title: Analytical direct solutions of the Risley prism systems for tracking and pointing.
abstract: The Risley prism systems, which had many different configurations, are only composed of two wedge prisms. The expressions of the direction cosines of the refractive ray of the two wedge prisms are given by nonparaxial ray tracing in a local coordinate referenced to the wedge prism, and the power of ray deviation of the two wedge prisms are shown by curves for systems using prisms of different materials and opening angles. The analytical direct solutions of the Risley prism systems are derived from the expressions of the direction cosines of the wedge prism through the coordinate transformation, and are also deduced from the two exact orientations for the same pointing position of precision tracking and pointing systems, which arise from applications of the Risley prisms to free-space communications. The exact expressions for the problem of precision tracking are generalized to investigate the synthesis of tracking a given target, i.e., to track a desirable path on some plane perpendicular to the optical axis of the system by controlling the circular motion of the two prisms.
authors.forename: Qi
authors.initials: Q
authors.lastname: Peng
authors.forename: Xinghui
authors.initials: X
authors.lastname: Wang
authors.forename: Ge
authors.initials: G
authors.lastname: Ren
authors.forename: Hongbin
authors.initials: H
authors.lastname: Chen
authors.forename: Lei
authors.initials: L
authors.lastname: Cao
authors.forename: Jihong
authors.initials: J
authors.lastname: Wang