Multiplex advantage, Fourier transform spectroscopy

The other principal advantage which applies to Fourier transform spectroscopy is the multiplex or "Fellgett" advantage 21,64) n yas P. Fellgett who first pointed out that there is an advantage when the data in all elements of a spectrum are obtained simultaneously instead of being measured for each element successively. In Fourier transform spectroscopy, the radiation in the Michelson interferometer is not separated into spectral elements. The interferogram contains... 

Applications of the Fourier transformation to spectroscopy have become widespread and are familiar to most chemists. They are attractive because they allow one to interpret experiments in which several different excitation signals are applied to a chemical system at the same time. The responses to those signals are superimposed on each other, but the Fourier transformation provides a means for resolving them. This capacity for simultaneous measurement is sometimes called the multiplex advantage of transform methods, and it is of great importance to applications in electrochemistry (see also Section A.6). 

For the three types of noise discussed above, the Fellgett advantage must be carefully evaluated. This multiplex advantage is an unquestioned benefit, for example, when detector noise dominates, as is the case in infrared Fourier transform spectroscopy. In visible/UV spectroscopy, the detector noise which is present can also be minimized with the multiplex advantage. Therefore it is not always necessary to cool photomultiplier tubes to reduce the thermionic emission for Fourier transform spectroscopy. 

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. 

The transform from the interferogram to the spectrum is carried out by the dedicated minicomputer on the instrument. The theory of Fourier-transform infrared spectroscopy has been treated, and is readily available in the literature.21,22,166 Consequently, the advantages of F.t.-i.r. dispersive spectroscopy will only be outlined in a qualitative sense (i) The Fellgett or multiplex advantage arises from the fact that the F.t.-i.r. spectrometer examines the entire spectrum in the same period of time as that required... 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

In infrared spectroscopy, the detector noise is usually much higher than the noise from other sources. In this case, multiplex recording provides an additional advantage. An interferogram contains the detector noise only once, independently of the number of spectral channels. Fourier transformation produces a spectrum where the SNR) of each spectral element is related to that of one line, SNR by ... 

In 1986, a Raman instrument based on NIR excitation (1064 nm) and a Michaelson interferometer became available [16]. This development revolutionized Raman spectroscopy. In addition to the advantages of throughput and multiplex inherent to Fourier Transform (FT) techniques, this instrument overcame the obstacle of fluorescence. Fluorescence was eliminated by excitation at a NIR wavelength where electronic transitions in most samples are absent. Availability of such NIR FT-Raman instruments was particularly useful in the studies of lignin. 

At last, it should be mentioned that, as always applies to Fourier methods , the major advantage of FTNMR is the multiplex advantage (see also (Chapter 1). Ernst and Anderson have shown that the gain in the signal-to-noise ratio between FTNMR and conventional NMR is proportional to the square root of the number of spectral elementsS . This result is the same as that obtained for infrared Fourier spectroscopy. In this context, it should be noted that a complete analogon to infrared Fourier spectroscopy is the nuclear magnetic Fourier-transfoim resonance with an incoherent rf-field (stochastic resonance) . Of course, Fourier methods depend on electronic computers to perform the Fourier transform of the measured data and were widely used when sufficiently cheap computers became available. The use of the compute- and of the mathematical treatment of the experimental... 

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