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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 3 — Mar. 1, 2007
  • pp: 776–784

First-order gradients of skew rays of axis-symmetrical optical systems

Psang Dain Lin and Chuang-Yu Tsai  »View Author Affiliations

JOSA A, Vol. 24, Issue 3, pp. 776-784 (2007)

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Current commercial software for analysis and design of optical systems use finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate, subject to gross error when the denominator is excessively small relative to the numerator. We avoid these problems and determine these gradients by the application of Snell’s law. We give the background and basics for determining the first-order gradients of skew rays of optical systems, whereby the differential vector of any ray can be estimated by the product of the developed gradient matrix and differential changes of system variables. The most important application is for optical design by use of optimization methods where the merit function is defined as the spot size. FD used for such optimization is slow for large systems and subject to inaccuracy. The presented methodology is shown to be accurate and computationally faster than traditional FD. Two illustrative examples are provided to validate the proposed method.

© 2007 Optical Society of America

OCIS Codes
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(220.4830) Optical design and fabrication : Systems design

Original Manuscript: June 29, 2006
Manuscript Accepted: September 22, 2006
Published: February 14, 2007

Psang Dain Lin and Chuang-Yu Tsai, "First-order gradients of skew rays of axis-symmetrical optical systems," J. Opt. Soc. Am. A 24, 776-784 (2007)

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