Diffuse-reflectance spectroscopy linearization function

For diffuse reflectance spectroscopy the Kubelka-Munk function, f Roo), is most appropriate [128, 129]. The K-M theory indicates that linear relationships of band intensity vs. concentration should result when intensities are plotted as the K-M function f Roo) = k/S, where k is the absorption coefficient and S is the scattering coefficient (cfr. Chp. 1.2.1.3). The use of the K-M equation for quantitative analysis by diffuse reflectance spectroscopy is common for measurements in the visible, mid-IR and far-IR regions of the spectrum. Measurement of scattered light (ELSD) allows quantitative analysis. 

It is usually considered more difficult to evaluate and quantify diffuse reflectance data than transmission data, because the reflectance is determined by two sample properties, namely, the scattering and the absorption coefficient, whereas the transmission is assumed to be determined only by the absorption coefficient. The absorbance is a linear function of the absorption coefficient, but its counterpart in reflection spectroscopy, the Kubelka-Munk function (sometimes also called remission2 function), depends on both the scattering and the absorption coefficient. Often, researchers list a number of prerequisites for application of the Kubelka-Munk function, but, in contrast, transmittance is routinely converted without comment into absorbance. 

While this is not an exact relationship, as many of the above assumptions are not accurately adhered to in practice, it is very useful for two reasons. First, other tfeatments of diffuse reflection do not allow Roc, to be converted into a simple parameter that varies approximately linearly with the concentration of a component of a powdered sample (similarly to absorbance [log(l/r)] for transmission spectroscopy). If 5 can be assumed to be constant among a group of samples and the baseline of the spectrum is at a constant value (vide infra), this relationship can be used to quantitatively determine the concentration, c, of an absorbing analyte by preparing a Beer s law plot of the K-M function vs. concentration. 

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