High-bandwidth demodulation in MF-AFM: a Kalman filtering approach

Emerging multifrequency atomic force microscopy (MF-AFM) methods rely on coherent demodulation of the cantilever deflection signal at multiple frequencies. These measurements are needed in order to close the z-axis feedback loop and to acquire complementary information on the tip-sample interaction. While the common method is to use a lock-in amplifier capable of recovering low-level signals from noisy backgrounds, its performance is ultimately bounded by the bandwidth of low-pass filters. In light of the demand for constantly increasing imaging speeds while providing multifrequency flexibility, we propose to estimate the in-phase and quadrature components with a linear time-varying Kalman filter. The chosen representation allows for an efficient high-bandwidth implementation on a field programmable gate array. Tracking bandwidth and noise performance are verified experimentally, and trimodal AFM results on a two-component polymer sample highlight the applicability of the proposed method for MF-AFM.