Robust approaches for model-free small-angle scattering data analysis

The small-angle neutron scattering data of nanostructured magnetic samples contain information regarding their chemical and magnetic properties. Often, the first step to access characteristic magnetic and structural length scales is a model-free investigation. However, due to measurement uncertainties and a restricted q range, a direct Fourier transform usually fails and results in ambiguous distributions. To circumvent these problems, different methods have been introduced to derive regularized, more stable correlation functions, with the indirect Fourier transform being the most prominent approach. Here, the indirect Fourier transform is compared with the singular value decomposition and an iterative algorithm. These approaches are used to determine the correlation function from magnetic small-angle neutron scattering data of a powder sample of iron oxide nanoparticles; it is shown that with all three methods, in principle, the same correlation function can be derived. Each method has certain advantages and disadvantages, and thus the recommendation is to combine these three approaches to obtain robust results.

Automated summary

The small-angle neutron scattering data of nanostructured magnetic samples can provide information about their chemical and magnetic properties. Different methods have been compared to derive regularized, more stable correlation functions from the data. It is shown that, in principle, the same correlation function can be obtained using the indirect Fourier transform, singular value decomposition, and an iterative algorithm. It is recommended to combine these three approaches to obtain robust results.