Higher-harmonic AFM imaging with a high-bandwidth multifrequency Lyapunov filter

Abstract

A major difficulty in multifrequency atomic force microscopy (MF-AFM) is the accurate estimation of amplitude and phase at multiple frequencies for both z-axis feedback and material contrast imaging. A lock-in amplifier is typically chosen for its narrowband response and ease of implementation. However, its bandwidth is limited due to post mixing low-pass filters and multiple are required in parallel for MF-AFM. This paper proposes a multifrequency demodulator in the form of a model-based Lyapunov filter implemented on a Field Programmable Gate Array (FPGA). System modelling and simulations are verified by experimental results demonstrating high tracking bandwidth and off-mode rejection at modelled frequencies. Additionally, AFM scans with a five-frequency-based system are presented wherein higher harmonic imaging is performed up to 1 MHz.