Calculations of radiant heating by inhomogeneous hot gases require knowledge of spectral transmittances of inhomogeneous optical paths. Determination of these transmittances is a difficult problem that can be attacked by means of the Curtis-Godson approximation, which replaces each inhomogeneous optical path with a hypothetical homogeneous path that has the same transmittance. The authors have tested the accuracy of the Curtis-Godson approximation experimentally. Infrared spectral transmittances of inhomogeneous hot samples of H2O and CO2 were measured. Each inhomogeneous hot gas specimen consisted of two or three homogeneous zones in series. The transmittance of each zone was measured, as was the transmittance of the entire multizone assembly. The measured transmittance of each inhomogeneous path was compared with a transmittance calculated from the homogeneous zonal transmittances, using the Curtis-Godson approximation in conjunction with a random band model. The measured and calculate inhomogeneous transmittances concurred to within about 0.02. The error appeared to be due more to the band model theory than to the Curtis-Godson approximation.
Burton Krakow, Harold J. Babrov, G. Jordan Maclay, and Abraham L. Shabott, "Use of the Curtis—Godson Approximation in Calculations of Radiant Heating by Inhomogeneous Hot Gases," Appl. Opt. 5, 1791-1800 (1966)