Multi-frequency data analysis in AFM by wavelet transform

Scanning Probe Microscopy 2017

Pukhova, V.^1 ; Ferrini, G.^2

Department of Quantum Electronics and Optoelectronic Devices, Saint Petersburg Electrotechnical University LETI, Saint Petersburg

197376, Russia^1

Interdisciplinary Laboratories for Advanced Materials Physics (I-LAMP), Dipartimento di Matematica e Fisica, Università Cattolica Del Sacro Cuore, Brescia

25121, Italy^2

关键词: Dynamic force spectroscopy;    Fourier transform analysis;    Mathematical apparatus;    Methodological approach;    Multi-frequency signals;    Spectral evolution;    Time-frequency representations;    Tip-sample interaction;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/256/1/012004/pdf
DOI  :  10.1088/1757-899X/256/1/012004

来源: IOP

【 摘 要 】

Interacting cantilevers in AFM experiments generate non-stationary, multi-frequency signals consisting of numerous excited flexural and torsional modes and their harmonics. The analysis of such signals is challenging, requiring special methodological approaches and a powerful mathematical apparatus. The most common approach to the signal analysis is to apply Fourier transform analysis. However, FT gives accurate spectra for stationary signals, and for signals changing their spectral content over time, FT provides only an averaged spectrum. Hence, for non-stationary and rapidly varying signals, such as those from interacting cantilevers, a method that shows the spectral evolution in time is needed. One of the most powerful techniques, allowing detailed time-frequency representation of signals, is the wavelet transform. It is a method of analysis that allows representation of energy associated to the signal at a particular frequency and time, providing correlation between the spectral and temporal features of the signal, unlike FT. This is particularly important in AFM experiments because signals nonlinearities contains valuable information about tip-sample interactions and consequently surfaces properties. The present work is aimed to show the advantages of wavelet transform in comparison with FT using as an example the force curve analysis in dynamic force spectroscopy.