一种大口径平面镜的瑞奇-康芒检测数据处理方法

张泊泊; 鄂可伟; 李世杰; 李晶; 刘焕玉; 郭永康; 张东旭; 薛勋; 赵建科

doi:10.37188/CO.2025-0017

一种大口径平面镜的瑞奇-康芒检测数据处理方法

doi: 10.37188/CO.2025-0017

cstr: 32171.14.CO.2025-0017

张泊泊^{1, 2,},
鄂可伟^1, ,,
李世杰^2,,
李晶^1,,
刘焕玉^1,,
郭永康^3,,
张东旭^{1, 2,},
薛勋^1,,
赵建科^1,

1.
中国科学院西安光学精密机械研究所, 陕西西安 710119
2.
西安工业大学光电工程学院, 陕西西安 710021
3.
中国科学院南京天文仪器有限公司江苏南京 210042

基金项目: 西部青年学者项目（No. E3295111）；陕西省科技厅项目（No. 2024ZC-KJXX-031）；陕西省教育厅项目（No. 24JC044）；西安市科技局项目（No. 23GXFW0034）

详细信息

作者简介:
鄂可伟（1991—），男，甘肃临夏人，博士，高级工程师，硕士生导师，2017年于四川大学获得博士学位，主要从事光学波面和光学检测技术方面的研究。E-mail：ekewei@opt.ac.cn

中图分类号: O436
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出版历程
- 网络出版日期: 2025-07-09

Data processing method for Ritchey-Common test for large-aperture mirrors

ZHANG Bo-bo^{1, 2
,},
E Ke-wei^{1
, ,},
LI Shi-jie^2
,,
LI Jing^1
,,
LIU Huan-yu^1
,,
GUO Yong-kang^3
,,
ZHANG Dong-xu^{1, 2
,},
XUE Xun^1
,,
ZHAO Jian-ke^1
,

1.
Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
2.
School of Opto-electronical Engineering, Xi’an Technological University, Xi’an 710021, China
3.
Nanjing Astronomical Instruments Co., LTD, Chinese Academy of Sciences, Nanjing 210042, China

Funds: Western Young Scholars Program (No. E3295111); Project of Shaanxi Provincial Science and the Technology Department (No. 2024ZC-KJXX-031); Project of the Education Department of Shaanxi Province (No. 24JC044); Project of Xi’an Science and Technology Bureau (No. 23GXFW0034)

More Information

Corresponding author: ekewei@opt.ac.cn

摘要

摘要:
针对现有大口径平面反射镜面形检测中数据处理方法存在通用性较低、检测中数据易受环境影响等问题，本文提出了一种结合光线追迹法获取灵敏度矩阵的数据处理方法，对瑞奇-康芒法检测获得的数据进行处理分析，实现了对大口径平面镜的高精度面形检测。首先，在Zemax软件中建立了瑞奇-康芒光学检测模型，并采用光线追迹算法获得了灵敏度矩阵，使用灵敏度矩阵计算并分离检测过程中存在的误差。其次，对基于灵敏度矩阵的数据处理算法进行了仿真验证。将该算法应用于口径200 mm平面镜的瑞奇-康芒法检测实验，通过与直接采用干涉仪检测结果的交叉对比，结果显示该方法相比直接采用泽尼克拟合去除像差的方法具有更高的检测精度，避免了近似拟合对数据处理结果的影响，验证了该数据处理方法的正确性。进一步将该方法应用于口径为2.2 m平面镜的制造流程中，最终获得的面形结果均方根误差优于1/50$\lambda $。该方法为大口径平面镜的瑞奇-康芒检测提供了一种高效可靠的数据处理算法，具有明显的工程应用价值。
- 大口径平面镜 /
- 瑞奇-康芒法检测 /
- 灵敏度矩阵 /
- 光线追迹 /
- 数据处理算法
Abstract:
Addressing limitations in existing data processing methods for large-aperture flat mirror figure measurement – specifically low generality and susceptibility to environmental instabilities, this paper proposes a novel data processing approach. This method integrates ray tracing to generate a sensitivity matrix and applies it to process and analyze data obtained via the Ritchey-Common test. Consequently, high-precision figure detection of large-aperture flat mirrors is achieved. The investigation commences with the development of a Zemax-based Ritchey-Common optical model, from which a sensitivity matrix is rigorously derived through advanced ray tracing algorithms. This matrix enables precise separation of systematic errors inherent in the measurement process, demonstrating superior accuracy compared to conventional Zernike polynomial aberration correction methods while eliminating approximation-induced artifacts in data interpretation. Subsequent numerical verification of the sensitivity matrix algorithm confirms its theoretical validity and computational robustness. Experimental validation encompasses dual-scale implementation: Primary verification employs a 200-mm aperture test mirror, where cross-comparative analysis with direct interferometric measurements achieves sub-wavelength consistency (RMS<λ/40). Full-scale application in the manufacturing process of a 2.2-meter class planar mirror demonstrates exceptional surface figure control, attaining final surface accuracy better than λ/50 RMS. The methodology exhibits significant improvements in measurement repeatability and environmental stability. This research establishes a generalized computational framework that effectively addresses the scalability challenges in ultra-precision optical testing, providing both theoretical advancement and practical engineering solutions for next-generation large-aperture optical systems fabrication.
- large-aperture flat mirror /
- Ritchey-Common Test /
- sensitivity matrix /
- ray tracing /
- data processing algorithm

