Watched a Nominal Semidestructor advertising video recently about weighing an eyebrow hair with an analog meter movement. Paul Groke built his scale as follows: he oriented the needle horizontally, connected up an optointerruptor to an opamp that drove the current through the meter movement so as to maintain the optointerruptor half interupted, then dropped his eyelash on the end of the needle. Then the current required to restore the zero position gave a measurement of the weight. Result: 75 micrograms or something. I guess he calibrated it previously.
(The circuit is very simple: the opamp has a resistor from its output to its inverting input, which is connected to the photodiode, and its noninverting input is held at a fixed bias voltage. Then the output is just connected to the meter movement, which is then connected to a resistor to ground. So the current flowing through the resistor keeps the inverting input equal to the bias voltage, and that current is just the photocurrent, so the output is maintained at a voltage above the bias voltage proportional to the photocurrent by the factor of the resistance.)
The nice thing about this kind of Kibble balance is that, except for elastic deformation, the movement is in the same position when it’s balanced as when it’s empty. The magnetic field can be wildly nonuniform over the range of the meter’s movement, but you don’t care because once you’re taking a reading you’re back at the same position; all that’s changed is the strength of the magnetic field (which is hopefully linear in the current) and the bending of the balance beam.
(This version of the ampere balance used to be called a “watt balance” because the power needed to restore the position is what’s proportional to the weight. Kibble proposed it in 01975, and after he died in 02019 they renamed the instrument after him. The full-fledged Kibble balance includes some other refinements and can measure mass by reference to voltage, current, gravity, and speed.)
It occurred to me that a simpler and higher-resolution version of the instrument would use electrical contacts instead of an optointerruptor, ideally gold-plated spherical ball bearings to ensure a well-defined point of contact. Then you include a small ac or noise component in the coil current in order to get intermittent contact and thus a continuously varying feedback signal (“stochastic resonance”). Such electrical contacts can detect movements of nanometers rather than the microns you get from an optointerruptor. At this point thermal deformation and creep of the balance apparatus become more significant sources of error than the sensor.