Transfer matrix method for four-flux radiative transfer

We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion approximation, predicts the specular and diffuse reflection and transmission of multilayer composite films for diffuse or collimated incidence. The model shows remarkable agreement with numerical Monte Carlo simulations for a range of absorption and film thicknesses, as well as for an example multilayer slab.