Maximum entropy reconstruction of spin densities involving non uniform prior

Conference · Mon Sep 01 04:00:00 EDT 1997

OSTI ID:541900

Schweizer, J; Ressouche, E ^[1]; Papoular, R J ^[2]; Tasset, F ^[3]; Zheludev, A I ^[4]

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1. DRFMC/SPSMS/MDN CEA-Grenoble (France)
2. CEA-Saclay, Gif sur Yvette (France). Lab. Leon Brillouin
3. Inst. Laue Langevin, Grenoble (France)
4. Brookhaven National Lab., Upton, NY (United States). Physics Dept.

Diffraction experiments give microscopic information on structures in crystals. A method which uses the concept of maximum of entropy (MaxEnt), appears to be a formidable improvement in the treatment of diffraction data. This method is based on a bayesian approach: among all the maps compatible with the experimental data, it selects that one which has the highest prior (intrinsic) probability. Considering that all the points of the map are equally probable, this probability (flat prior) is expressed via the Boltzman entropy of the distribution. This method has been used for the reconstruction of charge densities from X-ray data, for maps of nuclear densities from unpolarized neutron data as well as for distributions of spin density. The density maps obtained by this method, as compared to those resulting from the usual inverse Fourier transformation, are tremendously improved. In particular, any substantial deviation from the background is really contained in the data, as it costs entropy compared to a map that would ignore such features. However, in most of the cases, before the measurements are performed, some knowledge exists about the distribution which is investigated. It can range from the simple information of the type of scattering electrons to an elaborate theoretical model. In these cases, the uniform prior which considers all the different pixels as equally likely, is too weak a requirement and has to be replaced. In a rigorous bayesian analysis, Skilling has shown that prior knowledge can be encoded into the Maximum Entropy formalism through a model m({rvec r}), via a new definition for the entropy given in this paper. In the absence of any data, the maximum of the entropy functional is reached for {rho}({rvec r}) = m({rvec r}). Any substantial departure from the model, observed in the final map, is really contained in the data as, with the new definition, it costs entropy. This paper presents illustrations of model testing.

• Research Organization: Brookhaven National Lab., Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 541900
• Report Number(s): BNL--64549; CONF-9707105--; ON: DE97008973; BR: KC0202010
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BRAGG REFLECTION
CRYSTAL STRUCTURE
DATA ANALYSIS
INTERMETALLIC COMPOUNDS
MOLECULAR STRUCTURE
NEUTRON DIFFRACTION
RADICALS
X-RAY DIFFRACTION