Scattering Functions for Rayleigh Atmospheres of Arbitrary Thickness

A complete quantitative solution, in the form of equations and tables of functions, is given for the problem of the magnitudes and polarizations of the directional and total fluxes of radiation emerging from the upper and lower boundaries of a plane-parallel Rayleigh atmosphere. An extension of previous work, which applied only to investigation of the earth's atmosphere in visible sunlight, the results of the present study can be used for investigations of the earth's atmosphere by short ultraviolet radiation as well as of the atmosphere of other planets that have much greater optical thickness in a wide range from ultraviolet to infrared. Numerical values are given for Chandrasekhar's X-, Y-, K-, and L-functions for optical thicknesses from 0.15 to 100.0 and for all directions. Simple formulas are also given for using the tabulations to calculate the effect of ground reflection, the average intensity of the emerging radiation, the components of its net flux, and the internal radiation field at any level within the atmosphere.