Comparison and optimization of smoothing procedures for small-angle X-ray scattering curves. Polynomial fitting and modified frequency filtering

The filter theory allows one to compare the efficiencies of smoothing procedures widely used in the field of small-angle X-ray scattering. This method is demonstrated for polynomial fitting and modified frequency filtering. Optimized and objective smoothing parameters are determined for both procedures through the knowledge of variance reduction factors, transfer functions of the filters, the largest value of the spatial frequencies of the scattering curve and the distortions caused by the smoothing procedures. The comparison of the efficiency of polynomial fitting and frequency filtering clearly shows the superiority of the latter; therefore, this method has to be preferred.