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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 18 — Jun. 20, 2013
  • pp: 4137–4150

Analysis and design of prisms using the derivatives of a ray. Part I: derivatives of a ray with respect to boundary variable vector

Psang Dain Lin  »View Author Affiliations

Applied Optics, Vol. 52, Issue 18, pp. 4137-4150 (2013)

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A computational scheme based on differential geometry is proposed for determining the first- and second-order derivative matrices of a skew ray as it is reflected/refracted at a flat boundary surface. In the proposed approach, the position and orientation of the boundary surface in 3D space are described using just four variables. As a result, the proposed method is more computationally efficient than existing schemes based on all six variables. The derivative matrices enable the cross-coupling effects of the system variables on the exit ray to be fully understood. Furthermore, the proposed method provides a convenient means of determining the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. The validity of the proposed approach as an analysis and design tool is demonstrated using a corner-cube mirror and laser tracking system for illustration purposes.

© 2013 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(080.1753) Geometric optics : Computation methods
(080.2468) Geometric optics : First-order optics

Original Manuscript: February 26, 2013
Revised Manuscript: April 22, 2013
Manuscript Accepted: April 26, 2013
Published: June 13, 2013

Psang Dain Lin, "Analysis and design of prisms using the derivatives of a ray. Part I: derivatives of a ray with respect to boundary variable vector," Appl. Opt. 52, 4137-4150 (2013)

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