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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 8 — Aug. 1, 2011
  • pp: 1600–1609

Determination of second-order derivatives of a skew ray with respect to the variables of its source ray in optical prism systems

Psang Dain Lin and Wei Wu  »View Author Affiliations


JOSA A, Vol. 28, Issue 8, pp. 1600-1609 (2011)
http://dx.doi.org/10.1364/JOSAA.28.001600


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Abstract

The second-order derivative of a scalar function with respect to a variable vector is known as the Hessian matrix. We present a computational scheme based on the principles of differential geometry for determining the Hessian matrix of a skew ray as it travels through a prism system. A comparison of the proposed method and the conventional finite difference (FD) method is made at last. It is shown that the proposed method has a greater inherent accuracy than FD methods based on ray-tracing data. The proposed method not only provides a convenient means of investigating the wavefront shape within complex prism systems, but it also provides a potential basis for determining the higher order derivatives of a ray by further taking higher order differentiations.

© 2011 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(080.1753) Geometric optics : Computation methods
(080.2468) Geometric optics : First-order optics

History
Original Manuscript: May 20, 2011
Manuscript Accepted: June 13, 2011
Published: July 12, 2011

Citation
Psang Dain Lin and Wei Wu, "Determination of second-order derivatives of a skew ray with respect to the variables of its source ray in optical prism systems," J. Opt. Soc. Am. A 28, 1600-1609 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-8-1600

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