Neutron diffraction and inelastic scattering, in common with many other experimental techniques used in materials science (e.g. X-ray diffraction, light scattering), uses the measurement of the change in momentum/energy of scattered particles in order to provide information on the positions and motions of atoms (or electrons) in real space. It is always impossible to measure complete information in energy/momentum space, without errors, and in any case phase information is lost. The analysis of all neutron scattering data is therefore an inverse problem.
In this talk I will describe a number of typical neutron scattering experiments and the associated data analysis challenges, from the ‘inverse problem’ viewpoint. The inverse methods that are used to solve these problems typically involve the generation of either a mathematical or physical model, calculating the predicted data set corresponding to the model and comparison to experiment. In some cases the parameters that define the model can then be directly varied in some fashion to ‘fit’ the model to the experimental data. In other cases the models are an ‘aid to interpretation’ of the data.
While particular mathematical techniques (e.g. Bayesian analysis) can be applied to these problems in order to in some way deal with data errors or incompleteness, I will stress the central importance of ensuring the physical sense of the model via the use of appropriate constraints. In the end it must be remembered that the goal is not to produce a unique solution to a mathematical problem, but rather an always approximate model which gives us a useful insight into the system/problem of interest.
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