It is shown that the average transmission function in the atmosphere can be calculated from the fractional absorption as measured in the laboratory for frequency intervals involving either large or small optical thicknesses. These relations are very general and are independent of any special assumptions as to the shape of the pressure broadened lines, of the variation of spacing, intensity, or half-width of the lines, of the extent of the overlapping of the lines, or of the distribution of the radiating gases in the atmosphere. The optical thickness is considered large or small for a particular interval depending on the intensities and half-widths of the lines contributing to the absorption. The solutions of radiation transfer problems can be obtained from the average transmission function calculated by the above method. A number of examples are given of the application of these results to particular problems. It is shown that in general for pressure broadened lines the fractional absorption is a function only of pressure times optical thickness for large optical thicknesses, and of optical thickness times a function of the pressure for small optical thicknesses.
© 1952 Optical Society of AmericaFull Article | PDF Article
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