The oldest method of resolving the problem of stray or scatter light effects is derivative spectroscopy. In this situation, it is not the original spectra (log 1/R) but what are referred to as the derivatives which are drawn on for the further calculation.|
By the formation of derivatives it is possible, for example, for a parallel displacement of the spectra (displacement of the base line) to be corrected. Maximum values in the original spectrum become zero points in the first derivative. If in Figure 1 the XY graphic for the wavelength 1930 nm, the maximum of the water bands, has been represented, then in the first derivative of the spectra (Figure 2) zero positions are provided for all samples at this wavelength. In the first derivative of the spectra, the interesting wavelengths are therefore always on the flank of the bands of the original spectrum, in Figure 2 at 1860 nm instead of 1930 nm. In the second derivative, the bands again lie on the wavelengths of the original spectrum.
With the first derivative, it is therefore possible for parallel displacements of the spectra to be corrected. If the second derivative is formed, then it is additionally possible for differences in the overall rise of the spectra (the trend) to be corrected. Higher derivatives than the second derivative are rarely used.
|Figure 1: Transformed spectra (first derivative)|
of Pathlength of the light trough the sample
Derivative spectroscopy is very widespread in the field of spectroscopy in the near-infra-red. Because of the formation of derivatives, even fine absorption bands can also be emphasised in the spectrum. This is therefore important in near-infra-red spectroscopy, because the bands in the near-IR spectral range are on the one hand, as a rule, overtones or combination modes of fundamental modes in the mid-infra-red, and such overtones always have broader bands. On the other hand, water is the most important absorber in the near-IR spectral range, and exhibits broad absorption bands at 1450 and 1930 nm. Water is, in turn, present in a large number of investigation matrices. In order to draw fine absorption bands out against a background of broad and mutually-overlapping bands, derivatives may be used.
|Figure 2: XY graphic of the transformed |
absorption values at 1860-nm and the moisture contents
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