# Topic 3: Algorithms in computational biophotonics

Here, we study efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform. The transform is used as a numerical tool facilitating a polar convolution of two radially symmetric functions. This is relevant for applications in tissue optics and optoacoustics, where a recurrent task is to perform a beam-shape convolution in order to yield the material response to an extended laser beam from its Greens-function response. The latter results from a more complex measurement process modeled in terms of a Monte Carlo approach and is, in the worst case, known on a finite sequence of coordinate values, only. The considered applications require the repeated (hundreds of times) calculation of a forward and reverse Fourier-Bessel transform. Thus, time-efficiency is key and fast numerical procedures are valuable.

The figure below illustrates the laser profile convolution procedure for different irradiation source profiles (ISP). Colums from left to right: Gaussian ISP, Flat-top ISP, and Donut ISP. Rows from top to bottom: increasing scattering anisotropy factor.

We applied the developed convolution procedure to the problems of finite-size beam-shape convolution in polar coordinates and the prediction of photoacoustic transients observed in actual experiments, see here (in the linked article we address the important issue of testing research code by illustrating a sequence of unittest).