Simple Bayesian method for improved analysis of quasi-two-dimensional scattering data

A new method is presented for the analysis of small angle neutron scattering data from quasi-two-dimensional systems such as flux lattices, Skyrmion lattices, and aligned liquid crystals. A significant increase in signal to noise ratio and a natural application of the Lorentz factor can be achieved by taking advantage of the knowledge that all relevant scattering is centered on a plane in reciprocal space. The Bayesian form ensures that missing information is treated in a controlled way and can be subsequently included in the analysis. A simple algorithm based on Gaussian probability assumptions is provided which provides very satisfactory results. Finally, it is argued that a generalized model-independent Bayesian data analysis method would be highly advantageous for the processing of neutron and x-ray scattering data.