The extended Kubelka–Munk theory and its application to spectroscopy

The Kubelka–Munk theory is one of the main theories of light flux through homogeneous isotropic media. In this work, we used the extended solution of this theory, applied to a specimen on top of an arbitrary substrate, to obtain the overall spectral reflectance and transmittance. A complete colorimetric study can be derived from these calculations and this is shown by analyzing the effect of the different properties of the system (scattering and absorption coefficients, thickness, particle radius, surrounding medium) on its coordinates on the color space. Along with the analytical solutions to the original two-flux and the more modern four-flux models, we present a computing tool based on a Monte Carlo algorithm, which is very adequate in this context. In it, both the energy and the media are discretized, and the interaction is converted into probability of scattering and absorption. This numerical procedure also introduces new capabilities in the model, since it admits properties such as inhomogeneity in the layers, or more complex light–matter interactions, and offers solutions with temporal resolution, something applicable, for example, to pulses or transient states.