Wavenumber filters

The number of sites controls the quality of the array as a wavenumber filter, i.e., its ability to suppress seismic energy crossing simultaneously the array with a different slowness than the one on which the array is steered. 

Figure 9.22 illustrates how a CARS experiment might be carried out. In order to vary (vj — V2) in Equation (9.18) one laser wavenumber, Vj, is fixed and V2 is varied. Here, Vj is frequency-doubled Nd YAG laser radiation at 532 nm, and the V2 radiation is that of a dye laser which is pumped by the same Nd YAG laser. The two laser beams are focused with a lens L into the sample cell C making a small angle 2a with each other. The collimated CARS radiation emerges at an angle 3 a to the optic axis, is spatially filtered from Vj and V2... 

A detailed description of LES filtering is beyond the scope of this book (see, for example, Meneveau and Katz (2000) or Pope (2000)). However, the basic idea can be understood by considering a so-called sharp-spectral filter in wavenumber space. For this filter, a cut-off frequency kc in the inertial range of the turbulent energy spectrum is chosen (see Fig. 4.1), and a low-pass filter is applied to the Navier-Stokes equation to separate the... 

In the mid-IR, unlike NIR, it is customary to use microns or micrometers (um) for the wavelength scale, not nanometers (nm). Also, for filter-based instruments the wavelength scale is traditionally used instead of the wavenumber (cm ) frequency based scale this tends to be historical based on thin film interference filter technology. 

This filtering preprocessing method can be used whenever the variables are expressed as a continuous physical property. One example is dispersive or Fourier-Transform spectral data, where the spectral variables refer to a continuous series of wavelength or wavenumber values. In these cases, derivatives can serve a dual purpose (I) they can remove baseline offset variations between samples, and (2) they can improve the resolution of overlapped spectral features. 

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... 

Table 7.1 are continuous wave (CW), not pulsed. Second, frequency stability to < 1 cm" is important to assure Raman shift precision and avoid line broadening. Although the Raman shift axis is usually calibrated periodically, the laser frequency must remain stable between calibrations. Third, lasers vary significantly in output linewidth, from hundreds of reciprocal centimeters to much less than 1 cm". For the majority of samples of analytical interest, a laser linewidth below 1 cm" is sufficient. Laser linewidths are often quoted in terms of frequency rather than wavenumber, in which case 1 cm" equals 30 GHz. Lasers are available with < 1 MHz linewidths (< 10 em ), but such lasers would be unnecessarily narrow for most analytical Raman applications. Fourth, lasers differ in their output of light at wavelengths other than the laser line itself. Gas lasers (Ar+, Kr+, He-Ne) emit atomic lines (plasma lines), and solid-state lasers luminesce, both of which can interfere with Raman scattering. Essentially all lasers require a bandpass filter or monochromator to reduce these extraneous emissions. 

Some workers reserve the term LES for the case where the filter scale A corresponds to a wavenumber in the k A inertial range, and the term VLES when the residual field begins before the inertial range [128]. The reason for... 

The low-pass filter between the FT-IR spectrometer and the microscope restricts the high-wavenumber range beyond 3850 cm" in order to avoid artifacts due to Fourier fold-over. 

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