Implementation of atomic force microscopy resonance modes based on asymptotic dynamics using Costas Loop

Asymptotic nonlinear dynamics of Atomic Force Microscopy (AFM) based on Krylov-Bogoliubov-Mitropolsky (KBM) averaging technique applied to Euler-Bernoulli model of vibrating cantilever allows rigorous definition, analysis, and design of possible AFM resonance modes. The paper uses this asymptotic dynamics for new design, and implements the newly defined AFM resonance modes including Amplitude Modulation with Frequency Imaging (AM-FI) and Frequency Modulation with Amplitude Imaging (FM-AI), where the cantilever is kept in resonance by feedback. Implementation of these modes is based on modified Costas Phase Locked Loop (PLL) that in addition to its main function -servo the phase set-point, measures frequency, phase and amplitude of the incoming signal. Comparative analysis of experimental scan images for different AFM resonance modes is provided including some quantitative measurements.