4 Spectral Analysis in the NIR Spectroscopy
75
be obtained by substituting w k = −3/35, 12/35, 17/35, 12/35, −3/35 (k = −2, −1,
0, 1, 2) into Eq. (4.3). It is noted that if one tries to increase the effect of smoothing
by increasing the number of the point of w k , a band shape would be distorted. This
distortion may lead to the decrease in spectral resolution and band intensity.
There are other methods for the noise reduction such as wavelets, eigenvector
reconstruction, and artificial neural networks (ANN) [2, 3, 19, 20].
4.3.2 Baseline Correction Methods
As described above in NIR spectra baselines vary for various reasons [1–3]. An
observed NIR spectrum, A(λ), can be represented as follows;
A(λ) = α A 0 (λ) + β + e(λ)
(4.4)
Here, A 0 (λ), α, β, and e(λ) are a real spectrum, a multiplicative scatter factor
(amplification factor), an additive scatter factor (offset deviation), and noise, respectively. There are several methods to eliminate or reduce the effects of α and β. We
explain three of them.
Derivative methods
Derivative methods are utilized in NIR spectra for both resolution enhancement
and baseline correction [1–3]. (Chap. 7) A derivative spectrum is an expression of
derivative values, d
n A/dλ
n (n = 1, 2, …), of a spectrum A (λ) as a function of λ.
The second derivative, d
2 A/dλ
2 , is most often encountered. The superimposed peaks
in an original spectrum turn out as clearly separated downward peaks in a secondderivative spectrum. Another important property of second-derivative method is the
removal of the additive and multiplicative baseline changes in an original spectrum.
Figure 4.10a displays NIR spectra of 16 kinds of linear low-density polyethylene
(LLDPE) and one kind of high-density polyethylene (HDPE), and Fig. 4.10b shows
the second derivative obtained with the Savitzky–Golay method of the spectra as
shown in Fig. 4.10a [21]. It can be seen from Fig. 4.10b that the second derivative is
powerful in removing additive and multiplicative baseline variations of the spectra,
and at the same time, it enables to detect a number of bands clearly. A drawback
in the derivative methods is that the SN ratio deteriorates every time a spectrum is
differentiated.
Let us explain derivative methods using equations. If the band shape is a Gaussian
shape as below;
A(x) = αexp
−
x − x 0
w
2
,
(4.5)
75
be obtained by substituting w k = −3/35, 12/35, 17/35, 12/35, −3/35 (k = −2, −1,
0, 1, 2) into Eq. (4.3). It is noted that if one tries to increase the effect of smoothing
by increasing the number of the point of w k , a band shape would be distorted. This
distortion may lead to the decrease in spectral resolution and band intensity.
There are other methods for the noise reduction such as wavelets, eigenvector
reconstruction, and artificial neural networks (ANN) [2, 3, 19, 20].
4.3.2 Baseline Correction Methods
As described above in NIR spectra baselines vary for various reasons [1–3]. An
observed NIR spectrum, A(λ), can be represented as follows;
A(λ) = α A 0 (λ) + β + e(λ)
(4.4)
Here, A 0 (λ), α, β, and e(λ) are a real spectrum, a multiplicative scatter factor
(amplification factor), an additive scatter factor (offset deviation), and noise, respectively. There are several methods to eliminate or reduce the effects of α and β. We
explain three of them.
Derivative methods
Derivative methods are utilized in NIR spectra for both resolution enhancement
and baseline correction [1–3]. (Chap. 7) A derivative spectrum is an expression of
derivative values, d
n A/dλ
n (n = 1, 2, …), of a spectrum A (λ) as a function of λ.
The second derivative, d
2 A/dλ
2 , is most often encountered. The superimposed peaks
in an original spectrum turn out as clearly separated downward peaks in a secondderivative spectrum. Another important property of second-derivative method is the
removal of the additive and multiplicative baseline changes in an original spectrum.
Figure 4.10a displays NIR spectra of 16 kinds of linear low-density polyethylene
(LLDPE) and one kind of high-density polyethylene (HDPE), and Fig. 4.10b shows
the second derivative obtained with the Savitzky–Golay method of the spectra as
shown in Fig. 4.10a [21]. It can be seen from Fig. 4.10b that the second derivative is
powerful in removing additive and multiplicative baseline variations of the spectra,
and at the same time, it enables to detect a number of bands clearly. A drawback
in the derivative methods is that the SN ratio deteriorates every time a spectrum is
differentiated.
Let us explain derivative methods using equations. If the band shape is a Gaussian
shape as below;
A(x) = αexp
−
x − x 0
w
2
,
(4.5)