五角棱镜扫描系统中调整误差及制造角差的影响分析  

Influences of alignment error in pentaprism scanning system and fabrication angle error on measuring accuracy of optical surface

作　　者：马冬梅[1] 刘志祥[1,2] 马磊[1,2] 卞江[1,2] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所,吉林长春130033 [2]中国科学院研究生院,北京100039

出　　处：《光学精密工程》2008年第12期2517-2523,共7页Optics and Precision Engineering

基　　金：中国科学院长春光学精密机械与物理研究所二期创新工程资助项目

摘　　要：为了精确测量光学表面的表面斜率,从而实现光学表面面形的高精度测量,全面分析了五角棱镜扫描系统中的调整误差及五角棱镜的制造角差对测量光束的指向精度和被测面表面斜率测量精度的影响。根据旋转变换矩阵和光线矢量追迹理论,运用MATLAB编写了精确计算测量光束指向误差和测角仪测量值的程序,通过对各误差组合的计算结果进行二维二次多项式拟合,推导出在一定角度范围内,用于计算指向误差和测角仪测量值的二阶近似公式。分析结果表明,测角仪的俯仰角和五角棱镜的制造角差对沿扫描方向的指向误差和测角仪垂直方向的测量值的影响是常量,五角棱镜在扫描过程中的偏摆角和滚动角与其成二次函数关系;五角棱镜的偏摆角和滚动角、测角仪的偏摆角与垂直扫描方向的指向误差和测角仪水平方向的测量值均成线性关系。当导轨的滚动角为10″、偏摆角为10″,系统的各项调整误差为±3″时,沿扫描方向的最大测角误差为0.0010666″。The influences of the alignment error in pentaprism scanning system and the angle error of pentaprism fabrication on the line-of-sight accuracy of measuring beam and the slope measuring accuracy of optical surface were analyzed in order to realize the high precision measurement for a optical surface. According to rotation transform matrix and vectorial ray tracing theory, a program used to accurately compute the line-of-sight error and angle measurement error of autocollimator was written by MATLAB. Meanwhile, by a 2D second-order polynomial fitting to the computed results of each error combination, the second-order approximations for computing the line-of-sight error and angle measure-ment value of autocollimator in a certain range were derived. The analysis result indicates that the influences of the pitch angle of autocollimator and the fabrication angle error of pentaprism on the lineof-sight error of in-scan direction and the vertical angle measurement of autocollimator are constants, and there are quadratic with the yaw angle and roll angle of pentaprism in the scanning. The line-ofsight error of cross-scan direction and horizontal angle measurement of autocollimator are linear with the yaw angle and roll angle of pentaprism in the scanning. When the rail error is 10″ in roll. 10″ in yaw, and the misalignments of the system are ±3″, the max angle measurement error in scan direction is 0. 001 066 6″.

关 键 词：光学测量 五角棱镜扫描系统 误差分析 光线矢量追迹 MATLAB 

分 类 号：TH741[机械工程—光学工程] TB92[机械工程—仪器科学与技术]