中文摘要：

针对光电自准直系统现有简化模型的局限，研究了一种基于矢量运算的的建模方法。以矢量运算理论为基础，通过对分划板任意点经光电自准直系统成像进行一般性分析，建立了分划板点坐标、平面镜转角与回像点坐标相互关系的数学模型，并提出了理想自准直系统的概念。通过数值仿真，分析了回像轨迹与平面镜转角的关系以及简化模型的原理性误差。根据分析的结论，进行了激光自准直实验验证。文中建立的模型对于大范围、高精度的光电自准直系统设计、误差分析与补偿具有一定的指导意义。

英文摘要：

In view of the limitation of the simplified model, this paper proposes a modeling method for photoelectric auto-collimating system based on vector operation. With the theory of vector operation, arbitrary point imaging of the reticle is analyzed in that method. The mathematical model is derived from the relation of the reticle point coordinates, the reflector space angle and the image point coordinates. With its special case, this paper puts forward an ideal auto-collimating system. Finally, principle error of the simplified model and the corresponding relationship between image trace and reflector space angle are discussed and also simulation and laser auto-collimator experiment results validate the proposed model. The presented model has some practical significance in the design, error analysis and compensation of photoelectric auto-collimating system with large range and high precision.