On the Use of the Inverted Abel Integral for Evaluating Spectroscopic Sources

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Abstract
A numerical method for evaluating the inverted Abel integral employing cubic spline approximations is described along with a modification of the procedure of Cremers and Birkebak, and an extension of the Barr method. The accuracy of the computations is evaluated at several noise levels and with varying resolution of the input data. The cubic spline method is found to be useful only at very low noise levels, but capable of providing good results with small data sets. The Barr method is computationally the simplest, and is adequate when large data sets are available. For noisy data, the method of Cremers and Birkebak gave the best results.