Optimal scan trajectories for high-speed scanning probe microscopy

A novel method is presented which enables the systematic analysis and design of scan trajectories for highspeed scanning probe microscopy. The analysis is based on a family of universal metrics for spatial resolution which utilize Voronoi tessellations. The scan trajectories are designed in the framework of mathematical optimization in which the specifications on spatial resolution, speed and frequency content are captured in an objective function and a set of constraints. We demonstrate the method by designing scan trajectories that are based on Lissajous curves. Experimental results are obtained on a custom-built atomic force microscope. By employing the Lissajous scan trajectories, frame rates as high as 1 frame/s are achieved using a low-bandwidth commercial nanopositioner.