Meaning of Successive Iteration of the Auxiliary Equation in the Theory of Radiative Transfer.

Abstract

The solution of the problem of the transfer of electromagnetic radiation through a non-homogeneous, partly absorbing, plane-parallel atmosphere obeying Rayleigh's law of scattering is obtained from the definition of the source matrix. The solution derived here is exactly the same as the solution of the auxiliary equations given by Sekera. It is shown that a successive iteration of the auxiliary equations is equivalent to including successive higher orders of scattering. The method clearly shows the advantages of using Stokes parameters and characteristic functions introduced by Chandrasekhar in solving similar problems for homogeneous non-absorbing atmospheres. The expressions for the Stokes parameters of the diffuse radiation for a Lambert-type ground reflection underlying the atmosphere are also given.