Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations

The reduced scattering cross section per unit of volume Σs′ ≡ Σs(1 − g) is an important parameter to describe light propagation in media with scattering and absorption. Mie calculations of the asymmetry factory g for nonabsorbing spheres and Qsca, the ratio of the scattering cross section Σs and the particle cross section, show that Qsca(1 − g) = 3.28x0.37(m − 1)2.09 is true to within a few percent, when the Mie parameters for relative refractive index m and size x are in the ranges of 1 < m ≤ 1.1 and 5 < x < 50, respectively. A ratio of reduced scattering cross sections for radiation at two wavelengths is also independent of the size within the range mentioned, even for mixtures of different size spheres. The results seem promising for biomedical applications.