基于Zernike多项式的人眼波前像差拟合算法

J4 ›› 2013, Vol. 30 ›› Issue (2): 146-153.

基于Zernike多项式的人眼波前像差拟合算法

曹正林

南京邮电大学地理与生物信息学院，江苏南京 210003

收稿日期:2012-02-23 修回日期:2012-10-04 出版日期:2013-03-28 发布日期:2013-03-14
通讯作者: 曹正林（1978—）江苏宿迁人，讲师，博士，主要从事计算机辅助生物医学工程方面的研究。 E-mail:caozl@njupt.edu.cn
基金资助:
国家自然科学基金资助（61271082）

Human eye’s wave-front aberration fitting algorithm based on Zernike polynomial

School of Geography and Biological Information, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Received:2012-02-23 Revised:2012-10-04 Published:2013-03-28 Online:2013-03-14

摘要/Abstract

摘要： 采用改进的Gram-Schmidt正交化法对矛盾方程的广义增广矩阵进行正交三角化，导出求解基于Zernike多项式的人眼波前像差拟合系数的算法。通过拟合给定模式系数和一般数学波面的两种方式对算法进行了验证。验证结果表明，该算法与直接构造法方程组解法的计算精度相当。该算法避免了因构造法方程组而引入的计算误差，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。

关键词: 非线性光学, 波前像差拟合系数, 改进的Gram-Schmidt正交化法, Zernike多项式

Abstract: A new precise algorithm for computing the fitting coefficients of the Zernike polynomial was presented. The new algorithm orthogonalized and triangulated the matrix of inconsistent equation group by using improved Gram-Schmidt orthogonalization method. The Zernike coefficients were worked out directly. The algorithm was verified by fitting the given coefficients and normal mathematical surface respectively. The new algorithm has equivalent computational precision to the algorithm of constructing normal equation group. By avoiding constructing normal equation group, the computational error introduced by constructing normal equation group is eliminated. The new algorithm is easy to be programmed and proved to be an efficacious algorithm.

Key words: nonlinear optics, wave-front aberration fitting coefficients, improved Gram-Schmidt orthogonalization method, Zernike polynomial

中图分类号:

R778.2

曹正林. 基于Zernike多项式的人眼波前像差拟合算法[J]. J4, 2013, 30(2): 146-153.

参考文献

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