长条形镜面面形拟合技术研究

闫力松; 杨甬英; 马冬林; 韩西萌

doi:10.3788/CO.20181106.1011

长条形镜面面形拟合技术研究

doi: 10.3788/CO.20181106.1011

cstr: 32171.14.CO.20181106.1011

闫力松^{1, 2, ,},
杨甬英¹,
马冬林²,
韩西萌³

1.
浙江大学现代光学仪器国家重点实验室, 浙江杭州 310027
2.
华中科技大学光电学院, 湖北武汉 430074
3.
中国航天科工集团第九总体设计部, 湖北武汉 430000

基金项目:

国家自然科学基金 61036015

详细信息

作者简介:
闫力松(1988-), 男, 黑龙江齐齐哈尔人, 博士, 讲师, 2010年中国科学院长春光学精密机械与物理研究所获得博士学位, 现工作于华中科技大学光学与电子信息学院, 主要从事光学检测方面的研究。E-mail:yanlisong@hust.edu.cn

中图分类号: O439;O436.1
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出版历程
- 收稿日期: 2017-10-13
- 修回日期: 2017-11-29
- 刊出日期: 2018-12-01

Surface fitting technology of rectangular mirror

1.
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
2.
School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China
3.
The 9th Designing of China Aerospace Science Industry Corp, Wuhan 430000, China

Funds:

National Natural Science Foundation of China 61036015

More Information

Corresponding author: YAN Li-song, E-mail:yanlisong@hust.edu.cn

摘要

摘要: 为了解决长条形镜面面形拟合中各项不正交，无法在调整中利用像差指导计算机辅助装调的问题，本文建立了一套合理的拟合模型。该模型以矩阵求解正交化Zernike多项式系数为基础，将离散的数据点作为定义域，对已选取的Zernike项进行定义域内正交化计算，并以获得的各正交项为基底，实现对长条形镜面及其他异形光学镜面的正交化多项式拟合求解。进而确定在干涉检测中加工误差与装调误差的分离，为光学镜面的最终面形收敛提供保障。根据本文实验结果，对一口径600 mm×260 mm，PV与RMS值分别为5.889λ及1.002λ的长条形光学镜面进行拟合，利用Metropro去像散后，面形未得到收敛，PV与RMS值分别变为7.448λ及1.725λ。而采用本文算法处理后，其PV与RMS值分别收敛为4.666λ及0.679λ，验证了本文方法对于长条形镜面拟合的正确性。
- 干涉测量 /
- 面形拟合 /
- 长条形反射镜 /
- 正交化
Abstract: In order to solve the non-orthogonal problems in the surface fitting to rectangular mirror, and realize the computer aided adjustment based on aberration, a reasonable fitting model is established in this paper. The model is based on the method by using matrix to solve the orthogonal Zernike polynomial coefficients, through the matrix solving method, and using the discrete data points as the domain, the orthogonalization calculation is performed on the selected Zernike term, and the orthogonal terms obtained are used as the basis to realize the orthogonal polynomial fitting solution for the rectangular mirror and other irregular optical mirrors to determine the separation of the machining error and the alignment error in the interference detection, thus guaranteeing convergence of the final shape of the optical mirror. According to the experimental results, a rectangular mirror with size of 600 mm×260 mm and PV and RMS values of 5.889λ and 1.002λ is fitted. After anastigmatism with Metropro, the surface shape is not converged, and the PV and RMS values become 7.448λ and 1.725λ respectively. But according to the algorithm described in this paper, the PV and RMS values converge to 4.666λ and 0.679λ respectively, which verifies the correctness of the proposed method for rectangular mirror surface fitting.
- interferometry /
- surface fitting /
- rectangular mirror /
- orthogonalization

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图 1 长条形镜面检测光路图

Figure 1. Optical pathway diagram of surface testing for rectangular mirror

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图 2 检测光路图

Figure 2. Testing optical pathway setup

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图 3 检测结果

Figure 3. Testing results

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图 4 Metropro去像散结果

Figure 4. Results of Metropro anastigmatism

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图 5 正交化去像散结果

Figure 5. Anastigmatism results of proposed method

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map

参考文献(22)

