The two-path method (utilizing a mirror) is shown to provide sufficient information to solve for the true radial brightness distribution of a luminous medium in the presence of self-absorption. In the case where self-absorption is not large, an approximate solution to the problem is shown to be no more difficult than a solution for the “optically thin” approximation.
MARK P. FREEMAN and S. KATZ, "Determination of the Radial Distribution of Brightness in a Cylindrical Luminous Medium with Self-Absorption," J. Opt. Soc. Am. 50, 826-828 (1960)