Probabilistic bounds for complete scanning in non-raster atomic force microscopy

Non-raster methods in atomic force microscopy seek to reduce imaging time through efficient means of information acquisition. In this work we consider the local raster-scan algorithm for imaging biopolymers and other string-like samples. Through feedback control, the scheme drives the tip along the sample to ensure measurements are collected from information-rich areas. Noise in the system, however, can cause the tip to deviate from the sample and the algorithm to fail. In this paper we use a geometric analysis to derive the probability that a loss of tracking event is due to noise. This probability is expressed in terms of the user-defined scan parameters. In turn, this allows us to quantify the probability that the sample will be scanned completely.