Dispersion Fourier transformation

J. R. Birch and T. J. Parker, Dispersive Fourier Transform Spectroscopy in K. J. Batton, ed., Infrared and Millimeter Waves, Vol 2 Instrumentation, Chapter 3 Academic Press, New York, pp. 137-271, 1979. 

As in all Fourier transform methods in spectroscopy, the FTIR spectrometer benefits greatly from the multiplex, or Fellgett, advantage of detecting a broad band of radiation (a wide wavenumber range) all the time. By comparison, a spectrometer that disperses the radiation with a prism or diffraction grating detects, at any instant, only that narrow band of radiation that the orientation of the prism or grating allows to fall on the detector, as in the type of infrared spectrometer described in Section 3.6. 

In the infrared spectral range in general Fourier transform (FT) interferometers are used. In comparison with dispersive spectrometers FTIR enables higher optical throughput and the multiplex advantage at equivalent high spectral resolution. In... 

We now apply these results to compute 1 v(2>) the Fourier transform of Kuv(x), in terms of its imaginary part Im OL p). Causality asserts that J uv(p) is an analytic function of p0 in Imp0 > 0, and hence that there exists a dispersion relation relating the real and imaginary parts of... 

Figure 3.6 The first set of Fourier transformations across <2 yields signals in V2, with absorption and dispersion compronents corresponding to real and imaginary parts. The second FT across /, yields signals in V, with absorption (i.e., real) and dispersion (i.e., imaginary) components quadrants (a), (b), (c), and (d) represent four different combinations of real and imaginary components and four different line shapes. These line shaptes normally are visible in phase-sensitive 2D plots.

Figure 4.12 shows Fourier-transformed EXAFS data of a highly dispersed (H/M =... 

From Table 2 it is observed that the dispersive NIR ensembles (NIR and NIR R) result in the best cross validated models. The potential advantages of Fourier transform spectroscopy [5] are in practice outnumbered by a more reproducible setup and saimpling procedures. 

It is only since 1980 that in situ spectroscopic techniques have been developed to obtain identification of the adsorbed intermediates and hence of reliable reaction mechanisms. These new infrared spectroscopic in situ techniques, such as electrochemically modulated infrared reflectance spectroscopy (EMIRS), which uses a dispersive spectrometer, Fourier transform infrared reflectance spectroscopy, or a subtractively normalized interfacial Fourier transform infrared reflectance spectroscopy (SNIFTIRS), have provided definitive proof for the presence of strongly adsorbed species (mainly adsorbed carbon monoxide) acting as catalytic poisons. " " Even though this chapter is not devoted to the description of in situ infrared techniques, it is useful to briefly note the advantages and limitations of such spectroscopic methods. 

The IR spectra in Fig.7 indicate the preferential adsorption of NO on the Co sites. It may be conjectured that the Mo sulfide species are physically covered by the Co sulfide species or that Co-Mo mixed sulfide species are formed and the chemical natures of the Co and Mo sulfides are mutually modified. The Mo K-edge EXAFS spectra were measured to examine the formation of mixed sulfide species between Co and Mo sulfides. The Fourier transforms are presented in Fig.8 for MoSx/NaY and CoSx-MoSx/NaY. The structural parameters derived from EXAFS analysis are summarized in Table 1. The structure and dispersion of the Mo sulfides in MoSx/NaY are discussed above. With the Co-Mo binary sulfide catalyst, the Mo-Co bondings are clearly observed at 0.283 nm in addition to the Mo-S and Mo-Mo bondings. The Mo-Co distance is close to that reported by Bouwens et al. [7] for a CoMoS phase supported on activated carbon. Detailed analysis of the EXAFS results for CoSx-MoSx/NaY will be presented elsewhere. It is concluded that the Co-Mo mixed sulfides possessing Co-S-Mo chemical bondings are formed in CoSx-MoSx/NaY. 

In recent years, infrared spectroscopy has been enhanced by the possibility of applying Fourier transform techniques to it. This improved spectroscopic technique, known as Fourier transform infrared spectroscopy (FTIR), is of much greater sensitivity than conventional dispersive IR spectroscopy (Skoog West, 1980). Moreover, use of the Fourier transform technique enables spectra to be recorded extremely rapidly, with scan times of only 0-2 s. Thus it is possible to record spectra of AB cements as they set. By comparison, conventional dispersive IR spectroscopy requires long scan times for each spectrum, and hence is essentially restricted to examining fully-set cements. 

Ifourth(fd, 2 Q) was multiplied with a window function and then converted to a frequency-domain spectrum via Fourier transformation. The window function determined the wavenumber resolution of the transformed spectrum. Figure 6.3c presents the spectrum transformed with a resolution of 6cm as the fwhm. Negative, symmetrically shaped bands are present at 534, 558, 594, 620, and 683 cm in the real part, together with dispersive shaped bands in the imaginary part at the corresponding wavenumbers. The band shapes indicate the phase of the fourth-order field c() to be n. Cosine-like coherence was generated in the five vibrational modes by an impulsive stimulated Raman transition resonant to an electronic excitation. 

Figure 5.3 Schematics of a typical dispersive spectrometer. After Williams [7]. From R. Williams, Spectroscopy and the Fourier Transform, VCH Publishers, New York, NY. Wiley-VCH, 1996. Reproduced by permission of Wiley-VCH...

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