Zernike多项式拟合人眼波前像差的一种新算法

曹正林; 廖文和; 沈建新

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Zernike多项式拟合人眼波前像差的一种新算法

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- Zernike多项式拟合人眼波前像差的一种新算法
- A new algorithm for human eye’s wave-front aberration fitting with Zernike polynomial
- 光学精密工程 2006年14卷第2期页码：308-314
- 作者机构：
  
  南京航空航天大学机电学院,江苏南京,210016
- 作者简介：
- 基金信息：
- DOI：
  中图分类号： R778.2;TP391
- 收稿日期：2005-06-15，
  
  修回日期：2005-12-14，
  
  网络出版日期：2006-04-30，
  
  纸质出版日期：2006-04-30
- 稿件说明：
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曹正林, 廖文和, 沈建新. Zernike多项式拟合人眼波前像差的一种新算法[J]. 光学精密工程, 2006,14(2):308-314.

CAO Zheng-lin, LIAO Wen-he, SHEN Jian-xin. A new algorithm for human eye’s wave-front aberration fitting with Zernike polynomial[J]. Optics and precision engineering, 2006, 14(2): 308-314.
曹正林, 廖文和, 沈建新. Zernike多项式拟合人眼波前像差的一种新算法[J]. 光学精密工程, 2006,14(2):308-314. DOI：

CAO Zheng-lin, LIAO Wen-he, SHEN Jian-xin. A new algorithm for human eye’s wave-front aberration fitting with Zernike polynomial[J]. Optics and precision engineering, 2006, 14(2): 308-314. DOI：

摘要

提出一种用于计算人眼波前像差函数中Zernike多项式拟合系数的精确算法。介绍了人眼波前像差的概念以及用Zernike多项式表示的人眼波像差函数

采用Householder变换对矛盾方程的广义增广矩阵进行正交三角化

导出求解拟合系数的算法。给出了人眼大、小瞳孔的像差测量计算实例

并对比了直接构造法方程组的计算结果和精度。对比多只眼睛的计算结果表明

该算法与直接构造法方程组的计算精度相当

各项拟合系数的相对误差都在10%以内。该算法避免了构造法方程组引入的计算误差

易于编程

是一种比较理想的求解Zernike多项式拟合系数的算法。

Abstract

A new precise algorithm for computing the fitting coefficients of the Zernike polynomial was presented. The concept of human eye’s aberration and the mathematical function of wave-front aberration expressed by Zernike polynomial were introduced. The matrix of inconsistent equation group of the algorithm was orthogonalized and triangulated by Householder transformation

and the Zernike coefficients were given directly. The fitting coefficients of the Zernike polynomial of the big and small pupil were computed respectively by using this new algorithm and by constructing normal equation group. The computational results show that two algorithms have equivalent computational precision with relative error of each order coefficient in less than 10%. By avoiding the computational error introduced by constructing normal equation group

the algorithm is easy to used in programming and has proved to be an efficacious algorithm.

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references

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. 鄢静舟,孙厚环,高志强,等. 用Zernike多项式进行波面拟合的一种新算法[J]. 数学物理学报,2000,20(3):378-385. YAN J ZH,SUN H H,GAO ZH Q,et al.A new algorithm for wave-front fitting using Zernike polynomial[J].Acta Mathematica Scientia,2000,20(3):378-385.(in Chinese)

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