基于灵敏度矩阵的瑞奇-康芒检测数据处理

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

基于灵敏度矩阵的瑞奇-康芒检测数据处理

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:
张泊泊（1997—），男，陕西西安人，硕士，研究生，学生，主要从事大口径光学系统波前检测方面的研究。Email：zhangbobo@st.xatu.edu.cn

鄂可伟（1991—），男，甘肃临夏人，博士，高级工程师，硕士生导师，主要从事光学波面和光学检测技术方面的研究。主要学习经历：2008.09——2012.07 兰州交通大学本科；2012.09——2017.07 四川大学硕博连读。E-mail：ekewei@opt.ac.cn

李世杰（1988—），男，四川广安人，博士，副教授，博士生导师，主要从事先进光学制造与检测技术方面的研究。E-mail：lishijie@xatu.edu.cn

李晶（1987—），女，河北石家庄人，博士，高级工程师，硕士生导师，主要从事光学系统检测技术方面的研究。E-mail：lijing@opt.ac.cn

刘焕玉（1998—），女，陕西榆林人，硕士，工程师，主要从事光学波面和光学检测技术方面的研究。E-mail：296974266@qq.com

郭永康（1994-），男，安徽芜湖人，本科，工程师，主要从事光学系统波前检测技术方面的研究。E-mail：1034658571@qq.com

张东旭（1998—），男，河南驻马店人，硕士，研究生，学生，主要从事凸非球面检测技术方面的研究。E-mail：zdx4800@163.com

薛勋（1986—），男，陕西蒲城人，博士，高级工程师，硕士生导师，主要从事弱目标模拟与探测技术方面的研究。E-mail：xx@opt.ac.cn

赵建科（1973—），男，陕西宝鸡人，硕士，高级工程师，硕士生导师，主要从事光电仪器研发和光学测试方面的研究。E-mail：zjk@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

Research on data processing for Ritchey-Common test based on sensitivity matrix

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, Shaanxi, China
2.
School of Opto-electronical Engineering, Xi’an Technological University, Xi’an 710021, Shaanxi, China
3.
Nanjing Astronomical Instruments Co., LTD , Chinese Academy of Sciences, Nan’jing 210042, Jiangsu, 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:
针对现有瑞奇-康芒法检测大口径平面反射镜的数据处理方法中存在通用性较低、检测中的数据易受环境稳定性影响等问题，本文提出了一种灵敏度矩阵分析结合光线追迹的数据处理方法，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，相比直接采用泽尼克拟合方式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，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，验证了该数据处理算法的正确性。进而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:
To address the limitations of conventional data processing approaches in Ritchey-Common method-based inspection of large-aperture planar mirrors, particularly their restricted applicability and environmental sensitivity, this study presents a novel hybrid analytical methodology integrating sensitivity matrix decomposition with rigorous ray tracing simulations. The proposed framework establishes a comprehensive solution for high-precision surface figure characterization through systematic error decoupling and numerical optimization. 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-康芒法测量光路

Figure 1. Ritchey-Common method to measure the flat

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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 仿真模型以及获取到的两角度下波前数据 (a) 瑞奇角为46°时波前数据 (b) 瑞奇角为58°时波前数据

Figure 3. The simulation model and the obtained wavefront data at two angles (a) Wavefront data at angle 46° (b) Wavefront data at angle 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 (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 θ；(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 瑞奇康芒法检测现场 (a) 2.6 m球面镜 (b) 球面镜检测结果 (c) 2.2 m平面镜

Figure 8. Ritchey-Common testing site (a) 2.6 m spherical mirror (b) sphere test results (c) 2.2 m flat mirror

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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对比 (a)不移除球面镜误差 (b) 移除球面镜误差 (c)球面镜面形误差的影响

Figure 11. Spherical mirror surface figure error: Pre- vs. Post-Removal Analysis (a) Without Removing Spherical Mirror Error (b) With Spherical Mirror Error Removed (c) Influence of Spherical Mirror Surface Error

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表 1 验证实验数据及处理结果（λ）

Table 1. Validation of 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. Plane mirror surface shape detection results

Ritchey angle	results1	results 2	results 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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