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 Sigma'(s) identical withSigma(s)(1 - g) is an important parameter to describe light propagation in media with scattering and absorption. Mie calculations of the asymmetry factor g for nonabsorbing spheres and Q(sca), the ratio of the scattering cross section Sigma(s) and the particle cross section, show that Q(sca)(1 - g) = 3.28x(0.37)(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.