Efficient polar convolution based on the discrete Fourier-Bessel transform for application in computational biophotonics

TL;DR

This paper presents efficient algorithms for the discrete Fourier-Bessel transform to enable fast 2D polar convolution of radially symmetric functions, with applications in computational biophotonics such as tissue optics and optoacoustics.

Contribution

It introduces a novel, efficient numerical method for the forward and reverse discrete Fourier-Bessel transform tailored for polar convolution tasks in biophotonics.

Findings

Algorithms outperform straightforward quadrature methods.

Application demonstrates computational efficiency in tissue optics simulations.

Versatile approach applicable to various biophotonics problems.

Abstract

We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to applications in computational biophotonics. In our survey of the numerical procedure we account for the circumstance that the objective function might result from a more complex measurement process and is, in the worst case, known on a finite sequence of coordinate values, only. We contrast the performance of the resulting algorithms with a procedure based on a straight forward numerical quadrature of the underlying integral transform and asses its efficienty for two benchmark Fourier-Bessel pairs. An application to the problem of finite-size beam-shape convolution in polar coordinates, relevant in the context of tissue optics and optoacoustics, is used to illustrate the versatility and computational efficiency of the numerical procedure.