Volumetric optical properties of fully anisotropic participating media

The average absorption and scattering properties of participating media (PM) are usually found from experiments, either a physical measurement or, if possible, a numerical ray-tracing experiment. The analysis of the experimental results is not simple when the medium is fully anisotropic, i.e., extinction depends on the orientation of the incident radiation. Common approaches require a full solution of the radiative transfer equation (RTE) in the sample, and an iterative optimization procedure to find the optical properties. We present an approximate analysis method that is based on treating the sample as a single control volume. This leads to a direct, non-iterative solution, using a set of algebraic equations rather than a full solution of the RTE. The procedure computes a representation of the optical properties for the most general case of anisotropy, which is compatible with the discrete ordinate method or the finite volume method approaches. We discuss experimental error, the error due to the single control volume approximation, and the effect of the optical thickness of the sample. The performance and robustness of the procedure are demonstrated for several test cases.