The radiative transfer approach is used to study the thermal microwave emission from an inhomogeneous slab of random medium bounded by different dielectrics on both sides. The random medium can have nonuniform absorption, scattering and temperature profiles. With the method of invariant imbedding, the boundary value problem of the radiative transfer equations is cast into an initial value problem starting at zero slab thickness. The invariant imbedding equations so obtained are in the form of first-order ordinary differential equations and incorporate the boundary conditions. Random fluctuations of a structure both laminar and with three-dimensional variations are considered and illustrated. The frequency, angular, and polarization dependences of brightness temperatures are discussed.
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