The application of Bayesian statistics and maximum entropy to Ion beam analysis techniques

The elimination of some blurring property, such as the detector response function, from spectra has received a considerable amount of attention. The problem is usually complicated by the presence of noise in the data, and in general, there exists an infinite set of possible solutions which are consistent with the data within the bounds imposed by the noise. Such a problem is known, generally, as an ill-defined inverse problem. Many techniques have been developed in an attempt to solve inverse problems, for example the problem of deconvolution, but these techniques employ ad hoc modifications to solve different problems. Bayesian Statistics has been proved to be the only consistent method for solving inverse problems of the type where the information is expressed in terms of probability distributions. This dissertation presents results of applying the Bayesian formalism, together with the concepts of maximum information entropy and multiresolution pixons, to various inverse problems in ion beam analysis; The results of this method of deconvoluting Rutherford Backscattering Spectrometry (RBS) and Proton Induced X-ray Emission (PIXE) spectra are compared to the results from other deconvolution techniques, namely Fourier Transforms, Jansson's method and maximum entropy (MaxEnt) without pixons. All the deconvolution techniques show an improvement in the resolution of the RBS spectra but only the MaxEnt techniques show a significant improvement in the resolution of the PIXE spectra. The MaxEnt methods also produce physically acceptable results. The MaxEnt formalism was applied to the extraction of depth profiles from RBS and PIXE spectra and yielded good results. The technique was also used to deconvolute the beam profile from one-dimensional nuclear microprobe scans.

Grantor dc:publisher.institution

Department of Physics

Year dc:date.issued

1997

Author dc:creator

• Padayachee, Jayanethie

Advisors dc:contributor.advisor

• Prozesky, Victor M
• Britton, David T

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/16143

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/16143