  A general approach for the calculation of the incoherent intensity scattered
by a random medium with rough boundaries has been developed using a Green
function formalism. The random medium consists of spherical particles whose
physical repartition is described by a pair-distribution function. The boundary
contribution is included in the Green functions with the help of scattering
operators which can represent any existing theory of scattering by rough
surfaces. By using a standard procedure, we derive the integral Bethe-Salpeter
equation under the ladder approximation and, by differentiation, the vectorial
radiative transfer equation. Furthermore, with the help of our formalism, the
boundary conditions necessary to solve the radiative transfer equation are
expressed in terms of the scattering operators of the rough surfaces. Finally,
using the reciprocity properties of the Green functions, we are able to include
the enhanced backscattering contributions to take into account every state of
polarization of the incident and the scattered waves.
