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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. 29, Iss. 6 — Jun. 1, 2012
  • pp: 1035–1046

The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface

Magdalena Marciano-Melchor, Esperanza Navarro-Morales, Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Román Suárez-Xique  »View Author Affiliations


JOSA A, Vol. 29, Issue 6, pp. 1035-1046 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001035


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Abstract

The aim of this paper is to obtain expressions for the k-function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a parabolic refracting surface. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type, while the refracted wavefront, at the caustic region, locally has singularities of the cusp ridge and swallowtail types.

© 2012 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(120.5710) Instrumentation, measurement, and metrology : Refraction

History
Original Manuscript: December 13, 2011
Revised Manuscript: March 1, 2012
Manuscript Accepted: March 1, 2012
Published: May 29, 2012

Citation
Magdalena Marciano-Melchor, Esperanza Navarro-Morales, Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Román Suárez-Xique, "The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface," J. Opt. Soc. Am. A 29, 1035-1046 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-6-1035

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