Theory of anisotropic scattering of radiation - Explicit expression for the resolvent function

Astronomy and Astrophysics – Astrophysics

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Integral Equations, Light Scattering, Optical Thickness, Planetary Atmospheres, Planetary Radiation, Anisotropy, Atmospheric Models, Linear Equations, Numerical Integration

Scientific paper

The anisotropic scattering of light in a homogeneous plane-parallel layer of finite optical thickness is investigated analytically. The linear integral equation for the resolvent function of Sobolev (1969) is solved using auxiliary functions related to the generalized Ambartsumian-Chandrasekhar functions. Explicit expressions are then obtained which permit the determination of the reduced source function and radiation intensity for parallel-ray illumination of a medium of finite optical thickness without integrating over the optical depth. These formulas are applicable to the calculation of radiation intensity in planetary atmospheres.

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