Wavenumber interferogram

If a single sharp absorption occurs at a wavenumber v, as shown in the wavenumber domain spectmm in Figure 3.15, the cosine wave corresponding to is not cancelled out and remains in the I 5) versus 5 plot, or interferogram, as it is often called. For a more complex set of absorptions the pattern of uncancelled cosine waves becomes more intense and irregular. 

The cosine Fourier transform given by Eq. (2) is only applicable if the interferogram is perfectly symmetrical about <5 = 0. In practice additional wavenumber-dependent phase shifts are present, owing to beamsplitter characteristics or refraction effects, and cause the interferogram to appear partially asymmetric. The modulated part of Eq. (1) then becomes... 

Figure 4. Three-dimensional representation of the time-resolved data near 8 = 0 as they appear following one interferometric scan. The sampling interval employed was 1.2656 jxm, corresponding to a Nyquist wavenumber of 3950.7 cm 1. Selection of an interferogram at any time delay following the photolysis laser pulse is possible, and is shown here for t = 150/is. Reproduced with permission from Ref. 37.

Figure 6. Interferograms before and after normalizing for the variations of C02 laser fluence with functional form similar to that shown in Figure 5. The data shown correspond to emission from vibrationally excited HF, generated from the IRMPD of CH2F2, and are for a delay of 20 jis after photolysis, taken with one laser shot per interferometric mirror position and a Nyquist wavenumber of 7901.4 cm-1.

FT-Raman instruments are calibrated with an internal laser, which is used to provide the exact location of the movable mirror in the interferometer. Thus the intensity of the interferogram is known as a function of the mirror location (distance in cm), and this is converted through a fast Fourier transform to reciprocal distance or wavenumber (cm-1) in the spectral domain. 

Thus, we need only take a one-sided interferogram. From Eq. 13 we can also see why spectroscopy associated with the Michelson interferometer is called Fourier transform spectroscopy. Movement of the mirror which corresponds to a change in retardation provides a signal which is a function of distance. This signal is then decoded by a Fourier transform to give a spectrum which is a function in the reciprocal space. This is why wavenumbers (cm-1) are such a convenient unit to use with this type of spectroscopy. 

The digitized (ADC) discrete interferogram is Fourier transformed (DFT) by a PC to yield a wavenumber dependent spectrum. Sampling points are determined by the interference pattern of a monochromatic HeNe laser beam which is transferred collinearly with the IR beam. The resulting high wavenumber accuracy constitutes the third advantage of FTIR. 

Phase correction in contrast to the theoretical expectation, the measured interferogram is typically not symmetric about the centerburst (.v = 0). This is a consequence of experimental errors, e.g., frequency-dependent optical and electronic phase delays. One remedy is to measure a small part of the interferogram doublesided. Since the phase is a weak function of the wavenumber, one can easily interpolate the low resolution phase function and use the result later for phase correction. If there is considerable background absorption, phase errors may falsify the intensities of bands in the difference spectra. To avoid such phase errors for difference spectroscopy, the background absorbance should therefore be less than one. 

For monochromatic radiation of wavenumber v(= 1/A), the interferogram can be described by a cosine function ... 

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