A simple computational approach is proposed for the evaluation of cuspoid diffraction catastrophes, which are fundamental tools for the description of wave fields in proximity to stable caustics. In particular, on representing the Pearcey and the swallowtail functions in terms of convergent series expansions, the action of the Weniger transformation on them is numerically studied for both real and complex values of the cuspoid arguments. Numerical experiments, aimed at giving evidence of the effectiveness and implementative ease of the proposed method, together with some quantitative comparisons to previously published results, are also presented. (c) 2008 Optical Society of America
Borghi, R. (2008). On the numerical evaluation of cuspoid diffraction catastrophes. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION, 25(7), 1682-1690 [10.1364/JOSAA.25.001682].
On the numerical evaluation of cuspoid diffraction catastrophes
BORGHI, Riccardo
2008-01-01
Abstract
A simple computational approach is proposed for the evaluation of cuspoid diffraction catastrophes, which are fundamental tools for the description of wave fields in proximity to stable caustics. In particular, on representing the Pearcey and the swallowtail functions in terms of convergent series expansions, the action of the Weniger transformation on them is numerically studied for both real and complex values of the cuspoid arguments. Numerical experiments, aimed at giving evidence of the effectiveness and implementative ease of the proposed method, together with some quantitative comparisons to previously published results, are also presented. (c) 2008 Optical Society of AmericaI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
