  Displacement calibration of nanomechanical plate resonators presents a
challenging task. Large nanomechanical resonator thickness reduces the
amplitude of the resonator motion due to its increased spring constant and
mass, and its unique reflectance. Here, we show that the plate thickness,
resonator gap height, and motional amplitude of circular and elliptical drum
resonators, can be determined in-situ by exploiting the fundamental
interference phenomenon in Fabry-Perot cavities. The proposed calibration
scheme uses optical contrasts to uncover thickness and spacer height profiles,
and reuse the results to convert the photodetector signal to the displacement
of drumheads that are electromotively driven in their linear regime. Calibrated
frequency response and spatial mode maps enable extraction of the modal radius,
effective mass, effective driving force, and Young's elastic modulus of the
drumhead material. This scheme is applicable to any configuration of
Fabry-Perot cavities, including plate and membrane resonators.
