Analytical model for diffuse light reflection from an aqueous highly-forward-scattering medium

The aim of the present study is to develop a method for calculating the diffuse component of the bidirectional reflectance of a strongly absorbing and highly-forward scattering medium like seawater. The relevance of this issue is due to the widespread use of the bidirectional reflectance in the processing of ocean color measurements. 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 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 phase function, as well as for the two-term Henyey-Greenstein function that models light scattering in seawater. It is shown that for optical parameters typical to seawater, the first two terms of the expansion (i. e. the sum of quasi-single- and quasi-double-scattering contributions) prove to be sufficient to describe the bidirectional reflectance with high accuracy over a wide range of illumination/viewing angles.

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