Generalization of the Fedorova-Schmidt method for determining particle size distributions

This article reports the integral transform that determines the particle size distribution of a given sample from the small-angle scattering intensity under the assumption that the particle correlation function is a polynomial of degree M. The Fedorova-Schmidt solution [Fedorova & Schmidt (1978). J. Appl. Cryst. 11, 405-411] corresponds to the case M = 3. The procedure for obtaining a polynomial approximation to a particle correlation function is discussed in the cases M = 3 and 4 and applied to the cases of polydisperse particles of tetrahedral, octahedral or cubic shape.