Numerical evaluation of Hankel transforms for oscillating functions

Joanne Markham, José Angel Conchello

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

Six methods for the numerical calculation of zero-order Hankel transforms of oscillating functions were evaluated. One method based on Filon quadrature philosophy, two published projection-slice methods, and a third projection-slice method based on a new approach to computation of the Abel transform were implemented; alternative versions of two of the projection-slice methods were derived for more accurate approximations in the projection step. These six algorithms were tested with an oscillating sweep signal and with the calculation of a three-dimensional diffraction-limited point-spread function of a fluorescence microscope. We found that the Filon quadrature method is highly accurate but also computationally demanding. The projection-slice methods, in particular the new one that we derived, offer an excellent compromise between accuracy and computational efficiency.

Original languageEnglish
Pages (from-to)621-630
Number of pages10
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume20
Issue number4
DOIs
StatePublished - Apr 2003

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