Application of inverse Abel techniques in in-line holographic microscopy

In this paper, we compare two well-established techniques, namely the BASEX and the Fourier–Hankel, as regards their efficiency of retrieving the three-dimensional distribution of cylindrically symmetric objects in the presence of noise. This situation is commonly encountered in pump–probe experiments where the refractive index profile of elongated structures, such as plasma strings or transient refractive index changes, is under study. We performed numerical experiments for a variety of objects, with respect to the spatial distribution and size, and for various statistical distributions and levels of noise. In this area of application, the BASEX can surpass the Fourier–Hankel technique in respect of reconstruction quality, spatial resolution and robustness to noise especially after proper tuning of the basis set functions width.