Intensity, 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. 

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. 

The intensity recorded in the interferogram, henceforth called hologram, is given by... 

Recently, a systematic experimental study has clearly proved the effect on a gaseous medium of both ASE and picosecond pedestal prior to the arrival of the ultrashort intense laser pulse [26]. The study has been based on sequences of electron density maps obtained from optical interferograms with femtosecond resolution and has been supported by numerical simulation of the ionization of the medium. 

The final step in obtaining the spectrum by the FTIR method is turning back the data obtained as a result of the repetitive interference action of the moving mirror into an intensity wavelength line. It is here that Fourier Transform mathematics is utilized. It is the signal intensity that is stored in a digital representation of the Interferogram. This information is then Fourier transformed by the computer into the frequency spectrum. 

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... 

Obviously, it is difficult to find a schematic representation for a compound absorbing 10 different frequencies. In such a case, M0 can be dissociated into many vectors, each of which precesses around the field with its own frequency (Fig. 9.7 shows a simplified situation). As the system returns to equilibrium, which can take several seconds, the instrument records a complex signal due to the combination of the different frequencies present, and the intensity of the signal decays exponentially with time (Fig. 9.9). This damped interferogram, called free induction decay (FID), contains at each instant information on the frequencies of the nuclei that have attained resonance. Using Fourier transform, this signal can be transformed from the time domain into the frequency domain to give the classical spectrum. 

Figure 10.11—Optical arrangement of a Fourier transform IR spectrometer, a) A 90c Michelson interferometer including the details of the beam splitter (expanded view) b) optical diagram of a single beam spectrometer (based on a Nicolet model). A weak intensity HeNe laser (632.8 nm) is used as an internal standard to measure precisely the position of the moving mirror using an interference method (a simple sinusoidal interferogram caused by the laser is produced within the device). According to the Nyquist theorem, at least two points per period are needed to calculate the wavelength within the given spectrum.

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