基于Zernike多项式波面拟合中边界误差的影响分析  

Effect analysis of edge errors in wavefront fitting with zernike polynomials

作　　者：侯溪[1] 伍凡[1] 杨力[1] 陈强[1] 

机构地区：[1]中国科学院光电技术研究所

出　　处：《红外与激光工程》2006年第z2期72-75,共4页Infrared and Laser Engineering

摘　　要：波面拟合实质上就是把携带测量表面信息的离散点采样数据拟合成与实际波面尽可能一致的数学上的波面函数;在光学检测中,由于 Zernike 多项式在单位圆域里具有正交性而通常被选作拟合基函数.Zernike拟合首先需要进行归一化处理,而待拟合的离散数据组的中心点和半径坐标值是归一化处理所需要的必要参数.简单介绍了基于 Zernike 多项式的波面拟合方法,重点分析了被拟合数据组边界误差(中心点和半径值误差)对拟合结果的影响.分析结果表明边界误差将影响到各项 Zernike 拟合系数精度,其影响程度与边界误差大小有关.因此,在实际的波面拟合分析中有必要采用一些有效的方法以提高待拟合数据组中心点和半径值的确定精度.In the analysis of interferometric test data and optical system performance,it is often convenient to represent the optical wavefront in Zernike polynomial form.The normalization process is the first step in wavefront fitting,and the center and radius value of discrete data set are the basic parameters.The wavefront fitting method is simply introduced,and the effect of edge errors including center and radius error is mainly analyzed.The results of analysis show that the edge errors will affect the accuracy of Zernike fitting coefficients,and the effect extent depends on the amount of edge errors.Therefore,it is necessary that some effective methods are used in wavefront fitting to further improve the accuracy of determining the basic parameters of the data edge.

关 键 词：光学测量 干涉计量 波面拟合 边界误差 ZERNIKE多项式 

分 类 号：O432.2[机械工程—光学工程]