Wavelet analysis of higher harmonics in tapping mode atomic force microscopy.

Higher harmonics have been widely used to characterize nanomechanical properties of the sample surface in tapping mode atomic force microscopy. They are usually analyzed by the Fourier transform method which provides time-averaged amplitude and phase information. In this paper, we apply the analytic wavelet transform to analyze higher harmonics. The intuitive descriptions of higher harmonics are obtained by the time-frequency analysis of the tip motion signal. The temporal evolutions of the higher harmonics are analyzed. The higher harmonics extracted by the analytic wavelet transform are closely related to the wavelet parameters. Different time and frequency features of higher harmonics can be analyzed through adjusting the wavelet parameters. Moreover, the root-mean-square amplitude and the peak amplitude obtained by the analytic wavelet transform can provide better characterization of sample properties than the amplitude obtained by the Fourier transform method.