The Fourier Transform Spectrometer

The Fourier transform spectrometer (FTS) is a dual-beam interferometer, which is most frequently of the Michelson type, as shown in Fig.6.32. If the arms of the interferometer have equal lengths the path difference between the two interferring beams would be 0. If the mirror is moved A/2 an optical path difference of A is introduced. For the case of monochromatic radiation and equally intense beams the intensity at the detector will be 

If the light source emits a spectrum B(t ) we then obtain 

The part of the above expression that depends on A is called the interferogram 

The spectrum B u) can be calculated fi om the interferogram J(A) as its Fourier cosine transform 

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Two main categories of monochromators can be distinguished one is the dispersive monochromator where an energy spectrum dispersed in space is obtained with a reflection or a transmission diffraction grating (more rarely now with a prism). The other is the Fourier transform spectrometer (FTS). The principles of these two types of spectrometers are described below. 

These instruments (Figure 10.7) can be divided into two categories the Fourier transform spectrometers, which undertake a simultaneous analysis of the whole spectral region from interferometric measurements, and numerous specialized analysers for the second category. Dispersive-type spectrometers are also used for the near-IR. 

The Fourier transform spectrometer is based on the interferometer introduced in 1881 by Michelson. The basic configuration of the Michelson... 

The main advantages of the Fourier transform spectrometer over conventional dispersive spectrometers are (i) higher energy throughput, because no slits are required, (ii) higher optical resolution, and (iii) ability for simultaneous monitoring of all spectral information for an extended period. 

We will now describe in some detail the Fourier transform spectrometer constructed by Ekkers and Flygare.5 The following requirements for their instrument working in the frequency range from 4 to 8 GHz with a maximum bandwidth of 50 MHz were carefully considered. 

The optimum sensitivity of the Fourier transform spectrometer obtained by calculating the signal-to-noise ratio of a pulse Fourier transform spectrometer relative to a conventional absorption spectrometer has also been given. Suppose that a spectral range F has to be investigated in a total time, T. Both experiments will use a superheterodyne detection system with a balanced mixer. The noise is assumed to be white with a power density Pg per spectral unit. The S/N ratio is defined as the ratio of the peak signal amplitude to the rms noise amplitude. 

There are two reasons for the increased sensitivity with the Fourier transform spectrometer. First, the steady-state spectrometer wiht 5 KHz modulation has significant 1/f noise. To improve the sensitivity, the modulation frequency could have been increased to 100 KHz to reduce the noise to white noise. However, the resolution... 

A final point worth noting is that most steady-state spectrometers use Stark modulation. This modulation gives rise to Stark lobes, which are very helpful for assignments and dipole moment measurements. However, Stark lobes complicate the Zeeman spectrum and can lead to distortion of the Zeeman transitions and the baseline. The Fourier transform spectrometer eliminates this complication. The microwave molecular Zeeman effect in trans-crotonaldehyde has also been reported.16... 

Jacquinotl2,13 recognized that the light gathering capability of a Michel son interferometer is greater than that of a dispersive instrument operating that the same resolving power. The improvement offered by the Fourier transform spectrometer can be expressed asl"... 

The IR spectra of the samples under study were recorded in the range of400-4000 cm" by a standard method with potassium bromide [15] making use of the Fourier transform spectrometer Equinox 55 (Broker). 

We will describe four types of instruments prism and grating instruments, the Fabry-Perot interferometer and the Fourier transform spectrometer. A large number of varieties of these different types are used in spectroscopic research and various applications. Spectroscopic instruments have been discussed in [6.6,7,66]. 

Fig. 2.8 The Fourier transform spectrometer is based on a Michelson interferometer with a moving mirror. The signal on the detector will be a composition of many superimposed iiequen-cies, each the result of the interference of a different wavelength...

Fig. 2.9 A monochromatic light beam passing through the Fourier transform spectrometer creates an oscillating response on the detector (a). The signal fiom polychromatic light creates an interferogram (b), which can be deconvoluted by a Fourier transform to recover the frequency domain spectrum. The frequencies forming the interferogram will be represented by peaks whose amplitude is proportional to the intensity of the the light of that frequency impinging on the detector (c)...

The dynamical results on the 0( D) reactions with H2S, NH3 and CH4, to be reported in ie following Sections, were obtained without time-resolution of the observations. In this case, the photolysis laser was allowed to free-run it had no phase relationship with the data acquisition of the Fourier transform spectrometer. 

To compute the convolution of these two functions, Eq. 2.19 requires that/(v) be reversed left to right [which is trivial in this case, since/(v) is an even function], after which the two functions are multiplied point by point along the wavenumber axis. The resulting points are then integrated, and the process is repeated for all possible displacements, v, of/( relative to B v). One particular example of convolution may be familiar to spectroscopists who use grating instruments (see Chapter 8). When a low-resolution spectrum is measured on a monochromator, the true spectrum is convolved with the triangular slit function of the monochromator. The situation with Fourier transform spectrometry is equivalent, except that the true spectrum is convolved with the sine function/(v). Since the Fourier transform spectrometer does not have any slits,/(v) has been variously called the instrument line shape (ILS) Junction, the instrument function, or the apparatus function, of which we prefer the term ILS function. 

The introduction of the Helium-Neon laser had a significant impact on the evolution of the optical part -the interferometer- of the Fourier transform spectrometer. It allowed for the direct calibration of the interferometer mirror displacement which resulted in a much more precise measurement of the interferogram signal and hence a much improved spectral recovery. 

The retrieval method has been used extensively for temperature profile retrieval in both the terrestrial and other planetary atmospheres. Examples of profiles obtained by this technique for Earth, Mars, Jupiter, Saturn, Uranus, and Neptune are shown in Fig. 8.2.2. Also included is a Titan profile obtained from radio occultation data. The profiles for Earth and Mars were derived from measurements obtained with the Fourier transform spectrometers carried on Nimbus 3, 4, and Mariner 9, respectively. In both cases data from the 15 ptm. CO2 absorption band were used. The profiles for the outer planets were obtained by inversion of measurements from the Voyager Fourier transform spectrometers. For Jupiter and Saturn, data from the S(0) and S(l) collision-induced H2 lines between 200 and 600 cm were used, along with measurements from the CH4 V4-band centered near 1300 cm . Because of the extremely low temperatures encountered on Uranus and Neptune, adequate signal-to-noise ratio for the retrieval of vertical thermal stmctures was obtained... 

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