Wavefronts and caustic of a spherical wave reflected by an arbitrary smooth surface
JOSA A, Vol. 26, Issue 11, pp. 2295-2305 (2009)
http://dx.doi.org/10.1364/JOSAA.26.002295
Enhanced HTML 
Acrobat PDF (544 KB)
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
OCIS Codes
(080.0080) Geometric optics : Geometric optics
(120.5700) Instrumentation, measurement, and metrology : Reflection
ToC Category:
Geometric Optics
History
Original Manuscript: July 10, 2009
Manuscript Accepted: August 30, 2009
Published: October 9, 2009
Citation
Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, and Ramón Silva-Ortigoza, "Wavefronts and caustic of a spherical wave reflected by an arbitrary smooth surface," J. Opt. Soc. Am. A 26, 2295-2305 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-11-2295
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
Log in to access OSA Member Subscription
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
Log in to access OSA Member Subscription
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
Log in to access OSA Member Subscription
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
Log in to access OSA Member Subscription
Related Journal Articles 
- Preservation of far-UV aluminum reflectance by means of overcoating with C60 films (AO)
- Exact computation of image disruption under reflection on a smooth surface and Ronchigrams (AO)
- Describing the structure of ronchigrams when the grating is placed at the caustic region: the parabolical mirror (JOSAA)
- Lava lamp optics (AO)
- Wavefronts, caustics, and ronchigrams of a spherical wave reflected by a spherical mirror (JOSAA)
Related Conference Papers
- Measurement of Very Low Residual Reflections in Lensed-Fiber Pigtailed Semiconductor Optical Amplifier
- Ultra-Thin Folded Imager
- New Optics Using Negative Refraction
- Determination of the Modal Reflection Coefficients in Air-Core Photonic-Bandgap Fiber Terminations
- The role of spherical aberration on THz pulse propagation
« Previous Article | Next Article »
OSA is a member of 