Lock-in amplifiers

Figure C3.4.5. Typical scheme of a single-colour pump-probe experiment utilizing lock-in-amplifier detection.

Thus we are challenged by the problem of measuring a small signal against the background of one much stronger. The problem is usually solved by one of two means (a) lock-in-amplifier detection and (b) a boxcar type of detection (to some extent we can include double-input optical multichannel detection in this category). 

A very practical way to infer the contact area was later developed by Carpick et al. [65] and Lantz et al. [66]. In these experiments, a small (up to nanometer) lateral modulation, djc, is applied to the sample, and torsion of the cantilever is monitored with a lock-in amplifier to detect the lateral force response, dF (Fig. 5). In this way, the lateral stiffness, [51], given by... 

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

In a steady state experiment the PIA signal Y is proportional to neq. Measuring the PIA with a lock-in amplifier means exciting the sample with a periodic time-dependent pump photon flux. The latter can be approximated by a square wave that switches between a constant flux and zero photons with a frequency /= 1/r. As shown in Refs. [32] and [33] the PIA signal, measured with a lock-in amplifier Y, shows the same functional dependence on p as ncq in Eq. (9.5). For the monomo-lecular (p-1) and bimolecular (//=2) case the influence of r depends on t, the lifetime of the observed states, as follows ... 

The detection of the AC component allows one to separate the contributions of the faradaic and charging currents. The former is phase shifted 45° relative to the applied sinusoidal potential, while the background component is 90° out of phase. The charging current is thus rejected using a phase-sensitive lock-in amplifier (able to separate the in-phase and out-of-phase current components). As a result, reversible electrode reactions yield a detection limit around 5 x 10 7m. 

Time-resolved microwave conductivity measurements with electrodes in electrochemical cells can conveniently be made with pulsed lasers (e.g., an Nd-YAG laser) using either normal or frequency-doubled radiation. Instead of a lock-in amplifier, a transient recorder is used to detect the pulse-induced microwave reflection. While transient microwave experiments with semiconducting crystals or powders have been performed... 

Measurements of the interfaeial eapacitance (the differential double layer capacity Cdl) have been used widely, the method has been labelled tensammetry [46Bre, 52Bre, 51Dosl, 52Dosl, 63Bre]. Various experimental setups based on arrangements for AC polarography, lock-in-amplifier, impedance measurement etc. have been employed. In all reports evaluated in the lists of data below the authors have apparently taken precautions in order to measure only the value of Cdl-... 

The amplitudes of the signals with frequencies 2co and Iw can easily be measured using lock-in amplifiers. The 2w signal is used as control signal in the feedback electronics so that its value is kept constant. The feedback output is then the topographic image [modulated by e(x,y)]. Since the term B-f(Rlz) in Eq. (17) is kept constant by the feedback, the 1 w signal obtained simultaneously with another lock-in amplifier provides a map of surface... 

The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in amplifier and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148-156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-... 

By the use of tuned or lock-in amplifiers these various harmonics can be detected the results remain advantageously confined to the faradaic current... 

Such measurement provides the magnitude of birefringence, but not its sign. In addition, identical transmission values will be observed for multiple birefringence orders, that is, whenever the optical path difference, dAn, becomes a multiple of X. The main interest of this method arises from its excellent time resolution, below 1 ms, that is readily achieved using a low-power (e.g., 5 mW) continuous-wave laser and a photodiode. If the sample is initially isotropic, it is possible to follow the birefringence order to obtain quantitative results. For improved accuracy, a second (reference) photodiode or a beam chopper and a lock-in amplifier can be used. 

B. Prasad and R. Lai, A capacitative immunosensor measurement system with a lock-in amplifier and potentiostatic control by software. Meas. Sci. Technol. 10,1097—1104 (1999). 

Since the flow system can be made with such a fast response, it becomes important to improve the response of the infrared detector. Use of a liquid-nitrogen-cooled Hg-CdTe detector, with 200 to 1000 Hz chopping and a lock-in amplifier, permits the IR... 

The rest of the detector signal is noise filtered and amplified by a lock-in amplifier. The output of the lock-in amplifier is monitored by an oscilloscope, and recorded as the laser scans across the gas s absorption line. The result is a spectral profile of the gas absorption, impressed on the depth of the locked resonance dip. This is then analyzed using (5.6) to find an experimental effective absorption path length. 

Photomultipliers are generally used to convert the spectral radiation to an electrical current and often phase-sensitive lock-in amplifiers are used to amplify the resulting current. AES and AFS require similar read-out systems because both methods are measuring small signals. The difficulty associated with both these methods is the separation of the signal for the atomic transition of interest from the background radiation emitted by excited molecular species produced in the atom reservoir. AFS phase locks the amplifier detection circuit to the modulation frequency of the spectral source. Modulation of the source is also used in AAS. 

This technique is of high accuracy and is meant to be used in precision measurement instrumentation, for it is inherently insensitive to the DC-offset and the AC-noise in the sinusoidal signal which can be substantially reduced by a great variety of electronic devices ranging from various electronic analogue filters, and digital filters to the most effective lock-in amplifiers. 

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