中国空间科学技术

中国空间科学技术 ›› 2021, Vol. 41 ›› Issue (5): 28-36.doi: 10.16708/j.cnki.1000-758X.2021.0064

• 论文 • 上一篇    下一篇

五棱镜面形误差对中心入射光线的转向角影响

温中凯，徐明明，张庆君，李爽   

  1. 1 南京航空航天大学 航天学院，南京211106
    2 中国空间技术研究院 遥感卫星总体部，北京100094
  • 出版日期:2021-10-25 发布日期:2021-09-29

Influence of the surface error of pentaprism on the steering angle of central incident ray

WEN Zhongkai，XU Mingming，ZHANG Qingjun，LI Shuang   

  1. 1 College of Astronautics, Nanjing University of Aeronautics and Astronautics，Nanjing 211106, China
    2 Institute of Remote Sensing Satellite, CAST，Beijing 100094, China
  • Published:2021-10-25 Online:2021-09-29

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摘要： 针对五棱镜面形误差引起出射光线转向角误差，进而影响空间光电跟瞄系统多光轴标校精度的问题，提出了一种研究五棱镜面形误差对出射光线转向角影响的新方法。首先，在五棱镜不规则度较小的前提下，利用最佳拟合球面矢高适当简化了五棱镜的工作面模型，推导出了出射光线转向角计算公式，并将影响出射光线转向角误差的因素限定在了6个非独立随机变量的共同作用上。然后，结合五棱镜的典型应用场景，提出了一种降维分析方法，去除了6个变量间的相互关联，推导出了降维后的转向角误差计算公式。计算结果表明，该公式计算主截面方向和垂直于主截面方向上转向角误差的最大相对误差分别仅为2.14%和0.31%，完全符合精度分析要求。最后，通过试验对五棱镜进行了技术测试，结果表明：主截面方向和垂直于主截面方向上转向角误差的试验测试平均值与降维公式计算结果的偏差分别在±0.25″和±0.15″以内，这是完全可以接受的。因此，提出的简化模型以及降维分析方法均是可行的，为五棱镜面形误差的相关研究提供了一种新的研究思路与分析方法。

关键词: 五棱镜, 面形误差, 转向角误差, 最佳拟合球面矢高, 降维分析

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