Control techniques for high-speed dynamic mode imaging in atomic force microscopes

This paper proposes a new dynamic mode of operation in an Atomic Force Microscope (AFM) where the deflection signal is used for force regulation instead of its derivatives such as the amplitude and phase. This mode is especially useful in AFMs with high speed positioning systems with bandwidths of the order of ≈ 1/10 times the natural frequency of the scanning probe. We formulate this problem in an optimal control setting and employ multiobjective optimization techniques to design the regulating controller. Furthermore, we present a method to estimate the tip-sample interaction force and extract the sample topography information from this estimate. The overall scheme facilitates high speed imaging that can potentially exploit fast scanning devices without compromising on the bandwidth and resolution. Simulation results show a regulation bandwidth of 10−15% of the natural frequency of the probe.