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图 1 瑞奇-康芒法测试平面镜光路图

Figure 1. Optical path schematic of Ritchey-Common method for measuring the flat mirror

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图 2 瑞奇-康芒测量仿真模型

Figure 2. Ritchey-Common measurement simulation model

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图 3 瑞奇角为(a) 46°时；(b) 58°时的波前数据

Figure 3. Wavefront data (a) at 46° and (b) at 58°

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图 4 光瞳面与平面镜坐标转换

Figure 4. Coordinate transformation from pupil plane to plane mirror

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图 5 导入面形与计算结果对比。(a)导入面形数据；(b)本文方法计算结果；(c) 残差计算结果

Figure 5. Comparison of imported surface shape data and calculation results. (a) Import of surface data; (b) calculation results of this method; (c) residual calculation results

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图 6 200 mm平面镜瑞奇-康芒检测实验。(a)检测现场；(b)角度1检测结果；(c)角度2检测结果

Figure 6. Ritchey-Common test for a 200-mm flat mirror. (a) Experimental setup; (b) measurement results at incidence angle θ₁；(c) measurement results at incidence angle θ₂

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图 7 使用450 mm平面干涉仪直接检测平面镜。(a) 200 mm平面镜；(b) 450 mm平面干涉仪；(c)检测结果

Figure 7. Direct detection of a plane mirror using 450-mm interferometer. (a) 200 mm flat mirror; (b) 450 mm flat interferometer; (c) measurement results

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图 8 大口径平面镜瑞奇-康芒法检测实验。(a) 2.6 m参考球面镜；(b) 球面镜面形检测结果；(c) 2.2 m待测平面镜

Figure 8. Ritchey-Common test experiment of large-aperture flat mirror. (a) 2.6-m reference spherical mirror; (b) measurement results of spherical mirror; (c) 2.2-m flat mirror test specimen

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图 9 数据处理结果。(a)拟合结果1；(b)拟合结果2；(c)拟合结果3

Figure 9. Data processing results. (a) Fitting result 1; (b) fitting result 2; (c) fitting result 3

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图 10 球面镜坐标到平面坐标的转换

Figure 10. Conversion from spherical mirror coordinates to plane coordinates

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图 11 去除球面镜面形误差前后数据处理结果对比。(a)未移除球面镜误差面形；(b) 移除球面镜误差后面形；(c)去除球面镜面形误差的前后残差

Figure 11. Comparison of data processing result before and after removal of reference sphere surface errors. Surface figure (a) without/(b) reference surface errors correction; (c) Residual error map from error removal process

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表 1 验证实验数据及处理结果(λ)

Table 1. Verify experimental data and processing results

	θ₁ = 41°	θ₂ = 45°	Calculation results	Residual error
(1)	PV=0.2036 RMS=0.0229	PV=0.3406 RMS=0.0259	PV=0.4060 RMS=0.0159	PV=0.0986 RMS=0.0067
(1)
(2)	PV=0.1878 RMS=0.0205	PV=0.3429 RMS=0.0265	PV=0.4700 RMS=0.0158	PV=0.0979 RMS=0.0066
(2)
(3)	PV=0.2037 RMS=0.0201	PV=0.3220 RMS=0.0257	PV=0.4460 RMS=0.0160	PV=0.0986 RMS=0.0067
(3)

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表 2 平面镜面形检测结果

Table 2. Detection results of planar mirror surface shape

Ritchey angle	Result 1	Result 2	Result 3
41.7°	PV=0.2374 RMS=0.0174	PV=0.3379 RMS=0.0175	PV=0.3337 RMS=0.0177
41.7°
48.4°	PV=0.2406 RMS=0.0168	PV=0.1929 RMS=0.0173	PV=0.2055 RMS=0.0172
48.4°

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