Similarity relations for anisotropic scattering in absorbing media

The validity of the similarity parameter SIGMA(s)' = SIGMA(s) (1-g), the reduced scattering coefficient, where g is the average cosine of the scattering phase function is investigated. Attenuation coefficients alpha and diffusion patterns are obtained from solutions of the transport equation for isotropic scattering and Rayleigh-Gans scattering, applied to infinite media. Similarity is studied for the attenuation coefficient alpha, as well as for the Kubelka-Munk absorption and backscattering coefficients in the positive and negative directions, and for predictions of the internal reflection at interfaces. Similarity between solutions of the Boltzmann equation for highly forward scattering and isotropic scattering (g = 0) exist only when SIGMA(a) much less than SIGMA(s) (1 - g). However, because similarity between results, both with g > 0.9, is independent of the value of the absorption coefficient, it is advantageous to simulate highly forward scattering media like biological tissues with g > 0.9, e.g., by Monte Carlo simulations, instead of using isotropic scattering or diffusion theory. Monte Carlo simulations on slabs confirm the deviations from the diffusion approximation and show the behavior near boundaries. Application of similarity may save calculation time in Monte Carlo simulations, because simulation with a lower value for g will increase the mean free path.