Statistical detection of the hidden distortions in diffusive spectra

Abstract

The detection of an unknown substance in small concentration represents an important problem in spectroscopy. Usually this detection is based on the recognition of specific `labels' i.e. the visual appearance of new resonance lines that appear in the spectrograms analysed. But if the concentration of the unknown substance is small and visual indications (e.g. resonance peaks in diffusive spectra) are absent then the detection of the unknown substance constitutes a problem. We suggest a new methodology for the statistical detection of an unknown substance, based on the transformation of fluctuations obtained from initial spectrograms into ordered quantized histograms (QHs). The QHs obtained help to detect, statistically, the presence of unknown substances using the characteristics of conventional quantum spectra adopted from quantum mechanics. The averaging of the QHs helps to calculate the ordered `fluctuation fork' (FF), which provides a specific `noise ruler' for the detection and quantification of the trace substance. The quantitative parameters of the FF are the length (D) (defined as the maximal value of the FF along OX axis), maximum value of the width (W) (which coincides with the maximal value of standard deviation along OY axis) and the total area (A) of the FF occupied on OXY plane. The sensitivity of these parameters to the concentration of trace substance forms the basis on which it is possible to analyse the concentration of the unknown substance, despite the fact that visual indications in diffusive spectra are absent. This methodology can provide the foundations for a new fluctuations treatment spectroscopy, which can be effective in the analysis of fluctuations (noise) accompanying the basic spectrogram. Application of the new methodology to near infrared (NIR) spectra obtained for petrol of octane ratings 95 and 98, and their mixtures, confirms the effectiveness and sensitivity of new methodology. In another experiment on the detection of protein (IgG1) in phosphate buffer saline it was possible to show the sensitivity of the new methodology to concentrations as low as 0.1 μg ml−1 (i.e. 10−5%). Conventional analysis of NIR spectra would lead to a level of detection of 0.1%, at best. The applicability of the new method as a general approach to the analysis of fluctuations within complex diffusive spectrograms is discussed.