光电自准直系统的建模方法研究

Research on the Model of Photoelectric Auto-collimating System

针对现有自准直模型包含系统信息量有限的不足,提出了一种基于厚透镜对光线变换的建模方法。以应用光学中厚透镜对光线变换的理论为基础,结合矢量运算和坐标系旋转方法建立了光电自准直系统数学模型。通过数值仿真,对模型中包含的平面镜的转角、透镜的厚度、焦距及表面曲率半径、光源和探测器位置等系统主要参数对光电自准直系统的成像影响进行了分析,并通过对像点几何中心的提取,分析了透镜成像畸变对光电自准直系统测量精度的影响。文章建立的模型,为系统参数的提取和优化、分析像点轨迹变化的影响因素以及自准直测量误差的分析和补偿提供了理论支持。

Aiming at the deficiency of existing models with limited system parameters, proposed is a modeling method for photoelectric auto-collimating system based on beam transformation theory of thick lens. With the theory of thick lens beam transformation on applied optics, combined vector operation and coordinate system rotation method, a mathematical model for photoelectric auto-collimating system is constructed. Via numerical simulation, the effects of such factors as reflector space angle, the thickness, focal length and surface curvature radius of lens and the position coordinates of light source and detector, on the imaging results of the optoelectric auto-collimating system were analyzed. By abstracting geometrical centers of image points, the corresponding relationship between measuring error of photoelectric auto-collimating system and image trace for incremental dimension of thick lens was analyzed. The proposed model provides theoretical support for extraction and optimization of system parameters, analysis of the factors affecting image trace, error analysis and compensation of photoelectric auto-collimating system.