非球面非零位横向剪切干涉检测与波前重建

本文分析了非球面非零位检测中3种典型的非球面度及其变化率、调整误差、回程误差以及干涉仪系统误差,提出了非球面度变化率是影响检测误差的主要因素,并给出了非球面非零位检测面形加工误差的确定方法.对基于Zernike多项式拟合的最小二乘法和系数转换法进行了对比研究,分析了剪切量和多项式拟合阶数对波前重建精度的影响,并给出了数值模拟结果.为了验证以上方法的可行性及检测精度,针对一单点金刚石车削的抛物面反射镜,利用顶点球作为测试波前进行非零位横向剪切干涉检测,并用最小二乘法进行波前重建.实验结果表明,在非球面度变化率最大的反射镜边缘处面形误差最大,达到0.203μm,研究结果为横向剪切干涉仪用于非球面加工过程中在位检测提供了技术支撑.

Non-Null Lateral Shearing Interferometric Testing of Aspheric Surface and Wavefront Reconstruction

Three typical asphericities and their corresponding variation rate, adjustment error, retrace er- ror and interferometer systematic error in non-null aspheric surface testing were analyzed in this paper to propose that the variation rate of asphericity is the main factor affecting testing error and then give the method of determining surface machining error. A comparative study on the least square method and the coefficient conversion method which were based on the Zernike polynomials fitting was made to analyze the influence of shear value and the polynomials fitting order on wavefront reconstruction accuracy, and give the numerical simulation results. In order to verify the feasibility and testing accuracy of the above methods, the non-null lateral shearing interferometric testing was performed on a parabolic reflector sur- face generated by single point diamond turning process. During the testing, a vertex sphere was used as a testing wavefront and the least square method was used for wavefront reconstruction. Experimental results show that the largest form error of 0. 203 p~m was located near the edge of the reflector where the variation rate of aspherieity was at the maximum value. The study provides a very decisive technical support for the application of lateral shearing interferometer to in-situ to.glin~r n~nh,~.; ,-f~ n..- 1_, ~