Optimisation-based adaptive scan for atomic force microscopy imaging

© 2018 Dr. Kaixiang WangAtomic force microscopy (AFM) is widely used in nanotechnology for imaging chemical structures and small biological cells. Unlike scanning electron microscopy, AFM is able to achieve a nanoscale resolution for both electrically conductive and insulated samples because it uses a mechanical probe with a sharp tip to directly interrogate the sample. However, as the probe needs to scan over the sample surface in a line-by-line manner, the imaging process can take up to an hour. To meet the new demands of imaging fast nanoscale dynamic processes, such as chemical reactions and biological structure movements, the imaging speed of AFM needs to be substantially improved. However, in practice, increasing AFM imaging speed tends to deteriorate AFM imaging accuracy due to actuator dynamics and nonlinearities and insufficient bandwidth of a vertical contact force regulation system. This leads to the imaging speed-accuracy trade-off. To investigate this trade-off, the study begins with constructing a unified model framework for a large class of AFM systems with various actuators, controllers, scan patterns and samples to be imaged. Based on the model framework, the inverse relationship between the scan rate and lateral tracking and vertical regulation accuracy is theoretically verified. In order to improve the imaging speed-accuracy trade-off for a given AFM system, this research proposes an optimisation-based adaptive scan method that allows the scan rate to be changed during imaging. In particular, an extremum-seeking algorithm is employed to search for the scan rate that optimises some user-defined local imaging performance metric. The stability of the proposed method is subsequently analysed to inform theoretical performance guarantees, and the result is verified in both simulation and experiment on a commercial AFM platform. Furthermore, through extensive experiments, the various tuning degrees of freedom of the proposed method are investigated and it is shown that the proposed method can achieve a better imaging speed-accuracy trade-off than conventional fixed-rate scan method