Lyapunov Estimator for High-Speed Demodulation in Dynamic Mode Atomic Force Microscopy

Abstract

In dynamic mode atomic force microscopy (AFM), the imaging bandwidth is governed by the slowest component in the open-loop chain consisting of the vertical actuator, cantilever, and demodulator. While the common demodulation method is to use a lock-in amplifier (LIA), its performance is ultimately bounded by the bandwidth of the postmixing low-pass filters. This brief proposes an amplitude and phase estimation method based on a strictly positive real Lyapunov design approach. The estimator is designed to be of low complexity while allowing for high bandwidth. In addition, suitable gains for high performance are suggested such that no tuning is necessary. The Lyapunov estimator is experimentally implemented for amplitude demodulation and shown to surpass the LIA in terms of tracking bandwidth and noise performance. High-speed AFM images are presented to corroborate the results.