Illustration of failure of continuum models of diffuse reflectance

Continuous models are widely used to model diffuse reflection from particulate samples. They are embodied in various theories, including diffusion theory, the equation of radiation transfer, and Kubelka-Munk. Using a simple system, it is shown that such models do not simultaneously predict the fractions of incident light that are transmitted directly and diffusely. Discontinuous models do have the capability to do so, but have a variety of limitations as well.