# Dual-Slope Diffuse Reflectance Instrument for Calibration-Free Broadband Spectroscopy
## 4 Discussion
Further evaluation was carried out to estimate the recovered concentration of II given the measured change in absorption. The true concentration (in volume fraction) of II in the phantom was \(5.7\times 10^{-6}\), given the phantom volume and the amount of ink added. The same II was measured in transmission in non-diffuse solutions of known concentrations to yield spectra of the total attenuation coefficient (\(\mu_{t}\); assuming only unscattered light is detected). To yield thespectrum of absorption (\(\mu_{a}\); needed to recover concentration in the diffuse experiment) for II, the single scattering albedo (\(a\)) must be assumed (\(\mu_{a}=\mu_{t}(1-a)\)). This must be considered for II since it is not in solution in water but instead a suspension of carbon particles. Wavelength independent values of \(a=0\) to \(a=0.15\) were assumed which yielded recovered concentrations of \(5.2\times 10^{-6}\) to \(6.1\times 10^{-6}\), respectively. This range of low albedo values of pure II indicates that its scattering coefficient is much smaller than the absorption coefficient, which is consistent with the literature [35; 36]. The range resulted in measurement errors of \(-8.8\%\) to \(7.0\%\) (given true value of \(5.7\times 10^{-6}\)). Therefore, it is expected that DS CW-bDRS is capable of recovering accurate chromophore concentrations given that the extinction spectra is known (not the case here since the albedo for II was not measured). For NIR746A (N7) and N8, the concentration recovery was not carried out due to temporal and spectral instability of the dyes (discussed below). Future experiments will be undertaken to validate the accurate chromophore concentration recovery of DS CW-bDRS using soluble and stable dyes. Moving on from II, the next two dyes were expected to feature a more interesting spectrum (Figure 3). NIR746A (N7) was added after II and the change of absorption presented in Figure 4c. The expected peak between 700 nm and 800 nm was present. However, upon closer examination, the exact peak location is shifted about 12 nm higher for the DS CW-bDRS measurement compared to the expected spectrum (Figure 5a). When the next and final dye, NIR869A (N8), was added, yet again there was a peak present in approximately the expected location (Figure 4b). But, as with N7, there was an approximate 12-nm shift to longer wavelengths in the DS CW-bDRS measurement. This is consistent with a bathochromic shift, which is possible for these dyes given the manufacturer information and previous studies [37; 38]. The hypothesis is that, when in milk, the dyes exhibit a bathochromic shift due to the different bulk polar nature of milk versus water. To test this possibility, two further measurements were done on N8. N8 was measured in transmission (in a semi-micro cuvette), both in water and in the MW mixture (Figure 5b). The results show that the transmission spectral absorbance for N8 in milk matches the DS CW-bDRS peak location, whereas the transmission spectral absorbance of N8 in water matches the manufacturer provided spectra. Thus, this transmission experiment supports the hypothesis that these dyes exhibit a bathochromic shift of about 12 nm when in the MW mixture. However, it is unknown if the amplitude of the absorption peak is also effected (hyperchromic or hypochromic shift) for these dyes. The dyes were also found to be temporally unstable, as extended time in solution caused N7 to lose its near-infrared absorption peak, and N8's peak shifted roughly 200 nm to the blue. These spectral and temporal instabilities stopped the analysis of the concentrations of these dyes in the diffuse phantom. But, despite this, DS CW-bDRS was still capable of distinguishing the dye's spectral features. Summarizing the discussion above, these results on the liquid phantom serve to validate the DS CW-bDRS instrument's ability to measure spectral features and absolute values of absorption in a diffuse medium.