Classical Least Squares

Mid-infrared (MIR) laser spectroscopy was used to detect the presence of residues of high explosives (HEs) on fabrics. The discrimination of the vibrational signals of HEs from a highly MIR-absorbing substrate was achieved by a simple and fast spectral evaluation without preparation of standards using the classical least squares (CLS) algorithm. Classical least squares focuses on minimizing the differences between the spectral features of the actual spectra acquired using MIR spectroscopy and the spectral features of calculated spectra modeled from linear combinations of the spectra of neat components: HEs, fabrics, and bias. Samples in several combinations of cotton fabrics/HEs were used to validate the methodology. Several experiments were performed focusing on binary, ternary, and quaternary mixtures of TNT, RDX, PETN, and fabrics. The parameters obtained from linear combinations of the calculated spectra were used to perform discrimination analyses and to determine the sensitivity and selectivity of HEs with respect to the substrates and to each other. However, discrimination analysis was not necessary to achieve successful detection of HEs on cotton fabric substrates. The RDX signals (mRDX？>？0.02？mg) on cotton were used to calculate the limit of detection (LOD). The signal-to-noise ratios (S/N) calculated from the spectra of cotton dosed with decreasing masses of RDX until S/N？≈？3 resulted in a LOD of 15–33？μg, depending on the vibrational band used. Linear fits generated by comparing the mass dosed RDX with the fraction predicted were also used to calculate the LOD based on the uncertainty of the blank and the slope. This procedure resulted in a LOD of 58？μg. Probably the most representative value of the method LOD was calculated using an interpolation of a threshold determined using the predicted average value for the blank plus 3.28 times the standard deviations (p-value threshold) for low surface dosages of RDX (LOD？=？40？μg). The contribution demonstrates that to achieve HE detection on fabrics using the proposed algorithm, i.e., determining the presence/absence of HEs on the substrates, the library must contain the spectra of HEs, substrates, and potential interferents or that these spectra be added to the models in the field. If the model does not contain the spectra of the fabric components, there is a high probability of finding false positives for clean samples (no HEs) and a low probability for failed detection in samples with HEs. More work will be required to demonstrate that these new approaches to HE detection work on real-world