Spectral Derivatives

FIGURE3.17 Top Part of the spectrum of benzonitiile plotted in absorbance. Bottom The first derivative of this spectrum (Savitsky-Golay algorithm, 2nd order, 5 points). The intersecting dotted lines indicate that the top of the ahsorhance band has a slope of zero. 

FIGURE 3.18 Top A benzonitrile peak plotted in percent transmittance. Bottom Its first derivative (Savitsky-Golay algorithm, 2 order, 5 points). 

FIGURE 3.20 Bottom Part of the absorbance spectrum of a mixture of polystyrene and a polycarbonate. Top The second derivative of this spectrum (Savitsky-Golay algorithm, 2 order, 5 points). Note how the negative lobes of the 2nd derivative point at the peaks in the spectrum. 

The areas of the features in derivative spectra are proportional to the area of the peaks in the absorbance spectrum from which they were calculated. Hence, the size of features in derivative spectra calculated from absorbance peaks is proportional to concentration. Thus derivatives can be used to obtain quantitative calibrations. First derivatives are used on data to remove offset from standard spectra, and second derivatives are used to remove offset and slope [10], 

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Radiometric quantities are important to describe and measure UV and VUV radiation. They are usually subdivided into energetic, spectral and photonic terms. Energetic terms (Tab. 3-9) are based on the energy of the radiation and they refer to all relevant wavelengths. Eor each of these terms a spectral derivative can be defined (Bolton, 1999) which is correlated with a specific wavelength X. Eor example, the extraterrestrial solar spectrum incident on the upper atmosphere is represented by the mean spectral irradiance Eq in W m nm over a defined wavelength interval AX in nm (CIE, 1989). Further, each of the spectral units can easily be transferred to photon-based units, which themselves are related to radio-metric units (cf Braun et al., 1991). 

Auger electrons can be emitted if the inner-shell vacancy is created by the absorption of an X-ray quantum or by electron bombardment. However, in the latter case an electron continuum due to the scattered electrons tends to mask the frequently weak Auger lines in the case of solid samples. Spectral derivation techniques can then be used to enhance the signals. For gases the background is weak and causes no problems. 

The functions used to change the decay functions in FSD increase the noise level faster than do the polynomial functions used for spectral derivatives because exponential functions tend to increase more rapidly at high spatial frequencies than polynomials. As a consequence, the effect on the data at high spatial frequencies in the Fourier domain signal (the region where the SNR is the lowest) is most severe. The general rule is that as the FWHH is narrowed by a factor of 2, the SNR of the spectmm decreases by an order of magnitude. In practice, the... 

One shortcoming of FSD is that the altered FWHH affects all the component bands of an overlapped feature differently if their individual FWHHs are different. The value (y — y ) from Eq. 10.12 will differ for each component peak if their respective widths are not identical. Thus, it is possible that narrow component bands will be over-deconvolved so that sidelobes are seen in the spectrum, whereas the widths of other bands will scarcely be altered. For this reason many workers prefer spectral derivatives, as the FWHH is adjusted individually that is, there is no dependence on width with spectral derivatives. Although differentiation has this advantage over FSD, it should be noted that derivatives may be used to correct slowly varying baselines while FSD retains the baseline. Consequently, very broad bands may be eliminated when the derivative of the spectrum is calculated and will be narrowed minimally only with FSD. 

Despite some of the problems associated with FSD and spectral derivatives, both techniques are powerful and usefiil tools if applied judiciously. With care, highly overlapped bands can be resolved into a reasonable number of component bands. The assignment of each new band should be validated through careful spectral interpretation. Even so, it may be an easy matter for a spectroscopist to carry out FSD under conditions that happen to yield the number of bands that he or she is looking for In other words, as in the case for curve fitting, operator bias can have a significant effect on the results of FSD. 

Neural networks have been applied to IR spectrum interpreting systems in many variations and applications. Anand [108] introduced a neural network approach to analyze the presence of amino acids in protein molecules with a reliability of nearly 90%. Robb and Munk [109] used a linear neural network model for interpreting IR spectra for routine analysis purposes, with a similar performance. Ehrentreich et al. [110] used a counterpropagation network based on a strategy of Novic and Zupan [111] to model the correlation of structures and IR spectra. Penchev and co-workers [112] compared three types of spectral features derived from IR peak tables for their ability to be used in automatic classification of IR spectra. 

Monobasic acids are determined by gas chromatographic analysis of the free acids dibasic acids usually are derivatized by one of several methods prior to chromatographing (176,177). Methyl esters are prepared by treatment of the sample with BF.—methanol, H2SO4—methanol, or tetramethylammonium hydroxide. Gas chromatographic analysis of silylation products also has been used extensively. Liquid chromatographic analysis of free acids or of derivatives also has been used (178). More sophisticated hplc methods have been developed recentiy to meet the needs for trace analyses ia the environment, ia biological fluids, and other sources (179,180). Mass spectral identification of both dibasic and monobasic acids usually is done on gas chromatographicaHy resolved derivatives. 

Mass spectral fragmentation patterns of alkyl and phenyl hydantoins have been investigated by means of labeling techniques (28—30), and similar studies have also been carried out for thiohydantoins (31,32). In all cases, breakdown of the hydantoin ring occurs by a-ftssion at C-4 with concomitant loss of carbon monoxide and an isocyanate molecule. In the case of aryl derivatives, the ease of formation of Ar—NCO is related to the electronic properties of the aryl ring substituents (33). Mass spectrometry has been used for identification of the phenylthiohydantoin derivatives formed from amino acids during peptide sequence determination by the Edman method (34). 

Mass Spectroscopy. A coUection of 125,000 spectra is maintained at Cornell University and is avaUable from John WUey Sons, Inc. (New York) on CD-ROM or magnetic tape. The spectra can be evaluated using a quaHty index algorithm (63,76). Software for use with the magnetic tape version to match unknowns is distributed by Cornell (77). The coUection contains aU avaUable spectral information, including isotopicaUy labeled derivatives, partial spectra, and multiple spectra of a single compound. 

If the perturbations thus caused are relatively slight, the accepted perturbation theory can be used to interpret observed spectral changes (3,10,39). The spectral effect is calculated as the difference of the long-wavelength band positions for the perturbed and the initial dyes. In a general form, the band maximum shift, AX, can be derived from equation 4 analogous to the weU-known Hammett equation. Here p is a characteristic of an unperturbed molecule, eg, the electron density or bond order change on excitation or the difference between the frontier level and the level of the substitution. The other parameter. O, is an estimate of the perturbation. 

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