Abel's inversion applied to experimental spectroscopic data with off axis peaks

Many mathematical techniques for solving Abel's integral equation have been proposed over the years in the literature. Often these methods handle test functions with known solutions and Gaussian type profiles quite accurately. For experimental data and non-Gaussian shapes, however, these methods are inadequate. An experimental study of the uniformity of the plasma emission on the Gaseous Electronics Conference Reference Cell has as its goal to provide immediate feedback regarding the plasma uniformity. Therefore a rapid, accurate, and sturdy computational method of data analysis is required. The first round of experiments indicate off axis or donut shaped plasmas within the reference cell. The analysis and conclusions are presented herein.