Noncontact Subnanometer Resolution Displacement Sensing With Wide Bandwidth Based on Squeeze Film Damping Effect

Displacement sensors with subnanometer resolution and wide bandwidth are essential for micro–nano manufacturing, measurement, and motion control systems. However, the current displacement sensing methods have various limitations, such as requirements for the optical or electrical properties of the target sample, the need to be in contact with the sample surface, and the contradiction between the accuracy and bandwidth. This study proposes a displacement sensing method with wide bandwidth and subnanometer resolution, which is not only insensitive to the material properties of the measured sample but it is also not in contact with the sample. The squeeze film damping (SFD) force exerted on the resonant microcantilever plate is sensitive to the plate–sample displacement (film height), which can be converted into the cantilever vibration amplitude. The resulting amplitude variations can be measured by the optical lever method. Herein, the mathematical model of the resonant cantilever and SFD force is established. The effects of driving amplitude and frequency on displacement sensing are studied. Evidently, increasing the driving amplitude and using a resonant driving frequency can improve sensing sensitivity and resolution. Experiments reveal that the proposed method is insensitive to sample material changes, has a resolution of 0.21 nm [standard deviation (STD)], a range of
$5 \mu \text{m}$
, a bandwidth of about 515 Hz, and can be utilized in gantry vibration measurement.