Relations between interaction force and frequency shift in large-amplitudedynamic force microscopy

Large-amplitude dynamic force microscopy based on measuring shifts of the r esonance frequency of the force sensor has proved to be a powerful imaging tool. General expressions relating arbitrary interaction forces to resonanc e frequency shifts are derived using variational methods and Fourier expans ion 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 con volution product involving the interaction force and a weakly divergent ker nel. The convolution can be inverted, thus enabling one to recover unequivo cally interaction potentials and forces from measured frequency shift data. (C) 1999 American Institute of Physics. [S0003-6951(99)02429-8].