General method for determining the first order gradients of skew rays of optical systems with non-coplanar optical axes

Psang-Dain Lin, C. Y. Tsai

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Current commercial software for the analysis and design of optical systems uses finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate and are subject to gross error when the denominator is excessively small relative to the numerator. This paper avoids these problems and determines the gradient matrix of the exit ray traveling along an optical system with a non-coplanar axis. To achieve this, the gradient matrix of the rays reflected/refracted by flat or spherical boundary surfaces are first determined by directly differentiating the skew-ray tracing equations. By introducing a Jacobian matrix, which represents the partial derivatives specifying the rates of changes between boundary variables and element variables, one can obtain the gradient matrix of the exit ray of an element with respect to its independent variables. This methodology will be useful in the analysis of rays and in design of optical systems with non-coplanar axis. A right-angle prism is used as illustrative example to validate its applications.

Original languageEnglish
Pages (from-to)621-628
Number of pages8
JournalApplied Physics B: Lasers and Optics
Volume91
Issue number3-4
DOIs
Publication statusPublished - 2008 Jun 1

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rays
gradients
matrices
methodology
reflected waves
estimates
ray tracing
prisms
computer programs
approximation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)

Cite this

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abstract = "Current commercial software for the analysis and design of optical systems uses finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate and are subject to gross error when the denominator is excessively small relative to the numerator. This paper avoids these problems and determines the gradient matrix of the exit ray traveling along an optical system with a non-coplanar axis. To achieve this, the gradient matrix of the rays reflected/refracted by flat or spherical boundary surfaces are first determined by directly differentiating the skew-ray tracing equations. By introducing a Jacobian matrix, which represents the partial derivatives specifying the rates of changes between boundary variables and element variables, one can obtain the gradient matrix of the exit ray of an element with respect to its independent variables. This methodology will be useful in the analysis of rays and in design of optical systems with non-coplanar axis. A right-angle prism is used as illustrative example to validate its applications.",
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General method for determining the first order gradients of skew rays of optical systems with non-coplanar optical axes. / Lin, Psang-Dain; Tsai, C. Y.

In: Applied Physics B: Lasers and Optics, Vol. 91, No. 3-4, 01.06.2008, p. 621-628.

Research output: Contribution to journalArticle

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