Relating Near-Infrared Light Path-Length Modifications to the Water Content of Scattering Media in Near-Infrared Spectroscopy: Toward a New Bouguer–Beer–Lambert Law

In near-infrared spectroscopy (NIRS), the linear relationship between absorbance and an absorbing compound concentration has been strictly defined by the Bouguer-Beer-Lambert law only for the case of transmission measurements of nonscattering media. However, various quantitative calibrations have been successfully built both on reflectance measurements and for scattering media. Although the lack of linearity for scattering media has been observed experimentally, the sound multivariate statistics and signal processing involved in chemometrics have allowed us to overcome this problem in most cases. However, in the case of samples with varying water content, important modifications of scattering levels still make calibrations difficult to build due to nonlinearities. Moreover, even when calibration procedures are successfully developed, many preprocessing methods used do not guarantee correct spectroscopic assignments (in the sense of a pure chemical absorbance). In particular, this may prevent correct modeling and interpretation of the structure of water. In this study, dynamic near-infrared spectra acquired during a drying process allow the study of the physical effects of water content variations, with a focus on the first overtone OH absorbance region. A model sample consisting of aluminum pellets mixed with water allowed us to study this specifically, without any other absorbing interaction terms related to the dry mass-absorbing constituents. A new formulation of the Bouguer-Beer-Lambert law is proposed, by expressing path length as a power function of water content. Through this new formulation, it is shown that a better and simpler prediction model of water content may be developed, with more precise and accurate identification of water absorbance bands.