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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. 9 — Sep. 1, 2011
  • pp: 1860–1863

Surfaces refracting and reflecting collimated beams

Cristian E. Gutiérrez and Federico Tournier  »View Author Affiliations

JOSA A, Vol. 28, Issue 9, pp. 1860-1863 (2011)

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We describe necessary and sufficient conditions for image transformations so that surfaces refracting or reflecting collimated beams exist. The surfaces are given by explicit formulas. When these conditions are not satisfied, we show that a surface can be found so that it minimizes the L 2 distance between its gradient and the image 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: April 1, 2011
Manuscript Accepted: May 24, 2011
Published: August 22, 2011

Cristian E. Gutiérrez and Federico Tournier, "Surfaces refracting and reflecting collimated beams," J. Opt. Soc. Am. A 28, 1860-1863 (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]
  2. R. A. Hicks and R. K. Perline, “Blind-spot problem for motor vehicles,” Appl. Opt. 44, 3893–3897 (2005). [CrossRef] [PubMed]
  3. D. L. Shealy, “Geometrical Methods,” in Laser Beam Shaping: Theory and Techniques, F.M.Dickey and S.C.Holswade, eds. (Marcel Dekker, 2000), pp. 163–213.
  4. C. E. Gutiérrez and Qingbo Huang, “The refractor problem in reshaping light beams,” Arch. Ration. Mech. Anal. 193, 423–443 (2009). [CrossRef]
  5. C. E. Gutiérrez, “Reflection, refraction and the Legendre transform,” J. Opt. Soc. Am. A 28, 284–289 (2011). [CrossRef]

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