The absorption of radiation by molecular bands is calculated when the source emits its energy in discrete spectral lines. The results are compared with those for a blackbody source. The absorption of flame radiation by the molecular bands of an absorbing medium is derived for a number of different conditions when the spectral lines do not overlap. These results are then extended to the case when the overlapping of the spectral lines in either the source or absorber can be described either by the Elsasser model or by the statistical model. When the same spectral lines are involved in the emission and absorption processes, the absorptance of flame radiation is always greater than the absorptance of blackbody radiation by the same medium. All of the above results are derived both for the case when the absorbing medium is homogeneous and when the pressure, temperature, and amount of absorbing gas vary along the path.
Gilbert N. Plass, "The Theory of the Absorption of Flame Radiation by Molecular Bands," Appl. Opt. 4, 161-166 (1965)