A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ν,  ν>-1, using wavelets. The philosophy behind the proposed algorithm is to replace the part tf(t) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing Fν(p) as a Fourier-Bessel series with coefficients depending strongly on the input function tf(t). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive