Centre frequency

In Lakestani (10) modelling work performed within the PISC III project is validated against experiments. Figure 1 shows the pulse echo response from the lower edge of a 10 mm vertical strip-like crack at centre depth 55 mm. The probe has the size 20 mm by 22 ram, is of SV type with angle 45 and has centre frequency 2.2 MHz and an assumed bandwidth of 2 MHz. The calibration is perfomed by a side-drilled hole of diameter 9.5 mm and centre depth 60 mm (the... 

The sample frequency of the ADC (analogue to digital converter) should be 8 times higher than the test frequency (centre frequency of the spectrum). In dependence of the application, different ADC- boards are used. A standard board (20520) provides 8 bit resolution and up to 100 Msamples/s in single shot mode. For manual tests, up to 400 Msamples/s can be reached in the repetition mode. For scanning systems with high frequencies boards up to 400 Msamples/s (single shot) are available. 

With the advent of short pulsed lasers, investigators were able to perfonn time resolved coherent Raman scattering. In contrast to using femtosecond pulses whose spectral widtii provides the two colours needed to produce Raman coherences, discussed above, here we consider pulses having two distinct centre frequencies whose difference drives the coherence. Since the 1970s, picosecond lasers have been employed for this purpose [113. 114], and since the late 1980s femtosecond pulses have also been used [115]. Flere we shall briefly focus on the two-colour femtosecond pulsed experiments since they and the picosecond experiments are very similar in concept. 

The design of a system for working with short pulses follows the same principles as other pulsed ultrasonic systems such as ultrasonic flaw detectors, but in this case it is necessary to achieve very much greater stability and higher bandwidth. A schematic circuit is shown in Fig. 5.4 A very short impulse is generated by a step recovery diode. The pulse has a width of half the period of the centre frequency of the lens if it is shorter than that the energy in the pulse is reduced without any improvement in the signal bandwidth. Thus the lens acts as a sort of matched filter with poor time resolution but optimal... 

Fig. 10.5. Signals reflected from the top and bottom surfaces of a 15 ym thick coating of polyethylene terephthalate on a stone-finish rolled steel substrate, using a short pulse of centre frequency 230 MHz and half-power bandwidth 110 MHz z = +40 (with the top surface of the polymer as datum) (Sinton etal. 1989).

Filters and delay lines of the form shown in Fig. 6.34(b) are made which exploit the surface acoustic wave (see Section 6.5.2 above). The SAW is propagated in the direction normal to the overlap of the interdigitated electrodes, the wavelength launched being related to the electrode spacing and width. For a combined space and half-width of 15 /nn (2sulfacc = 30 /nn) the structure will propagate a centre frequency of 100 MHz. That is it operates as a filter. 

Doppler splittings [89]. In both spectra the scan range was 1 MHz about the centre frequency. 

The Morlet wavelet can be understood to be a linear bandpass filter, centred at frequency m = coo/a with a width of /(aoa). Some Morlet wavelets and their Fourier spectra are illustrated in Fig. 4.4.4. The translation parameter b has been chosen for the wavelet to be centred at time f = 0 (top). With increasing dilatation parameter a the wavelet covers larger durations in time (top), and the centre frequency of the filter and the filter bandwidths become smaller (bottom). Thus depending on the dilatation parameter different widths of the spectrum are preserved in the wavelet transform while other signals in other spectral regions are suppressed. 

Fig. 6.2.7 [Fral] Timing diagram for multi-slice imaging by the STEAM method. The third rf pulse is used for slice selection. It is repeated with different centre frequencies for acquisition of different slices.

A closely related technique can be used for multi-slice imaging (Fig. 6.2.7) [Fral]. The scheme of Fig. 6.2.5(c) is appended by further slice-selective 90° pulses with different centre frequencies, so that the magnetization of other slices is selected [Fral]. In this way, the otherwise necessary recycle delay can effectively be used for acquisition of additional slices. However, the contrast in each slice is affected by a different Ty weight, because is different for each slice. The technique can readily be adapted to line-scan imaging by applying successive slice-selective pulses in orthogonal gradients [Finl]. 

Equations 1.16 and 1.17 are based on the assumption that all the molecules undergoing the transition m —> do so at the same frequency v. In reality they will have slightly different transition frequencies centred around the centre frequency Vq due predominately to collisional interactions between molecules. Doppler broadening also makes a small contribution giving a Gaussian shape to the line (Figure 1.4), but the overall result is a profile approximated by the Lorentz shape function 5 (v) ... 

When V = V(f the centre frequency and maximum of the line profile, the peak absorption coefficient is given by... 

The significance of Equation 1.30 is that at the centre frequency Vq of the Doppler broadened line, the maximum absorption coefficient aa max is always independent of the Doppler width. As long as the pressure is below a critical value pc, which corresponds to the onset of a significant contribution due to collisional broadening, then... 

The key to their success has been a broad bandwidth BWO phase locked to an 8-12 GHz synthesiser that defines the BWO centre frequency. The locked source was frequency modulated by a second 20-40 MHz synthesised sweeper. The Fabry-Perot cavity comprised a pair of 120 mm diameter X 240 mm radius of... 

Solid state sources are not able presently to achieve the required power output over such a wide band 10% of the centre frequency would represent a typically good -3 dB power bandwidth. For single component measurements it is not necessary to scan the entire waveguide band, the 6-8 GHz FWHM of typical lines at 50-200 GHz, could be adequately covered by a Gunn device. This would be an attractive method for dedicated measurements at atmospheric pressure of flame combustion products in smoke stack and engine exhaust effluents, e.g. oxygen and carbon monoxide whose concentrations at >1 ppm are particularly important. 

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