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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

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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 magnifi cation 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

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

Cristian E. Gutiérrez, "Reflection, refraction, and the Legendre transform," J. Opt. Soc. Am. A 28, 284-289 (2011)

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  1. R. A. Hicks and R. Bajcsy, “Reflective surfaces as computational sensors,” Image Vis. Comput. 19, 773–777 (2001). [CrossRef]
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  3. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, 1962).
  4. C. E. Gutiérrez and Q. Huang, “The refractor problem in reshaping light beams,” Arch. Ration. Mech. Anal. 193, 423–443 (2009). [CrossRef]

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