Pure component spectra

If we examine the first column of the matrix in equation [23] we see that each Kw, is the absorbance at each wavelength, w, due to one concentration unit of component 1. Thus, the first column of the matrix is identical to the pure component spectrum of component 1. Similarly, the second column is identical to the pure component spectrum of component 2, and so on. 

This will cause CLS to calculate an additional pure component spectrum for the G s. It will also give us an additional row of regression coefficients in our calibration matrix, Kc , which we can, likewise, discard. 

Number 3 - There are many well-established techniques for choosing which wavelength regions to use when modeling with PLS/PCR. First, I advise people to make sure that the pure component spectrum actually has a band in the location being modeled. If this is not possible, at least only include regions that look like... 

The useful aspect of this follows we can determine the regions in the series of spectra in which there is only one component. The spectral vectors are all parallel and the average over all spectra in the region is a good estimate for the pure component spectrum. The main difficulty with this approach is to decide when exactly the deviation from a straight line starts and thus, which selection of spectra we need to average. 

The progression from the target ( 3 in Figure 4.8), to the realization of Rh4(CO)i2 in Figure 4.9 can be followed. Snapshots of the SA optimization for recovery of the pure component spectrum of Rh4(CO)i2 are shown in Figure 4.10. Further refinements are made to the estimate as the optimization proceeds. For j=50 and k=5000, a pure component spectral recovery can require a few hours cpu time on a good workstation. SA typically encounters and evaluates 10 -10 local minima before the global minimum is achieved. 

To address the issue of inter-correlations between pure chemical species, it is possible to impose additional application-specific constraints to improve the interpretability of SMCR results. For example, one might know the location of a pure component peak in the spectrum, or can obtain a sufficiently relevant pure component spectrum in the lab. Such additional constraints can be applied mathematically during the iterative SMCR process to improve the interpretability of the results.4 Of course, if such extra constraints... 

Selectivity describes the degree of spectral interferences, and several measures have been proposed. Most definitions refer to situations where pure-component spectra of the analyte and interferences are accessible [19-21, 28]. In these situations, the selectivity is defined as the sine of the angle between the pure-component spectrum for the analyte and the space spanned by the pure-component spectra for all the interfering species. Recently, equations have been presented to calculate selectivity for an analyte in the absence of spectral knowledge of the analyte or interferences [25-27], These approaches depend on computing the NAS, defined as the signal due only to the analyte. Methods have been presented to compute selectivity values for N-way data sets (see Section 5.6.4 for the definition of N-way) [29, 30],... 

Using the formulations of the calibration set listed in Table 8.19 and the pure-component spectra measured earlier, we can generate a set of simulated calibration spectra without performing any experimental work and investigate some important properties of the calibration set. The first step is to estimate the matrix of extinction coefficients, E, using the pure-component spectra. Assuming the path length, 1=1, the ith pure-component spectrum can be represented by... 

While there many examples of multivariate analysis involving NMR time domain data,24-36 Yvi II be assumed in this review that the data matrix of interest is (or is derived from) the frequency domain data /y(otherwise specified. In most situations the NMR spectrum of the /th sample (different mixture, time, etc.) can be described as the linear combination of comp pure component spectrum, each with a concentration... 

In a spectral region where [PJ [P2], [R] is approximately equal to i. Conversely, if [P2] 2> [Pi], then [R] is approximately equal to S2. An implicit assumption is that each pure-component spectrum contains a characteristic peak that is not overlapped by peaks appearing in the spectra of other pure components [122]. With the introduction of relative concentrations in the preceding equations, this ratio approach allows quantitative analyses without external calibration [123]. 

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