Abel inversion using Bessel function as a radial basis function for sparse spectroscopic data

Abstract

A stable and reliable Abel inversion code is developed for the calculation of the reconstruction of circularly symmetric two-dimensional functions from its projection. This technique differs from earlier methods by using Bessel function to expand the radial emissivity. The matrix inversion associated with the Abel inversion technique is achieved with the help of the singular value decomposition method. It is shown with the help of simulated data that Abel inversion by this technique generates a good reconstruction of the source functions and gives very good and accurate results for sparse data. A comparison is made with the results from other methods using both experimental noisy data and source functions with different amounts of noise added to them.