Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations

Nonparaxial ray tracing through Risley prisms of four different configurations is performed to give the exact solution of the inverse problem arisen from applications of Risley prisms to free space communications. Predictions of the exact solution and the third-order theory [Appl. Opt. 50, 679 (2011)] are compared and results are shown by curves for systems using prisms of different materials. The exact solution for the problem of precision pointing is generalized to investigate the synthesis of the scan pattern, i.e., to create a desirable scan pattern on some plane perpendicular to the optical axis of the system by controlling the circular motion of the two prisms.