Sequential Cycloid Scanning for Time-resolved Atomic Force Microscopy

We report sequential atomic force microscope (AFM) imaging with a cycloid scan pattern where one lateral axis of the nanopositioner follows a sinusoid superimposed on a slow triangular signal. Due to the abrupt slope change in a triangular signal, large peaks appear in the tracking error. To smoothen the sharp turning points and reduce the error, an optimization technique is employed. To achieve a highperformance tracking, we utilized an internal model controller which includes a model of the reference signals while additional internal models are also added to the controller to deal with the system nonlinearities. The experiment is conducted on a two degrees of freedom microelectromechanical system nanopositioner within a scan area of $5 \ \mu\mathrm{m}\times 10 \ \mu\mathrm{m}$ and the pitch size of 44.2 nm as the scanning time is 80.6 msec. The peak of tracking error in x-axis is negligible due to the optimal trajectory while the root mean square value of tracking error is obtained as 4.9 nm and 4.4 nm for x- and y-axis, respectively. A sequence of contact mode constant height AFM images are acquired at 12.4 fps.