Fourier transform Fellgett advantage

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... 

The resolution of the light into its various frequency components is accomplished by (i) gratings or prisms in dispersive instruments, (ii) interferometers (such as the Michelson124 interferometer see below) in Fourier transform spectrometers (Fellgett s125 advantage), or (iii) for X rays, bent LiF crystal or graphite monochromators. 

There are three well known advantages one gains by doing Fourier transform spectroscopy that are usually discussed in terms of their relationship to grating spectroscopy. They are called the Fellgett advantage, the Jacquinot advantage, and Connes accuracy. 

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... 

The Fellgett or multiplex advantage deals with the fact that a Fourier transform spectrometer records data from the entire spectral region throughout the experiment. This is quite different to the case with a dispersive spectrometer, as the grating or prism instrument only measures a narrow bandwidth at any time. The measurement bandwidth of the dispersive spectrometer is regulated by the instrument s exit slit. This difference has important effects on the acquisition of data. 

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 mentioned in the introduction to this chapter, visible/UV Fourier transform instruments are still found mainly as unique, one-of-a-kind instruments in a few spectroscopy laboratories. The research topics being pursued with these Fourier transform instruments include atomic spectrochemical measurements, atomic and molecular emission spectroscopy from hollow cathode discharges, and molecular absorption spectroscopy for accurate frequency standards and molecular constants. In each of these research efforts, the Fourier transform method has proven useful. In part, the success of this method is derived from the fundamental advantage originally stated by Jacquinot, and to some extend from the advantage stated by Fellgett. 

The advantages of Fourier transform spectrometry over the use of a scanning monochromator (often referred to as dispersive spectrometry) is fully valid only when the detector noise is independent of the power of the radiation incident on the detector. When the detector is photon shot-noise limited [as it generally is for a photomultiplier tube (PMT), and often is for other sensitive detectors used in the near-infrared, visible, and ultraviolet spectral regions], the noise level is proportional to the square root of the incident power. For a boxcar spectrum, this means that shot noise is proportional to the square root of the number of resolution elements in the spectrum, This disadvantage therefore precisely offsets Fellgett s advantage when continuous broadband sources are employed. It should also be... 

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