Page 122 - Photodetection and Measurement - Maximizing Performance in Optical Systems

System Noise and Synchronous Detection

System Noise and Synchronous Detection 115

reference and input. The sum frequency f ref + f input is filtered out by the lock-in while
f ref - f input is shown on the display (after filtering at the chosen time constant).
Now readjust the frequency to be a few hertz from the reference. The display will
show the detected amplitude, oscillating fast between positive and negative extremes.
Switch the display to show magnitude (R) of magnitude/phase (Rq) mode. The display
should stop oscillating, and give a more or less constant value. The two 90°-phased
detectors are now added as sums of squares, giving the amplitude with the phase vari-
ation removed. Now increase TC to 1s, and the signal should drop almost to nothing.
This is because the acceptance bandwidth of the synchronous filter has become
narrower (about ±0.16Hz) than the separation between reference and input. Adjust
the frequency carefully to line them up, and the signal appears again.
Now set TC = 10ms, and adjust the input frequency to give the peak detected ampli-
tude in Rq mode. Note the amplitude, and then adjust the frequency above and below
the center to reduce the amplitude to half its peak value. In 6db/octave filter mode I
got 7174Hz and 7228Hz (54Hz), and with the 12dB/octave filter I obtained 7186Hz,
7215Hz (29Hz). This gives an idea of the detection bandwidth of the synchronous
filter in the two modes. Clearly, the 12db/octave setting is about half as wide as the
single-pole response.
Go back to the TC = 1ms setting and XY display mode with an input frequency
about 15Hz above or below the reference. The amplitude display needle should be
vibrating rapidly around the zero reading. It is clearly not able to follow the 15Hz
beat signal with full amplitude, but at least you can see it trying! (With a digital display
all you get is fuzz.) If your lock-in has a connector output for the display voltage, you
should be able to see the sinusoidal beat signal on a scope, which doesn’t have any
problem following the 15Hz beat. Offset by 50Hz, and the scope will show the 50Hz
beat, unless of course you attenuate it by increasing the filter time constant to 10ms
or longer.
Depending on what equipment you have, these experiments can be done in differ-
ent ways. Instead of the external variable oscillator, you may be able to use the inter-
nal reference oscillator, if the lock-in has one. If not, two watch-crystal oscillators of
nominally identical frequencies can be used. You can usually pull one of the oscilla-
tors either by loading with a small (100pF) variable capacitor or applying brief jabs
of a soldering iron to the crystal package to sweep one past the other with tempera-
ture tuning! Just be careful that there is no mutual electrical interference between
the two generators, or they might lock together. All these experiments make great
hands-on class demonstrations.

5.8 Spread Spectrum References
You may have noticed that in Fig. 5.14, one of the waveforms W(7,16) is not
“square,” but is nevertheless applied to a binary multiplier in Fig. 5.15. This
suggests that there is nothing sacred about sine waves or single-frequency
square waves and multipliers. More generalized source modulation and syn-
chronous detection with an identical waveform works, and can be useful. In Fig.
5.6 we saw the importance of being able to choose our modulation frequency to
avoid strong interfering signals. But what if the locations of these are unknown,
or change from day to day, or are even being actively adjusted to coincide with
your modulation and hence ruin your experiment. This is a scenario of “elec-

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