A Versatile Analytical Expression for the Inverse Abel Transform Applied to Experimental Data with Noise

A method for reconstruction of radially distributed plasma emission coefficients from projections with noise is proposed. The method represents the projections based on overlapping piecewise polynomial least squares fitting to take the inversion. Parameters that affect the inversion accuracy are analyzed and discussed in detail. Results for profiles with various shapes are presented and compared with those obtained with other methods. It is shown that for data with different numbers of points and different levels of noise, our method is more accurate and yields markedly better results for very sparse data. In addition, excellent results have been obtained from experimental intensities of an arc plasma without filtering of noise.