A simple computational approach is proposed for the evaluation of umbilic diffraction catastrophes which, together with cuspoids, describe the whole hierarchy of the structurally stable diffraction patterns that can be produced by optical diffraction. In this paper, after expanding the double integral representations of hyperbolic and elliptic umbilics as convergent power series, the action of the Weniger transformation on them is studied. Exact expressions for the "on-axis" umbilic field have also been found, which extend previously published results to complex values of the control parameter. Numerical experiments aimed at giving evidence of the effectiveness and implementative ease of the approach are eventually presented. (C) 2010 Optical Society of America
Borghi, R. (2010). On the numerical evaluation of umbilic diffraction catastrophes. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION, 27(7), 1661-1670 [10.1364/JOSAA.27.001661].
On the numerical evaluation of umbilic diffraction catastrophes
BORGHI, Riccardo
2010-01-01
Abstract
A simple computational approach is proposed for the evaluation of umbilic diffraction catastrophes which, together with cuspoids, describe the whole hierarchy of the structurally stable diffraction patterns that can be produced by optical diffraction. In this paper, after expanding the double integral representations of hyperbolic and elliptic umbilics as convergent power series, the action of the Weniger transformation on them is studied. Exact expressions for the "on-axis" umbilic field have also been found, which extend previously published results to complex values of the control parameter. Numerical experiments aimed at giving evidence of the effectiveness and implementative ease of the approach are eventually presented. (C) 2010 Optical Society of AmericaI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
