Reduction of the standard problem in radiative transfer for a medium of finite optical thickness

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Atmospheric Refraction, Atmospheric Scattering, Optical Thickness, Planetary Atmospheres, Radiative Transfer, Atmospheric Attenuation, Chandrasekhar Equation, Data Reduction, Polynomials, Transmittance

Scientific paper

The problem of determining the reflection and transmission by a homogeneous atmosphere with an arbitrary phase function is discussed. Taking advantage of well-known as well as new symmetry relations, a general reduction procedure for the problem is presented, whereby the solution can be expressed in Chandrasekhar's X- and Y-functions. Several alternative paths in the reduction procedure and other checking possibilities are explicitly pointed out. The connection between various constraints is shown. Some practicing examples, including isotropic and linear-anisotropic scattering, are worked out.

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