Interferogram measurement

If I (5) is other than a few discrete narrow lines, the tool to evaluate / (5) from I[s) is the Fourier transform, where I ) is the interferogram measured with a two-beam (Michelson) interferometer. This is the fundamental idea of Fourier transform spectroscopy. We have left aside the question of whether the Fourier integral Eq. (2.12) exists and whether it is meaningful or not. For the mathematical requirements on I (s), the reader is referred to the literature 34). it is sufficient to say here that, for all physically and experimentally reasonable interferograms I s), these requirements are usually met. 

In practice, the interferogram measured is not mirror symmetrical about the point d = 0. Call up the interferogram of the file MIR GLYCIN or ACQUIS in order to verify that. This asymmetry originates from experimental errors, e.g., wavenumber-dependent phase delays of the optics, the detector/ amplifier unit, or the electronic filters. The Fourier transformation of such an asymmetrical interferogram generally yields a complex spectrum C(v) rather than a real spectrum S(r) as known from spectrometers based on the dispersive technique. That is why phase correction is necessary. 

If the doublet has a separation of Av(= vi — V2), the two cosine waves in Figure 2.4b become out of phase after a retardation of 0.5(A and are once more back in phase after a retardation of (Av) To go through one complete period of the beat frequency, a retardation of (Av) is therefore required. An interferogram measured only to half this retardation could not readily be distinguished from the interferogram of a source with the profile shown in Figure 2.3c. The narrower the separation of the doublet, the greater is the retardation before the cosine waves become in phase. It is therefore apparent that the spectral resolution depends on... 

A more detailed discussion of phase correction is given in Chapter 4. At this point it is sufficient to say that if the phase angle 0 in an interferogram measured with a continuous broadband source varies only slowly with wavenumber (as is... 

Wavenumbers measured by an FT-IR spectrometer are determined by the translation of the movable mirror, the movement of which is determined by using the interferogram measured... 

The interferogram measured is read into the computer, accumulated, and stored. This process is repeated until the number of accumulations reaches that instructed by the user. In Figure 5.3 , the abscissa axis represents the numbering of sampling points denoted by m. 

In this method, an operation is required for alternating between measuring the target sample and the reference sample at a frequency sufficiently higher than the modulation frequency inherent in an interferogram measured by an FT-IR spectrometer. By this operation, the difference spectrum and the sum spectrum can be obtained, respectively, as the alternating-current component and the direct-current component of the modulated signal. These two components can be separated by an electronic filter, and their ratio can then be calculated. 

To measure an interferogram using a Michelson interferometer the mirror is moved back and forth once. This is called a scan. The interferograms measured while scanning are Fourier transformed to yield a spectrum, hence the term Fourier Transform Infrared (FTIR) spectroscopy. 

FIGURE 2.28 An illustration of what the interferogram measured hy the laser detector on an FTIR might look like. Note that each maximum in the interferogram corresponds to a different value of the integers n = 0,1, 2,... 

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