长条形镜面面形拟合技术研究 -

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长条形镜面面形拟合技术研究

doi:10.3788/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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- 被引次数:0
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 China61036015

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 4Metropro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

下载: 全尺寸图片幻灯片

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