TY - JOUR
T1 - Uniform asymptotic expansions for wave propagators via fractional transformations
AU - Alonso, M. A.
AU - Forbes, G. W.
PY - 1997
Y1 - 1997
N2 - By use of the fractional Fourier transformation, a new representation is developed for the wave propagator of scalar diffraction theory, and its asymptotic form is then derived by using the fractional Legendre transformation. The resulting expression remains valid in the presence of caustics and automatically accounts for the associated and problematic phase shifts. Although the derivation is long, the final result is simple and takes a form that is strikingly similar to the conventional expression. The new asymptotic method that is established here has both extended validity and significant advantages.
AB - By use of the fractional Fourier transformation, a new representation is developed for the wave propagator of scalar diffraction theory, and its asymptotic form is then derived by using the fractional Legendre transformation. The resulting expression remains valid in the presence of caustics and automatically accounts for the associated and problematic phase shifts. Although the derivation is long, the final result is simple and takes a form that is strikingly similar to the conventional expression. The new asymptotic method that is established here has both extended validity and significant advantages.
UR - http://www.scopus.com/inward/record.url?scp=3943102646&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.14.001279
DO - 10.1364/JOSAA.14.001279
M3 - Article
AN - SCOPUS:3943102646
SN - 1084-7529
VL - 14
SP - 1279
EP - 1292
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 - 6
ER -