Theoretical bounds on a non-raster scan method for tracking string-like samples

In this paper, we study the performance of a non-raster-scan algorithm for imaging string-like samples in an atomic force microscope. The algorithm yields high-speed imaging through a feedback control law that steers the tip along the sample, thereby reducing the imaging time by eliminating unnecessary measurements. Under simplifying assumptions, we derive expressions for bounds on the control parameters to ensure accurate tracking of the sample.