Synthetic reflectance and transmittance spectra of particulate materials evaluated from four-flux radiative transfer models

Two simplified versions of the four-flux radiative transfer model (the standard one and a novel extended form) are put into context with respect to the generalized approach. Collimated-collimated, collimated-diffuse, and diffuse-diffuse reflectance and transmittance (R&T) spectra of anatase (TiO 2 ) pigments in a polymeric aqueous medium are generated by these four-flux models. To this end, it has been necessary to evaluate previously the scattering and absorption cross sections, average pathlength parameters, and forward scattering ratios that enter these models. The evaluation has been carried out assuming no interaction between neighboring particles, or assuming the presence of particle aggregates in the composite medium. In the first case, the Lorenz-Mie theory has been applied to obtain the expansion of the phase function in Legendre polynomials. For particulate media containing aggregates, the coefficients in this expansion are derived using a transition matrix formalism. Additionally, parameters such as scattering and absorption cross sections, albedo, and asymmetry parameter have been determined. Evaluating synthetic R&T spectra of these materials can be useful to validate inversion procedures using spectral gradient and simulated annealing methods. Quantifying the dependent scattering effect in R&T spectra, both collimated and diffuse, is now possible. This has been done mostly at the level of cross sections, albedos, and asymmetry parameters of particle aggregates, but not for parameters that can be directly correlated with spectrophotometric measurements like R&T.