A Generalization of Abel Inversion to non axisymmetric density distribution

Abel Inversion is currently used in laser-plasma studies in order to estimate the electronic density $n_e$ from the phase-shift map $delta phi$ obtained via interferometry. The main limitation of the Abel method is due to the assumption of axial symmetry of the electronic density, which is often hardly fulfilled. In this paper we present an improvement to the Abel inversion technique in which the axial symmetry condition is relaxed by means of a truncated Legendre Polinomial expansion in the azimutal angle. With the help of simulated interferograms, we will show that the generalized Abel inversion generates accurate densities maps when applied to non axisymmetric density sources.