A generalization of Abel inversion to non-axisymmetric density distribution

• Published in: Optics communications Vol. 199; no. 1; pp. 143 - 148
• Main Authors: Tomassini, P., Giulietti, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.11.2001; Elsevier Science
• Subjects: Chemistry; Colloidal state and disperse state; Disperse systems; Exact sciences and technology; General and physical chemistry; General, apparatus, technics of preparation; Interferometry; Plasma diagnostics; 52.70.−m; Plasma diagnostics; Interferometry; Theoretical study; Laser plasma interaction; Optical interferometry; Electron density; Plasma diagnostic
• ISSN: 0030-4018; 1873-0310
• DOI: 10.1016/S0030-4018(01)01575-9

Abel inversion is currently used in laser-plasma studies in order to estimate the electronic density n e from the phase-shift map δ φ 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 polynomial expansion in the azimuthal 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.