Abstract

It is shown that the equations relating the radial profiles of the volume emission and absorption coefficients to the transmission and emitted intensity profiles in self-absorbing cylindrically symmetric sources, can be written in such a way that the problem of spatially resolving the volume emission coefficient gives rise to a Volterra integral equation of the second kind in a standard form. The theory of equations of this type is invoked to show the formal convergence of an iterative solution to the problem, subject only to a finite transmission and bounded slope to the absorption coefficient. A prescription for applying this iterative procedure is given that involves a series of numerical integrations and Abel inversions, and the convergence of some numerical solutions is demonstrated.

© 1968 Optical Society of America

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