Response Measurement Accuracy for Off-Resonance Excitation in Atomic Force Microscopy

Displacement measurement in atomic force microscopy (AFM) is most commonly obtained indirectly by measuring the slope of the AFM probe and applying a calibration factor. Static calibration techniques operate on the assumption that the probe response approximates single mode behavior. For off-resonance excitation or different operating conditions the contribution of higher modes may become significant. In this paper, changes to the calibrated slope-displacement relationship and the corresponding implications on measurement accuracy are investigated. A model is developed and numerical simulations are performed to examine the effect of laser spot position, tip mass, quality factor and excitation frequency on measurement accuracy. Free response conditions and operation under nonlinear tip-sample forces are considered. Results are verified experimentally using a representative macroscale system. A laser spot positioned at a nominal position between x = 0.5 and 0.6 is determined to minimize optical lever measurement error under conditions where the response is dominated by contributions from the first two modes, due to excitation as well as other factors.