The mean scattering cross section of a polydispersion upon which electromagnetic radiation is incident is found to depend primarily upon the ratio of the third to second moment of the size distribution function, i.e., the volume—surface mean diameter, and is only weakly dependent on the shape of the size distribution function. This result is applicable to mean diameters ranging from very large to very small compared with the wavelength of incident light. Mean scattering coefficients are presented for polydispersions with refractive indices varying from m-1«1 to m=1.85. The results of this investigation can be used to measure mean particle size, as represented by the ratio of third to second moment of size distribution function, to an accuracy comparable to experimental accuracy even though the size distribution function is not known.
RICHARD A. DOBBINS and G. STEPHEN JIZMAGIAN, "Optical Scattering Cross Sections for Polydispersions of Dielectric Spheres," J. Opt. Soc. Am. 56, 1345-1349 (1966)