Demodulation method

Mishuk et a/.675,676 have applied the modified amplitude demodulation method to electrochemically polished pc-Bi in aqueous NaF solution. The curves of the real component of the nonlinear impedance Z" as a function of the electrode potential, unlike pc-Cd and pc-Pb, intersect for various cNaF at E - -0.62 V (SCE),674 i.e., at Ea=0 for pc-Bi, as obtained by impedance.666-672 The different behavior of pc-Bi from pc-Cd and pc-Pb at a > 0 has been explained by the semimetallic nature of pc-Bi electrodes. A comparison of inner-layer nonlinear parameter values for Hg, Cd, and Bi electrodes at a < 0 shows that the electrical double-layer structure at negative charges is independent of the metal.675,676... 

The reduction of Cd(II) ions on DME was also investigated in 1 M perchlorate, fluoride and chloride solutions using dc, ac admittance, and demodulation methods [27]. It was found that in the perchlorate supporting electrolyte, the reduction mechanism is also CEE, and that the rate constant of the chemical step is quite close to the value characteristic for fluoride solutions. The theories available at present could not be applied to the Cd(II) reduction in chloride solution because of the inapplicability of the Randles equivalent circuit. 

Also in the demodulation method, controlled-current perturbation is applied, which means that here, too, eqn. (84) is to be used to substitute El by a term containing the squared amplitude of the current density,. ... 

In studying a system by a nonlinear impedance method, use is made of the system s nonlinear characteristics. A variant of the nonlinear impedance method called the amplitude demodulation method was first applied in the electrochemistry of semiconductors, in particular to diamond electrodes, in [83] (see the quoted paper for the theory of the method and the experimental set-up). A perturbing current signal of a high frequency oo, modulated in amplitude at a low frequency 2, is applied to electrochemical cell the demodulated low-frequency voltage signal is to be measured at the frequency 2. In accordance with the theory of the method [83], under the condition of formation of a depletion layer in a semiconductor electrode, the in-phase component of the cell response Re h is inversely proportional to d(C 2)/dE. Hence, for the acceptor concentration in the semiconductor we have [compare Eq. (1)] ... 

Excitation with continuous lighi the phase and demodulation method Principles... 

DIRECT DEMODULATION METHOD AND ITS APPLICATION TO HARD X-RAY IMAGING... 

The direct demodulation algorithm provides a general approach to handle a large variety of image restoration or reconstruction problems. Computer simulations and analysis results for COS-B and CGRO 7-ray data show that in comparison with traditional techniques, e.g. maximum entropy method, cross-correlation deconvolution or likelihood approach, the direct demodulation method has high sensitivity, high resolution ability and capability to effectively reduce the effect of statistical fluctuations and noise in data and to simultaneously restore both the extended and discrete features in the object. 

The direct demodulation method of producing images does not rely on a position sensitive detector. Prom the point of view of the direct approach restoring N objective intensities from M image intensities observed with a position sensitive detector and that from M modidated counts measured by scan observation with a simple collimated counter are the same mathematical problem extract N undetermined quantities from M linear equations. 

Allowing the use of different demodulation methods or raw signal analysis ... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

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. 

As we have seen in Section 9.5.3, in the case of resistance thermometry, the signal produced by a low-temperature thermometer is very low (microvolt range). Low-pass filters are not sufficient to narrow the detection bandwidth in order to get a suitable signal to noise ratio (S/N). Bandpass filters are needed. The most commonly used method is the synchronous demodulation, usually simply called lock-in technique, as shown in the block diagram of Fig. 10.7. 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

The decay parameters [a (X) and rj are recovered from the experimentally measured phase shift and demodulation factor by the method of non-linear least squares (24,25). The goodness-of-fit between the assumed model (c subscript) and the experimentally measured (m subscript) data is determined by the chi-squared (x2) function ... 

One of the most convenient methods for determining lifetime, as well as one of the best suited to low-cost applications, involves using frequency-modulated excitation (49). Upon excitation by a frequency modulated source, the finite lifetime of the emitter causes a phase-shift and demodulation of the emission relative to the excitation waveform as shown schematically in Fig. 6. 

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