After 1981, the development of software for the analysis of energy-dispersive spectra from nuclear decay has more or less followed the technical development of personal computers, and major emphasis has been on the user’s request for simplified and intuitive handling. All programs can analyse big singlet peaks correctly and with an acceptable level of accuracy, though it may seem that uncertainties of fitted parameters and of peak-areas are significantly underestimated by some programs.
A few general statements are:
- All programs run under WINDOWS®
- All commercial programs have software protection units
- All reasonable programs can read various spectrum formats
- All reasonable programs can make reliable automatic spectrum analyses
- All reasonable programs provide a software update service
- All reasonable programs provide on-line help and hotline
- All reasonable programs provide spectrum oriented analyses but not peak-list oriented analysis.
In the last years Dr. Westmeier GmbH has developed new programming strategies and algorithms for the analysis of nuclear radiation spectra. Principles of the new developments are:
- Physics, no numerology
- Fuzzy Logic
- Repeated analyses
The meaning of categories is as follows:
PHYSICS, NO NUMEROLOGY
It is not meaningful (though current practice) that simple mathematical recipes are used for the description of physical dependences such as peak shape or shape of the baseline under peaks, even when simple functions are easily fitted. The real shape of peaks, baseline and other spectral dependences comes from the interactions after emission of photons or alpha particles with matter and detector material. The relevance of this statement is particularly apparent when one surveys the tailing of alpha peaks. The correct description comes from the mathematical description of energy loss in interactions whereby one has to consider all possible interactions between emission and registration. This leads to a more complicated mathematical function which can be least-squares fitted though. In this way one can replace the simplified shape description (e.g. the Gaussian Distribution) by the physically correct description. This yields much improved results in the fitting process. Improvements are in particular apparent when one fits small peaks sitting in the shoulder of a big one or on high background. The “Physics, no numerology” approach is used for description of peak shape, baseline, background, efficiency and other dependences.
A completely new strategy towards programming automatic spectrum analysis has been introduced by us in recent years. The heart of the method lies in the fact that there are often various different ways in which a solution to a problem can be found. Some ways may be good for one situation but poor for another; some procedures are generally usable whereas others may be suitable only for very specific cases. The modern approach to handling this dilemma of “how to do it right?” is called Fuzzy Logic where one
- uses all available methods and algorithms
- assigns weights to the various results, based on the applicability of the respective method (this is the key issue!)
- discards inapplicable methods
- calculates the weighted average of valid results.
When the least-squares fit of a region is finished results are subjected to residuum analysis and statistical checks. This may reveal presence of yet another peak or show that a peak is statistically insignificant. In this case the complete fit operation of the region is repeated, however, this time with the improved set of potential peaks. The analysis of these fit results may reveal other changes which are then tried out. In this way multiple analyses will finally yield the best possible fit of peaks to the data. When one judges the statistical relevance of fitted results one must keep in mind that an improved reduced chi-quares variable is always found when more parameters are fitted to the same set of data points.
The .PDF file Paradigm Shift gives a comprehensive overview of this innovative method of spectrum analysis.
The .PDF file Hardware and Software Applications in Nuclear Spectrometry gives an overview over recent developments in the field.