Extension of the Kubelka–Munk theory to an arbitrary substrate: a Monte Carlo approach

In this work we review and-to some extent-upgrade one of the main theories of light flux through homogeneous isotropic media, namely, the Kubelka-Munk (K-M) theory, and in particular the later expansion made by Kubelka to obtain the reflectance of a specimen when a substrate lies underneath. We have completed this solution by calculating the transverse energy density in the specimen and the transmission of the whole. We show that this last result-compatible with Kubelka's upgrade for layered media-also allows for the calculation of the specimen/substrate absorption split. In order to validate these expressions, the results were reproduced by means of a Monte Carlo simulation working on a layered medium under the same assumptions as the K-M theory. Interestingly, the numerical procedure introduces new capabilities in the model regarding the history of any absorbed or outgoing elemental light beam, such as the recording of its time-of-flight through a given system.