A method is proposed for calculating the diffuse component of the bidirectional reflectance distribution function (BRDF) of a medium with relatively strong absorption, such as seawater. Our approach is based on the expansion of the reflectance in orders of scattering through large angles (compared to the characteristic single-scattering angle), which leads to the reflectance expansion in inverse powers of the absorption coefficient. Explicit expressions for the first two terms of the expansion are derived. The first term reproduces the well-known result of quasi-single-scattering approximation, and the second one corresponds to the contribution of quasi-double scattering (the small-angle multiple scattering before, between, and after two events of large-angle scattering). To validate our analytical results, we carry out numerical integration of the radiative transfer equation for the Henyey–Greenstein (HG) phase function, as well as for the two-term HG and Morel et al (for Case I water) ones. For optical parameters typical to seawater, our analytical formula is in excellent agreement with the results of numerical radiative transfer calculations over a wide range of illumination/viewing angles. Remarkably, the relative contribution of the quasi-double scattering proves to be rather sensitive to the shape of the phase function in the backward hemisphere.
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