A new method for the evaluation of small-angle scattering data

TLDR

The study introduces a numerical method for simultaneous smoothing, desmearing, and Fourier transformation of X‑ray and neutron small‑angle scattering data. The method models the distance distribution with 20–30 cubic B‑splines, fitting coefficients via weighted least‑squares to optimally smooth and desmear the data while suppressing oscillations through a stabilization routine. It yields radius‑of‑gyration estimates that outperform the Guinier approximation.

Abstract

A new numerical method is presented for simultaneous smoothing, desmearing and Fourier transformation of X-ray and neutron small-angle scattering data. The method can only be applied to scattering curves from dilute particle systems, i.e. for scattering media whose distance distributions are zero beyond a certain value. The distance distribution of the scattering medium is approximated by a linear combination of about 20 to 30 cubic B-splines. These spline functions have a restricted extension in real space. Their coefficients are adjusted by a weighted least-squares operation so that the series, after being Fourier transformed and smeared according to the geometry and wavelength distribution, represents an optimum smoothed approximation of the experimental data. Tendencies towards oscillations in the least-squares operation are suppressed by a new stabilization routine. The method offers a new possibility for the estimation of the radius of gyration, which is generally superior to the Guinier approximation.