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".