Radiative characteristics of beds of spheres containing an absorbing and scattering medium

The aim of this paper is to characterize the radiative behavior of beds made of spherical particles containing an homogeneous absorbing and scattering medium whose radiative properties (extinction coefficient, scattering albedo, and scattering phase function) are known. In the beds studied, the spherical particles could be far apart, close to each other, or even compressed. When the particles are sufficiently distant from each other to scatter independently, the radiative properties of the whole bed are determined from the radiative characteristics of one particle alone. These characteristics are determined using a Monte Carlo procedure applied to one bead alone. On the other hand, when particles get closer to each other independent scattering theory is no longer valid, and dependent scattering effects have to be taken into account. We then apply a Monte Carlo procedure to the whole bed and identify the extinction coefficient, scattering albedo, and scattering phase function of the equivalent homogeneous absorbing and scattering medium that best matches the radiative behavior of the bed. The simulation permits us to characterize the evolution of the radiative properties of the bed with the inside medium properties and the characteristics of the bed. Moreover, we investigate the limit of validity of the independent scattering hypothesis.