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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 1 — Jan. 1, 2002
  • pp: 129–131

Two theorems in catoptrics

J. Rubinstein and G. Wolansky  »View Author Affiliations

JOSA A, Vol. 19, Issue 1, pp. 129-131 (2002)

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Two general theorems in the theory of mirrors are presented. The first one asserts that a mirror that reflects a parallel beam into a beam with zero mean curvature must be harmonic. The second one provides a universal characterization of the spot diagram of rays from a reflected parallel beam as they intersect a plane orthogonal to their direction of propagation.

© 2002 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(230.4040) Optical devices : Mirrors

Original Manuscript: March 28, 2001
Revised Manuscript: June 4, 2001
Manuscript Accepted: June 4, 2001
Published: January 1, 2002

J. Rubinstein and G. Wolansky, "Two theorems in catoptrics," J. Opt. Soc. Am. A 19, 129-131 (2002)

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  1. J. A. Kneisly, “Local curvature of a wave front in an optical system,” J. Opt. Soc. Am. 54, 229–235 (1964). [CrossRef]
  2. O. N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972).
  3. J. B. Keller, H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Opt. Soc. Am. 40, 48–52 (1950). [CrossRef]
  4. J. Rubinstein, G. Wolansky, “A class of elliptic differential equations related to optical design,” available as preprint.
  5. J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray deflections,” Opt. Rev. (to be published).

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