Relations between interaction force and frequency shift in large-amplitude dynamic force microscopy

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Abstract
Large-amplitude dynamic force microscopy based on measuring shifts of the resonance frequency of the force sensor has proved to be a powerful imaging tool. General expressions relating arbitrary interaction forces to resonance frequency shifts are derived using variational methods and Fourier expansion of the tip motion. For interactions with a range much shorter than the vibration amplitude, the frequency shift can be expressed in terms of a convolution product involving the interaction force and a weakly divergent kernel. The convolution can be inverted, thus enabling one to recover unequivocally interaction potentials and forces from measured frequency shift data.