Abstract

The aim of the present work is to obtain expressions for both the wavefront train and the caustic associated with the light rays reflected by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in free space. To this end, we obtain an expression for the k-function associated with the general integral of Stavroudis to the eikonal equation that describes the evolution of the reflected light rays. The caustic is computed by using the definitions of the critical and caustic sets of the map that describes the evolution of an arbitrary wavefront associated with the general integral. It is shown that the expression for the caustic is the same as that—reported in the literature—obtained by using an exact ray tracing. The general results are applied to a parabolic mirror. 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 reflected wavefront at the caustic region locally has singularities of the cusp ridge and swallowtail types.

© 2009 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
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
J. Opt. Soc. Am. A 29(6) 1035-1046 (2012)

Wavefronts, caustics, and ronchigrams of a spherical wave reflected by a spherical mirror

Jorge Castro-Ramos, Magdalena Marciano-Melchor, Mariana Marcelino-Aranda, Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, Román Suárez-Xique, and José Miguel Zárate-Paz
J. Opt. Soc. Am. A 30(2) 177-188 (2013)

Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens

Salvador Alejandro Juárez-Reyes, Magdalena Marciano-Melchor, Mariana Marcelino-Aranda, Paula Ortega-Vidals, Edwin Román-Hernández, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, Román Suárez-Xique, Gerardo Francisco Torres del Castillo, and Mercedes Velázquez-Quesada
J. Opt. Soc. Am. A 31(2) 448-459 (2014)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (84)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription