光栅横向剪切干涉仪及其系统误差分析

System Errors Analysis of Grating Lateral Shearing Interferometer

在分析光栅横向剪切干涉仪典型结构及系统参数配置,给出其适用范围的基础上,系统研究了该干涉仪结构最显著的系统误差:几何光程误差和探测器倾斜误差。采用Zernike多项式给出波前重建前后系统误差项的解析表达式;对其大小与被测数值孔径(NA)、衍射光会聚点间距d、剪切率s之间的关系进行了定量分析。几何光程彗差和像散、探测器倾斜像散和离焦是剪切干涉差分波前中最主要的误差项,波前重建后主要导致几何光程球差和彗差,探测器倾斜彗差。重建波前误差随着NA、d的增加而迅速增大,随着s的减小而增大。特别是小剪切(s≤0.05)时,波前重建对系统误差有增益效应,重建波前的系统误差值远大于差分波前。小剪切情况下,当d>2μm、NA>0.1时,重建波前误差的均方根值远大于1nm。

Based on analysis of the typical structure and system configuration parameters of grating lateral shearing interferometer, we systematically study the most significant errors of the interferometer system： geometric optical path difference and detector tilt error. We give the analytical expression of systematic errors before and after wavefront reconstruction in the form of Zernike polynomials. The relationship between the system errors and the measured numerical aperture （NA）, the distance of diffracted light converging point d, the shear ratio s are quantitatively analyzed. The most important errors for differential wavefront of shearing interferometer are the coma and astigmatism of geometric optical path difference, the astigmatism and defocus of detector tilt. These error terms will cause the errors of spherical aberration and coma of geometric optical path difference, the coma and astigmatism of detector tilt through wavefront reconstruction. The error of reconstructed wavefront increases rapidly with the increasing of NA, d, but increases with the decreasing of s. Especially, the wavefront reconstruction has gained effect on system errors with small shear ratio （a≤0.05）, and the system errors of wavefront reconstruction is much larger than the differential wavefront. The root-mean-square （RMS） of reconstructed wavefront error is much greater than lnm under small shear ratio when d〉2 μm, NA〉0. 1.