Bayesian Spectral Analysis of Reflectivity Data

Abstract

The analysis of neutron and x-ray reflectivity data to obtain scattering-length density profiles is akin to the notorious phaseless Fourier problem, well-known in many fields such as crsytallography. Current methods of analysis culminate in the refinement of a few parameters of a functional model, and are often preceded by a long and laborious process of trial-and-error. A discussion of the use of maximum entropy for obtaining “free-form” solutions of the density profile, as an alternative to the trial-and-error phase when a functional model is not available, and the suggestion for a novel experimental procedure designed to alleviate the ambiguity problems inherent in traditional reflectivity measurements, are given in Sivia et al. (1990). In this paper we consider the Bayesian spectral analysis approach, which is appropriate for optimising the parameters of a simple (but adequate) type of model when the number of parameters is not known.