Transfer matrix method for four-flux radiative transfer

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We develop a transfer matrix method for four-flux radiative transfer, which is ideally suited for studying transport through multiple scattering layers. The model predicts the specular and diffuse reflection and transmission of multilayer composite films, including interface reflections, for diffuse or collimated incidence. For spherical particles in the diffusion approximation, we derive closed-form expressions for the matrix coefficients and show remarkable agreement with numerical Monte Carlo simulations for a range of absorption values and film thicknesses, and for an example multilayer slab.