Optimized Reduced Spectrum Models of Diffuse Reflectance for NIR-SWIR Absorbing-Dye Formulations

This study describes a measurement-optimized parametric model of diffuse reflectance, based on the reduction of absorption spectra for Near Infrared (NIR) and Short-Wave Infrared (SWIR) absorbing dyes on substrates using critical feature isolation and projection. The critical features are identified through a structural analysis of the peaks, troughs, and points of inflection within the Kubelka-Munk absorption spectra, which is calculated from diffuse reflectance measurements. These critical features are then parameterized and projected into a reduced feature subspace using Lorentzian decompositions to effectively capture the fundamental characteristics of the absorbing dyes, while removing processing and measurement noise. A Kramers-Kronig analysis then characterizes the dielectric responses and provides an estimation of the reduced spectra reflectance. The model parameters for the analytical reduction are further refined using a nonlinear multivariable optimization function between the analytically predicted reflectance and the measured reflectance. This results in an enhanced measurement-optimized model that is capable of incorporating measurement and processing artifacts to improve application-specific reflectance predictions. Furthermore, the reduced, enhanced functions establish a parametric dataspace that can support the mapping of functions between individual NIR-SWIR absorbing dye components and the diffuse reflectance predictions for new mixture and substrate combinations.