TY - JOUR
T1 - Using rays better. IV. theory for refraction and reflection
AU - Forbes, G. W.
PY - 2001
Y1 - 2001
N2 - A new ray-based method is extended to include the modeling of optical interfaces. The essential idea is that the wave field and its derivatives are always expressed as a superposition of ray contributions of flexible width. Interfaces can be analyzed in this way by introducing a family of surfaces that smoothly connects them. Even though the ray-to-wave link may appear to be obscured at caustics, the standard Fresnel coefficients (for plane waves at flat interfaces between homogeneous media) are shown to be universally applicable on a ray-by-ray basis. Thus, in the interaction at the interface, the surface’s curvature and any gradients in the refractive indices influence only the higher asymptotic corrections. Further, this method finally gives access to such corrections.
AB - A new ray-based method is extended to include the modeling of optical interfaces. The essential idea is that the wave field and its derivatives are always expressed as a superposition of ray contributions of flexible width. Interfaces can be analyzed in this way by introducing a family of surfaces that smoothly connects them. Even though the ray-to-wave link may appear to be obscured at caustics, the standard Fresnel coefficients (for plane waves at flat interfaces between homogeneous media) are shown to be universally applicable on a ray-by-ray basis. Thus, in the interaction at the interface, the surface’s curvature and any gradients in the refractive indices influence only the higher asymptotic corrections. Further, this method finally gives access to such corrections.
UR - http://www.scopus.com/inward/record.url?scp=0012645242&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.18.002557
DO - 10.1364/JOSAA.18.002557
M3 - Article
C2 - 11583273
AN - SCOPUS:0012645242
VL - 18
SP - 2557
EP - 2564
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
SN - 1084-7529
IS - 10
ER -