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.
© 2010 Optical Society of America
Original Manuscript: April 28, 2010
Manuscript Accepted: May 17, 2010
Published: June 21, 2010
Riccardo Borghi, "On the numerical evaluation of umbilic diffraction catastrophes," J. Opt. Soc. Am. A 27, 1661-1670 (2010)