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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. 2 — Feb. 1, 2011
  • pp: 284–289

Reflection, refraction, and the Legendre transform

Cristian E. Gutiérrez  »View Author Affiliations


JOSA A, Vol. 28, Issue 2, pp. 284-289 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000284


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Abstract

We construct in dimension two a mirror that reflects collimated rays into a set of directions that amplify the image and an optical lens so that collimated rays are refracted into a set of directions with a prescribed magnification factor. The profiles of these optical surfaces are given by explicit formulas involving the Legendre transformation.

© 2011 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(230.4040) Optical devices : Mirrors
(080.4225) Geometric optics : Nonspherical lens design
(080.4228) Geometric optics : Nonspherical mirror surfaces

History
Original Manuscript: October 28, 2010
Manuscript Accepted: November 8, 2010
Published: February 1, 2011

Citation
Cristian E. Gutiérrez, "Reflection, refraction, and the Legendre transform," J. Opt. Soc. Am. A 28, 284-289 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-2-284

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