Reflection and transmission of polarized light: The adding method for homogeneous atmospheres

A mathematical justification is given for the multiple interface reflection expansion arising when using the adding method for solving numerically the equation of transfer of polarized light in a homogeneous atmosphere. The ratio of convergence is investigated analytically as a function of the optical thicknesses of the layers. The proof is based on manipulations with the positivity properties of the reflection and transmission operators, whose existence may be based on recent existence and uniqueness results for the solution of the equation of polarized light transfer