## 3 Results and Discussion
### Comparision of Analysis Methods  
The three different analysis methods were compared based on their ease of implementation and performance in determining adulterant concentration (Table 1). Table 1 lists the pixel-based detected concentrations of adulterants in each sample. A linear relationship between the pixel-based detected percentage of adulterants and actual concentration of adulterants in the mixture was developed for quantitative analysis. Table 1 shows that the adulterant contents determined using univariate and bivariate imaging were very similar, with slightly better performance observed for the latter method. Figure 6: Combined color-coded Raman chemical images for each adulterant at four different concentrations generated using three different analysis methods. This behavior was ascribed to the suppression of noise by image multiplication, whereas some false positive pixels were calculated for Sudan-I (inside the black box in Figure 6) using the univariate method. The pixels marked in Figure 6 corresponded to high-frequency noise in the spatial domain, which was viewed as Sudan dye pixels during image thresholding. However, when the bivariate method was used and images were multiplied, this noise was suppressed, as the adulterant pixel intensity was enhanced. The obtained results revealed that the SAM method underestimated the adulterant content (particularly in the case of Sudan-I) for low-concentration samples and overestimated it in the case of highly concentrated samples (e.g., mixture 4), as compared to the results of the univariate and bivariate methods. This behavior was attributed to the fact that in low-concentration samples, the minor peaks of adulterants were not clearly distinguished from those of the paprika powder background, while being fairly intense in the case of concentrated samples. To re-state this, the SAM algorithm calculates the similarity between the spectra of the reference material and investigated pixels. If the pixel spectra are strongly influenced by those of the background material (paprika powder), the calculated angles lie between those of paprika powder and the adulterant of interest. Thus, the above pixels are considered to be sub-pixels and are missed during image thresholding. In order to correct this sub-pixel effect, the threshold values were also tested as slightly higher and lower than the calculated median values. However, for the higher threshold value, some of the background pixels were identified as adulterants (over-classifying) and at the lower threshold value, some adulterants pixels were missed (under-classifying). In an another approach, to check the similarity between the adulterant particles detected using the three analysis methods, the binary images of same-concentration samples generated using these methods were linked together for pixel-to-pixel comparison, as shown in Figure 7. At each concentration level, the binary images generated using the three different methods were combined and the detected adulterant pixels for each method were color coded--pixels in green represent the results from the univariate method, blue represents the bivariate method, and red represents the multivariate (SAM) analysis. Combination pixels that were detected using two methods (any combination of two methods from the three used analysis methods) were represented in orange, pink, and baby blue and pixels detected as adulterants by all methods are shown in black. As can be seen, the majority of pixels in these images were black, implying that all of the three methods assigned the same pixels as adulterants. However, some pixels corresponding to relatively small spots were determined as adulterants by the univariate and bivariate methods (brown color) but not by SAM, probably due to the latter method viewing them as subpixels and thus not classifying them as adulterants for the reason mentioned above. However, the visual evaluation of the spectra of these pixels confirmed their assignment as adulterants.