Interferometer Fourier

Fig. 26. Block diagram of the optics of the triangle common-path interferometer Fourier transform spectrometer S, light source BS, beam splitter M1, M2,M 3, plane mirrors r, lens d, self-scanning photodiode array. [Redrawn from Okamoto et al. (139) with permission.]...

Figure 7.13 (a) Infrared interferometer Fourier transform instrument (b) GC infrared lightpipe sample cell (c) HPLC infrared mieroliquid sample cell. 

Figure Bl.2.6. Schematic representation of a Michelson interferometer. From Griffiths P R and de Flaseth J A 1986 Fourier transfonn infrared spectroscopy Chemical Analysis ed P J Hiving and J D Winefordner (New York Wiley). Reprinted by pemiission of Jolm Wiley and Sons Inc.

For radiofrequency and microwave radiation there are detectors which can respond sufficiently quickly to the low frequencies (<100 GHz) involved and record the time domain specttum directly. For infrared, visible and ultraviolet radiation the frequencies involved are so high (>600 GHz) that this is no longer possible. Instead, an interferometer is used and the specttum is recorded in the length domain rather than the frequency domain. Because the technique has been used mostly in the far-, mid- and near-infrared regions of the spectmm the instmment used is usually called a Fourier transform infrared (FTIR) spectrometer although it can be modified to operate in the visible and ultraviolet regions. 

If was nof until fhe developmenf of Fourier fransform infrared (FTIR) specfromefers (see Section 3.3.3.2) fhaf fhe possibilify of using an infrared laser routinely was opened up. The intensify advanfage of an infrared interferometer, wifh which a single specfrum can be obfained very rapidly and fhen many specfra co-added, coupled wifh fhe developmenf of more sensitive Ge and InGaAs semiconductor infrared defectors, more fhan compensate for fhe loss of scatfering intensify in fhe infrared region. 

Gc/k instmments are all of the gc/fdr variety that utilize an interferometer and requke a Fourier transform of the signal as opposed to employing a monochrometer and mechanical scanning. At least 3 scan/second are needed across the capillary gc peaks which are from 3 to 6 seconds wide. 

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). 

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... 

It is the self-coherence function that is measured in Fourier transform spectroscopy. Writing the measured on-axis intensity at the output of the Michelson interferometer as... 

We are now ready to derive an expression for the intensity pattern observed with the Young s interferometer. The correlation term is replaced by the complex coherence factor transported to the interferometer from the source, and which contains the baseline B = xi — X2. Exactly this term quantifies the contrast of the interference fringes. Upon closer inspection it becomes apparent that the complex coherence factor contains the two-dimensional Fourier transform of the apparent source distribution I(1 ) taken at a spatial frequency s = B/A (with units line pairs per radian ). The notion that the fringe contrast in an interferometer is determined by the Fourier transform of the source intensity distribution is the essence of the theorem of van Cittert - Zemike. 

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