Interferogram Interferometer

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. 

In a Fourier transform IR instrument the principles are the same except that the monochromator is replaced by an interferometer. An interferometer uses a moving mirror to displace part of the radiation produced by a source (Fig. 5.4) thus producing an interferogram which can be transformed using an equation called the Fourier transform in order to extract the spectrum from a series of overlapping frequencies. The advantage of this technique is that a full spectral scan can be acquired in about 1 s compared to the 2-3 min required for a dispersive instrument... 

Bergdolt (Ref 12) used the Mach-Zehnder interferometer and a short duration light source with a rotating mirror cameraito obtain interferograms of projectiles and the air flow patterns around them... 

Howard has applied his method to high-resolution infrared spectroscopic data obtained by dispersive techniques and to both experimental and simulated Fourier interferograms. The method in the latter application explicitly renders the data as they would be observed by an interferometer having a path difference exceeding the mechanical limits of the instrument used for the observation. Details on both the method and its application constitute Chapters 9 and 10. 

In the operating mode customarily used, which is to determine the existence, location, and intensity of the spectral lines, the interferometer produces an interferogram that is symmetric about the zero displacement position. If the zero displacement position (the maximum point on the central fringe ) is taken as the origin of the interferogram function, the Fourier transform of this will produce an infrared spectrum that is real and symmetric about... 

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). 

Fig. 24 Interferogram of the two monochromatic sources that would be obtained for a finite maximum path difference of the interferometer. (a) Finite interferogram. (b) Recorded spectrum. The two lines are completely merged into one.

The simplest case, that of two large infrared lines, is shown in Fig. 31(a). A smooth curve was fitted to the base line as shown. A spline-fitting computer program developed by De Boor (1978) was used to obtain this fit very conveniently. After the fit was obtained, the data were adjusted to a flat base line, as shown in Fig. 31(b), and the data field was extended by padding with zeros to yield an overall data field of 28 = 256 points. Taking the Fourier transform, we obtained the interferogram function shown in Fig. 32. (Even though it was not obtained directly from the interferometer as recorded... 

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