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

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 *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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