Wavelet Transforms to Probe the Torsional Modes of a Thermally Excited Cantilever across the Jump-to-Contact Transition: Preliminary Results

The response of the torsional modes of a thermally excited cantilever across the jump-to-contact transition shows a modification of the oscillation amplitude, frequency, and damping. The measurement of these parameters is important because their analysis provides nanoscale information on the physical, chemical, and topographic properties of the sample. The tip-surface interaction potential is usually reconstructed by Fourier analysis of the cantilever oscillations around its equilibrium position. However, Fourier analysis can be correctly interpreted only in the case of stationary systems. The wavelet transform analysis overcomes these limitations, revealing the temporal evolution of the spectral content of a temporal trace. The one-dimensional time signal from the photodiode is converted into a two-dimensional time-frequency topography, which simultaneously exhibits the time and frequency behavior of the cantilever thermal fluctuations. In the present study, we show preliminary data obtained using wavelet transforms to analyze thermally excited torsional cantilever modes during jump-to-contact transition on a highly oriented pyrolitic graphite surface in air.