TY - JOUR
T1 - Wavefronts, light rays and caustic of a circular wave reflected by an arbitrary smooth curve
AU - Marciano-Melchor, Magdalena
AU - Montiel-Pĩa, Enrique
AU - Romn-Hernndez, Edwin
AU - Rosado, Alfonso
AU - Santiago-Santiago, José Guadalupe
AU - Silva-Ortigoza, Gilberto
AU - Silva-Ortigoza, Ramón
AU - Surez-Xique, Romn
PY - 2011/5
Y1 - 2011/5
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 curve after being emitted by a point light source located at an arbitrary position in the two-dimensional 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 two-dimensional map that describes the evolution of an arbitrary wavefront associated with the general integral. The general results are applied to circular and parabolic mirrors. The main motivation to carry out this research is to establish, in future work, the caustic touching theorem in a two-dimensional optical medium and to study the diffraction problem by using the k-function concept. Both problems are important in the computation of the image of an arbitrary object under reflection and refraction.
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 curve after being emitted by a point light source located at an arbitrary position in the two-dimensional 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 two-dimensional map that describes the evolution of an arbitrary wavefront associated with the general integral. The general results are applied to circular and parabolic mirrors. The main motivation to carry out this research is to establish, in future work, the caustic touching theorem in a two-dimensional optical medium and to study the diffraction problem by using the k-function concept. Both problems are important in the computation of the image of an arbitrary object under reflection and refraction.
KW - caustics
KW - eikonal
KW - reflector
KW - wavefronts
UR - http://www.scopus.com/inward/record.url?scp=79955791745&partnerID=8YFLogxK
U2 - 10.1088/2040-8978/13/5/055705
DO - 10.1088/2040-8978/13/5/055705
M3 - Artículo
SN - 2040-8978
VL - 13
JO - Journal of Optics (United Kingdom)
JF - Journal of Optics (United Kingdom)
IS - 5
M1 - 055705
ER -