Bridging the continuum-discontinuum gap in the theory of diffuse reflectance

A system of equations described by Benford relate the absorption and remission properties of a layer of a material to the properties of any other thickness of the material. R, the fraction of light remitted from an infinitely thick sample, may be calculated from Benford's equations by increasing the sample thickness until the total remission converges to its upper limit. The fractions of light absorbed (a₀) and remitted (r₀) by a very thin layer may be similarly calculated. The relationship A(r,t) = [(1 - r)² - t²] / r = (2 - a - 2r) a / r = 2 a₀ / r₀ = (1 - R)² / R describes an Absorption/Remission Function for the material as a function of a, r and t, the fractions of light absorbed, remitted and transmitted by a specified layer. This is a more general expression than the widely used Kubelka-Munk equation, but gives results equivalent to it for the case of infinitesimal particles.