Combining Spiral Scanning and Internal Model Control for Sequential AFM Imaging at Video Rate

We report on the application of internal model control for accurate tracking of a spiral trajectory for atomic force microscopy (AFM). With a closed-loop bandwidth of only 300 Hz, we achieved tracking errors as low as 0.31% of the scan diameter and an ultravideo frame rate for a high pitch (30 nm) spiral trajectory generated by amplitude modulation of 3 kHz sinusoids. Design and synthesis procedures are proposed for a smooth modulating waveform to minimize the steady-state tracking error during sequential imaging. To obtain AFM images under the constant-force condition, a high bandwidth analogue proportional-integral controller is applied to the damped z-axis of a flexure nanopositioner. Efficacy of the proposed method was demonstrated by artifact-free images at a rate of 37.5 frames/s.