抽样点对基于Zernike多项式曲面拟合精度的影响

在光学测量中,常以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,用拟合得到的曲面方程去反应实际波面或面形的属性。现研究了用不同精度的测量设备得到的抽样数据进行基于Zernike多项式的曲面拟合,研究了测量设备精度和抽样点数目对拟合精度的影响,得出通过增加抽样点可以对由较低精度设备测得的抽样数据进行较高精度拟合的结论。

The influence of sampling points on the precision of curved surface fitting based on Zernike polynomials

In optical measurement,Zernike polynomials are often used as basic set of polynomials for the fitting of measured discrete data.The wavefront and curved surface are interpreted in the form of linear combinations of Zernike polynomials,which are used to describe the property of actual wavefront and surface.In this article investigation is made on the curved surface fitting of the sampling data obtained by different preccision instruments based on Zernike polynimials,and on the influence of the precision of instrments and amount of sampling points on fitting precision.The conclusion can be drawn that the precision of fitting with sampling discrete data obtained by lower precision instrument improves with larger set of sampling points.