78
Y. Ozaki et al.
Since, in general, spectrum data take discrete values, and the calculation of derivatives with various orders is performed by algebraic differences between data taken at
closely spaced wavelengths. Transformation to first- and second-derivatives is then
dA i = A i+k − A i−k
d
2 A i = d(A i+k − A i−k )
= A i+2k − 2 A i + A i−2k
(4.8)
Multiplicative scatter correction (MSC)
MSC is an effective method for correcting vertical variations of the baseline (additive
baseline variation) and inclination of the baseline (multiplicative baseline variation)
[17]. The idea of MSC originates from the fact that light scattering has the wavelength
dependence different from that of chemically based light absorbance. Thus, we can
use data from a number of wavelengths to distinguish between light absorption and
light scattering.
MSC corrects spectra according to a simple linear univariate fit to a standard spectrum. α and β are estimated by least squares regression using the standard spectrum.
As the standard spectrum, a spectrum of a particular sample or an average spectrum
is used. Figure 4.10c shows the NIR spectra as shown in Fig. 4.10a after the MSC
treatment [21]. The spectra demonstrate the potential of MSC in correcting offset and
amplification in the NIR spectra. Generally, MSC improves essentially the linearity
in NIR spectra. While it is generally an very useful technique, care must be exercised
since the use of MSC may generate unwanted artifacts.
Standard normal variate (SNV)
Standard normal variate (SNV) is also a powerful method for correcting vertical
baseline drift of a set of spectra [22]. For each spectrum A(λ), SNV is calculated as
A SNV (λ) =
A(λ) − ˙
A
/σ , where ˙
A and σ are mean and standard deviation of the
intensities in the spectrum, respectively. Therefore, mean and standard deviation of
the intensities for each spectrum after SNV are standardized as 0 and 1, respectively.
4.3.3 Resolution Enhancement Methods
Resolution enhancement methods are very important to unravel overlapping bands
and elucidating the existence of obscured bands [2, 3]. In NIR spectroscopy derivative methods, difference spectra, mean centering, and Fourier self-deconvolution
are employed as resolution enhancement methods. Note that PCA loadings plots are
often effective for resolution enhancement [21]. 2D correlation spectroscopy can also
make resolution enhancement, but since it is not a pretreatment method, it will be
Y. Ozaki et al.
Since, in general, spectrum data take discrete values, and the calculation of derivatives with various orders is performed by algebraic differences between data taken at
closely spaced wavelengths. Transformation to first- and second-derivatives is then
dA i = A i+k − A i−k
d
2 A i = d(A i+k − A i−k )
= A i+2k − 2 A i + A i−2k
(4.8)
Multiplicative scatter correction (MSC)
MSC is an effective method for correcting vertical variations of the baseline (additive
baseline variation) and inclination of the baseline (multiplicative baseline variation)
[17]. The idea of MSC originates from the fact that light scattering has the wavelength
dependence different from that of chemically based light absorbance. Thus, we can
use data from a number of wavelengths to distinguish between light absorption and
light scattering.
MSC corrects spectra according to a simple linear univariate fit to a standard spectrum. α and β are estimated by least squares regression using the standard spectrum.
As the standard spectrum, a spectrum of a particular sample or an average spectrum
is used. Figure 4.10c shows the NIR spectra as shown in Fig. 4.10a after the MSC
treatment [21]. The spectra demonstrate the potential of MSC in correcting offset and
amplification in the NIR spectra. Generally, MSC improves essentially the linearity
in NIR spectra. While it is generally an very useful technique, care must be exercised
since the use of MSC may generate unwanted artifacts.
Standard normal variate (SNV)
Standard normal variate (SNV) is also a powerful method for correcting vertical
baseline drift of a set of spectra [22]. For each spectrum A(λ), SNV is calculated as
A SNV (λ) =
A(λ) − ˙
A
/σ , where ˙
A and σ are mean and standard deviation of the
intensities in the spectrum, respectively. Therefore, mean and standard deviation of
the intensities for each spectrum after SNV are standardized as 0 and 1, respectively.
4.3.3 Resolution Enhancement Methods
Resolution enhancement methods are very important to unravel overlapping bands
and elucidating the existence of obscured bands [2, 3]. In NIR spectroscopy derivative methods, difference spectra, mean centering, and Fourier self-deconvolution
are employed as resolution enhancement methods. Note that PCA loadings plots are
often effective for resolution enhancement [21]. 2D correlation spectroscopy can also
make resolution enhancement, but since it is not a pretreatment method, it will be