Modulation as a function

Another light pulse of frequency comes at a time delay ta and interacts with the vibrationally excited molecules. The intensity of the probe light transmitted through the interface is modulated as a function of the delay. The modulation is Fourier-transformed to provide the frequency and phase of the vibrational coherence. 

The signals S+ and S are now amplitude-modulated as a function of tp, therefore, a double hypercomplex Fourier transformation of these data, following for instance the States-Haberkom-Ruben procedure, yields a pure-absorption 2D spectrum with sign discrimination in the 12 j dimension [169]. 

Fig. 4. Nonlinear conductance oscillations at low field from a 6 /mi junction, (a) shows the oscillations as a function of both B and V. (A smoothed background has been subtracted to emphasize the oscillations.) The brightest (and darkest) lines, corresponding to tunneling between the lowest modes, break the V-B plain into regions I, II, and III. Additional positively-sloped bright and dark lines in II arise from other ID channels in the wires and are disregarded in our theoretical analysis. Also present is a slow modulation of the strength of the oscillations along the abscissa, (b) Absolute value of the peak of the Fourier transform of the conductance at a fixed V in region II as a function of V. Its slow modulation as a function of V is easily discerned.

Linear combinations of these phase-modulated signals yield two new data sets that are purely amplitude-modulated as a function of fj. 

Adding the signals results in a data set that is cosine-modulated as a function of t,... 

Figure 22. Refractive index modulation as a function of the external angle of the probe beam with respect to the sample normal for the material given in [20], when the writing beams are arranged at a constant 55° and 75° to the sample normal. A) angular variation if reorientational birefringence is dominant B) angular variation if Pockels response were the primary source of index contrast.

The amplitude modulation of the antiphase proton magnetization 2/,-5 2, generated prior to the generation of zero and double quantum coherences by the first Sn 90° pulse, obeys a sine law of the type sin[/7cA] with j=V( Sn, H). This amplitude modulation as a function of the coupling constant varying from 0 to 200 Hz is presented in Figure S for two fixed delays, A = 3.8 and 62 ms. 

Tris(4-bromophenyl)ammoniumyl hexachloro antimonate is commercially available (e.g., Fluka product, 5g cost 70). It is commonly used as an oxidizing reagent by means of electron transfer and is elegantly applied to induce cycloadditions and cyclodimerization ([2 -I- 2] reactions) by Bauld [115]. However, aromatic amine radical cations as the oxidizing reagent can be easily obtained anodically [116] and their redox potentials (between -1-1 V and -1-2 V vs. NHE) modulated as a function of different substituents for utilization if indirect oxidation reactions are to be conducted. Therefore, such a redox catalysis process appears to be a cheap and elegant method to selectively achieved in situ oxidation, provided that polar solvents, electrolytes, and room temperatures are acceptable experimental conditions to perform a given reaction. 

Because the intensity of a diffracted beam is modulated as a function of the crystal thickness, using one diffracted beam to form an image results for a... 

A 2D NMR experiment can lead to a data set that is either phase modulated or amplitude modulated as a function of fj, depending on the particular experiment and coherence pathways selected. A regular ID spectrum consists of absorption A(p) and dispersion peaks corresponding to the real and imaginary parts of the spectral lines, respectively. In 2D experiments, phase modulation in fj results in twisted 2D real lineshapes as a result of the Fourier transformation of bi-exponential time domain... 

Fig. 20a,b. Far field mode pattern the upper spot with a long stripe line is the slab-mode pattern and the lower one is the rib of waveguiding propagation mode (a), and output intensity modulation as a function of applied DC voltage (b)... 

Prior to the advent of the above methods that allowed the presentation of phase-sensitive displays, 2D data sets were collected that were phase-modulated as a function of ti rather than amplitude-modulated. Phase-modulation arises when the sine and cosine modulated data sets collected for each ti increment are combined (added or subtracted) by the steps of the phase cycle, meaning each FID per tj increment contains a mixture of both parts. Here it is the sense of phase precession that allows the differentiation of positive and negative frequencies. This method is inferior to the phase-sensitive approach because of the unavoidable mixing of absorptive and dispersive lineshapes, so is generally only suitable for routine, low-resolution work. 

For the phase-sensitive COSY experiment both p = 1 pathways must be preserved during ti. Recall that for a pure-phase 2D spectrum the signal detected in ta must be amplitude-modulated as a function of tt. Such a signal can only be obtained if both of the counter-rotating coherences are retained since the retention of only one of these unavoidably leads to a phase-modulated... 

FIGURE 14. Density modulation as a function of the number of line pairs per millimeter ... 

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