Weniger transformation is a powerful nonlinear sequence transformation that, when applied to the sequence of the partial sums of a divergent or a slowly convergent series, can convert it to a fast-converging sequence. Weniger transformation is not yet well known in optics. Diffraction catastrophes are fundamental tools for evaluating an optical field in proximity to caustics and singularities. The action of the Weniger transformation on the power series representation of diffraction catastrophes is numerically studied for two particular cases, corresponding to the Airy and the Pearcey functions. The obtained results clearly show that Weniger transformation could become a computational tool of great importance for summing several types of series expansions in optics.
© 2007 Optical Society of America
Original Manuscript: September 11, 2006
Revised Manuscript: October 10, 2006
Manuscript Accepted: October 20, 2006
Published: January 12, 2007
Riccardo Borghi, "Evaluation of diffraction catastrophes by using Weniger transformation," Opt. Lett. 32, 226-228 (2007)