Numerical evaluation of Hankel transforms for oscillating functions.
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.
Markham
Joanne
J
Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, Missouri 63110, USA. joanne@npg.wustl.edu
Conchello
José-Angel
JA
D000465:Algorithms; D021621:Imaging, Three-Dimensional; D008853:Microscopy; D008962:Models, Theoretical; D055095:Optics and Photonics