General theory of amplitude-modulation atomic force microscopy.

We present a general analytical theory that enables one to determine accurately the unknown tip-sample interactions from the experimental measurement of the amplitude and phase of the oscillating tip in amplitude-modulation atomic force microscopy (AM-AFM). We apply the method to the known Lennard-Jones-type forces and find excellent agreement with the reconstructed results. AM-AFM, widely used in air and liquid, is now not only an imaging tool but also a quantitative force measurement tool.