A new method for the determination of particle size distributions from small-angle neutron scattering measurements

The determination of a particle size distribution p(R) from small-angle scattering data is an example of a practical linear inverse problem for which there is no unique solution. It is shown (i) how the maximum entropy algorithm may be used to extract a unique solution which is the most uniform function compatible with the data set and is necessarily positive, and (ii) how the Backus-Gilbert [Geophys. J. R. Astron. Soc. (1968), 16, 169-205] method may be used to judge the significance of features in distributions derived from a data set of given statistical accuracy. As an illustration, void size distributions are presented for a sample of irradiated stainless steel which was successively annealed at increasing temperatures.