A Pragmatic Smoothing Method for Improving the Quality of the Results in Atomic Spectroscopy

Abstract

A new smoothing method for improvement on the quantification of spectral signals, which requires the previous knowledge of the functions that should be quantified, is presented. These functions are used as weighted coefficients in the proposed smoothing algorithm. This method is extremely effective in reducing the scatter of signals obtained by the multichannel analyzer and it could be applied in atomic and nuclear spectroscopies, preferably to these techniques where net counts are a linear function of the acquisition time, like total reflection X-ray fluorescence, micro X-ray fluorescence, etc. If this algorithm is properly applied, it does not distort the form or the intensity of the signal, so it is well suited for use in all kinds of spectroscopic techniques. However, it should not be applied to data obtained from systems depending on time, e.g., control sciences, time series, sound analysis, etc. We applied this method over simulated data and real experimental measurements. As with all smoothing techniques, the proposed method improves the precision of the results, but when it was applied to computer-simulated spectra, we found a systematic enhancement on the accuracy of the results. We still do not have an answer for this apparent paradox. We also have to evaluate, in spectral analysis, the improvement produced by this smoothing procedure over detection and quantification limits. When this algorithm is applied over experimental results, it is mandatory that the sought characteristic functions, required for this weighted smoothing method, should be obtained from a system with strong stability. If the sought signals are not perfectly clean, this method should be applied with care.

An “ad-hoc” modified likelihood function applied to optimization of data analysis in atomic spectroscopy

“…For these reasons, an improvement on the quality of the results over those obtained by least squares approaches seems to be unrealistic. However, in another work we developed a new smoothing method [6] which was applied to simulated spectroscopic data, producing results with better accuracy than those obtained from the least squares approach.…”

“…In spectral analysis, we still have to evaluate the improvement produced by this method in conjunction with a new smoothing procedure [6], over Detection and Quantitation Limits, when they are applied over real experimental results. These kind of evaluations are formally required in all spectroscopic techniques, in order to establish their metrological traceability, defining carefully their operational procedures.…”

“…( 8) is implicitly applied over Eq. (6). Taking into account that ∆𝐹 𝑖 = 0 𝑎𝑛𝑑 ∆𝑏𝑔 𝑖 = 1, the uncertainty of the parameter α, is:…”

“…However, in another work [6] we devised a new smoothing method which was applied to simulated spectroscopic data, producing results with better accuracy than those obtained from the least squares approaches.…”

“…Being ∆ ( ) the uncertainty of the function ( ), and ∆ the uncertainty of every one of the k independent input variables.The Eq. (8) is implicitly applied over Eq (6)…”