Trade-off between the control bandwidth and the measurement accuracy in Atomic Force Microscopy

In Atomic Force Microscopy the force between the tip and the sample is controlled in a feedback loop in order to prevent damage to the tip and the sample during scanning, and also to convert the force measurement into an estimate of the sample topography. In this paper it is experimentally shown that within the design of the control system a direct trade-off has to be made between the bandwidth of the feedback loop and the accuracy of the topography estimation due to the dynamical uncertainty of the systems. Several method are suggested to reduce the dynamical uncertainty of the imaging system to allow both faster and more accurate AFM imaging. Moreover, a method is discussed and experimentally validated to compensate for the loss in imaging accuracy due to the hysteresis within the piezoelectric actuators