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

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4 Citations (Scopus)

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 axissymmetrical 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.

Original languageEnglish
Pages (from-to)3085-3100
Number of pages16
JournalApplied optics
Issue number14
DOIs
Publication statusPublished - 2014 May 10

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering

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