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。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。

A new precise algorithm for computing the fitting coefficients of Zernike polynomial of human eye’s wave-front aberration was presented. The matrix of inconsistent equation group was triangulated 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.