Mathematical model and simulation for testing aspheric surface by annular subaperture stitching interferometry

WANG Xiao-kun; ZHANG Xue-jun; WANG Li-hui

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Mathematical model and simulation for testing aspheric surface by annular subaperture stitching interferometry

Article | 更新时间：2020-08-12

- Mathematical model and simulation for testing aspheric surface by annular subaperture stitching interferometry
- Optics and Precision Engineering Vol. 14, Issue 4, Pages: 527-532(2006)
- 作者机构：
  
  1. 中国科学院长春光学精密机械与物理研究所,吉林长春,中国,130033
  2. 中国科学院研究生院北京,100039
- 作者简介：
- 基金信息：
- DOI：
  CLC： O436.1;TQ171.6+5
- Received：22 November 2005，
  
  Revised：18 June 2006，
  
  Published：2006
- 稿件说明：
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王孝坤, 张学军, 王丽辉. 环形子孔径拼接干涉检测非球面的数学模型和仿真研究[J]. 光学精密工程, 2006,14(4): 527-532

WANG Xiao-kun, ZHANG Xue-jun, WANG Li-hui, ZHENG Li-gong. Mathematical model and simulation for testing aspheric surface by annular subaperture stitching interferometry[J]. Editorial Office of Optics and Precision Engineering, 2006,14(4): 527-532
王孝坤, 张学军, 王丽辉. 环形子孔径拼接干涉检测非球面的数学模型和仿真研究[J]. 光学精密工程, 2006,14(4): 527-532 DOI：

WANG Xiao-kun, ZHANG Xue-jun, WANG Li-hui, ZHENG Li-gong. Mathematical model and simulation for testing aspheric surface by annular subaperture stitching interferometry[J]. Editorial Office of Optics and Precision Engineering, 2006,14(4): 527-532 DOI：

摘要

利用环形子孔径拼接干涉技术可以不需要补偿器、CGH等辅助元件就能够高分辨、低成本、高效地实现对大口径、大相对孔径非球面的检测。介绍了该技术的基本原理

并基于最小二乘法和Zernike多项式拟合建立了合理的数学模型

同时对其进行了计算机模拟实验

拼接前后全孔径相位分布残差的PV值和RMS值分别为0.0079 和0.0027

说明该拼接模型和算法是准确可行的

从而提供了除零位补偿外又一种定量测试非球面尤其是大口径非球面的途径。

Abstract

Annular subaperture stitching interferometry can test large-aperture

large relative aperture aspheric surfaces at high resolution

low cost and high efficiency without assistant parts. The basic principle of the stitching method was introduced

and the reasonable mathematical model and effective splicing algorithm were established based on least squares method and Zernike polynomial fitting. Meanwhile the computer simulation experiment was carried on

the PV and RMS of the full aperture phase distribution residual error are 0.0079 and 0.0027

respectively. The results show that this splicing model and algorithm are accurate and feasible

and it can provide another quantitive measurement for testing aspheric surfaces besides null compensation

especially for large aperture asphere.

关键词

Keywords

references

张学军,张云峰,余景池,等. FSGJ-1非球面自动加工及在线检测系统[J]. 光学精密工程,1997,5(2):70-76. ZHANG X J,ZHANG Y F,YU J CH,et al. FSGJ-1 aspheres automatic fabrication and on-line testing system[J].Optics and Precision Engineering,1997,5(2):70-76.(in Chinese)[2] HOU X,WU F. Annular subaperture interferometric testing technique for large aspheric surfaces[J]. SPIE,2005,5638:992-997.[3] MAURO M,LUCA P,ALESSANDRO M.Testing aspheric surfaces using mulitiple annular interferograms[J].Opt.Eng.,1993,32(5):1073-1079.[4] 鄢静舟,雷凡. 用Zernike 多项式进行波面拟合的几种算法[J]. 光学精密工程,1999,7(5):119-128. YAN J ZH,LEI F.Algorithms for wavefront fitting using Zernike polynomial[J]. Optics and Precision Engineering, 1999,7(5):119-128.(in Chinese)[5] JON F,PAUL D,PAUL E M,et al. An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces[J].SPIE,2003,5188:296-307.[6] PAUL E M, JON F, GREG F,et al.High precision metrology of domes and aspheric optics[J].SPIE,2005,5786: 113-121.

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Related Institution

Optical Technology Research Center, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences

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南京理工大学电子工程与光电技术学院

中国科学院长春光学精密机械与物理研究所光学技术研究中心

College of Fine Photoelectric Instrument and Engineering, Harbin Institute of Technology

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