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Applied Optics

Applied Optics


  • Vol. 7, Iss. 8 — Aug. 1, 1968
  • pp: 1635–1639

Spatial Resolution of the Volume Emission Coefficient in Strongly Self-Absorbing Sources of Cylindrical Symmetry

J. W. Birkeland and J. P. Oss  »View Author Affiliations

Applied Optics, Vol. 7, Issue 8, pp. 1635-1639 (1968)

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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)

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