Analysis of the trade-off between resolution and bandwidth for a nanoforce sensor based on diamagnetic levitation

Nanoforce sensors based on passive diamagnetic levitation with a macroscopic seismic mass are a possible alternative to classical Atomic Force Microscopes when the force bandwidth to be measured is limited to a few Hertz. When an external unknown force is applied to the levitating seismic mass, this one acts as a transducer that converts this unknown input into a displacement that is the measured output signal. Because the inertia effect due to the mass of such macroscopic transducers can not be neglected for time-varying force measurement, it is necessary to deconvolve the displacement to correctly estimate the unknown input force. A deconvolution approach based on a Kalman filter and controlled by a scalar parameter has been recently proposed. The adjustment of this parameter leads to a trade-off that is analysed in this paper in term of resolution and bandwidth of the estimated force. Associated tools to help the end-user to set this parameter are also described.