Complex force dynamics in atomic force microscopy resolved by wavelet transforms.

The amplitude and phase evolution of the oscillations of a cantilever after a single tip-sample impact are investigated using a cross-correlation wavelet analysis. The excitation of multiple flexural modes is evidenced and the instantaneous amplitude and phase evolution is extracted from the experimental data at all frequencies simultaneously. The instantaneous total force acting on the tip during a single impact is reconstructed. This method has general relevance for the development of an atomic force spectroscopy of single tip-sample interactions, that develop in a few oscillation cycles of the interacting cantilever eigenmodes and their harmonics.