection optical path, and the concave surface of the Hindle-Shell compensator is used as the reference surface, and the detection optical path is a common optical path system. The wavelength modulation interferometer is controlled to emit a plane wave, which is then converted into a spherical wave by the spherical standard mirror. The positions of the wavelength modulation interferometer and the CGH compensator are adjusted so that the interference fringes in the alignment area are zero fringes, thereby achieving alignment between the wavelength modulation interferometer and the CGH compensator. The wavelength modulation interferometer emits a plane wave, which is then passed through the spherical standard mirror and a spherical wave. The spherical wave then passes through the reference area and forms a mark line on the detection optical path. The position of the high-order convex aspherical surface to be tested is adjusted to the mark line, thereby aligning the CGH compensator with the high-order convex aspherical surface to be tested. The Hindle-Shell compensator is positioned between the CGH compensator and the high-order convex aspherical surface to be measured. The position of the Hindle-Shell compensator is adjusted until the interference fringes in the main region of the CGH compensator are zero. S3: Connect the wavelength meter to the light source of the wavelength modulation interferometer via an optical fiber. Control the wavelength modulation interferometer by a computer to change the wavelength of the output plane wave to achieve phase shift. This generates interference fringes on the concave surface of the Hindle-Shell compensator. These interference fringes are formed by interference between the aspherical wavefront reflected from the higher-order convex aspherical surface to be measured and the reference wavefront of the concave surface of the Hindle-Shell compensator, with the concave surface of the Hindle-Shell compensator as the reference surface. At least 20 interference fringes and the corresponding wavelength data for each fringe are recorded by computer. The average of all interference fringes is used to obtain the detection result W, which is the surface shape detection result carrying systematic errors, and its expression is as follows: ； in, The surface shape detection result of the high-order convex aspherical surface to be tested. This refers to the systematic error introduced into the Hindle-Shell compensator due to machining accuracy and material uniformity. The systematic error introduced by the wavelength variation is represented by λ, which represents the wavelength. S4: Calculate the systematic error introduced by the Hindle-Shell compensator due to machining accuracy and material uniformity. The process is as follows: Remove the CGH compensator and place an auxiliary concave spherical mirror on the side of the Hindle-Shell compensator away from the wavelength modulation interferometer. Control the wavelength modulation interferometer to emit a plane wave. The plane wave becomes a spherical wavefront after passing through a spherical standard mirror. After passing through the Hindle-Shell compensator, the spherical wavefront is reflected by the auxiliary concave spherical mirror along the original optical path. The reflected spherical wavefront interferes with the reference wavefront of the spherical standard mirror. The interference fringes obtained in the wavelength modulation interferometer are the systematic errors introduced by the Hindle-Shell compensator due to manufacturing precision and material uniformity. ; Calculate the systematic error introduced by wavelength variation The process is as follows: Based on the wavelength data corresponding to each interference fringe recorded by the computer, the corresponding wavefront residual map is obtained. Each wavefront residual map is then processed to the same size as the corresponding interference fringe. The average of all wavefront residual maps is the systematic error introduced by the wavelength variation. ; The calculation formula for the detection result of the higher-order convex aspherical surface shape is as follows: 。 2. The method for detecting the surface shape of a large-diameter, high-order convex aspherical surface as described in claim 1, characterized in that, The wavelength modulation interferometer used is the MST wavelength modulation interferometer.

3. The method for detecting the surface shape of a large-diameter, high-order convex aspherical surface as described in claim 1, characterized in that, The diameter of the Hindle-Shell compensator is larger than the diameter of the high-order convex aspherical surface to be measured, and the diameter of the CGH compensator is less than 300 mm.

4. The method for detecting the surface shape of a large-diameter, high-order convex aspherical surface as described in claim 1, characterized in that, In step S4, the process of obtaining the wavefront residual map is as follows: The wavelength data corresponding to all interference fringes recorded by the computer are imported into the detection system simulated by ZEMAX, and the corresponding wavefront residual map is obtained through the wavelength data corresponding to each interference fringe.

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