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Numerical evaluation of Hankel transforms for oscillating functions.

Joanne Markham·José-Angel Conchello
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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.

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AlgorithmsImaging, Three-DimensionalMicroscopyModels, TheoreticalOptics and PhotonicsJournal ArticleResearch Support, U.S. Gov't, P.H.S.

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Joanne Markham, José-Angel Conchello. 2003. Numerical evaluation of Hankel transforms for oscillating functions.. https://doi.org/10.1364/josaa.20.000621

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