ИСТИНА

The inverse Abel transform allows extraction of radially-resolved values of an axially symmetric function by analyzing its projections along observation axis. In the context of laser induced plasma, the Abel inversion can be used to obtain spatial profiles of temperature and electronic density, thereby facilitating a range of different applications such as measuring Stark broadening parameters. Despite the inherent advantages of Abel inversion, its practical application is complicated by a number of intricacies, namely, symmetry distortion, self-absorption, temporal evolution of plasma, and experimental noise. The latter, in particular, can drastically alter the reconstructed profile from a noiseless counterpart and, moreover, excessive data points can result in noise amplification. While reduced sampling [1] helps to improve the precision, it also reduces the trueness of reconstructed profile. The present work demonstrates that regularization can effectively handle noisy data, providing an efficient means of achieving both high precision and trueness in a single step. Instead of reducing the number of points we have applied the algorithm of Abel inversion with regularization. The method of regularization described in the literature [2] involves applying a penalty to a solution of inverse transform along the radial coordinate. It was augmented with penalty for non-smoothness along the height coordinate. The new method was applied to analysis of data obtained from ablation of calcium carbonate in a vacuum chamber at 10 torr. Through this, we were able to obtain spatial distributions of relative atomic and ionic concentrations, temperature and electronic density. Temperature was measured using Saha-Boltzmann plot and electron density was determined from the Stark broadening of spectral lines.