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

1977/10/01 by O. Glatter, Otto Glatter · 1,279 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Computational physics #Fourier series #Fourier transform #Least-squares function approximation #Mathematical analysis #Mathematics #Nuclear Physics and Applications #Optics #Physics #Scattering #Small-angle scattering #Smoothing #Soil and Unsaturated Flow #X-ray Diffraction in Crystallography

paper · doi:10.1107/s0021889877013879

published in Journal of Applied Crystallography 10(5), 415-421 (Wiley)

openalex publication_date 1977/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

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