This paper exemplifies methods to estimate sample properties, including topographical properties, from a high bandwidth estimate of tip-sample interaction forces between the probe tip and the sample surface in an atomic force microscope. The tip-sample interaction force is the most fundamental quantity that can be detected by the probe tip. The fact that sample features as well as physical properties of the sample are a function of tip-sample interaction model chosen is exploited, and the property estimates are obtained by fitting appropriate physical models to the force estimate data. The underlying idea is to treat the non-linear tip-sample interactions as a disturbance to the cantilever subsystem and design a feedback controller that ensures the cantilever deflection tracks a desired trajectory. This tracking allows scanning speeds as high as 1/10th of the cantilever resonance frequency compared to typical scanning modes that regulate derivatives of the probe deflection such as amplitude or phase, providing much lower scan speeds. The high bandwidth disturbance rejection and consequent estimation provides estimates of the tip-sample interaction force.

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