Signal oscillation

Consider a monochromatic beam The detected signal oscillates as the two components alternately come into and out of phase as the path difference (p) is varied and gives rise to an interference pattern, the ac portion of which is a modulated cosine wave. The simplest equation representing this is... 

In the Third-Harmonic Generation (THG) experiment an input beam at frequency w is incident into the nonlinear sample and an optical signal oscillating at frequency 3w is generated through the nonlinear interaction inside of the material. This is described by w, w, w) ... 

The second set-up utilizes a fixed magnetic field and a rotating polarizer the signal oscillates between two extreme values which correspond either to the background absorption alone or to the latter plus the absorption by the tt component of the element (Figure 13.15). 

Figure 5.4. The concentration distribution in a diffusion couple of a fictitious system A/B that has two compounds, a line compound ABj and one with considerable nonstoichiometry AjBj. The reactants have some solubility in each other. If both compounds form during annealing at (dotted line in the phase diagram) a line profile over the diffusion couple shows a distribution of [B] as indicated. In the vertical parts of this graph (in the coexistence regions) the concentration signal oscillates between two values, depending on which of the two crystallites happens to be measured (by SEM).

Typical xSR spectrum (number of detected positrons against muon lifetime). The exponential muon decay is superposed upper spectrum) by a signal oscillating with the muon precession frequency v (x B. The lower spectrum shows the slowly relaxing asymmetry curve with the exponential removed... 

Frequency The rate at which a signal oscillates, or changes polarity, expressed as hertz or number of cycles per second. 

Optimization of smoothing and differentiation parameters and of the differentiation order is reached if all shoulders and inflection points are resolved and if the signals oscillate around the zero line. 

Advanced signal processing techniques provides more elaborated approaches to the analysis and interpretation. In our study, we continue to promote the use of a continuous wavelet transform. We believe that its higher computational complexity are comparable to the Fourier transformation but the continuous wavelet transform makes the convenient assessment of amplitude, scale and phase of signal oscillations. Wavelet transform allows us to isolate a given structure in time and frequency space. Let us define the wavelet trans-... 

Ample evidence of the effectiveness of this expedient has been gathered within ESIS TC4. As the examples in Figure 2 show, signal oscillations can be practically suppressed and thus the point of fracture initiation can be easily identified and the critical load easily determined. 

The previously described techniques probe primarily electronic states. Vibrational information can be obtained from observed vibronic progressions, band shapes, and signal oscillations due to coherent motions of nuclear wavepackets. A more direct... 

After an initial transmission decrease around time zero, a positive signal appears with a small delay, which then dominates. In addition, pronounced signal oscillations are observed with a couple of frequencies in the range up to 700 cm, as can be seen from the Fourier transforms. The transmission decrease at time zero is caused by ESA, which takes place as soon as the molecule is promoted to the Sj... 

Already in early investigations transfer times of about 100 fs or less were observed for HBT in tetrachloroethylene [7], 2-(2 -hydroxyphenyl)benzoxazole (HBO) in cyclohexane [33], and for methyl salicylate (MS) [34] and OH BA [35] in gas phase. For a number of ESIPT molecules, very fast transfer times were found even at cryogenic temperatures [36]. Pioneering work was performed on 2-(2 -hydroxy-5 -methylphenyl)benzotriazole (TINUVIN P), and for the first time oscillatory signal contributions associated with the ESIPT were observed [37]. Meanwhile ultrafast ESIPT and subsequent signal oscillations due to coherent wavepacket motions were also found in HBO [38], OHBA [39], and a number of other ESIPT compounds [13, 40-43]. 

The spectral position and shape of the SE reflects the fluorescence of the enol form. The onset of the SE is a clear signature for the proton transfer itself. The signal oscillations result from a wavepacket motion in the excited-state potential of the keto form. Wavepackets in the electronic ground state of the enol configuration which might be excited by impulsive stimulated Raman processes [44, 45] do not contribute since the enol absorption spectrum is at much shorter wavelengths than the applied probe pulses. 

The oscillatory signal contributions are due to the motion of a nuclear wavepacket on the PES of the electronically excited product state and allow the identification of the participating vibrational modes. A wavepacket in a vibrational mode leads to periodic variations of the optical transition energy and to an oscillatory spectral shift of the Sj emission and the transient S - S j absorption spectra, as depicted in Figure 4.8. The amplitude of the signal oscillations exhibits a wavelength dependence that reflects the slope of the emission spectrum [31, 41]. 

The phase of the signal oscillations gives hints about the specific mechanisms leading to the coherent excitation of the modes. At the time a vibration starts, the... 

Fig. 2.8 HD-OKE signal from iodo-benzene sample at 273 K. In the inset we show the fast relaxation time scale, where several signal oscillations take place...

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