A posteriori determination of the useful data range for small-angle scattering experiments on dilute monodisperse systems

Small-angle X-ray and neutron scattering (SAXS and SANS) experiments on solutions provide rapidly decaying scattering curves, often with a poor signal-to-noise ratio, especially at higher angles. On modern instruments, the noise is partially compensated for by oversampling, thanks to the fact that the angular increment in the data is small compared with that needed to describe adequately the local behaviour and features of the scattering curve. Given a (noisy) experimental data set, an important question arises as to which part of the data still contains useful information and should be taken into account for the interpretation and model building. Here, it is demonstrated that, for monodisperse systems, the useful experimental data range is defined by the number of meaningful Shannon channels that can be determined from the data set. An algorithm to determine this number and thus the data range is developed, and it is tested on a number of simulated data sets with various noise levels and with different degrees of oversampling, corresponding to typical SAXS/SANS experiments. The method is implemented in a computer program and examples of its application to analyse the experimental data recorded under various conditions are presented. The program can be employed to discard experimental data containing no useful information in automated pipelines, in modelling procedures, and for data deposition or publication. The software is freely accessible to academic users.