Fourier-type components

Fig, 4. Sections through the even-ordered spherical harmonic functions, Pq, P2, P4 and P( which are in effect Fourier-type components of orientation distributions such as that shown in Fig. 3. ... 

Principal component analysis has been used in combination with spectroscopy in other types of multicomponent analyses. For example, compatible and incompatible blends of polyphenzlene oxides and polystyrene were distinguished using Fourier-transform-infrared spectra (59). Raman spectra of sulfuric acid/water mixtures were used in conjunction with principal component analysis to identify different ions, compositions, and hydrates (60). The identity and number of species present in binary and tertiary mixtures of polycycHc aromatic hydrocarbons were deterrnined using fluorescence spectra (61). 

A special type of data pre-treatment is the transformation of data into a smaller number of new variables. Principal components analysis is a natural example and we have treated it in Section 36.2.3 as PCR. Another way to summarize a spectrum in a few terms is through Fourier analysis. McClure [29] has shown how a NIR... 

Larger frequency shifts lead to more sensitive structural discriminations. In the IR, the (i-shcct amide I is distinctively lower in frequency than other structural types, particularly for aggregates, a form often seen in unfolding experiments. However, owing to the high signal-to-noise ratio (S/N) of Fourier transform IR (FTIR), one can detect components having smaller frequency separations. This effective resolution... 

Direct NIR or MIR measurements of whole soil can be made using attenuated total reflectance (ATR) and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) samplers. This type of measurement detects only components on the surface and so has severe limitations when information about the bulk soil is needed [4],... 

Platinum and palladium porphyrins in silicon rubber resins are typical oxygen sensors and carriers, respectively. An analysis of the characteristics of these types of polymer films to sense oxygen is given in Ref. 34. For the sake of simplicity the luminescence decay of most phosphorescence sensors may be fitted to a double exponential function. The first component gives the excited state lifetime of the sensor phosphorescence while the second component, with a zero lifetime, yields the excitation backscatter seen by the detector. The excitation backscatter is usually about three orders of magnitude more intense in small optical fibers (100 than the sensor luminescence. The use of interference filters reduce the excitation substantially but does not eliminate it. The sine and cosine Fourier transforms of/(f) yield the following results ... 

FIGURE 10.2 Concept of (a) aperture type and (b) apertureless type near-field microscopes (c) is the Fourier transform function of (a) and (b), which shows propagation and evanescent light components. 

Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFT).6 When IR radiation is directed onto the surface of a solid sample, two types of energy reflectance can occur specular and diffuse. The specular component is the radiation that reflects directly off the sample surface (i.e., not absorbed by the sample). Diffuse reflectance is the radiation that penetrates into the sample and then emerges. Diffuse reflectance accessories are designed to optimize the diffuse reflected energy and suppress the specular component. The optics therefore selectively directs the scattered radiation to the IR detector. 

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