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As you do, I was watching a video about levelling granite surface plates used in precision machine shops and labs. They're ground and lapped to a high level of flatness (I think AA plates are flat to within around 0.005mm) and a key tool for this process is a set of electronic differential levels like these.

These devices are used to measure the relative inclination of different parts of the plate and the paths are integrated to give a map of global roughness across the plate. The manufacturers of these levels claim that they can measure .1 arcseconds repeatably. If I did the maths right, across a 1m surface plate that corresponds to vertical displacement of 4.8e-7m.

My question is, how do these things work? I'm not electronic engineer but I assume each unit contains a (hinged or flexible) pendulum ~0.1m in length with capacitive plates on both sides charged from an AC source. As the pendulum flexes or rotates around the hinge, the relative change in capacitance between the plates on either side would result in a voltage difference between the two capacitors that you could then feed into an amplifier to measure the change in pendulum displacement and thus the change in the orientation of the level. Combine this with another level as shown in the video and you can measure the relative change in orientation between the units.

I've left some of the maths in here for you lot to enjoy working out for yourselves but if anyone has an idea of what the circuitry looks like inside these things, I'd like to know whether my assumption was even close. I've been playing around with a circuit sim to try and build something that can measure very small changes in relative capacitance but alas, I've got nothing that really works.

HJCee
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Obviously you don't need instrumentation like that to make granite surface plates extremely flat (they were made long before such electronics existed). You need three plates and a great deal of patience. See Foundations of Mechanical Accuracy on creating a master flat plane.

I don't know what's in that particular set of instrumentation, but one approach to detecting angles very close to vertical is a pendulum with differential capacitive sensor. It's not all that hard, with reasonable care, to detect fF of capacitive difference and ~10aF RMS is possible with extreme care over a 1Hz bandwidth. You can also make a closed-loop system using actuation to servo the gaps. Think excitation with kHz AC and synchronous demodulation, for starters.

I have an inexpensive mechanical master machinist level that has a resolution of 0.0002"/10" or about 0.005mm in 200mm. Smaller B grade (toolroom) plates are supposed to be about that good in overall flatness.

Spehro Pefhany
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    I learned a few things here, today. Thanks. Also, reading at page 24ff in that reference you offered us, it reminds me of the many, many, many hours I spent with red rouge on glass surfaces polishing them until reaching almost a 20th wave of flatness (struggling for 0.1 fringe or about 1.2E-6 Inch.) – jonk May 18 '21 at 00:19
  • Thanks for your comment and I would second your book recommendation, it's actually how I started on this path! Could you recommend any resources for reading more about differential capacitance sensing? I've done a bit of googling but nothing's jumping out as a good starting point. – HJCee May 18 '21 at 08:57