A metrological approach for the calibration of force transducers with interferometric readout

We introduce an experimental calibration method for force transducers with interferometric readout. The head of the transducer is compressed on the pan of a weighing scale until the first maximum of interference is reached. An optomechanical feedback loop makes sure that the force applied remains constant during the integration time of the weighing scale. At the end of the integration time, the transducer is forced to move to the next maximum of interference, where it is again locked into position to allow the user to read the corresponding increase in weight on the scale. Repeating a similar procedure for a series of consecutive maximum-to-maximum steps, one can finally plot the weight indicated by the scale as a function of the displacement of the head of the transducer, and, from there, extract its spring constant. The method relies only on measurements of weights and laser wavelengths, both of which can be, in principle, referred to metrological standards.