Nyquist wavenumber

Here vmax is the maximum wavenumber present (Nyquist wavenumber). Radiation v above vmax must be removed by suitable optical filtering or additional features and noise will be folded back onto the spectrum. Aliasing, as this phenomenon is called, places constraints on the operation of real... 

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.

Figure 8. Three-dimensional representation of the time evolution of the IR chemiluminescence spectra following the IRMPD of CH2F2 in the presence of O atoms. Conditions were 28.5mTorr CH2F2, 12.0mTorr O atoms, 5.09 Torr total pressure, unapodized FWHM resolution of 6.04 cm 1, Nyquist wavenumber 7901.4 cm"1 with the signal obtained for 1 shot per sampling point. The data were digitized at 30 /is resolution, but are shown here with 150/is between spectra and have been corrected for the instrument function. Emission from HF near 4000 cm-1 and CO near 2000 cm-1 is clearly seen. Reproduced with permission from Ref. 40.

Data were summed up to 25 /total pressure 4.5Torr, un-apodized FWHM 9.31 cm-1. Nyquist wavenumber 3950.7 cm-1, 4 shots per point, fluence 82 J cm-2. The positions of the CO v, v—1 band origins are shown together with the detector cut-off point at 1840 cm-1. Reproduced with permission from Ref. 40. 

Figure 19, Emission spectra at 50, 200, and 500 fts following the IRMPD of CF2HC1 (24 mTorr) in the presence of O atoms (11.3 mTorr) and Ar (4.05 Torr), obtained from FTIR emission experiments. Data are unapodized with resolution (FWHM) 3.18cm 1, Nyquist wavenumber 3950cm-1, and were obtained at one C02 laser pulse per sampling point. The P, R envelope of the (0,0,1) - (0,0,0) transition of COz is clearly seen in the 500-/JS data. Reproduced with permission from Ref. 82.

Figure 25. FTIR emission spectra at two times following the IRMPE of 70njTorr PhNCO. Unapodized FWHM 3.18 cm 1, Nyquist wavenumber 3950.7 cm the spectrum is corrected for the instrument response function and the maxima of ot spectra have been scaled to unity.

Figure 5.7. Atomic emission spectrum of platinum measured at a resolution of 0.11 cm showing the performance of a Bruker 120 HR spectrometer operating in the ultraviolet with a Nyquist wavenumber of 63,200cm The resolving power for this spectrum is 4.7 x 10 and the measurement time was 24 hours. (Reproduced by permission of Bruker Optics.)...

Nyquist (45) states that the vp=0 frequencies occur at higher wavenumbers in the vapor phase than in the condensed phase. He has modified the n-constant values in (1) to better match the slightly different band positions in the gas-phase spectra. These values are shown in Table 4 together with those for the condensed phase. 

A single-mode He Ne laser has an emission at 632.8 nm (visible, red) which corresponds to a frequency of 15,800 wavenumbers. The reference He Ne laser beam is coupled to the moving mirror of the interferometer by either its own beamsplitter in parallel with the infrared beamsplitter, or directly through the infrared optics. The laser radiation is detected separately from the infrared radiation and is recorded as a cosine wave, as indicated by Equation 6. According to the Nyquist sampling criterion, to correctly sample the He Ne signal data would have to be collected at twice its frequency. 

The closer the high-wavenumber end of the spectrum is to the Nyquist frequency, the faster must be the filter cutoff. So-called brick-wall filters have been designed, but they tend to affect the phase of the signal near the Nyquist frequency to a far... 

In a coherent picture then the imaging experiment reduces to a series of measurements as a function of the wavenumber in three-dimensional space and taking the inverse Fourier transform of the NMR signal returns the real space image. At this level of approximation, the field of view and spatial resolution are given directly by the Nyquist sampling theorem. 

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