Review: Formulae for Absorption Spectroscopy Related to Idealised Cases

Abstract

Over the years, a wide variety of formulae have been developed to describe absorption and scatter of light from particles with idealised characteristics. Many of these have been found to be very useful in spectroscopy. The solutions that are mathematically exact are generally limited to light that is travelling in one direction (as in the Bouguer–Lambert law) or two directions (as in the Kubelka–Munk equation). Many of the equations are well known in a form quite different from that presented by those who developed them. The most successful of these mathematical treatments have tended to be presented in terms of absorption by, and scatter from, layers of material. In order to be applicable to real samples, the layer should be representative of the sample. These formulae allow one to predict or model the remission, transmission and/or absorption for a sample, given scattering and absorption coefficients that accurately represent the sample. The inverse problem—using spectral data to calculate absorption coefficients that accurately represent the material of which the sample is composed—is conceptually more complex for scattering samples, owing to the fact that the processes of absorption and scattering influence each other. To the extent that real samples can be represented as a series of plane parallel layers well separated by layers of air, a solution to this “inverse problem” has been realised for scattering samples, analogous to the use of Beer's law for clear solutions. This review summarises the relevant theory in a way that assumptions and limitations can be clearly understood, and misconceptions can be avoided.