Based on the elementary concept of ruled surfaces, a new method relating to a structural analysis of the scan field distributed over the interior of the Risley prisms is proposed that opens the way to a re-examination of the pointing accuracy that predicted the existing noniterative solution of the Risley prism pointers for precision tracking of targets [Li, J. Opt. Soc. Am. A 28, 667 (2011) [CrossRef] and Li, Appl. Opt. 50, 4302 (2011) [CrossRef] ]. After taking the thickness and the air gap of the two prisms into consideration, the refined version of the closed-form analytic solution is obtained, which predicts the correct results for detecting and tracking targets traversing across both the near and far zones of the beam-steering field in front of the pointer if the linear size of the target, the diameter of the laser beam, or their combination is greater than a small fraction of the central thickness of the prism. For very tiny targets, a method for pointing accuracy enhancement is proposed based on tracking a virtual target.

中文翻译：

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Risley棱镜指针生成的直纹曲面：I.基于指针内部扫描场结构分析的指向精度评估和增强

基于直纹面的基本概念，提出了一种与分布在 Risley 棱镜内部的扫描场结构分析相关的新方法，为重新检查预测现有非迭代解的指向精度开辟了道路用于精确跟踪目标的 Risley 棱镜指针 [Li, J. Opt. 社会。是。A 28 , 667 (2011) [CrossRef] 和 Li, Appl。选择。50 , 4302 (2011) [CrossRef] ]。在考虑两个棱镜的厚度和气隙后，得到了封闭形式解析解的改进版本，它预测了检测和跟踪穿过光束近区和远区的目标的正确结果 -如果目标的线性尺寸、激光束的直径或它们的组合大于棱镜中心厚度的一小部分，则指针前方的转向场。针对非常微小的目标，提出了一种基于跟踪虚拟目标的提高指向精度的方法。