Fourier transform spectrometry

Multiplex (Fellgett) advantage, all frequencies are scanned simultaneously and the signal-to-noise ratio S/n) cx /N where N is the number of scans. Also scans are faster so many scans can improve the S/n). 

Throughput (Jacquinot) advantage, about 150 times greater throughput than a dispersive instmment that has several slits. 

Registration (Connes) advantage with internal wavelength reference (He-Ne laser). 

Although the FFT is done using complex arithmetic recall that cos (x) = 

Thus you can see the analogy to a projection of a specific cosine component from the interferogram, although the details of the Cooley-Tukey algorithm are much more complicated. If we apply the projection idea to many (thousands) cos(nx) waves, we can find a fine-grained bar graph that 

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S.P. Davis, M.C. Abrams and J.W. Brault, Fourier Transform Spectrometry, Academic Press, Orlando, FL (2001). 

Remote Sensing by Fourier Transform Spectrometry. By Reinhard Beer... 

The newer instruments (Figure 2.4c) utilize a radiofrequency pulse in place of the scan. The pulse brings all of the cycloidal frequencies into resonance simultaneously to yield a signal as an interferogram (a time-domain spectrum). This is converted by Fourier Transform to a frequency-domain spectrum, which then yields the conventional m/z spectrum. Pulsed Fourier transform spectrometry applied to nuclear magnetic resonance spectrometry is explained in Chapters 4 and 5. 

From A. R Thorne, "Fourier Transform Spectrometry in the Ultraviolet,"Anal. Chem. 1991,63.57A]... 

Great advances have occurred in the application of IR techniques to the study of transient phenomena, in the quant identification of trace contaminants and in the resolution of the spectra of mixts. The new techniques are known as Fourier Transform spectrometry. The following description will be necessarily brief but it is intended to highlight potential new areas of application in the study of rapid reaction phenomena ... 

In Fourier transform spectrometry, the wavelength components of light are not physically separated. Instead, the light is analyzed in the time frame of reference (the time domain) by passing it through a Michelson interferometer. The Michelson interferometer is so constructed that light is separated into two beams by a beamsplitter. One beam strikes a stationary mirror and is reflected back to the beamsplitter. 

Fuller MP, Griffiths PR. 1978. Diffuse reflectance measurements by infrared fourier transform spectrometry. Anal. Chem. 50 1906-1910. 

For readers interested in greater detail, Fourier transform techniques are treated in the following references (a) Marshall, A.G. Verdun, F.R. Fourier Transforms in NMR, Optical, and Mass Spectrometry Elsevier Amsterdam, 1986 (b) Griffiths, P.R., DeHaseth, J.A. Fourier Transform Infrared Spectrometry Wiley-Interseience New York, 1986 (c) Chamberlain, J. The Principles of Interferometric Spectroscopy Wiley-Interscience Chichester, 1979 (d) Bell, R. J. Introductory Fourier Transform Spectrometry Academic Press New York, 1972. 

Kolboe and Ellefsen (1962) and Michell et al. (1965) provided preliminary results indicating the feasibility of employing infrared spectroscopy to determine the lignin content of finely ground wood and pulp samples embedded in potassium chloride. Further development and refinement of this technique have led to methods for determination of lignin based on multiple internal reflectance infrared spectrometry (Marton and Sparks 1967) and diffuse reflectance Fourier transform spectrometry (Schultz et al. 1985). Lignin contents have also estimated by 13C CP/MAS/NMR spectrometry (Haw et al. 1984, Hemmingson and Newman 1985) (see Chap. 4.5). 

Ferraro JR, Basile LJ (1978) Fourier transform infrared application to national problems In Ferraro JR, Basile U (eds) Fourier transform infrared spectroscopy - applications to chemical systems, Vol 4 Academic Press, New York, 275-302 Ferraro JR, Rein AJ (1985) Application of diffuse reflectance spectroscopy in the far-infrared region In Ferraro JR, Basile LJ (eds) Fourier transform infrared spectroscopy -applications to chemical systems, Vol 4 Academic Press, New York, 244-282 Frank IE, Feikema J, Constantine N, Kowalski BR (1984) Prediction of product quality from spectral data using the partial least squares method J Chem Inf Comput Sci 24 20-24 Fuller MP, Griffiths PR (1980) Infrared microsampling by diffuse reflectance Fourier transform spectrometry Appl Spectrosc 34 533-539... 

Pakdel H, Grandmaison JL, Roy C (1989) Analysis of wood vacuum pyrolysis solid residues by diffuse reflectance infrared Fourier transform spectrometry Can J Chem 67 310-314 Perkins WD (1986) Fourier transform-infrared spectroscopy Part I Instrumentation J Chem Educ 63 A5-A10... 

TeVrucht, M.L.E. Griffiths, P.R. Quantitative investigation of matrices for diffuse reflectance infrared fourier transform spectrometry. Talanta 1991, 38, 839-849. 

Williams, R. Application of fourier transform spectrometry in the ultraviolet, visible, and near-IR. Appl. Spectrosc. Rev. 1989, 25, 63-79. 

Fourier transform spectrometry [67] makes use of a Michelson interferometer (Fig. 29) to produce the interferogram. With the aid of a beam splitter the radiation is split into two parts each of which is directed to a mirror. When shifting the... 

Figure 1.5 (a) Energy profile showing the diffracted radiation outside the area defined by a single aperture (b) Corresponding profile obtained with masks located before and after the sample. Reproduced from Infrared Fourier Transform Spectrometry by P. R. Griffiths and J. A. de Haseth 2007, p. 307. 

The Fourier transform provides a unique relation between a function and its transform, i.e., there is no loss of information when we replace a function by its Fourier transform, or vice versa. This property is, of course, crucial in Fourier transform spectrometry, since it allows us to measure a time-dependent function and obtain from it the spectrum, i.e., its representation in the frequency domain. 

As described in Section 4.4 for pulsed Fourier transform spectrometry of protons, a short, powerful, rf pulse (on the order of a few microseconds) excites all of the 13C nuclei simultaneously. At the same time, the broadband decoupler is turned on in order to remove the 13C— H coupling. Since the pulse frequencies are slightly off resonance for all of the nuclei, each nucleus shows a free induction decay (FID), which is an exponentially decaying sine wave with a frequency equal to the difference between the applied frequency and the resonance frequency for that nucleus. Figure 5.2a shows the result for a single-carbon compound. 

R. Beer, Remote Sensing by Fourier Transform Spectrometry, John Wiley Sons, Inc., New York, 1992. 

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