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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 9 — Sep. 1, 2013
  • pp: 1719–1726

Aspherical lens design

Cristian E. Gutiérrez  »View Author Affiliations

JOSA A, Vol. 30, Issue 9, pp. 1719-1726 (2013)

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Given a three-dimensional surface G , not necessarily rotationally symmetric, and away from a point source, we design a surface F such that the lens sandwiched between the two surfaces refracts radiation into a given direction or into a given point. The surface F satisfies a system of first-order partial differential equations that can be solved in terms of G and the refractive indices of the media involved.

© 2013 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(080.4225) Geometric optics : Nonspherical lens design

ToC Category:
Geometric Optics

Original Manuscript: January 14, 2013
Manuscript Accepted: March 30, 2013
Published: August 2, 2013

Cristian E. Gutiérrez, "Aspherical lens design," J. Opt. Soc. Am. A 30, 1719-1726 (2013)

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  1. G.-I. Kweon and C.-H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103 (2007). [CrossRef]
  2. C. E. Gutiérrez, “Reflection, refraction and the Legendre transform,” J. Opt. Soc. Am. A 28, 284–289 (2011). [CrossRef]
  3. D. L. Shealy, “Theory of geometrical methods for design of laser beam shaping systems,” Proc. SPIE 4095, 163–213 (2000). [CrossRef]
  4. R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).
  5. C. E. Gutiérrez and Q. Huang, “The refractor problem in reshaping light beams,” Arch. Ration. Mech. Anal. 193, 423–443 (2009). [CrossRef]
  6. C. E. Gutiérrez and Q. Huang, “The near field refractor,” Geometric Methods in PDE’s, Conference for the 65th Birthday of E. Lanconelli, Vol. 7, Lecture Notes of Seminario Interdisciplinare di Matematica (Università degli Studi della Basilicata, 2008), pp. 175–188.
  7. C. E. Gutierrez and Q. Huang, “The near field refractor,” Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire (in press).

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