The Lock-in Amplifier

As was noted before, several techniques based on the electronic analysis of signals have been developed to increase the signal-to-noise ratio without requiring large measurement times. In this section, we will focus our attention on the lock-in amplifier and in the next section on photon counter systems. 

Most common lock-in amplifiers can be operated at frequencies ranging from a few Hz up to 100 kHz. This fact is important in analyzing the temporal evolution of optical signals for example, fluorescence decay time measurements. Although this particular application of lock-in amplifiers is beyond the scope of this section, it is instructive to mention that this can be done by tuning the relative phase (the time delay) between the signal intensity and the reference signal provided by the chopper. 

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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 ... 

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. 

The output of the lock-in amplifier is input to a sample-and-hold amplifier or directly to the analog-to-digital converter. This signal is converted to a digital and thus machine-readable form. 

Fig. 1. The relationship of the sample and the various pieces of equipment necessary to automatically measure the current, and the parallel and perpendicular voltages. A standard contact configuration is shown in the main drawing, whereas a van der Pauw configuration is shown in the inset. The lock-in amplifier is used in ac photoconductivity measurements. [From Look and Farmer (1981), copyright by The Institute of Physics.]...

To minimize the current flow through the sample, an ac four-point probe technique was used to monitor the conductivity of the sample with a lock-in amplifier (Stanford Research Systems, model SR 830 DSP). The lock-in amplifier enabled us to measure very low voltages without noise problems. 

The prism at the outlet of the laser serves to separate the laser emission of the gas fluorescence and allows for a clean excitation of the sample. For excitation using solid-state lasers, this element is dispensable. The lens (element 5) collects the fluorescent signal and focuses on the aperture of the monochromator. The filter is used to eliminate excitation that is spread over the surface of the sample. The optical chopper serves to modulate the light at a defined frequency, which serves as reference for the lock-in amplifier. A data acquisition system controls the pace of the monochromator and reads the signal of the lock-in, generating the sample s emission spectrum. 

This equation shows that the alternating capacitance of different frequencies corresponds to each order of the nonlinear dielectric constant. Signals corresponding to 333, 3333 and 33333 were obtained by setting the reference signal of the lock-in amplifier in Figure 16.1 to frequency cop, 2 ujp and 3 uip of the applied electric field, respectively. 

The control of the monochromator stepping motor, the PEM retardation level, and the lock-in amplifiers, are carried out by a standard IBM-compatible personal computer. It communicates with the PAR lock-in amplifier via a 1200 baud serial link,... 

Similarly, the 100 kHz component of the photocurrent detected by the lock-in amplifier is given as... 

When an analyzer is inserted into the optical path, from a matrix calculation of A D S M P /0, the 50 kHz signal detected by the lock-in amplifier can be expressed as... 

Measurement Setup. The buffer capacity measuring setup is shown in Fig. 14. Since the current source is not floating, the grounded counter electrode works as a reference electrode as well. In this case, the current at low frequency will cause a certain polarization in spite of the very large area of the counter electrode. This polarization potential of the counter electrode will be superposed on the output of the ISFET amplifier and interfere with the measurement. Therefore an additional saturated calomel electrode (denoted S.C.E. in Fig. 14) is used to measure separately the polarization potential, and the signal is sent to the lock-in amplifier for subtraction. The measured current and voltage are presented in effective (root-mean-square or RMS) values. 

A lock-in amplifier uses phase-sensitive detection, in conjunction with a potentio-stat, to measure the complex impedance. The algorithm is fimdamentally different from that of the Fourier-based analyzers. These analyzers perform an assessment of the Fourier coefficients of the input and output signals, whereas the lock-in amplifier measures the amplitudes of the two signals and the phase angle of each signal with respect to some reference signal. Thus, the impedance is measured in polar, rather than Cartesian, coordinates. 

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