# Dual-Slope Diffuse Reflectance Instrument for Calibration-Free Broadband Spectroscopy
## 4 Discussion  
The experiment involved a liquid phantom and sought to validate the Dual-Slope Continuous Wave broadband Diffuse Reflectance Spectroscopy (DS CW-bDRS) instrument (Sections 2.2 and 3). This was done by measuring a highly scattering phantom as dyes were progressively added (Figure 4). The expectation was that the DS CW-bDRS (in combination with Multi-Distance Frequency-Domain Near-Infrared Spectroscopy; MD FD-NIRS) instrument would be able to measure the known spectral features of the dyes and the absolute absorption of the phantom. First, before any dyes were added (just Milk and Water; MW), the phantom was measured to yield an absorption spectrum dominated by water (Figure 4a). This MW spectra had the expected spectral features of water (hump at about 750 nm and sharp increase starting at about 800 nm) [41]. Further, the expected MW spectrum agrees (within error) with the experimental data for the spectral range between 690 nm and 830 nm, where the reduced scattering coefficient is interpolated (not extrapolated) from the MD FD-NIRS measurement. Below 690 nm, the agreement is lost likely due to the very low water absorption, such that, even low absorption, contributions from fat, proteins, or other milk constituents in the MW medium may become detectable. Above 830 nm, the agreement also degrades possibly because of incorrect reduced scattering values (from extrapolation) or contributions from other absorbers in the milk other than water. Overall, the quantitative agreement between the expected and measured MW spectra are quite good with a coefficient of determination (\(R^{2}\)) of 0.98, indicating an accurate measurement of absolute absorption by DS CW-bDRS. Further, the absorption measured by MD FD-NIRS agrees within error with DS CW-bDRS at all points of comparison except for NIR869A (N8). For N8, the difference between the measurements is about 10%, and the combined errors for the two measurements amount to about 8% (dominated by uncertainty in the distances; Section 3). Admittedly, the reduced scattering found by MD FD-NIRS is used to find the absorption for DS CW-bDRS; thus, the measurements are related (Section 2.3). However, the observed agreement demonstrates a reliable absolute measurement of the slope of diffuse reflectance with the DS CW-bDRS instrument, given the accurate measurements with the scanning MD method used by MD FD-NIRS in controlled laboratory conditions. In the case of N8, where the two instruments do not agree, the most likely explanation is instrumental error (distance uncertainty and boundary conditions). The distance uncertainty accounts for most of the difference between the measurements, and the remaining unaccounted disagreement may be explained by uncertainties in boundary conditions (true depth of fibers in phantom, existence of meniscus, etc.). These distance uncertainties and boundary effects may have changed for each measurement, since after the addition of each dye the instruments needed to be re-setup and placed on the phantom. This may explain why instrumental errors impacted differently the measurements of different dyes. Additionally, there is evidence that the NIR dyes are not stable over time (discussed below), and the two measurements are not simultaneous (5-10 min between measurements). Any of these considerations may have led to the lack of agreement for N8. However, given the existence of these considerations and the close agreement in six out of eight cases, we find that the results serves to validate the absolute absorbance measured by DS CW-bDRS. Focusing on the individual dye additions allows for validation of the measurement of spectral features. The first dye added was India Ink (II), which is expected to have a flat or decreasing spectral dependence with wavelength [35]. The change in the absorption spectrum observed confirmed this wavelength dependence and, again, agreed with the measurements at two wavelengths with MD FD-NIRS (Figure 4d).