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Quantifying the tip-sample interaction at the nanoscale in AmplitudeModulation mode AFM is challenging, especially when measuring in liquids. Here,we derive formulas for the tip-sample conservative and dissipative interactionsand investigate the effect that spurious resonances have on the measuredinteraction. Both direct and acoustic excitation are considered. We alsohighlight the differences between measuring directly the tip position or thecantilever deflection. We show that, when probing the tip-sample forces, theacoustically excited cantilever behavior is insensitive to spurious resonancesas long as the measured signal corresponds to the tip position, or if theexcitation force is correctly taken into account. Since the effectiveexcitation force may depend on the presence of such spurious resonances, weconsider the cases where the frequency is kept constant during the measurementso that the proportionality between excitation signal and actual excitationforce is kept constant. With the present work we show the advantages thatresult from the use of a calibration method based on the acquisition ofapproach-retract curves. Optical beam deflection based AFMs benefit from theuse of this calibration method, especially in presence of spurious resonancesin the cantilever transfer function.

Small amplitude Dynamic AFM: quantifying interactions with different tip detection and excitation schemes in presence of additional resonances