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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 13 — May. 1, 2014
  • pp: C83–C90

Analytical direct solutions of the Risley prism systems for tracking and pointing

Qi Peng, Xinghui Wang, Ge Ren, Hongbin Chen, Lei Cao, and Jihong Wang  »View Author Affiliations

Applied Optics, Vol. 53, Issue 13, pp. C83-C90 (2014)

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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.

© 2014 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2720) Geometric optics : Mathematical methods (general)
(120.5800) Instrumentation, measurement, and metrology : Scanners

Original Manuscript: December 18, 2013
Revised Manuscript: March 8, 2014
Manuscript Accepted: March 8, 2014
Published: April 25, 2014

Qi Peng, Xinghui Wang, Ge Ren, Hongbin Chen, Lei Cao, and Jihong Wang, "Analytical direct solutions of the Risley prism systems for tracking and pointing," Appl. Opt. 53, C83-C90 (2014)

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