Combined scheme of reconstruction of the particle size distribution function using small-angle scattering data

To analyze polydisperse systems of nanoparticles, the particle size distribution function can be determined from small-angle X-ray and neutron scattering data using some algorithms. The corresponding least squares problem is an ill-posed problem; correspondingly, a solution can strongly depend on the initial approximation and the parameters of search algorithms. A procedure based on solving a system of linear equations with regularization gives a stable solution, but it is not free of artifacts. Other algorithms that seek the distribution function both in an analytical form and in the form of a nonparametric histogram provide solutions that can depend on the search parameters and the initial approximation. In this work, a combined scheme of using these algorithms has been proposed to increase the stability of the solution and, thereby, its reliability.