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Birefringent media, like biological tissues, are usually assumed to be uniaxial. For biological tissues, the influence of linear birefringence on the scattering phase function is assumed to be neglectable. In order to examine this, a numerical study of the influence of linear birefringence on the scattering phase function and the resulting backscattering Mueller matrices was performed. It is assumed that the media consist of spherical scattering particles embedded in a nonabsorbing medium, which allows us to employ the Lorenz-Mie theory. In the Monte Carlo framework, the influence of linear birefringence on the components of the electric field vector is captured through the Jones N-matrix formalism. The Lorenz-Mie theory indicates that a given linear birefringence value Δn has a bigger impact on the scattering phase function for large particles. This conclusion is further supported by Monte Carlo simulations, where the phase function was calculated based on the refractive index once in the ordinary direction and once in the extraordinary one. For large particles, comparisons of the resulting backscattering Mueller matrices show significant differences even for small Δn values.

This paper deals with an efficient and accurate simulation algorithm to solve the vector Boltzmann equation for polarized light transport in scattering media. The approach is based on a stencil method, which was previously developed for unpolarized light scattering and proved to be much more efficient (speedup factors of up to 10 were reported) than the classical Monte Carlo while being equally accurate. To validate what we believe to be the new stencil method, a substrate composed of spherical non-absorbing particles embedded in a non-absorbing medium was considered. The corresponding single scattering Mueller matrix, which is required to model scattering of polarized light, was determined based on the Lorenz-Mie theory. From simulations of a reflected polarized laser beam, the Mueller matrix of the substrate was computed and compared with an established reference. The agreement is excellent, and it could be demonstrated that a significant speedup of the simulations is achieved due to the stencil approach compared with the classical Monte Carlo.