Application of derivative matrices of skew rays to design of compound dispersion prisms

Research output: Contribution to journalArticle

Abstract

Numerous optimization methods have been developed in recent decades for optical system design. However, these methods rely heavily on ray tracing and finite difference techniques to estimate the derivative matrices of the rays. Consequently, the accuracy of the results obtained from these methods is critically dependent on the incremental step size used in the tuning stage. To overcome this limitation, the present study proposes a comprehensive methodology for the design of compound dispersion prisms based on the first- and second-order derivative matrices of skew rays. The proposed method facilitates the analysis and design of prisms with respect to arbitrary system variables and provides an ideal basis for automatic prism design applications. Four illustrative examples are given. It is shown that the optical quantities required to evaluate the prism performance can be extracted directly from the proposed derivative matrices. In addition, it is shown in this study that the single-element 3D prism can have the same deviation angle and spectral dispersion as the 2D compound prism.

Original languageEnglish
Pages (from-to)1843-1850
Number of pages8
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume33
Issue number9
DOIs
Publication statusPublished - 2016 Sep 1

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Prisms
prisms
rays
Derivatives
matrices
Ray tracing
ray tracing
Optical systems
systems engineering
Tuning
Systems analysis
tuning
methodology
deviation
optimization
estimates

All Science Journal Classification (ASJC) codes

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

Cite this

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abstract = "Numerous optimization methods have been developed in recent decades for optical system design. However, these methods rely heavily on ray tracing and finite difference techniques to estimate the derivative matrices of the rays. Consequently, the accuracy of the results obtained from these methods is critically dependent on the incremental step size used in the tuning stage. To overcome this limitation, the present study proposes a comprehensive methodology for the design of compound dispersion prisms based on the first- and second-order derivative matrices of skew rays. The proposed method facilitates the analysis and design of prisms with respect to arbitrary system variables and provides an ideal basis for automatic prism design applications. Four illustrative examples are given. It is shown that the optical quantities required to evaluate the prism performance can be extracted directly from the proposed derivative matrices. In addition, it is shown in this study that the single-element 3D prism can have the same deviation angle and spectral dispersion as the 2D compound prism.",
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