Modulation depth

ENDOR, the ESEEM modulation depth will increase for nuclei with smaller... 

Here, results are shown from experiments performed in ASTER, reported by Biebericher et al. [512. 519], A SiH4-H2 (50 50 flow ratio, total flow 60 seem) plasma was generated at an RF excitation frequency of 50 MHz. The substrate temperature was 250°C. The RF signal was ampitude modulated (AM) by a square wave. The modulation frequency has been varied in a range of 1-400 kHz. The modulation depth was always 90%. The duty cycle was fixed at 50%. The pressure amounted to 0.2 mbar, and the average power was kept at 10 W. With a duty cycle of 50%, this leads to a power of 20 W during the plasma-on period. 

The third experimental knob is the relative amplitudes of the two laser fields. These are typically chosen to maximize the modulation depth without affecting the phase of the interference term. 

Additional information may by obtained from the modulation depth of the signal. For the simple case of one-dimensional, angle-resolved scattering into a single, uncoupled continuum (see Section IVC), the modulation depth is given by (see Eq. (4))... 

Once instrumental effects on M have been accounted for, useful information about the physical system may be deduced from the modulation depth. For isolated molecules, averaging over scattering angles and summing over continuum indices will reduce the ratio R. Further loss of modulation depth may be caused by decoherence in dissipative systems (vide infra), making this quantity a potentially useful observable for deducing structural and dynamical effects. 

Figure 4. Calculation of the modulation depth using the analytic model described in the text, with the lasers focused on the axis of the molecular beam (zm = 0). The dashed curve was obtained by setting pa — pi, at zm — 0. The solid curve is the maximum possible modulation depth, obtained by setting pa — pt, at an optimum location.

This procedure involves selecting a fluorophore of known lifetime and placing it in the microscope and measuring the phase and modulation depth [11]. Rearranging Eqs. (2.5 and 2.6) allows the expected phase and modulation to be predicted. These may then be used to compute the position of zero phase and the modulation depth of the light source. An advantage of the method is that it may be done under conditions exactly matching those of a sample. 

The calibration should be done for the specific objective in use. Some objectives have been shown to be interchangeable with minimal effect on the modulation depth and phase however, this is not easily predicted in advance and should never be assumed to be negligible. 

First pass analysis—data to modulation depth and phase shift... 

At present, two main streams of techniques exist for the measurement of fluorescence lifetimes, time domain based methods, and frequency domain methods. In the frequency domain, the fluorescence lifetime is derived from the phase shift and demodulation of the fluorescent light with respect to the phase and the modulation depth of a modulated excitation source. Measurements in the time domain are generally performed by recording the fluorescence intensity decay after exciting the specimen with a short excitation pulse. 

The zero crossing is independent of the amplitude of the cosine, hence effects of drift of Pin and of (varying) modulation depth M have been completely eliminated. 

In frequency-domain FLIM, the optics and detection system (MCP image intensifier and slow scan CCD camera) are similar to that of time-domain FLIM, except for the light source, which consists of a CW laser and an acousto-optical modulator instead of a pulsed laser. The principle of lifetime measurement is the same as that described in Chapter 6 (Section 6.2.3.1). The phase shift and modulation depth are measured relative to a known fluorescence standard or to scattering of the excitation light. There are two possible modes of detection heterodyne and homodyne detection. 

T = (Dq2) 1 is the collective diffusion time constant, DT the thermal diffusion coefficient. In Eq. (18), the low modulation depth approximation c( M c0, resulting in c(x,t)(l-c(x,t)) c0(l-c0)y has been made, which is valid for experiments not too close to phase transitions. Eqs. (16) and (20) provide the framework for the computation of the temperature and concentration grating following an arbitrary optical excitation. 

Xr is the readout wavelength and s the sample thickness. Q < 1 indicates thin, Q > 1 thick grating conditions,which are prevalent in the present case with Q 5. An extensive treatment of the diffraction theory of phase gratings has been given by Kogelnik [48]. All experiments discussed here have been conducted within the weak modulation depth limit, where the heterodyne or electric field diffraction efficiency Chet(t) is simply proportional to the refractive index modulation depth ... 

As predicted by the expressions for the critical divergence of the Soret coefficient in (12) and (13), the heterodyne diffraction efficiency of the induced concentration grating dramatically increases on approach of the critical point. Figure 2 shows normalized heterodyne diffraction efficiencies that have been recorded for different distances T — Tc. A few hundred milli-Kelvin away from Tc, the modulation depth, which is proportional to the heterodyne signal, exceeds the values typically found for small molecules and off-critical mixtures by nearly four orders of magnitude. 

Figure 4.17 Demonstration of the limited linear part of electro-optical modulators. In digital optocommunication applications, the full modulation depth (on/off) is used...

Modulation depths of 50% have been demonstrated with light passing through a l-/ m layer of a-Si H (Phelan et al., 1981). This device used plasma-deposited a-Si H sandwiched between two 25-nm gold contacts. Sapphire was used as the substrate (Fig. 5). The a-Si H was deposited using... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

Experimental three pulse electron spin echo spectra of two types of Chi in Na -A zeolite. Chi (( (D-CO-is the dominant copper species in site S2 in freshly prepared, hydrated Nai2 A and Cu +(0z)j(D20)2 in site S2 is the dominant species after partial dehydration under vacuum at room temperature. The different deuterium modulation depths characterize the different numbers of coordinated waters in these two Cu species. 

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