Accurate formulas for interaction force and energy in frequency modulation force spectroscopy

Frequency modulation atomic force microscopy utilizes the change in resonant frequency of a cantilever to detect variations in the interaction force between cantilever tip and sample. While a simple relation exists enabling the frequency shift to be determined for a given force law, the required complementary inverse relation does not exist for arbitrary oscillation amplitudes of the cantilever. In this letter we address this problem and present simple yet accurate formulas that enable the interaction force and energy to be determined directly from the measured frequency shift. These formulas are valid for any oscillation amplitude and interaction force, and are therefore of widespread applicability in frequency modulation dynamic force spectroscopy.