Interferogram spectroscopy

It is found that multiplication of the Fourier transform of the data by a carefully chosen window function is very effective in removing the artifacts around peaked functions. This process is called apodization. Apodization with the triangular window function is often applied to Fourier transform spectroscopy interferograms to remove the ringing around the infrared... 

In FT-Raman spectroscopy the radiation emerging from the sample contains not only the Raman scattering but also the extremely intense laser radiation used to produce it. If this were allowed to contribute to the interferogram, before Fourier transformation, the corresponding cosine wave would overwhelm those due to the Raman scattering. To avoid this, a sharp cut-off (interference) filter is inserted after the sample cell to remove 1064 nm (and lower wavelength) radiation. 

The growth and decay of all other species (including O3) were monitored by Fourier transform infrared (FT-IR) spectroscopy at a total pathlength of 460 meters and a spectral resolution of 1 cm". At this pathlength, the intense absorptions of H2O and CO limit the usable IR spectral windows to the approximate regions 750-1300, 2000-2300, and 2400-3000 cm". Each spectrum (700-3000 cm" ) was adequately covered by the response of the Cu Ge detector. Approximately 40 seconds were required to collect the 32 interferograms co-added for each spectrum. 

In spectroscopy, for example, the Fourier transform of an interferogram, fix) is sampled at regular intervals, Ax. Equation (36) is then replaced by the summation... 

Normally, time-resolved FT-IR spectroscopy (TRS FT-IR) possesses the same data characteristics. In a typical TRS FT-IR experiment, interferograms are assembled for a specific delay time after the photolysis pulse, and the data produced are normally finer-grained in frequency than in time. This type of experiment is complementary to experiments with fine-grained time information. It is particularly useful where a wide spectral range is necessary and works reasonably well for highly reproducible events which occur on relatively long timescales (fractions of seconds) (83). It is also an appealing system for use on shorter timescales, and it has... 

In detector noise limited spectroscopies such as PAS it is advantageous to enhance the throughput of energy (Jacquinot s advantage) by utilizing a Michel son interferometer. One then Fourier transforms (FTs) the resulting interferogram to yield a PA spectrum that qualitatively resembles an absorption spectrum. 

A Fourier transform infrared spectroscopy spectrometer consists of an infrared source, an interference modulator (usually a scanning Michelson interferometer), a sample chamber and an infrared detector. Interference signals measured at the detector are usually amplified and then digitized. A digital computer initially records and then processes the interferogram and also allows the spectral data that results to be manipulated. Permanent records of spectral data are created using a plotter or other peripheral device. 

Let the discrete spectrum, which consists of the coefficients of u(k) and v(k), be denoted by U(n) and V(n), respectively. The low-frequency spectral components U(n) are most often given by the most noise-free Fourier spectral components that have undergone inverse filtering. For these cases V(n) would then be the restored spectrum. However, for Fourier transform spectroscopy data, U(n) would be the finite number of samples that make up the interferogram. For these cases V(n) would then represent the interferogram extension. 

However, for illustration, only one side of the interferogram and its spectrum will be shown, usually the function of the positive spatial and spectral variable. In other operating modes of the interferometer, asymmetric interferograms are produced that have a complex Fourier transform. Asymmetric interferograms will not be treated in this work. For a more complete discussion of Fourier transform spectroscopy, the reader should consult Bell (1972), Vanasse and Strong (1958), Vanasse and Sakai (1967), Steel (1967), Mertz (1965), the Aspen International Conference on Fourier Spectroscopy (Vanasse et al., 1971), and the two volumes of Spectrometric Techniques (Vanasse, 1977, 1981). A review of early work, which includes several major contributions of his own, is given by Connes (1969). Another interesting paper on the earlier historical development of Fourier transform spectroscopy is that by Loewenstein (1966). 

FT Spectrometers FT spectrometers (Figure 3) differ from scanning spectrometers by the fact that the recorded signal is an interferogram [14] (see Chapter 6.2). They can be coupled to a microscope or macrochamber with an FPA detector. FT chemical imaging systems (CISs) are available for Raman, NIR, and IR spectroscopy. However, they can only be considered as research instruments. For example, most IR imaging systems are FT spectrometers coupled to microscopes. This type of spectrometer allows the acquisition of spectra in reflection, attenuated total reflection (ATR), or transmission mode. 

An advantage of Fourier transform spectroscopy is that the entire interferogram is recorded in a few seconds and stored in a computer. The signal-to-noise ratio can be improved by collecting tens or hundreds of interferograms and averaging them. 

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... 

Other processing techniques for analysis of F.t.-i.r. data have been developed in order to obtain the maximum of information from the spectra. The advances made in time-resolved techniques, which sample only a portion of the interferogram, permit obtaining of spectra in the microsecond domain this will lead to additional applications of F.t.-i.r. spectroscopy such as the study of dynamic and kinetic processes. 

In FT-IR spectroscopy, a pattern known as an interferogram is obtained in place of the normal spectrum. The interferogram is the Fourier transform of the normal spectrum. Therefore, the normal spectrum can be obtained by transforming the interferogram. The advantages of the FT-IR are simultaneous spectral acquisition and high signal to noise ratio. A detailed description of FT-IR can be found elsewhere [17]. 

Bouwman and Freriks (18.19) have also noted the advantages of FT spectroscopy and have used this technique to study the adsorption of CO on a silica-supported nickel catalyst at temperatures between 70 and 180°C. These authors point out that FT spectroscopy is particularly advantageous for in situ observation of heated samples since the radiation emitted by the sample is not modulated by the interferometer and hence does not contribute to the fluctuating portion of the interferogram. 

FT-IR spectrometers have interferometers with scanning velocities enabling the collection of tens of spectra per second at a spectral resolution of 8 cnr1 or less. With faster data collection capabilities, FT-IR spectroscopy can be used to monitor and observe dynamic gas-phase processes. To observe such a process, interferograms are sequentially collected and stored in the memory of the system. The interferograms are then processed at the end of the data acquisition. The result of this operation is a three-dimensional data cube where each vertical slice of the cube is the spectrum for a time slice in the experiment equal to the interferogram acquisition time. 

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