Lock-in techniques

As with alternating electrical currents, phase-sensitive measurements are also possible with microwave radiation. The easiest method consists of measuring phase-shifted microwave signals via a lock-in technique by modulating the electrode potential. Such a technique, which measures the phase shift between the potential and the microwave signal, will give specific (e.g., kinetic) information on the system (see later discussion). However, it should not be taken as the equivalent of impedance measurements with microwaves. As in electrochemical impedance measurements,... 

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. 

For capacity measurements, several techniques are applicable. Impedance spectroscopy, lock-in technique or pulse measurements can be used, and the advantages and disadvantages of the various techniques are the same as for room temperature measurements. An important factor is the temperature dependent time constant of the system which shifts e.g. the capacitive branch in an impedance-frequency diagram with decreasing temperature to lower frequencies. Comparable changes with temperature are also observed in the potential transients due to galvanostatic pulses. 

The charge distribution at metal electrode-electrolyte interfaces for liquid and frozen electrolytes has been investigated through capacity measurements using the lock-in technique and impedance spectroscopy. Before we discuss some of the important results, let us briefly consider some properties of the electrolyte in its liquid and frozen state. 

In parallel, Kasumov et al. [60] reported ohmic behavior of the resistance of A-DNA molecules deposited on a mica surface and stretched between rhenium-carbon electrodes (see Fig. 6). This behavior was measured at temperatures ranging from room temperature down to 1 K. Below 1 K a particularly unexpected result was observed proximity-induced superconductivity. The resistance was measured directly with a lock-in technique and no current-voltage curves were presented. This surprising proximity-induced supercon-... 

Before closing our discussion of transient phenomena it should be remarked that the emission transients are sometimes nonexponential, due to electric field effects (Makram-Ebeid, 1980), nonuniform doping, and other causes. When this problem exists, the standard boxcar or lock-in techniques (Fig. 9c) will give spurious results (White et al., 1979). Thus, the transients themselves should always be examined before any data are taken. Methods of dealing with nonexponential behavior are discussed elsewhere (Kirchner et al., 1981). 

Generally there are two different methods for measuring excited state spectra in the ms time regime. Typically, IR PIA spectra are not recorded with the lock-in technique but by referencing several hundred accumulated single beam spectra (by FTIR spectrometer) under illumination and in the dark, while UV/VIS PIA uses a lock-in detector to filter out signal changes due to photoexcitation. 

With lock-in techniques, small currents are measured with a very high S/N-ratio, so that the current density in the tip zone can be minimised. 

Pd(2-thpy)2 is dissolved in an n-octane matrix and is excited at low temperature (T < 2 K) by a c.w. source (non-pulsed, e.g. at A = 330 nm [61]). Additionally, microwave irradiation is applied and scanned in frequency. The microwave radiation can cause transitions between the triplet sublevels in the case of resonance, and thus, the previously different and non-thermalized steady state populations of the substates are usually altered. Under suitable conditions (see below) a change of the phosphorescence intensity will result due to microwave perturbation. Usually, this effect is very weak. Therefore, microwave pulse trains are applied, for example, with a repetition rate of 150 Hz. Thus, one can monitor the microwave-induced intensity changes by a phase-sensitive lock-in technique [90]. 

The transient triplet absorption for the common polyfluorene PF2/6 is shown in Fig. 9, the spectra was measured by quasi-cw photoinduced absorption. This lock-in technique allows the absorption of long-lived states to be measured with high sensitivity. It is possible to estimate the lifetime of the state using the quasi-cw experiment [46] however, more accurate methods in-... 

Because the capacitance of the wire connecting the sample to the outside world could not be measured precisely, we can only estimate the AC voltage at the source to be 0.5 jxV. We have also used the standard Lock-in technique with a low-frequency signal (7 MHz, 10 /.iV RMS) and observed similar interference patterns however, the measurement lasted much longer and was prone to sample s instability. 

In principle, there is no reason why only the time-independent response should be extracted from the total signal by addition of successive scans with unsynchronized field modulation. Because the time dependence is known for each voxel, the signal can be extracted for any voxel by a lock-in technique, where the reference function is given by the gradient modulation for the particular voxel. This can be executed simultaneously. 

Fig. 7. Diagram of a grating spectrometer with the optical components (Czerny-Turner mount and the electronics with the usual lock-in technique...

The disadvantage of the lock-in technique is that it retains contributions of the harmonic frequencies (2n + l)C0ref if they are present in the input signal (e.g., harmonics, noise), although their influence is attenuated by 1/3, 1/5, 1/7, etc. with increasing n. For example, when the frequency in Eq. (29) is three times the reference frequency in Eq. (30), the average signal obtained... 

For all nc-AFM measurements, a Kelvin probe force microscopy (KPFM) feedback controller was additionally activated for simultaneous topographic imaging [19]. In order to compensate for electrically or electronically induced artefacts, an ac voltage was applied between tip and sample and used in combination with lock-in techniques and a feedback controller to compensate for the contact potential difference (CPD) between tip and sample. With this method, nc-AFM is assiued to image the sample topography without any artefacts originating from different local surface potentials [20]. 

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