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.
© 2003 Optical Society of America
(000.4430) General : Numerical approximation and analysis
(100.3020) Image processing : Image reconstruction-restoration
(100.6890) Image processing : Three-dimensional image processing
(180.2520) Microscopy : Fluorescence microscopy
(180.6900) Microscopy : Three-dimensional microscopy
Joanne Markham and José-Angel Conchello, "Numerical evaluation of Hankel transforms for oscillating functions," J. Opt. Soc. Am. A 20, 621-630 (2003)