State estimation for high-speed multifrequency atomic force microscopy

A fundamental component in the z-axis feedback loop of an atomic force microscope (AFM) operated in dynamic mode is the lock-in amplifier to obtain amplitude and phase of the high-frequency cantilever deflection signal. While this narrowband demodulation technique is capable of filtering noise far away from the carrier and modulation frequency, its performance is ultimately bounded by the bandwidth of its low-pass filter which is employed to suppress the frequency component at twice the carrier frequency. Moreover, multiple eigenmodes and higher harmonics are used for imaging in modern multifrequency AFMs, which necessitates multiple lock-in amplifiers to recover the respective amplitude and phase information. We propose to estimate amplitude and phase of multiple frequency components with a linear time-varying Kalman filter which allows for an efficient implementation on a Field Programmable Gate Array (FPGA). While experimental results for the single mode case have already proven to increase the imaging bandwidth in tapping-mode AFM, multifrequency simulations promise further improvement in imaging flexibility.