Influence of spurious resonances on the interaction force in dynamic AFM

The quantification of the tip-sample interaction in amplitude modulation atomic force microscopy is challenging, especially when measuring in liquid media. Here, we derive formulas for the tip-sample interactions and investigate the effect of spurious resonances on the measured interaction. Highlighting the differences between measuring directly the tip position or the cantilever deflection, and considering both direct and acoustic excitation, we show that the cantilever behavior is insensitive to spurious resonances as long as the measured signal corresponds to the tip position, or if the excitation force is correctly considered. Since the effective excitation force may depend on the presence of such spurious resonances, only the case in which the frequency is kept constant during the measurement is considered. Finally, we show the advantages that result from the use of a calibration method based on the acquisition of approach-retract curves.