Interferometry, Fourier transform

The first Raman and infrared studies on orthorhombic sulfur date back to the 1930s. The older literature has been reviewed before [78, 92-94]. Only after the normal coordinate treatment of the Sg molecule by Scott et al. [78] was it possible to improve the earlier assignments, especially of the lattice vibrations and crystal components of the intramolecular vibrations. In addition, two technical achievements stimulated the efforts in vibrational spectroscopy since late 1960s the invention of the laser as an intense monochromatic light source for Raman spectroscopy and the development of Fourier transform interferometry in infrared spectroscopy. Both techniques allowed to record vibrational spectra of higher resolution and to detect bands of lower intensity. 

Modern infrared spectroscopy is performed using Fourier transform interferometry [22]. Hartstein and co-workers [23] were the first to show that... 

K. Krishnan, Advances in capillary gas chromatography-Fourier transform interferometry, Fourier Transform Infrared Spectrosc., 4 97-145 (1985). 

Painter P, Starsinic M, Coleman M (1985) Determination of functional groups in coal by Fourier transform interferometry. In Ferraro JR, Basile LJ (eds) Fourier transform infrared. spectroscopy - applications to chemical systems, Vol. 4. Academic Press, New York, 169-241... 

Painter, P. Starsinic, M. Coleman, M. Determination of functional groups in coal by fourier transform interferometry. In Fourier Transform Infrared Spectroscopy Application to Chemical Systems (J.R. Ferraro and L.J. Basile, Eds.), V. 4, Acad. Press, London, 1985, 169-241. 

In Sect. 2.2 the fundamentals of Stellar Interferometry are shown. Starting with the Young s double slit experiment the interferometric observables are explained, this is, the complex visibility function. The data synthesis relevant to the work of this thesis is then presented. Finally, in Sect. 2.3 the concept of Multi-Fourier Transform Interferometry is developed. 

G. Horlick, R. H. Hall, and W. K. Yuen, Atomic emission spectrochemical measurements with a Fourier transform spectrometer, in Fourier Transform Infrared Spectroscopy Techniques Using Fourier Transform Interferometry, J. R. Ferraro and L. J. Basile, Eds., Academic Press, New York, 1982, Vol. 3, p. 37. 

A rather new approach to time-resolved spectroscopy that uses modem optoelec-tronic-controlled step-scan methods of Fourier transform interferometry has been suggested [53]. When using step-scan interferometry, the initiation of a reversible event must occur at each mirror position. The time evolution at each mirror position subsequent to initiation is then measured at discrete time intervals. Data processing involves sorting by time in order to produce an interferogram for each sampling time. These interferograms are subsequently Fourier transformed to yield a set of time-resolved spectra. To quote the authors ... 

Interferometry is difficult in the uv because of much greater demands on optical alignment and mechanical stabiUty imposed by the shorter wavelength of the radiation (148). In principle any fts interferometer can be operated in the uv when the proper choice of source, beam spHtter, and detector is made, but in practice good performance at wavelengths much shorter than the visible has proved difficult to obtain. Some manufacturers have claimed operating limits of 185 nm, and Fourier transform laboratory instmments have reached 140 nm (145). 

The fundamental quantity for interferometry is the source s visibility function. The spatial coherence properties of the source is connected with the two-dimensional Fourier transform of the spatial intensity distribution on the ce-setial sphere by virtue of the van Cittert - Zemike theorem. The measured fringe contrast is given by the source s visibility at a spatial frequency B/X, measured in units line pairs per radian. The temporal coherence properties is determined by the spectral distribution of the detected radiation. The measured fringe contrast therefore also depends on the spectral properties of the source and the instrument. 

E.N. Lewis, RJ. Treado, R.C. Reeder, G.M. Story, A.E. Dowrey, C. Marcott and I.W. Levin, Fourier transform step-scan imaging interferometry high-definition chemical imaging in the infrared spectral region. Anal. Ghent., 67, 3377-3381 (1995). 

Figure 11.11—Multichannel detection, a) Multichannel detection with a diode array located in the focal plane. The light beam is diffracted by the concave dispersive system after travelling through the sample. Note the absence of an exit slit b) spectrum of a 1 1 000 solution of benzene in methanol. This spectrum represents a typical spectrum without smoothing and is obtained with commercial photodiodes (note in contrast to mid IR spectroscopy, interferometry followed by Fourier transform has led to few commercial achievements in this area).

Lewis, E.N. Treado, P.J. Reeder, R.C. Story, G.M. Dowrey, A.E. Marcott, C. 8c Levin, I.W., Fourier Transform Step-Scan Imaging Interferometry High-Definition Chemical Imaging in the Infrared Spectral Region Anal. Chem. 1995, 67, 3377-3381. 

Fourier transform (FT) IR spectroscopy is one of several nondispersive optical spectroscopies based on interferometry. A two-beam interferometer first proposed by Michelson is the basis of most modern FT-IR spectrometers, as exemplified by the schematic of the Bruker Equinox 55 spectrometer (Bruker Optik, Ettlingen, Germany) in Fig. 2. Simply described, the interferometer comprises a beam splitter and two mirrors. A collimated beam of IR energy is split at the beam splitter into equal halves. Half of the energy travels through the beam splitter to one of the mirrors, which is positioned at a fixed distance away from the beam splitter. The reflected beam travels perpendicular to the incident beam to a moving mirror. IR radiation reflects off the fixed and moving mirrors and recombines at the beam splitter. The recombined IR beam projects from the interferometer towards the detector on an optical path perpendicular to the source beam. 

Fourier transform infrared microspectroscopy couples both interferometry and microscopy into an integrated instmment. Since interferometry is an important... 

Perhaps the most dramatic example of the improvement in signal brought about by mathematical means is the application of the Fourier transform to infrared and NMR spectroscopy14 16). In the former instance, interferometry has become a practical possibility and in the latter it has permitted carbon-13 NMR to be developed. 

In spectral interferometry, the interference in the spectral domain is exploited. The spectral modulation period is essentially determined by a time delay. This is at the heart of Fourier transform infrared spectrometers (FTIRs). 

Fourier transform techniques are used throughout the whole spectroscopic region, particularly in the infrared and visible. As we pass from the microwave region to the far-infrared, Fourier transform methods are still used, but based now on interferometry rather than pulsed methods. Perhaps this region of the spectrum will, in... 

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. 

Nafie LA, Diem M (1979) Theory of high-frequency differential interferometry - application to the measurement of infrared circular and linear dichroism via Fourier-transform spectroscopy. Appl Spectrosc 33 130-135... 

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