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Manuscript Title: Calculation of the radial distribution of emitters in a cylindrical source.
Authors: R. Piessens
Program title: ABELA
Catalogue identifier: ABUE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)294
Programming language: Fortran.
Computer: IBM 370/155.
Operating system: OS/370.
RAM: 8K words
Word size: 32
Keywords: Astrophysics, Emitters, Radiative transfer, Data interpretation, Abel integral equation, Gauss-jacobi Quadrature, Least-squares Approximation.
Classification: 1.3, 21.2.

Nature of problem:
This program determines the radial distribution of the emission coefficient from measured spectral intensity distributions emitted by an extended source of radiation. It is assumed that the source is optically thin and axially symmetrical.

Solution method:
It is well-known that this problem can be solved by inverting the Abel integral equation. Using Clenshaw's method a least-squares polynomial is fitted to the observed radiance. The inversion of this polynomial is then carried out exactly by means of Gauss-Jacobi quadrature. This method of calculation is quite insensitive to small random errors in the data.