Representative Layer Theory for Diffuse Reflectance

Abstract

The fractions of light absorbed by and remitted from samples consisting of different numbers of plane parallel layers can be related with the use of statistical equations. The fractions of incident light absorbed (A), remitted (R), and transmitted (T) by a sample of any thickness can be related by an absorption/remission function, A(R,T):

A(R,T) = [(1 - R)² - T²]/R = (2 - A - 2R)A/R = 2A₀/R₀.

Being independent of sample thickness, this function is a material property in the same sense as is the linear absorption coefficient in transmission spectroscopy. The absorption and remission coefficients for the samples are obtained by extrapolating the measured absorption and remission fractions for real layers to the fraction absorbed (A₀) and remitted (R₀) by a hypothetical layer of infinitesimal thickness. A sample of particulate solids can be modeled as a series of layers, each of which is representative of the sample as a whole. In order for the layer to be representative of the properties of the individual particles of which it is comprised, it should nowhere be more than a single particle thick, and should have the same void fraction as the sample; further, the volume fraction and cross-sectional surface area fraction of each particle type in the layer should be identical to its volume fraction and surface area fraction in the sample as a whole. At lower absorption levels, the contribution of a particle of a particular type to the absorption of a sample is approximately weighted in proportion to its volume fraction, while its contribution to remission is approximately weighted in proportion to the fraction of cross-sectional surface area that the particle type makes up in the representative layer.