A combined averaging and frequency mixing approach for force identification in weakly nonlinear high-Q oscillators: Atomic force microscope

We present a polynomial force reconstruction of the tip-sample interaction force in Atomic Force Microscopy. The method uses analytical expressions for the slow-time amplitude and phase evolution, obtained from time-averaging over the rapidly oscillating part of the cantilever dynamics. The slow-time behavior can be easily obtained in either the numerical simulations or the experiment in which a high-Q resonator is perturbed by a weak nonlinearity and a periodic driving force. A direct fit of the theoretical expressions to the simulated and experimental data gives the best-fit parameters for the force model. The method combines and complements previous works (Platz et al., 2013; Forchheimer et al., 2012 [2]) and it allows for computationally more efficient parameter mapping with AFM. Results for the simulated asymmetric piecewise linear force and VdW-DMT force models are compared with the reconstructed polynomial force and show a good agreement. It is also shown that the analytical amplitude and phase modulation equations fit well with the experimental data.