In this paper the influence of the microscopic characteristics of a random medium on non polarized, incoherent steady light transport (ISLT) is investigated. After close examination of current diffusion models, the source term in those models is modified, allowing a complete modeling of experimental and simulated radial dependance of backscattered and transmitted intensities for media thicknesses larger than the transport length. The new model only presents an additional source with respect to the elementary point source model. Thanks to more than 200 Monte-Carlo simulations, this parameter is correlated to the backscattering part of the Mie phase function. Incoherent Steady Light Transport measurements on two industrial emulsions at various volume fractions validate experimentally this correlation. This establishes a complete link between the microscopic characteristic of the random medium (size, optical indexes and volume fraction) and its macroscopic description in terms of diffusion and source parameters, opening new potential applications of the ISLT technique to, for example, the evaluation of the particles interaction potential in concentrated suspensions.