For obtaining reliable nanostructural details of large amounts of sample --- and if it is applicable --- Small-Angle Scattering (SAS) is a prime technique to use. It promises to obtain bulk-scale, statistically sound information on the morphological
details of the nanostructure, and has thus led to many a researcher investing their time in it over the last eight decades of development. Due to pressure both from scientists requesting more details on increasingly complex nanostructures, as well as the ever improving instrumentation leaving less margin for ambiguity, small-angle scattering methodologies have been evolving at a high pace over the last few decades. As the quality of any results can only be as good as the data that goes into these methodologies, the improvements in data collection and all imaginable data correction steps are reviewed here. This work is intended to provide a comprehensive overview of all data corrections, to aid the small-angle scatterer to decide which are relevant for their measurement and how these corrections are performed. Clear mathematical descriptions of the corrections are provided where feasible. Furthermore, as no quality data exists without a decent estimate of its precision, the error estimation and propagation through all these steps is provided alongside the corrections. With these data corrections, the collected small-angle scattering pattern can be made of the highest standard allowing for authoritative nanostructural characterisation through its analysis. A brief background of small-angle scattering, the instrumentation developments over the years, and pitfalls that may be encountered upon data interpretations are provided as well.
Usually, equal time is given to measuring the background and the sample, or even a longer background measurement is taken as it has so few counts. While this seems the right thing to do, the relative error after background subtraction improves when m
ore time is spent counting the measurement with the highest amount of scattering. As the available measurement time is always limited, a good division must be found between measuring the background and sample, so that the uncertainty of the background-subtracted intensity is as low as possible. Herein outlined is the method to determine how best to divide measurement time between a sample and the background, in order to minimize the relative uncertainty. Also given is the relative reduction in uncertainty to be gained from the considered division. It is particularly useful in the case of scanning diffractometers, including the likes of Bonse-Hart cameras, where the measurement time division for each point can be optimized depending on the signal-to-noise ratio.
Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of size determin
ation methods in relation to the range of scattering vectors covered by the data is discussed. Improvements are presented to existing MC methods in which the particle shape is assumed to be known. A discussion of the problems with the ambiguous convergence criteria of the MC methods are given and a convergence criterion is proposed, which also allows the determination of uncertainties on the determined size distributions.
