Digital lock-in amplifiers

Figure 8.25 Absolute value of transfer function for digital lock-in amplifier as a function of normalized frequency and number of integration cycles.

For instance, when measuring luminescence typically at 200 frequencies between 10 Hz and 100 kHz, the ratio d between consecutive frequencies is ca. 1.0471. The frequency generation is easily accomplished using a modem digital lock-in amplifier, which has a built-in programmable frequency synthesizer. 

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. 

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. 

In this scheme, analog Fourier decomposition of the signal using lock-in amplifiers becomes impractical and a digital fast Fourier transformation is preferred. Such an analysis would lead to 22 linear combinations of the 16 Mueller matrix components of the sample. This is an overspecified system, and the extra information can be used as either an internal check of consistency or discarded. It is important to make proper choices of the angular velocities, and D2. Clearly, these frequencies cannot be simple multiplies of one... 

Recently developed digital signal-processing (DSP) lock-in amplifiers open new possibilities in measurement. It is possible, among others, to simultaneously measure two different frequency components of the input signal. 

In principle, Fourier transformation allows you to be much more specific, and to pick out or reject, e.g., a single frequency or a specific set of frequencies. For example, one can tune in to a particular frequency (the digital equivalent of a sharply tuned filter, or of a lock-in amplifier, see section 8.4), or selectively remove noise at, say, 60,120, and 180 Hz, while leaving signals at other frequencies unaffected. However, this requires that the selected frequency or frequencies precisely coincide with those used in the Fourier transformation, in order to avoid the so-called leakage to be described in section 7.4. 

Figure 9- 1.1b is a schematic of a typical double-beam-intime instrument. The beam from the hollow-cathode source is split by a mirrored chopper, one half passing through Ihe tlame and the other half around it. The two beams are then recombined by a half-silvered mirror and passed into a Czerny-Turner grating monochromator a photomultiplier tube serves as Ihe transducer. The output from the latter is the input to a lock-in amplifier that is synchronized with the chopper drive. The ratio between the reference and sample signal is then amplified and fed to the readout, which may be a digital meter or a computer. 

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