Zernike多项式波面拟合精度研究

Fitting Accuracy of Wavefront Using Zernike Polynomials

光学表面检测的绝大多数情况中,被测光学表面或光学系统的出射波面总是趋于光滑且连续的,这样的波面函数一定可以表示成一个完备的基底函数的线性组合。因此常用Zernike多项式作为基底函数对测量得到的离散数据进行拟合,把实际波面或面形表示为Zernike多项式各项的线性组合。文中研究了Zernike多项式阶数对拟合精度的影响,以及采样点数对拟合精度的影响。得出Zernike多项式拟合波面并非阶数越高越好,阶数过高会使拟合结果出现病态。因此拟合波面要选择合适阶数的Zernike多项式。当多项式阶数选定时,采样点数多有利于提高拟合精度,但采样点的多少并不是提高拟合精度的先决条件。

The vast majority of cases in optical surface testing,the output surface of measured optical surface or optical system always tends to be smooth and continuous,such wavefront functions must can be expressedas a complete the linear combination of the basement function.Zernike polynomials are often used as basic set ofpolynomials for the fitting of measured discrete data.The wavefront and curved surface are interpreted in theform of linear combinations of Zernike polynomial.The effects of fitting precision owing to Zernike polynomialsorder and sampling points are studied.The result is obtained that higher order Zernike polynomial fitting wavefront is not better,if order more than a certain range,fitting results will appear sick.Therefore,the wavefront fitting should choose appropriate order of Zernike polynomial.When the polynomial order is selected,more sampling points will help improve fitting accuracy.However,the number of sampling points is not a prerequisite forimproving the fitting precision.