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.

Milk is an example of a strongly scattering material, as its white colour indicates. For non-scattering samples, the Beer-Lambert law can be used to compute an absorption coefficient for a material and this absorption coefficient can be used to calculate or predict the absorption for a sample of any thickness of that material. However, absorption coefficients calculated for scattering samples are less directly applicable to other samples of the same material, because the processes of absorption and scattering affect each other. To overcome this, "absorbance" for a scattering sample should not be defined as { log(1/T) }, but as { − log(R + T) } or { − log(1-A) }. Interactions between absorption and scattering can be understood through consideration of a layer of single particles, here termed a "representative layer". A reasonable approximation for the "Beer's law absorbance" of a material is the { − log(1-A) } of the representative layer. Using the properties of the representative layer, the absorption and scattering properties of a sample can be understood based on the refractive index difference between the particles and the matrix, the size of the particles, the wavelength of the incident light, the concentration of the particles and the thickness of the sample. This review describes how the principles of representative layer theory can explain some of the light scattering properties of milk and examines several of the techniques used to separate the effects of absorption and scatter.

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 (a 0) and remitted (r 0) by a very thin layer may be similarly calculated. The relationship A(r,t) = [(1-r) 2-t 2 ] / r = (2-a-2r) a / r = 2 a 0 / r 0 = (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.

Since the commercial development of modern near-infrared spectroscopy in the 1970s, analysts have almost invariably used units of weight percent as the measure of analyte concentration, due largely to the historical precedent from other analytical methods, including other spectroscopic techniques. The application of the CLS algorithm to a set of binary and ternary liquid mixtures reveals that the spectroscopic measurement sees the sample differently; that the measured absorbance spectrum is in fact sensitive to the volume fraction of the various components of the mixture. Because there is not a one-to-one relationship between volume fraction and other measures of analyte concentration, nor is the relationship linear, this has important implications for the application of both the CLS algorithm and the various other, more conventional, calibration algorithms that are commonly used.