用旋转双棱镜系统控制光束指向时, 需要由光束的目标指向位置推算两棱镜的旋转角度(称为反向问题)。本文采用一阶近轴近似方法和非近轴光线追迹方法探讨了旋转双棱镜系统反向问题的完整解析解。首先, 基于一阶近轴理论, 利用中心算法分析了反向问题的近似解。然后, 基于矢量形式的斯涅尔定律对系统进行非近轴光线追迹, 用两步算法推算出反向问题的精确解。对比分析两种方法所得的反向解差异并设计实验对结果进行了比较和验证。结果表明, 针对一个确定的光束目标指向位置, 存在两套反向解。相对一阶近轴近似方法, 非近轴光线追迹法推算的反向解更加准确。对于大偏转角度的旋转双棱镜光束指向系统, 非近轴光线追迹法是推算其精确反向解的有效方法。

It is a key problem to calculate the rotation angles of the two prisms through the required pointing position of beams when a rotational double prism beam steering system is used to control the direction of optical beams (named inverse problem). This paper explores the entire analytical solutions of the reverse problem for the rotational double prism beam steering system by employing a first-order paraxial approximation method and a non paraxial ray tracing method. First, the centering algorithm is adopted to analyze the approximate solutions of the reverse problem based on first-order paraxial theory. Then, the nonparaxial ray is traced in the system based on Snell's law with the vector form and a two-step algorithm is applied to calculation of the accurate solutions of the inverse problem. The difference of the inverse solutions calculated with the two methods is analyzed and an experiment is designed to compare and validate the solutions. The results indicate that there are two reverse solutions for an required beam pointing position. Relative to the first-order paraxial approximation method, the reverse solutions derived from the nonparaxial ray tracing method are more accurate. For the rotational double prism beam steering system with large beam deviation, the nonparaxial ray tracing method has a potent effect on calculation of accurate reverse solutions.