Baseline corrections multiplicative scatter correction

NIR of the PE powder was carried out before compounding with Irganox 1010 and Irgafos 168. It was observed that the identification and selection of specific bands or unique spectral features in the spectra is difficult. The variation in baselines is due to differences in scattering properties of the analytes. Multiplicative scattering correction (MSC) or derivation can eliminate these variations [117, 118]. 

Compared to spectra obtained in the mid-infrared region, NIR spectra contain fewer, less resolved, peaks. Due to scattering and other effects, a set of NIR spectra on similar samples often exhibits constant baseline offsets from one to the next. To eliminate these baseline offset differences, reduce (but not eliminate) scattering effects, and increase the resolution of neighboring peaks, first- or second-deriva-tization is often applied to NIR spectra prior to their use in calculations. Other preprocessing techniques, such as standard normal variate (SNV) or multiplicative scatter correction (MSC), may be applied to more effectively reduce scattering effects that arise from particle size differences among samples.36... 

The MSC has been shown to work well in several empirical studies [9, 10], which showed an improvement in the performance of multivariate calibrations and a reduction in the number of factors in PCA. For example, NIR reflectance spectra of 20 powder samples of microcrystalline cellulose are shown in Figure 4.8a. Due to differences in particles size from sample to sample, there are significantly different baseline offsets. The same spectra are shown in Figure 4.8b after multiplicative scatter correction. The different baseline offsets observed in Figure 4.8a are so large that they mask important differences in the water content of these samples. These differences are revealed in the water absorption band at 1940 nm after the baseline offsets have been removed by MSC. 

Tablet spectra must usually be corrected for baseline shifting prior to analysis. Many techniques have been attempted, but second-derivative and multiplicative scatter correction calculations are most common. This baseline correction is critical even if an average tablet spectrum is used.

Methods used for preliminary examination of the data included smoothing the spectral data, multiplicative scatter correction, standard normal variance correction, baseline correction, and first- or second-derivative transformation of log (1/T) data. The smoothing and derivative transformations were based on the Savitzki-Golay second-order polynomial filter (22). 

MSC, multiple scatter correction SNV, standard normal variate BC, baseline correction ID, first-derivative transformation 2D, second-derivative transformation SEC, standard error of calibration R, coefficient of multiple correlation SEP, standard error of prediction r, validation correlation coefficient VCC, %, variation coefficient for calibration set-(SEC/Mean value) x 100 VCV, %, variation coefficient fa- validation set-(SEP/Mean value) x 100. 

More complex means of attacking the particle size question have also been attempted. These include experiments using mathematical modeling for simultaneous removal of particle size and water [29], the use of Fourier deconvolution [30], multiplicative scatter corrections [31 ], and principal components elimination [32]. Barnes et al. [33] introduced a procedure termed detrending that uses standard normal variate (SNV) with polynomial baseline correction [34]. These corrections for particle size may not always improve accuracy of NIRS analysis for two reasons. First, none of these procedures does a perfect job of removing particle size effects independent of absorption information. Second, particle size may be useful information in the calibration even though linear mathematics is used to derive the analytical equation. 

Numerous techniques have been developed to improve the robusmess and transportability of spectral calibration models [58-68]. Among them, the computation of first and second derivatives of spectral data with respect to the wavelength and the application of multiplicative scatter corrections (MSCs) certainly are the most popular ones. Derivatives of spectral data allow for efficient removal of baseline shifts and for magnification of small changes of the spectral signal. However, derivation of spectral data could increase the effects of noisy measurements. MSC was developed to... 

Thus, variations of the classical MSC method, such as extended multiplicative scatter correction (EMSC), have appeared to handle nonlinear baselines that may be better expressed by polynomial functions [16]. Recently, modifications of the EMSC algorithm, especially adapted to handle the Mie scattering effects caused by biological images, have also been implemented [17]. 

The simplest method which corresponds to these terms is multiplicative scatter correction (MSC). In this case, it is assumed that chemical variation is small compared to physical variation (i.e. variation introducing a constant (additive)/proportional (multiplicative) baseline effect) and thus the true signal may be replaced by a constant reference signal, usually the mean (or median) spectmm, m (it may also be a specific spectrum of the data set). The previous equation becomes... 

Artifact removal and/or linearization. A common form of artifact removal is baseline correction of a spectrum or chromatogram. Common linearizations are the conversion of spectral transmittance into spectral absorbance and the multiplicative scatter correction for diffuse reflectance spectra. We must be very careful when attempting to remove artifacts. If we do not remove them correctly, we can actually introduce other artifacts that are worse than the ones we are trying to remove. But, for every artifact that we can correctly remove from the data, we make available additional degrees-of-freedom that the model can use to fit the relationship between the concentrations and the absorbances. This translates into greater precision and robustness of the calibration. Thus, if we can do it properly, it is always better to remove an artifact than to rely on the calibration to fit it. Similar reasoning applies to data linearization. 

Plugge and van der Vlies have discussed the conformity index (Cl) for NIR analysis of ampicillin trihydrate [12,13]. The Cl is a metric used to determine the degree of conformity of a sample or batch with standards of known and acceptable quality. To use the Cl, reference spectra are first collected and baseline-corrected using a second-derivative or multiplicative scatter correction (MSC) spectrum. At every wavelength across the spectrum, the average absorbance and standard deviation are calculated for the baseline-corrected reference spectra, resulting in an average spectrum and a standard deviation spectrum. 

To calculate the corrected spectrum, 13 parameters need to be estimated, 2 for the constant and sloping baselines, 1 for the multiplicative factor and 10 for the loadings which describe the scattering curve. These parameters are estimated using a least squares fitting algorithm as before. 

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