Video-Rate Non-Raster AFM Imaging With Cycloid Trajectory

We demonstrate the application of the internal model principle in tracking a sequential cycloid trajectory to achieve video-rate atomic force microscope (AFM) imaging. To generate a sequential cycloid pattern, one axis of the nanopositioner traces a sinusoidal signal superimposed on a slow triangular wave. Discontinuities at turning points induce large peaks in the steady-state tracking error. To address this issue, a smooth trajectory is designed to reduce the magnitude of error by 60 nm compared with the triangular wave. This trajectory reduces the magnitude of error 10 times. The tracking controller includes the dynamics of the harmonic waveforms and the ramp signal as well as higher order harmonics of the scanning frequency, and an integrator to cope with the system nonlinearities at low frequencies. We perform experiments on a two degree of freedom microelectromechanical system nanopositioner at various scanning frequencies ranging from 500 to 2580 Hz within a scan area of $5\,\,\mu \text {m} \times 10\,\,\mu \text {m}$ . The root-mean-square value of tracking error remains below 6.1 nm with a pitch size of 44.2 nm. We acquire time-lapse AFM images in contact mode at scan rates as high as 20 frames per second.