22nd Day of Christmas: Lock-in Amplifier

This Advent during the 24 days leading up to Christmas I thought it would be fun to have a quick introduction of scientific apparatus, in particular tools used in atomic physics research. This is a way to say thanks to their hard work for our research, and a look at how many things are really needed to make a laboratory work!

Lock-in Amplifier

In atomic physics a lot of measurements involve very tiny data signals on a big background signal and likely big noise too. We have to be clever about how to set up the experiment so we can get the most out of our data signals. When we have a variable background that we control, we can use a lock-in amplifier to remove that base and amplify our measurement signal.

This method of signal separation works if we have some kind of a reference signal that has an effect on the measurement. This can be for example a signal generator¬†that turns a laser beam on/off at a specific pace (I’ll give some more examples below). Then the experimental signal measured will depend on whether the laser is on or off (are we interacting with the atoms or not), thus will depend on the pace of switching. Then we can feed the experimental signal and the reference of the signal generator to the lock-in amplifier, as shown on the left of the block diagram. The signal input is amplified, filtered around our frequency of interest, and fed into one input of a mixer. The reference is sensed, and the signal’s relative phase can be adjusted by the phase shifter before fed into the second input of the mixer. The mixer then returns a signal that contains the sum and the difference of the two inputs. Since the measurement signal and the reference should change at about the same pace as they are causally connected, their difference signal has a frequency close to zero, while their sum is at a high frequency. Then we apply a low-pass filter to just get the difference signal, effectively removing the reference signal from the measurement, leaving behind the experiment’s effect that we were looking for! This is then amplified and output.

Lock-in amplifier block diagram
Lock-in amplifier block diagram

These procedures have a number of settings, starting from using external or internal reference signal, the reference signal’s type (sine wave, square wave, …), the amplification of the different stages, the phase shift, the low-pass filter’s bandwidth, and more. Thus these devices can have quite the dashboard, with a lot of buttons and knobs, though the mental model of their operation is quite straightforward.

A lock-in amplifier
A lock-in amplifier

This procedure outlined on the block diagram above can be realized in an analog circuit, though now a lot of these devices use partly or wholly digital circuits. In some cases, now the whole device can be done in software too, for example in gnuradio, which is a quite powerful processing tool, being able to recreate a bunch of equipment like this purely in software.

For the input signal modulation, there are a lot of different options. For example, switching the beam on/off with an acousto-optic modulator, adjusting the beam power or polarization with an electro-optic modulator, using liquid crystals, or a beam copper: a wheel that has holes arranged periodically, and it transmits and blocks beams as they travel. It all depends on what makes the most sense for the given experiment.

Some care needs to be taken, as often the obvious modulation technique is not what gives the right signal. For example, when a laser beam is interacting with the atoms and the transmitted beam power needs to be measured, switching the beam on/off is not going to improve on anything. On the other hand, switching the frequency of the beam from being on-resonance and interacting with the atoms, to off-resonance when it travels through unperturbed will give the right kind of signal. When checking the interaction of two laser beams, there one can measure the result by switching one of them on/off. Also when measuring not the laser beam itself, but a secondary signal, such as scattered light, on/off sort of modulation can work. This also shows that it needs a lot of thinking to know what exactly is happening in the experiment, “what is it that we really measure?”

Lock-in amplifiers can do a number of other measurements, though this signal-recovery is the most commonly used ¬†function in the labs I’ve been, and there they are very useful equipment indeed.

Further info:

If you liked this, come back tomorrow for another apparatus! And send this link to someone who you think would be interested! :)