An improved method is proposed for applying the Abel integral equation to radiance data gathered from rotationally symmetric sources by side-on observation. The method involves dividing the data into a number of segments going out from the center. A least-squares polynomial is then fitted to each segment so that the inverted Abel integral equation can be integrated exactly to yield the emission coefficient. It is shown, with test curves approximating spectral line shapes from nonhomogeneous sources, that the method becomes superior to the other more common numerical methods of reducing such data as the number of data points becomes large. This superiority increases as the data scatter increases.
Clifford J. Cremers and Richard C. Birkebak, "Application of the Abel Integral Equation to Spectrographic Data," Appl. Opt. 5, 1057-1064 (1966)