[1]	刘晓梅, 向阳.宽视场成像光谱仪器前置远心离轴三反光学系统设计[J].光学学报, 2011, 31(6):0622005-1-0622004-4. http://cdmd.cnki.com.cn/Article/CDMD-80139-1013293705.htm LIU X M, XIANG Y. Design of telecentric off-axis three-mirror system of imaging spectrometer with wide field-of-view[J]. Acta Optica Sinica, 2011, 31(6):0622005-1-0622004-4.(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-80139-1013293705.htm
[2]	刘晓梅, 向阳.具有实入瞳的远心离轴三反系统研究与设计[J].光学学报, 2011, 31(11):1122002-1-1122002-4. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201111044.htm LIU X M, XIANG Y. Research and design of telecentric off-axis three-mirror system with real entrance pupil[J]. Acta Optica Sinica, 2011, 31(11):1122002-1-1122002-4.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201111044.htm
[3]	陈杨, 王跃明.大像场离轴三反望远镜畸变特性分析与设计[J].光学学报, 2013, 33(2):0222003-1-0222003-5. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QKV20132013051600111165 CHEN Y, WANG Y M. Design and distortion characteristics analysis of the large-image-field off-axis three-mirror telescope[J]. Acta Optica Sinica, 2013, 33(2):0222003-1-0222003-5.(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QKV20132013051600111165
[4]	常军, 翁志成, 姜会林, 等.用于空间的三反射镜光学系统设计[J].光学学报, 2003, 23(2):216-219. doi: 10.3321/j.issn:0253-2239.2003.02.018 CHANG J, WENG ZH CH, JIANG H L, et al.. Design on three-reflective-mirror system used in space[J]. Acta Optica Sinica, 2003, 23(2):216-219.(in Chinese) doi: 10.3321/j.issn:0253-2239.2003.02.018
[5]	杨新军, 王肇圻, 母国光, 等.偏心和倾斜光学系统的像差特性[J].光子学报, 2005, 34(11):1658-1662. http://d.old.wanfangdata.com.cn/Periodical/gzxb200511014 YANG X J, WANG ZH Q, MU G G, et al.. Aberration properties of the decentered and tilted optical systems[J]. Acta Photonica Sinica, 2005, 34(11):1658-1662.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gzxb200511014
[6]	TURNE T S. Vector aberration theory on spreadsheet analysis of tilted and decentered systems[J]. SPIE, 1992, 1752:184-195 doi: 10.1117-12.130730/
[7]	李旭阳, 李英才, 马臻, 等.消畸变长焦距相机光学系统设计[J].光学学报, 2010, 30(9):1359-1363. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201001877043 LI X Y, LI Y C, MA ZH, et al.. Optical system design of space camera with long focal length and correction of image distortion[J]. Acta Optica Sinica, 2010, 30(9):1359-1363.(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201001877043
[8]	潘君华.光学非球面的设计、加工与检验[M].苏州:苏州大学出版社, 2004:32-35. PAN J H. Design Manufacture and Test of Aspherical Optical Surfaces[M]. Suzhou:Soochow University Press, 2004:32-35.(in Chinese)
[9]	THOMPSON K P. Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry[J]. J. Opt. Soc. Am. A, 2005, 22(7):1389-1401. doi: 10.1364/JOSAA.22.001389
[10]	GUO P J, YU J C. Design and certification of a null corrector to test hyperboloid convex mirror[J]. SPIE, 2006, 6150:259:263. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1323209
[11]	YANG H S, SONG J B, LEE I W, et al.. Testing of steep convex aspheric surface with a Hartmann sensor by using a CGH[J]. Opt. Express, 2006, 14(8):3247-3254. doi: 10.1364/OE.14.003247
[12]	孙文卿, 陈磊, 李金鹏, 等.非圆孔径离散采样点正交多项式波前拟合[J].红外与金宝搏188软件怎么用工程, 2015, 44(3):1068-1072. doi: 10.3969/j.issn.1007-2276.2015.03.050 SUN W Q, CHEN L, LI J P, et al.. Discrete sampling points of non-circular aperture orthogonal polynomials wave-front fitting[J]. Infrared and Laser Engineering, 2015, 44(3):1068-1072.(in Chinese) doi: 10.3969/j.issn.1007-2276.2015.03.050
