Zernike多项式拟合人眼波前像差的一种新算法

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。

A new algorithm for human eye's wave-front aberration fitting with Zernike polynomial

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.