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

Determination of the Radial Profile of Absorption and Emission Coefficients and Temperature in Cylindrically Symmetric Sources with Self-Absorption

P. Elder, T. Jerrick, and J. W. Birkeland
Appl. Opt. 4(5) 589-592 (1965)

Measurements of Spectral Emission and Absorption of a High Pressure Xenon Arc in the Stationary and the Flashed Modes

Lothar Klein
Appl. Opt. 7(4) 677-685 (1968)

Determination of Self-Broadening Coefficients of CO, Using CO₂ Laser Radiation at 10.6 μ

R. R. Patty, E. R. Manring, and J. A. Gardner
Appl. Opt. 7(11) 2241-2245 (1968)

Science vs Fiction in Atomic Absorption

C. Th.J. Alkemade
Appl. Opt. 7(7) 1261-1269 (1968)

Application of High Temperature Infrared Emission Spectroscopy to Molten Salts

T. R. Kozlowski
Appl. Opt. 7(5) 795-800 (1968)