A non-uniform reference model for maximum-entropy density reconstructions from diffraction data

Abstract

Diffraction experiments provide information on the Fourier components of microscopic density distributions in crystals. To obtain the spatial densities themselves, an inverse Fourier problem has to be solved. The procedure is complicated by the presence of noise and incompleteness of the data. The application of the maximum-entropy (MaxEnt) principle was a breakthrough in density reconstruction, allowing high-quality density maps to be obtained without involving any a priori information concerning what the reconstructed density should look like. In this work, a procedure is proposed that incorporates a priori (e.g. theoretical) information into MaxEnt reconstructions of spin density distributions. It allows, on the one hand, the evaluation of the existing density models and, on the other, the precise investigation of what new information the experiment brings. Unlike traditional parameter-refinement techniques, the new method does not impose any strict constraints on the density to be reconstructed and is thus much more flexible. At the same time, it suppresses artifacts and yields high-quality density maps. The advantages of the new methods are illustrated by an example of spin density reconstruction based on real polarized neutron diffraction data.