五角棱镜扫描系统中调整误差及制造角差的影响分析-

五角棱镜扫描系统可以实现高精度测量光学表面面形，为了全面分析五角棱镜扫描系统中的调整误差及制造角差对指向误差和测角仪测量误差的影响。根据旋转变换矩阵和光线矢量追迹理论，运用MATLAB编写通用的五角棱镜扫描系统的光线矢量追迹函数及相关分析程序。同时通过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：在扫描测量过程中，测角仪的俯仰角和五角棱镜的制造角差对沿扫描方向指向误差和测角仪垂直方向测量值的影响是常量，五角棱镜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指向误差和测角仪水平方向测量值均成线性关系。当导轨误差滚动10"、偏摆10"，系统的各项调整误差为±3"时，沿扫描方向最大测角误差为0.0010666"。

Influences analysis of the pentaprism scannig system due to alignment error and fabrication angles error

The highly accurate measurement of optical surfaces can be realized by means of pentaprism scanning system, in order to analyze the influences on the line-of-sight error and angles measurement error of autocollimator due to alignment error and fabrication angles error of pentaprism scannig system. According to rotation transform matrix and vectorial ray tracing theory, a versatile vectorial ray tracing function and a relevant analysis program was written by MATLAB. Meanwhile, second-order approximations for computing the line-of-sight error and angle measurement of autocollimator in a certain range were derived by a 2D second-order polynomial fitting. The analysis result indicated that during the scanning measurement, the influences on the line-of-sight error of in-scan direction and vertical angle measurement of autocollimator are constants due to pitch angle of autocollimator and fabrication angles error of pentaprism, and there are quadratic with the yaw angle and roll angle of pentaprism; the line-of-sight 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 0.0010666".