用Zernike多项式进行波面拟合的几种算法  

Algorithms for Wavefront Fitting Using Zernike Polynomial

作　　者：鄢静舟[1] 雷凡[2] 周必方[1] 高志强[1] 

机构地区：[1]中国科学院南京天文仪器研制中心,南京210042 [2]北京市气象局,北京100089

出　　处：《光学精密工程》1999年第5期119-128,共10页Optics and Precision Engineering

基　　金：天文基金

摘　　要：介绍了几种实现波面Ｚｅｒｎｉｋｅ 多项式拟合的常用算法。为避免因直接构造法方程组而引入计算误差，这些方法归结为两种思路：一是从基底函数系入手，通过变换函数族的基底来改善法方程组状态；二是直接从矛盾方程组入手，应用Ｈｏｕｓｅｈｏｌｄｅｒ变换把系数矩阵正交三角化，直接求解拟合系数。特别是第二种方法由本文第一次提出，它避免了构造法方程组，从而避免了以前的方法因构造的法方程组出现严重病态而引入的计算误差，并且易于编程，因而是一种比较理想的实现Ｚｅｒｎｉｋｅ 多项式拟合的算法。Several algorithms for wavefront fitting using Zernike polynomial are studied. In order to avoid the computational error introduced by direct constructing normal equation group, the algorithms can be divided into two classes. One is Gram Schmidt or covariance matrix method, in which we transform the base function set to meliorate the condition of the normal equation group. The other is called Householder transformation method, in which the matrix of inconsistent equation group is orthogonalized and triangulated using Householder transformation, and then the Zernike coefficients can be worked out by using a backsubstitution technique. It is proposed for the first time. Being a method that can avoid the computational error effectively and can be easily performed, it has proven to be a feasible and efficacious algorithm.

关 键 词：波面拟合 ZERNIKE多项式 算法 

分 类 号：TH744.3[机械工程—光学工程]