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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

  • Vol. 18, Iss. 10 — Oct. 1, 2001
  • pp: 2557–2564

Using rays better. IV. Theory for refraction and reflection

G. W. Forbes  »View Author Affiliations


JOSA A, Vol. 18, Issue 10, pp. 2557-2564 (2001)
http://dx.doi.org/10.1364/JOSAA.18.002557


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Abstract

A new ray-based method is extended to include the modeling of optical interfaces. The essential idea is that the wave field and its derivatives are always expressed as a superposition of ray contributions of flexible width. Interfaces can be analyzed in this way by introducing a family of surfaces that smoothly connects them. Even though the ray-to-wave link may appear to be obscured at caustics, the standard Fresnel coefficients (for plane waves at flat interfaces between homogeneous media) are shown to be universally applicable on a ray-by-ray basis. Thus, in the interaction at the interface, the surface’s curvature and any gradients in the refractive indices influence only the higher asymptotic corrections. Further, this method finally gives access to such corrections.

© 2001 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)
(350.7420) Other areas of optics : Waves

History
Original Manuscript: December 14, 2000
Revised Manuscript: March 16, 2001
Manuscript Accepted: March 8, 2001
Published: October 1, 2001

Citation
G. W. Forbes, "Using rays better. IV. Theory for refraction and reflection," J. Opt. Soc. Am. A 18, 2557-2564 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-10-2557

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