Abstract: In order to solve the problem that the surface error of pentaprism will cause the steering angle error of the emergent ray, which affects the accuracy of the multi-optical axis calibration of space photoelectric tracking and aiming system, a new method was proposed to study the effect of the surface error of the pentaprism on the steering angle of the emergent ray. Firstly, the best fit spherical vector height was used to appropriately simplify the working surface model of pentaprism under the premise that the irregularity of the pentaprism is small. The steering angle formula of the emergent ray was derived, and the influence factors of the steering angle error of the emergent ray were limited to the joint action of six correlative random variables. Then, a dimensionality reduction analysis method by combining the typical application scenarios of pentaprism was proposed, which removes the correlation among the six variables, and the steering angle error calculation formula after dimensionality reduction was derived. The calculation results of the formula show that the maximum relative errors of the steering angle error in the direction of the principal section and the direction perpendicular to the principal section are only 2.14% and 0.31%, which meets the requirements of accuracy analysis. Finally, the technical test of the pentaprism was carried out through experiments, and the results show that the deviations of the steering angle errors in the direction of the principal section and the direction perpendicular to the principal section between the average values of the experimental test and the calculated results of the dimensionality reduction formula a ±0.25″ and ±0.15″, which is acceptable. Therefore, the simplified model and the dimensionality reduction analysis method proposed are both feasible, and provide a new research idea and analysis method for the related research of surface error of pentaprism.

Key words: pentaprism, surface error, steering angle error, best fit spherical vector height, dimensionality reduction analysis