Normalisation of standardisation of signal amplitude or intensity in Raman spectroscopy

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Spectroscopic techniques depend on measuring the intensity of a beam of radiation as it passes through or interacts with a sample. Reproducibility is maximized by splitting the radiation into an analyzing and a reference beam and comparing their intensities after the analyzing beam has interacted with the sample. For this to be sufficiently reliable an exact reproduction of sampling conditions, including path length and scattering properties 1 is required between the analyzing and reference beams. In Raman spectroscopy and other point-of-focus spectroscopic methods as well as increasingly complex ‘real world’ spectroscopic applications today, it is often unrealistic to control all factors affecting absolute signal level, particularly if one does not wish to perturb the system under investigation.

Where it is not realistic to control the factors affecting absolute signal intensity it is common practice to standardize the intensity of the spectra or individual bands by dividing the intensity at each point by that of a reference band. In datasets with one source of variation, e.g. solute concentration, it is usually straightforward to choose a band or region for standardization (such as solvent bands). In the absence of an solvent a the target peak for normalization can be introduced by addition of a carefully selected independent internal standard molecule.  This introduces a foreign substance into the sample, which may affect the behavior of the system under study and cancel out a primary advantage of spectroscopic methods; non-invasive sampling. There are also difficulties in using internal standards in spatially resolved mapping experiments, due to uneven partitioning of the internal standard within domains of the sample.

schemtic of the chemcical structure of triglycerides

Controlled Datasets

Spectroscopists often use a band or region within the signal of interest to standardize the intensity of the signal (a spectral internal standard). On occasion the dataset lends itself to an obvious choice for internal standard depending upon the eventual application. A useful case study to illustrate this principal is the Raman spectroscopic investigation of fatty acid composition of edible fats (see Figure 1). The molecular structure of fatty ester lipids involves an the ester group 3,4 that occurs in fixed numbers per fatty acid chain, making spectral bands related to this group an ideal candidate for studying molar quantities, as illustrated in Figure 2 a. In contrast to this molar constancy, the fatty acid chain is comprised of a variable number of CHx groups, which ultimately determines the mass of the fatty acid chain. Calculating the ratio of a band to a CHx mode allows correlation of that band with molal, or mass, quantities as illustrated in Figure 2d. Changing the band used for normalization has a dramatic influence on the information extracted from the spectrum, i.e. molar vs. molal quantification.

Raman intensity ratio against uynsaturation parameters illustrating effect of normalisation on the linearity of calibration

Employing the wrong normalization band induces systematic error into the analysis. Figure 2b and c show how employing the wrong normalization peak induces curvature in estimating unsaturation in fatty acid based lipids. However, the spectroscopists needs to be aware of much more subtle effects that can introduce systematic errors but which are not so readily evident. The two main carbon-hydrogen deformation modes, the scissor and the twist are not interchangeable, despite their apparent shared source. Most obvious is the difference in response of these two peaks to physical changes in the sample. The scissor band is readily affected by intermolecular forces, i.e. the crystalline state of the sample. The twist band is affected by intramolecular forces, i.e. the folding of the fatty acid chain and while these two changes do influence each other they do occur at different rates during phase transition. More importantly for normalization purposes is the chemical difference between the two modes. The twist band is derived purely from methylene modes (and not the methylenes adjacent to the terminals of the chain), whereas the scissor mode (taken as a whole of the coalesced bands in the region 1400-1500 cm-1) is derived from all the CHx groups present. Thus the scissor mode captures a more accurate description of the chain mass than the twist mode, with the result that the twist mode gives a curve against mass unsaturation Figure 2e). The twist mode requires a specifically devised parameter of unsaturated bonds against Raman active CH2 modes to produce a straight line (Figure 2f).

'Real-World' Datasets

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