Open AccessForward and inverse solutions for three-element Risley prism beam scanners
Author(s) -
Anhu Li,
Xingsheng Liu,
Wansong Sun
Publication year - 2017
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.25.007677
Subject(s) - prism , optics , ray tracing (physics) , singularity , inverse , inverse problem , beam (structure) , iterative method , lens (geology) , physics , computer science , mathematics , algorithm , mathematical analysis , geometry
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.