Time-frequency analysis of the tip motion in liquids using the wavelet transform in dynamic atomic force microscopy

The tip motion of the dynamic atomic force microscope in liquids shows complex transient behaviors when using a low stiffness cantilever. The second flexural mode of the cantilever is momentarily excited. Multiple impacts between the tip and the sample might occur in one oscillation cycle. However, the commonly used Fourier transform method cannot provide time-related information about these transient features. To overcome this limitation, we apply the wavelet transform to perform the time-frequency analysis of the tip motion in liquids. The momentary excitation of the second mode and the phenomenon of multiple impacts are clearly shown in the time-frequency plane of the wavelet scalogram. The instantaneous frequencies and magnitudes of the second mode are extracted by the wavelet ridge analysis, which can provide quantitative estimations of the tip motion in the second mode. Moreover, the relations of the maximum instantaneous magnitude (MIM) to the amplitude setpoint and the Young's modulus of the sample surface are investigated. The results suggest that the MIM can be used to characterize the nanomechanical property of the sample surface at high amplitude setpoints.