Exact Analytic Formulae of Beam Pointing Based on Achromatic Risley Prisms

Abstract

Abstract. The mathematic relationship between the given orientations of two-prism groups and the corresponding pointing position of outgoing beam is the basic prerequisite needed in applications of achromatic risley prisms to steer beam in free space. Based on vectorial law of refraction, this paper finishes the derivation of the analytic formulae of the relationship wanted. Then the test samplesobtained by the analytic formulae, the method of paraxial approximation and professional the optical software are compared respectively. The results prove the correctness of the analytic formulae, as well as its necessity and superiority in high-precision pointing solution when beam is steered over wide angular range.