Ruled surfaces generated by Risley prism pointers: I. Pointing accuracy evaluation and enhancement based on a structural analysis of the scan field inside the pointer

Abstract

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)JOAOD60740-323210.1364/JOSAA.28.000667 and Li, Appl. Opt. 50, 4302 (2011)APOPAI0003-693510.1364/AO.50.004302]. 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.