An efficient procedure for custom beam-profile convolution in polar coordinates: testing, benchmarking and application to biophotonics

Abstract

We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier–Bessel transform 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. Application to the problems of finite-size beam-shape convolution in polar coordinates and prediction of photoacoustic transients observed in experiments are used to illustrate the versatility and computational efficiency of the numerical procedure. Further, we address the important issue of testing research code written in the python scripting language by using its off-the-shelf unit testing library unittest.