Response quadrature

Figure 1-13 shows an example of a train of lock-in amplifiers used to demodulate DIRLD signals obtained with a spectrometer described in Figure 1-12. In order to obtain the time-dependent dynamic absorbance and DIRLD responses, quadrature lock-in amplifiers are used. These devices monitor signals both in phase and 90° out of phase (quadrature) with the sinusoidal strain reference signal. The monochromator is scanned one wavelength at a time through the spectrum. Data are collected on six separate channels (e.g., in-phase and quadrature dynamic dichroism, in-phase and quadrature dynamic absorbance, static dichroism, and normal IR absorbance)...

Phase cycling is widely employed in multipulse NMR experiments. It is also required in quadrature detection. Phase cycling is used to prevent the introduction of constant voltage generated by the electronics into the signal of the sample, to suppress artifact peaks, to correct pulse imperfections, and to select particular responses in 2D or multiple-quantum spectra. 

Response (FIR) filters have been implemented in the FPGA. Finally, the in-phase and quadrature signal pair is stored in a memory, also built inside the FPGA, according to the acquisition phase indicated by the pulse programmer. 

Fig. 11.2 Universal response curve for a two port interferometer as a function of phase offset. The positions of quadrature occur at the points of largest slopes where phase to intensity transduction is largest...

The universal interferometric response of a balanced two-port interferometer is shown in Fig. 11.2 as a function of the fixed phase offset between the two waves. The maximum slope of the intensity curve occurs when the fixed phase offset between the waves is an odd integer of = re/2. These conditions of maximum slope are called the conditions of phase quadrature. There are two quadrature conditions per cycle, with opposite slopes and hence opposite signed responses to modulated phase. These are the positions of maximum phase-to-intensity transduction and are the operating points for interferometric detection of protein or DNA on spinning discs. 

Fig. 23. The in-phase (/LF) an< quadrature (Qlf ) component of the demodulation response pertaining to the tris-oxalato Fe(III)/ tris-oxalato Fe(II) electrode reaction at the dropping mercury electrode in aqueous IMK2C2O4 + 0.05 M H2C2O4 solution. High frequency 100 kHz low frequency 170 Hz, = 0.21 A cm-2 Fe(III) concentration 1 mM. The thin solid lines represent the demodulation response in the absence of the redox couple [72].

The two copies of the COSY spectrum and the fi = 0 responses can all be separated without phase cycling if one is prepared to sacrifice digital resolution by increasing the fi-spectral width. The following spectmm was collected without phase cycling, with quadrature detection OFF,... 

In series with Csc are the capacitances associated with the Helmholtz layer and the electrolyte. It is easy to show that these are expected to be much larger under the circumstances that eqn. (36) is valid, and so the quadrature response of the semiconductor may be used to calculate a capacitance, Cobs, that is closely approximated by Csc. From eqn. (39), it is seen that... 

The criteria for SHAC voltammograms to yield reversible potentials are that the zero-current crossing potentials must be both frequency- and phase-independent. In practice one measures the in phase (/) and quadrature (Q) components of the second harmonic a.c. current by means of a phase-sensitive detector or lock-in amplifier. The response is illustrated in Figs 10-12 obtained during measurements on the oxidation of 9,10-diphenylanthracene (DPA) in acetonitrile (Fig. 10) and in acetonitrile containing pyridine (Figs... 

In the second method for phase separation it is necessary to apply 90° phase-shifted phase selection pulses between the evolution and detection periods and to measure the two quadrature components which evolve after the application of these pulses. The normal [S(rj,t2)] and shifted [5(fi,f2)] responses are then combined according to equation (8) to give the pure absorption two-dimensional spectrum. It will be noticed that the main computational difference between the two methods is that in the first the normal and changed signals are combined prior to transformation, whereas in the second the combination is done after transformation. It seems likely that techniques of this type will become widely used for the production of high quality two-dimensional spectra in molecules of real chemical interest. 

Impedance spectra are usually measured with automated frequency-response analysers using single sine wave applied fields. Measured data are resolved into real (in-phase) and imaginary (out of phase) or quadrature constituents. The frequency is usually swept over a certain range, either linearly or logarithmically. The measurements can also be done with sols between the electrodes, to study the dielectric response of colloids. We will return to that in sec. 4.5d. For general information on such techniques and their interpretation, see ref. 

This equation is fundamental for the explanation of many imaging methods. It describes the linear part of the complex transverse magnetization response in the presence of arbitrary magnetic-field gradient modulation G(t) and quadrature rf excitation jc(r). When the excitation is a delta pulse x(t) = Sit), the response yi ( ) is given by the kernel (cf. Section 4.2.1) of the outer integral in (5.4.7),... 

Although complex notation is often used for the sake of convenience, the electric field, E(r, t), is a classically measurable property and thus must be real, as given in Eq. (2.3). Its direct measurement at optical frequencies, however, is not practicable because of the slow response time of electric field detectors [16]. Instead, intensity (quadrature) detectors using the photoelectric effect are usually employed to record the cycle-averaged energy flux, (c/8Tr) E(r, r) [17], or photons. 

It is not heretical to consider the electromagnetic vacuum as a physical system. In fact, it manifests some physical properties and is responsible for a number of important effects. For example, the field amplitudes continue to oscillate in the vacuum state. These zero-point oscillations cause the spontaneous emission [1], the natural linebreadth [5], the Lamb shift [6], the Casimir force between conductors [7], and the quantum beats [8]. It is also possible to generate quantum states of electromagnetic field in which the amplitude fluctuations are reduced below the symmetric quantum limit of zero-point oscillations in one quadrature component [9]. 

After a single excitation pulse or a series of pulses the signal detection period begins where the response of the spin system to the pulse sequence is recorded. The basic configuration for quadrature detection [2.32, 2.33] is two detectors in the x,y-plane with a 90° phase difference where each detector may be assigned to the x- or y-axis. As illustrated in Fig. 2.6 there are two detection methods, in simultaneous detection both detectors are sampled at the same time whilst in sequential detection the detectors are sampled alternatively. 

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