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
Original Manuscript: February 26, 1968
Published: August 1, 1968
J. W. Birkeland and J. P. Oss, "Spatial Resolution of the Volume Emission Coefficient in Strongly Self-Absorbing Sources of Cylindrical Symmetry," Appl. Opt. 7, 1635-1639 (1968)