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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: Stephen A. Burns
  • Vol. 23, Iss. 7 — Jul. 1, 2006
  • pp: 1691–1698

Generalized Coddington equations found via an operator method

Charles E. Campbell  »View Author Affiliations


JOSA A, Vol. 23, Issue 7, pp. 1691-1698 (2006)
http://dx.doi.org/10.1364/JOSAA.23.001691


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Abstract

Generalized Coddington equations allow the optical properties of an arbitrarily oriented incoming astigmatic ray bundle to be found following refraction by an arbitrary surface. Generalized Coddington equations are developed using the abstract concept of vergence and refraction operators. After suitable incoming vergence and refraction operators have been formed, these operators are re-expressed in a common coordinate system via similarity transformations created from the series of space rotations necessary to align the coordinate systems. The transformed operators are then added together to produce the vergence operator of the refracted ray bundle. When properly applied, these generalized Coddington equations may be used with complex wavefronts and complex refracting surfaces if local surface curvature properties are known for both where the two intersect. The generalized Coddington equations are given in matrix form so that they may be easily implemented.

© 2006 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2730) Geometric optics : Matrix methods in paraxial optics

History
Original Manuscript: October 4, 2005
Manuscript Accepted: December 8, 2005

Citation
Charles E. Campbell, "Generalized Coddington equations found via an operator method," J. Opt. Soc. Am. A 23, 1691-1698 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-7-1691

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