Algorithm for misalignmental determination in computer-aided alignment of optical system

ZHANG Bin; ZHANG Xiao-Hui; HAN Chang-Yuan

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Algorithm for misalignmental determination in computer-aided alignment of optical system

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- Algorithm for misalignmental determination in computer-aided alignment of optical system
- Optics and Precision Engineering Vol. 8, Issue 3, Pages: 273-277(2000)
- 作者机构：
  
  中国科学院长春光学精密机械与物理研究所, 吉林长春130021
- 作者简介：
- 基金信息：
- DOI：
  CLC： TH703
- Received：25 February 2000，
  
  Revised：17 March 2000，
  
  Published Online：15 June 2000，
  
  Published：15 June 2000
- 稿件说明：
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张斌, 张晓辉, 韩昌元. 光学系统计算机辅助装调中的一种优化算法[J]. 光学精密工程, 2000,(3): 273-277

ZHANG Bin, ZHANG Xiao-Hui, HAN Chang-Yuan. Algorithm for misalignmental determination in computer-aided alignment of optical system[J]. Editorial Office of Optics and Precision Engineering, 2000,(3): 273-277
张斌, 张晓辉, 韩昌元. 光学系统计算机辅助装调中的一种优化算法[J]. 光学精密工程, 2000,(3): 273-277 DOI：

ZHANG Bin, ZHANG Xiao-Hui, HAN Chang-Yuan. Algorithm for misalignmental determination in computer-aided alignment of optical system[J]. Editorial Office of Optics and Precision Engineering, 2000,(3): 273-277 DOI：

摘要

如何快速、准确、稳定地确定失调量是光学系统计算机辅助装调技术的一个关键部分.本文首先进行数学建模

建立了失调量与引入像差的关系式

然后提出了求解失调量的伪逆及奇异值巩固逆算法

以解决直接按最小二乘法方程组求解所带来的数值不稳定性及解的不精确性问题.最后

利用本文所建立的数值分析模型

进行了模拟计算

计算结果表明

本文的计算方法是合理可行、有效的.

Abstract

How to determine the misalignment quickly

exactly and constantly is the key to the technology of computer-aided optical alignment. First

the mathematical simulation

which is the relationship between the misalignment and the aberrations is founded. Then

the concept of pseudoinverse and the algorithm of the singularity robust inverse are proposed in order to solve the problems of the numerical instability and the result inaccuracy which result from the solution for leastsquares method directly. Finally

the simulant calculation is processed using the numerical analysis model established in this essay. The result shows that the computation method is rational and effective.

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references

布耶哈马著.误差理论与广义逆矩阵[M].北京：测绘出版社,1980

杨簏引,马正午,孙宇,等编.电子计算机应用数学[M].北京：冶金工业出版社,1979.

史荣昌编著.矩阵分析[M].北京.北京理工大学出版社,1996.

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