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.
Journal of the Optical Society of America. A, Optics, image science, and vision