Frequency phase shift

J. R. Lakowicz, G. Laczko, H. Cherek, E. Gratton, and M. Limkeman, Analysis of fluorescence decay kinetics from variable-frequency phase shift and modulation data, Biophys. J. 46, 463—+77 (1984). 

Fig. 8.32. Bode plot showing experimental data and best and fit to the short circuit IMPS response of a dye sensitized cell. Dc photocurrent 6.3 mA. The upper solid line in each plot shows the fitted response in the absence of RC attenuation. Note the limiting high frequency phase shift is 45°, which is characteristic of diffusion control. The lower line illustrates the improved fit obtained by including the influence of r n. R = lOfl, C = 5 x 10 F.

In contrast to pulse methods described above, the phase-shift technique usually employs a continuous light source whose intensity is modulated by various means at some frequency /. The fluorescence response of the system is then also modulated at that frequency, albeit with some phase delay 0 and a reduced modulation depth m, as compared to the exciting light. "" From either of these quantities the fluorescence lifetime can be extracted. For a single-exponential decay the relationship between lifetime t, the modulation frequency /, phase shift 0, and the modulation depth m are given by tan(0) = /t and m = (1 -t-... 

The sum is as a pure sine wave at the fundamental frequency, phase-shifted, with double amplitude when (p = 0° and zero amplitude with

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FIGURE 10.71 Typical operating waveforms of the bridge inverter when operating with fixed-frequency, phase-shift control. 

Mansfeld F, Lin S, Chen Y, SMh H (1988) Minimization of high-frequency phase shifts in impedance measurements. Tech. rep. 

After amplification both signals change their initial phases due to the delay r of the amplifier unblank (r = 0.1 - 0.5 ms), phase shift in it and wave propagation in passive vibrator s elements. All the mentioned phase changes are proportional to the frequency. The most contribution of them has unblank delay z. Thus frequency variations changes the initial phases) f/, and j(/c) of both signals and their difference A - Vi ... 

For fluorescent compounds and for times in die range of a tenth of a nanosecond to a hundred microseconds, two very successftd teclmiques have been used. One is die phase-shift teclmique. In this method the fluorescence is excited by light whose intensity is modulated sinusoidally at a frequency / chosen so its period is not too different from die expected lifetime. The fluorescent light is then also modulated at the same frequency but with a time delay. If the fluorescence decays exponentially, its phase is shifted by an angle A([) which is related to the mean life, i, of the excited state. The relationship is... 

One advantage of the photon counting teclmique over the phase-shift method is that any non-exponential decay is readily seen and studied. It is possible to detect non-exponential decay in the phase-shift method too by making measurements as a fiinction of tlie modulation frequency, but it is more cumbersome. 

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

Nonciliated cells separate fields of ciliated epithelial cells from each other. Synchronized ciliary movement, with a beat frequency in human proximal airways under normal conditions of 8-15 EIz, propels mucus along the mucociliary escalator at a rate of up to 25 mm/min. Beat frequencies appear to slow to roughly 7 Hz in more distal airways. Cilia move in the same direction and in phase within each field but cilia in adjacent fields move in slightly different directions and are phase shifted. These beat patterns result in metachronal waves that steadily move mucus at higher velocities ( -12-18 mm/min) than would be achievable by summing the motion of individual cilia. 

With the downhole power available and the signal detection threshold at surface, Figure 4-254b gives the maximum depth that can be reached by the technique as a function of frequency. Assuming that phase-shift keying is used with two cycles per bit, in a 10 fi m area (such as the Rocky mountains) a depth of 2 km (6,000 ft) could be reached while transmitting 7 bits/s. 

Confirmation analysis In most cases, the occurrence of dynamic resonance can be quickly confirmed. When monitoring phase and amplitude, resonance is indicated by a 180° phase shift as the rotor passes through the resonant zone. Figure 44.44 illustrates a dynamic resonance at 500 rpm, which shows a dramatic amplitude increase in the frequency-domain display. This is confirmed by the 180° phase shift in the time-domain plot. Note that the peak at 1200 rpm is not resonance. The absence of a phase shift, coupled with the apparent modulations in the FFT, discount the possibility that this peak is resonance-related. 

Both lines are broadened independently and solely by adiabatic phase shift as in Lorentz and Weisskopf theories. They are Lorentzians of width (1 — cosa) and frequency shift (sin a). In general off-diagonal elements of f are not zero though they are less than diagonal elements. Consequently, the spectrum may collapse even in the adiabatic case when A 1/tc. However, adiabatic collapse is hardly ever achieved in the gas phase where l/rc > l/t0 > jS since A > 1/tc > j8 and hence only the resolved doublet limit is available. 

In the case were the arms are oriented at 45° from the x, y axes, the same equation holds but /i+ has to be replaced hy hx- If the incident light is a monochromatic plane wave of frequency Vopt, this time delay will appear as a phase shift between the aj-beam and y-beam ... 

Jablonski (48-49) developed a theory in 1935 in which he presented the now standard Jablonski diagram" of singlet and triplet state energy levels that is used to explain excitation and emission processes in luminescence. He also related the fluorescence lifetimes of the perpendicular and parallel polarization components of emission to the fluorophore emission lifetime and rate of rotation. In the same year, Szymanowski (50) measured apparent lifetimes for the perpendicular and parallel polarization components of fluorescein in viscous solutions with a phase fluorometer. It was shown later by Spencer and Weber (51) that phase shift methods do not give correct values for polarized lifetimes because the theory does not include the dependence on modulation frequency. 

For single exponential fluorescence decay, as is expected for a sample containing just one fluorophore, either the phase shift or the demodulation can be used to calculate the fluorescence lifetime t. When the excitation light is modulated at an angular frequency (o = 2itv, the phase angle f, by which the emission modulation is shifted from the excitation modulation, is related to the fluorescence lifetime by ... 

The output tracer signal is attenuated and shows a phase shift, but there is no change in frequency. All solutions to Equations (15.45) and (15.46) have these characteristics. Differentiate Pm tot — tot co tot to show that the maximum deviation occurs when cot tot =—tot. Some trigonometry then shows that the maximum deviation is... 

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