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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 14 — May. 10, 2014
  • pp: 3085–3100

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design

Psang Dain Lin  »View Author Affiliations


Applied Optics, Vol. 53, Issue 14, pp. 3085-3100 (2014)
http://dx.doi.org/10.1364/AO.53.003085


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Abstract

In a previous paper [Appl. Opt. 52, 4151 (2013)], we presented the first- and second-order derivatives of a ray for a flat boundary surface to design prisms. In this paper, that scheme is extended to determine the Jacobian and Hessian matrices of a skew ray as it is reflected/refracted at a spherical boundary surface. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustration purpose. It is found that these two matrices can provide the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. It is also possible to make the optical system designs more automatic, if the image defects can be extracted from the Jacobian and Hessian matrices of a skew ray.

© 2014 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

ToC Category:
Geometric Optics

History
Original Manuscript: January 22, 2014
Revised Manuscript: April 7, 2014
Manuscript Accepted: April 8, 2014
Published: May 8, 2014

Citation
Psang Dain Lin, "Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design," Appl. Opt. 53, 3085-3100 (2014)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-53-14-3085

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