Sampling amplitudes

Sample Amplitude (nm) Periodicity (pm) Difference in contact angle ... 

Figure 3.1. (a) Sine wave sampled at exactly twice its frequency b) lower-frequency wave sampled at the same frequency as in (a) (c) sine wave of higher frequency than the wave in a) and sampled at the same frequency. Note that the sampling amplitudes in (b) and (c) are indentical. 

Side band amplitude Amplitude of spining side bands is not greater than 2% of the sample amplitude at the rotational speed used... 

The sampling precision of the measured data depends on the signal amplitude. The difference between simulated and experimental data can be mainly explained by the low numerical precision of the measured data. 

We have perfomied some simulations of the eddy current distribution in a test object for a spiral coil and a circular one (see Fig. 4.1). Both coils had 9 turns and the excitation current was 6 mA. Figs. 4.1 show the cross section of the sample at the location of the crack and the amplitude of the eddy current density. One observes a 1.5 higher current density at the sides of the crack for the case of the circular coil. 

The ultrasound system should have more independent channels and allow the transmitter pulse to be individually adjustable in width and amplitude, and an increased frequency range for the logarithmic amplifier was desired. The digitization should be improved both with respect to sampling rate and resolution. 

The back wall echoes were sampled at 100 MHz and the length of these were 70 samples, yielding a size of the input data vectors, ) = 35. An example of such an echo is shown in Figure 2 together with its log spectral amplitude. 

Finally, the standard draft provides a detailed model of the acquisition data, which intends to describe all the possible shapes which can be taken by NDE data OD (scalar or complex), ID (sampled - cf ultrasonics A-scans - or unsampled - ef ultrasonics time/amplitude data), 2D (images) or 3D (volumes). 

The factor A has been measured for a variety of samples, indicating that the approximation can be applied up to quasi-atomic resolution. In the case of biological specimens typical values of are of the order of 5-7%, as detemiined from images with a resolution of better than 10 A [37,38]- For an easy interpretation of image contrast and a retrieval of the object infomiation from the contrast, such a combination of phase and amplitude hifomiation is necessary. 

Figure Bl.17.5 shows typical examples of the CTF for weak phase, weak amplitude or combined samples.

For a detailed discussion on the analytical teclmiques exploiting the amplitude contrast of melastic images in ESI and image-EELS, see chapter B1.6 of this encyclopedia. One more recent but also very important aspect is the quantitative measurement of atomic concentrations in the sample. The work of Somlyo and colleagues [56]. Leapman and coworkers and Door and Gangler [59] introduce techniques to convert measured... 

Most NC-AFMs use a frequency modulation (FM) teclmique where the cantilever is mounted on a piezo and serves as the resonant element in an oscillator circuit [101. 102]. The frequency of the oscillator output is instantaneously modulated by variations in the force gradient acting between the cantilever tip and the sample. This teclmique typically employs oscillation amplitudes in excess of 20 mn peak to peak. Associated with this teclmique, two different imaging methods are currently in use namely, fixed excitation and fixed amplitude. 

This corresponds to the physician s stethoscope case mentioned above, and has been realized [208] by bringing one leg of a resonatmg 33 kHz quartz tiinmg fork close to the surface of a sample, which is being rastered in the x-y plane. As the fork-leg nears the sample, the fork s resonant frequency and therefore its amplitude is changed by interaction with the surface. Since the behaviour of the system appears to be dependent on the gas pressure, it may be assumed that the coupling is due to hydrodynamic mteractions within the fork-air-sample gap. Since the fork tip-sample distance is approximately 200 pm -1.120), tire teclmique is sensitive to the near-field component of the scattered acoustic signal. 1 pm lateral and 10 mn vertical resolutions have been obtained by the SNAM. 

Other techniques to detennine the corrosion rate use instead of DC biasing, an AC approach (electrochemical impedance spectroscopy). From the impedance spectra, the polarization resistance (R ) of the system can be detennined. The polarization resistance is indirectly proportional to j. An advantage of an AC method is given by the fact that a small AC amplitude applied to a sample at the corrosion potential essentially does not remove the system from equilibrium. 

For many applications, it may be reasonable to assume that the system behaves classically, that is, the trajectories are real particle trajectories. It is then not necessary to use a quantum distribution, and the appropriate ensemble of classical thermodynamics can be taken. A typical approach is to use a rnicrocanonical ensemble to distribute energy into the internal modes of the system. The normal-mode sampling algorithm [142-144], for example, assigns a desired energy to each normal mode, as a harmonic amplitude... 

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