A Kalman filter for amplitude estimation in high-speed dynamic mode atomic force microscopy

A fundamental challenge in dynamic mode atomic force microscopy (AFM) is the estimation of the cantilever oscillation amplitude from the deflection signal, which might be distorted by noise and/or high-frequency components. When the cantilever is excited at resonance, its deflection is typically obtained via narrow-band demodulation using a lock-in amplifier (LIA). However, the bandwidth of this measurement technique is ultimately bounded by the low-pass filter, which must be employed after demodulation to attenuate the component at twice the carrier frequency. Furthermore, to measure the amplitude of multiple frequency components, such as higher eigenmodes and/or higher harmonics in multifrequency AFM, multiple LIAs must be employed. In this paper, the authors propose the estimation of amplitude and phase using a linear time-varying Kalman filter that is easily extended to multiple frequencies. Experimental results are obtained using square-modulated sine waves and closed-loop AFM scans, verifying the performance of the proposed Kalman filter.