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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: Stephen A. Burns
  • Vol. 23, Iss. 12 — Dec. 1, 2006
  • pp: 3133–3138

Two solvable problems of planar geometrical optics

Francesco Borghero and George Bozis  »View Author Affiliations


JOSA A, Vol. 23, Issue 12, pp. 3133-3138 (2006)
http://dx.doi.org/10.1364/JOSAA.23.003133


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Abstract

In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f ( x , y ) = c of any definite color and satisfying a differential condition, all the refractive index profiles n = n ( x , y ) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n = n ( x , y ) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.

© 2006 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)

History
Original Manuscript: February 21, 2006
Revised Manuscript: June 14, 2006
Manuscript Accepted: June 16, 2006

Citation
Francesco Borghero and George Bozis, "Two solvable problems of planar geometrical optics," J. Opt. Soc. Am. A 23, 3133-3138 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-12-3133

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