A technique for continuous measurement of the quality factor of mechanical oscillators

Thermal noise is a limit to precision measurement in many fields. The relationship of the quality factor of mechanical systems to the thermal noise has compelled many researchers to search for materials with low mechanical losses. Typical measurements of mechanical quality factor involve exciting a mechanical resonator and observing the exponential decay of the amplitude under free oscillations. Estimation of the decay time allows one to infer the quality factor. In this article, we describe an alternative technique in which the resonator is forced to oscillate at constant amplitude, and the quality factor is estimated by measuring the drive amplitude required to maintain constant oscillation amplitude. A straightforward method for calibration of the quality factor is presented, along with an analysis of the propagation of measurement uncertainties. Such a technique allows the quality factor to be measured continuously in real time and at constant signal to noise ratio.