TY - JOUR
T1 - Wavefronts and caustic of a spherical wave reflected by an arbitrary smooth surface
AU - Román-Hernández, Edwin
AU - Santiago-Santiago, José Guadalupe
AU - Silva-Ortigoza, Gilberto
AU - Silva-Ortigoza, Ramón
N1 - Funding Information:
Received 5 July 2000; revised 20 October 2000; electronically published 27 December 2000. Presented in part: North American Cystic Fibrosis Conference, Nashville, Tennessee, October 1997 (abstract 315). This study was approved by the institutional review boards of all the participating centers, and informed consent was received from the parents of the participating study subjects. Financial support: The Cystic Fibrosis Foundation (grants CFFA922 and R565) and the National Institutes of Health (grant R55 HL48888). Reprints or correspondence: Dr. Jane L. Burns, Division of Infectious Disease, CH-32, Children’s Hospital and Regional Medical Center, 4800 Sand Point Way NE, Seattle, WA 98105 (jburns@chmc.org).
PY - 2009/11/1
Y1 - 2009/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70449704638&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.26.002295
DO - 10.1364/JOSAA.26.002295
M3 - Artículo
SN - 1084-7529
VL - 26
SP - 2295
EP - 2305
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
IS - 11
ER -