Page 105 - Photodetection and Measurement - Maximizing Performance in Optical Systems

System Noise and Synchronous Detection

98 Chapter Five

magnitude of S cos(y). Hence the single-channel synchronous detector can be
used either to determine magnitude S (if the phase is known) or phase y (if the
magnitude is known), but not both simultaneously.
Figure 5.3d shows the response of the synchronous detector to a constant
level input. The signal is chopped to give a bipolar amplitude signal whose
average value is zero. This zero DC response simply corresponds to the zero of
response stretching from 0Hz to the start of the passband around f mod in the
frequency domain of Fig. 5.2. In Fig. 5.3e a synchronous signal is shown added
to the DC level. Once again, the DC component has been removed by the chop-
ping process, with only a finite negative average from the synchronous AC
component.
Therefore it is very important that the phase difference between reference
and signal has the value we need. With low-noise signals this can be achieved
by adjusting the phase for a maximum postfilter signal. However, close to the
maximum, the output varies only slowly with phase, like the cosine function
around zero angle. Hence it is usually better to adjust the phase for a minimum
filtered output signal, which can be much more precise, afterward shifting the
phase accurately by 90°.
A common feature of synchronous measurement systems is the provision of
two or more separate detection channels. If we use two multipliers driven by
90° phase-shifted signals, then the two demodulated outputs will vary as the
sine and cosine of the phase angles (Fig. 5.4). Each measurement channel
detects the projection of the rotating phasor R onto either the C or S axis. The
2 1/2
2
magnitude of the phasor can be calculated from R = (S + C ) . Three-phase
and higher-order systems can also be used and offer some advantages in terms
of the symmetry of the two resolved channels.
5.4 What Frequency Should We Use?
It is clear that the modulation frequency should if possible be above the 500Hz
region of so much man-made and natural interference, but the choice is not
arbitrary, as noise spectra are not flat even above 500Hz. One of the most
annoying and ubiquitous sources of optical interference is the fluorescent light-
ing used in most laboratory environments. These sources are more serious than
might at first be thought. Although the lights are driven by a more or less sinu-
soidal voltage source at 50/60Hz, the discharge process leads to a light output
that is a distorted, rectified sine wave. The frequency spectrum of this wave-
form exhibits strong components at harmonics of the 50/60Hz drive, which can
often be seen in detected light out to several kilohertz. Figure 5.5 shows a spec-
tral analysis of the output of a 10-kHz bandwidth transimpedance receiver with
interfering fluorescent room light. This was a system designed to measure low
levels of scattered light in an open environment. Despite optical filtration with
a 25-nm bandwidth interference filter to remove other nonsignal wavelengths
and an angular acceptance at the detector of only 5°, significant harmonics of
the 100Hz rectified line frequency are visible well beyond 2.5kHz.

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