The extended Kubelka–Munk theory and its application to spectroscopy

Abstract

The Kubelka–Munk theory is one of the main theories of light fux 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 refectance and transmittance. A complete colorimetric study can be derived from these calculations and this is shown by analyzing the efect of the diferent properties of the system (scattering and absorption coefcients, thickness, particle radius, surrounding medium) on its coordinates on the color space. Along with the analytical solutions to the original two-fux and the more modern four-fux 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 ofers solutions with temporal resolution, something applicable, for example, to pulses or transient states.