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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. 31, Iss. 4 — Apr. 1, 2014
  • pp: 891–899

Design of pairs of reflectors

Cristian E. Gutiérrez and Ahmad Sabra  »View Author Affiliations


JOSA A, Vol. 31, Issue 4, pp. 891-899 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000891


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Abstract

Given a 3D reflecting surface G, which is not necessarily rotationally symmetric, away from a point source, and a direction e, we design a reflecting surface F so that the system (G,F) reflects all rays into the direction e. We also solve the near-field problem when the direction e is replaced by a given point R. The surface F satisfies a system of first-order partial differential equations that can be explicitly solved in terms of G and e. We also apply the same ideas to designing refracting plates, of which the Schmidt corrector plate is an example.

© 2014 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(110.6770) Imaging systems : Telescopes
(080.4035) Geometric optics : Mirror system design
(080.4228) Geometric optics : Nonspherical mirror surfaces

ToC Category:
Geometric Optics

History
Original Manuscript: December 17, 2013
Revised Manuscript: February 21, 2014
Manuscript Accepted: February 24, 2014
Published: March 31, 2014

Citation
Cristian E. Gutiérrez and Ahmad Sabra, "Design of pairs of reflectors," J. Opt. Soc. Am. A 31, 891-899 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-891


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References

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  8. See the file far-field-concave.cdf at https://math.temple.edu/~gutierre/pair-reflectors-cdf/ .
  9. See the file far-field-convex.cdf at https://math.temple.edu/~gutierre/pair-reflectors-cdf/ .
  10. See the file cardioid-condenser.cdf at https://math.temple.edu/~gutierre/pair-reflectors-cdf/ .
  11. See the file near-field-reflectors.cdf at https://math.temple.edu/~gutierre/pair-reflectors-cdf/ .
  12. See the file mirror-and-corrector-plate.cdf at https://math.temple.edu/~gutierre/pair-reflectors-cdf/ .
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  18. L. G. Cook, “Flat field Schmidt telescope with extended field of view,” U.S. patent7,933,067 B1 (April26, 2011).

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