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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. 29, Iss. 11 — Nov. 1, 2012
  • pp: 2272–2280

Jacobian and Hessian matrices of optical path length for computing the wavefront shape, irradiance, and caustics in optical systems

Psang Dain Lin and Chien-Sheng Liu  »View Author Affiliations


JOSA A, Vol. 29, Issue 11, pp. 2272-2280 (2012)
http://dx.doi.org/10.1364/JOSAA.29.002272


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Abstract

The first- and second-order derivative matrices of the ray (i.e., R¯i/X¯0 and 2R¯i/X¯02) and optical path length (i.e., OPLi/X¯0 and 2OPLi/X¯02) were derived with respect to the variable vector X¯0 of the source ray in an optical system by our previous papers. Using the first and second fundamental forms of the wavefront, these four matrices are used to investigate the local principal curvatures of the wavefront at each boundary surface encountered by a ray traveling through the optical system. The proposed method not only yields the data needed to compute the irradiance of the wavefront but also provides the information required to determine the caustics. Importantly, the proposed methodology is applicable to both axisymmetric and nonaxisymmetric optical systems.

© 2012 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.1010) Geometric optics : Aberrations (global)
(080.2740) Geometric optics : Geometric optical design
(080.1753) Geometric optics : Computation methods

History
Original Manuscript: July 16, 2012
Revised Manuscript: September 6, 2012
Manuscript Accepted: September 9, 2012
Published: October 10, 2012

Citation
Psang Dain Lin and Chien-Sheng Liu, "Jacobian and Hessian matrices of optical path length for computing the wavefront shape, irradiance, and caustics in optical systems," J. Opt. Soc. Am. A 29, 2272-2280 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-11-2272

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