[13]	亓波, 陈洪斌, 刘顺发.Zernike多项式波面拟合的回归分析方法[J].光学精密工程, 2007, 15(3):396-400. doi: 10.3321/j.issn:1004-924X.2007.03.017 QI B, CHEN H B, LIU SH F. Regression analysis of wavefront fitting using Zernike polynomial[J]. Opt. Precision Eng., 2007, 15(3):396-400.(in Chinese) doi: 10.3321/j.issn:1004-924X.2007.03.017
[14]	薛建兴, 王启明, 古学东, 等.500 m口径球面射电望远镜瞬时抛物面拟合精度的预估与改善[J].光学精密工程, 2015, 23(7):2052-2059. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201507031 XUE J X, WANG Q M, GU X D, et al.. Estimation and improvement for fitting accuracy of instantaneous parabolic reflector in FAST[J]. Opt. Precision Eng., 2015, 23(7):2052-2059.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201507031
[15]	武鹏飞, 张赞, 郑义, 等.采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响[J].光学精密工程, 2016, 24(7):1564-1572. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201607004 WU P F, ZHANG Z, ZHENG Y, et al.. Influence of sampling point distribution in freeform surfaces fitting with radial based function model[J]. Opt. Precision Eng., 2016, 24(7):1564-1572.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201607004
[16]	徐乐, 张春雷, 代雷, 等.高精度非回转对称非球面加工方法研究[J].中国光学, 2016, 9(3):364-369. //www.illord.com/CN/abstract/abstract9413.shtml XU L, ZHANG CH L, DAI L, et al.. Research on manufacturing method of non-rotationally symmetrical aspheric surface with high accuracy[J]. Chinese Optics, 2016, 9(3):364-369.(in Chinese) //www.illord.com/CN/abstract/abstract9413.shtml
[17]	于新峰, 巩岩, 倪明阳, 等.基于运动学支撑的透镜光学表面面形及其复现性[J].光学精密工程, 2013, 21(8):2000-2007. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201308013 YU X F, GONG Y, NI M Y, et al.. Optical surface figure of lens under kinematic mount apparatus and its reproducibility[J]. Opt. Precision Eng., 2013, 21(8):2000-2007.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201308013
[18]	于树海, 王建立, 董磊, 等.基于最小二乘法拟合估计傅里叶望远镜的缺失分量[J].光学精密工程, 2015, 23(1):282-287. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201501035 YU SH H, WANG J L, DONG L, et al.. Estimation of missing components of Fourier Telescopy based on least square fitting[J]. Opt. Precision Eng., 2015, 23(1):282-287.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201501035
[19]	贺健康, 张立超, 才玺坤, 等.离子束溅射制备GdF₃光学薄膜沉积速率分布特性[J].中国光学, 2016, 9(3):357-363. //www.illord.com/CN/abstract/abstract9432.shtml HE J K, ZHANG L CH, CAI X K, et al.. Deposition rate distribution of GdF₃ optical coating prepared by ion beam sputtering[J]. Chinese Optics, 2016, 9(3):357-363.(in Chinese) //www.illord.com/CN/abstract/abstract9432.shtml
[20]	桑爱军, 孙敏, 陈绵书, 等.新多维矢量矩阵变换域的运动矢量估计[J].中国光学, 2015, 8(2):191-197. //www.illord.com/EN/abstract/abstract9267.shtml SANG A J, SUN M, CHEN M SH, et al.. Motion vector estimation in multi-dimensional vector matrix transform domain[J]. Chinese Optics, 2015, 8(2):191-197.(in Chinese) //www.illord.com/EN/abstract/abstract9267.shtml
[21]	VIRENDRA N M, DAI G M. Orthonormal polynomials in wavefront analysis:analytical solution[J]. J. Opt. Soc. Am. A, 2007, 24(9):2294-3016. doi: 10.1364/JOSAB.24.002294
[22]	DAI G M, VIRENDRA N M. Nonrecursive determination of orthonormal polynomials with matrix formulation[J]. Opt. Lett., 2007, 32(1):74-76. doi: 10.1364/OL.32.000074