title: Forward and inverse solutions for three-element Risley prism beam scanners.
abstract: Scan blind zone and control singularity are two adverse issues for the beam scanning performance in double-prism Risley systems. In this paper, a theoretical model which introduces a third prism is developed. The critical condition for a fully eliminated scan blind zone is determined through a geometric derivation, providing several useful formulae for three-Risley-prism system design. Moreover, inverse solutions for a three-prism system are established, based on the damped least-squares iterative refinement by a forward ray tracing method. It is shown that the efficiency of this iterative calculation of the inverse solutions can be greatly enhanced by a numerical differentiation method. In order to overcome the control singularity problem, the motion law of any one prism in a three-prism system needs to be conditioned, resulting in continuous and steady motion profiles for the other two prisms.
authors.forename: Anhu
authors.initials: A
authors.lastname: Li
authors.forename: Xingsheng
authors.initials: X
authors.lastname: Liu
authors.forename: Wansong
authors.initials: W
authors.lastname: Sun