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

Psang Dain Lin, Chuang Yu Tsai

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)776-784
Number of pages9
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number3
Publication statusPublished - 2007 Mar

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


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