## 3 Results and Discussion
### Quantification Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**VN**} \\ \cline{2-5}  & **LOD** & **SEN** & \(\gamma\) & \(\gamma^{-1}\) \\ \hline BC & 1.4 & 0.013 & 43 & 0.023 \\ SYN-S & 1.2 & 0.016 & 53 & 0.019 \\ NAT-S & 0.8 & 0.010 & 32 & 0.031 \\ NAT-S Low & 0.3 & 0.087 & 289 & 0.003 \\ \hline \hline \multicolumn{5}{c}{Noise = 0.0003} \\ \hline  & \multicolumn{4}{c}{**No Preprocessing**} \\ \cline{2-5}  & **LOD** & **SEN** & \(\gamma\) & \(\gamma^{-1}\) \\ \hline BC & 2.3 & 1.48 & 39 & 0.025 \\ SYN-S & 1.4 & 2.25 & 60 & 0.017 \\ NAT-S & 1.0 & 1.36 & 36 & 0.028 \\ NAT-S Low & 0.6 & 20.63 & 552 & 0.002 \\ KBr & 0.6 & 0.51 & 14 & 0.072 \\ KBr Low & 0.07 & 1.26 & 34 & 0.029 \\ \hline \hline \multicolumn{5}{c}{Noise = 0.037} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sensitivity, analytical sensitivity, the limit of detection (LOD), and noise of the models, with and without vector normalization (VN) preprocessing. MC was not able to compensate for the difference in the particle size. In contrast, the VN preprocessing method was able to compensate for these differences. The prediction of DNT in NAT-S-M shows peaks of high DNT concentrations (>10% DNT). This is because the particles of DNT were not homogenized. The models with no preprocessing provided bad predictions due to the difference in the baseline of the spectra. The above discussion demonstrates that VN preprocessing corrects the spectral variation due to changes in the particle size. To demonstrate the change in spectrum with the particle size, the tested soil was sieving for three particle sizes (\(d\)): \(d>0.85\) mm, 0.85 mm \(>d>0.25\) mm, and \(d<0.25\) mm. One hundred spectra were acquired at various locations on the sample surface for each value of \(d\), and the average and standard deviation of the spectra were determined (see Supplementary Materials: Figures S10 and S11). The background offset spectral decreases with \(d\), whereas the standard deviation increases with \(d\); however, this pattern is not consistent throughout the spectra. It is higher in the 1000-1200-cm\({}^{-1}\) and 1400-1600-cm\({}^{-1}\) regions. This can be explained by the fact that MC is not able to correct the background offset spectral completely in contrast to VN; VN is better because it scales the spectrum to unit vectors, whereas MC only changes the baseline. In the third sample, another type of natural soil (NAT2-S) was used to evaluate the NAT-S model. Two samples of NAT2-S were contaminated with 10% of DNT and mixed. Mappings of 10 \(\times\) 10 mm\({}^{2}\) (100 points) were generated with the %DNT predicted from the NAT-S model using VN preprocessing. The mappings are present in Supplementary Materials: Figure S12, while predictions for each point are illustrated in Figure 4d. It can be noticed from the figure that the predictions were lower than the true values. This indicates that the NAT-S model quantifies below the true value of 10% DNT; however, it is capable of predicting the existence of an explosive in a soil. This indicates that the technique should be used in known soil to have good quantification. Figure 4: Predictions for 100 pts. maps after applying VN, mean centering (MC), and no preprocessing: (**a**) simple mixture (NAT-S-M); (**b**) macroating the components (NAT-S-MM); (**c**) Averages for the predictions of NAT-S-M and NAT-S-MM (**d**) NAT2-S with VN preprocessing. To challenge the NAT-S model with other interferences, mixtures of other analytes in soil were prepared with a concentration of 10% (median of the model). The analytes used as interferences were BA, IBP, PETN, RDX, and TNT. BA and IBP do not have nitro groups but have aromatic rings and thus many common signals with DNT in the range of 1000-1600 cm\({}^{-1}\). PETN and RDX are nitro Aliphatic explosives. TNT is very similar to DNT but considered to be a more challenging interference. Predictions for these samples were generated using the calibration curves for DNT/NAT-S.