Small-aberration retrieval based on spot images

CHEN Xin-hua; JI Yi-qun; SHEN Wei-min

doi:10.3788/OPE.20122004.0706

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Small-aberration retrieval based on spot images

Article | 更新时间：2020-08-12

- Small-aberration retrieval based on spot images
- Optics and Precision Engineering Vol. 20, Issue 4, Pages: 706-711(2012)
- 作者机构：
  
  1. 苏州大学现代光学技术研究所,江苏苏州,215006
  2. 江苏省现代光学技术重点实验室,江苏苏州,215006
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20122004.0706
  CLC： TH703;TP391.4
- Received：30 September 2011，
  
  Revised：15 December 2011，
  
  Published Online：22 April 2012，
  
  Published：22 April 2012
- 稿件说明：
移动端阅览
陈新华, 季轶群, 沈为民. 基于星点图像的小像差复原[J]. 光学精密工程, 2012,(4): 706-711

CHEN Xin-hua, JI Yi-qun, SHEN Wei-min. Small-aberration retrieval based on spot images[J]. Editorial Office of Optics and Precision Engineering, 2012,(4): 706-711
陈新华, 季轶群, 沈为民. 基于星点图像的小像差复原[J]. 光学精密工程, 2012,(4): 706-711 DOI： 10.3788/OPE.20122004.0706.

CHEN Xin-hua, JI Yi-qun, SHEN Wei-min. Small-aberration retrieval based on spot images[J]. Editorial Office of Optics and Precision Engineering, 2012,(4): 706-711 DOI： 10.3788/OPE.20122004.0706.

摘要

提出了一种基于星点图像的小像差光学系统像差复原方法。应用标量衍射理论和Bessel级数

推导了以波像差的Zernike系数为参量的小像差光学系统点扩散函数的解析计算公式

利用该公式给出了基于星点图像的小像差复原问题的目标函数及梯度函数的表达式

并采用最优化方法进行求解。分别在理想情况和噪声情况下数值模拟了光学系统的像差复原

验证了本文提出的像差复原方法的有效性

并分析了星点目标尺寸对复原效果的影响。该方法以波像差的Zernike系数为优化变量

并利用推导得到的解析表达式计算目标函数及其梯度值

避免了常用像差复原算法中所需的傅里叶变换和有限差分等数值运算

提高了复原算法的运算速度。

Abstract

A small-aberration retrieval method based on spot images was introduced and an analytic formula to computer the point spread function for a small aberration optical system was derived according to the scalar diffraction theory and Bessel series. With this formula

the objective function and its gradient were given for the small-aberration retrieval method. Then

the optimized method was used to solve this problem. The effectiveness of this method was demonstrated by using the numerical simulation under ideal and noisy conditions

respectively

and the influence of the size of spot object on the retrieval results was also analyzed. This method uses aberration's Zernike coefficients as optimization variants and computes the objective function and its gradient with analytic expressions to avoid Fourier transform or numerical integral needed in common aberration retrieval methods. Therefore

it improves the speed of aberration retrieval greatly.

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Keywords

references

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