摘要
该文提出了一种用于计算全息数字波面干涉仪中实现波面Ｚｅｒｎｉｋｅ多项式拟合的精确算法．该算法不同于传统的直接构造法方程和Ｇｒａｍ－Ｓｃｈｍｉｄｔ正变化方法，而是用Ｈｏｕｓｅｈｏｌｄｅｒ变换对矛盾方程的广义增广矩阵进行正交三角化，直接求解拟合系数．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．
A precise algorithm for wavefront fitting using Zernike polynomial, which is applied in the computer-generated hologram digital wavefront interferometer, is studied. Differing from the conventional method of direct constructing normal equation group or the Gram-Schmidt orthogonalization method, the new algorithm orthogonalizes and triangulates the matrix of inconsistent equation group by using Householder transformation, and then the Zernike coefficients are worked out using a backsubstitution technique. It is proposed for the first time. By avoiding constructing normal equation group, the computational error introduced by constructing normal equation group is eliminated. It is also quite easy to be programmed and has proved to be an efficacious algorithm.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2000年第3期378-385,共8页
Acta Mathematica Scientia
基金
天文基金资助项目
