A new method for determination of particle-size distribution function from small angle scattering data

Abstract

A new numerical method is presented for calculating the particle-size distribution function of dilute particle systems from Small Angle Scattering data. The size distribution function, in order to be always positive, is approximated by the square of a combination of cubic B-splines. The coefficients of the combination are calculated in reciprocal space using the weighted least squares principle, which leads to a variational problem, solved by a Newton-Gauss-Marquardt iterative technique. A strategy is presented to enhance resolution in correspondence to the peaks of the distribution. Some results obtained on simulated and experimental points are presented, showing the accuracy of the method.