Blind source separation-based reconstruction algorithm of air bubbles holograms

Abstract

This article aims firstly to review some results on two-dimensional air bubble modeling necessary when calculating in-line holograms for such objects. Secondly, the blind source separation method (BSS) applied to estimate the most probable shape of the object that generates the holograms either theoretically or experimentally is recalled. The result of this study demonstrates that the opaque ring is the most probable theoretical model to simulate the hologram of bubbles and also to interpret the reconstructed images. Indeed, in [1], the opaque ring was a theoretical hypothesis. After the probabilistic method of this study, the theoretical hypothesis is validated and we can confirm the convergence of two methods (theoretical and probabilistic). Besides, we show that BSS is an interesting method for discriminating between opaque objects (e.g. a perfectly absorbing particle) and the symmetry of a revolution phase object. Finally, a note is made on the possibility of estimating the optical index of the bubble, which constitutes a perspective of this initial work.