离焦位置任意波长透射波前Zernike系数算法研究

Estimation of Zernike Coefficients for Any Wavelength Transmitted Wavefront at Defocus Position

基于Zernike多项式波前拟合法,提出计算离焦位置任意波长透射波前Zernike系数的算法,在聚焦位置Zernike系数基础上补偿离焦距离内Zernike系数变化量.以典型的消色差望远物镜为例,根据设计波长及权重优化其工作位置,计算不同波长的聚焦位置与工作位置的离焦量,使用该算法验证消色差系统工作位置任意波长Zernike系数.与在工作位置直接使用Conrady-Zernike公式对比表明,该算法对于与位置有关的Zernike系数计算效果明显,Z1的绝对误差由6.78降低到了1.41,Z4的绝对误差由6.83降低到了1.45.

Based on Zernike polynomials fitting wavefront,an algorithm of calculating Zernike coefficients for any wavelength transmitted wavefront at defocus position was put foward.The method compensates the change of Zernike coefficients of defocus distance based on Zernike coefficients at focus position.Using an achromatic system,the working position was optimized according to the wavelengths and weights,and the defocusing amount between focus position and working position was calculated,and the any wavelength wavefront Zernike coefficients at working position was verified by the algorithm.The result showed that the proposed algorithm is effective for calculating Zernike coefficients related to position,compared with using Conrady-Zernike formula in working position,the absolute error of Z1 decreased from 6.78 to 1.41,and the absolute error of Z4 decreased from 6.83 to 1.45.