Non-raster sampling in atomic force microscopy: A compressed sensing approach

Atomic force microscopy is a powerful tool that has had a tremendous impact in understanding systems with nanometer-scale features. In this work we explore the use of compressed sensing as a means of sampling data and generating an image. Under this approach only a small number of the pixels in an image, typically as few as 10%, need to be sampled to generate an accurate image. We show that when combined with time-optimal control to move the tip of the microscope between measurement locations, the imaging time is comparable to high-speed AFM systems while also greatly reducing the interactions with and force applied to the sample. In addition, the approach can significantly reduce the imaging time in applications such as force mapping in which the tip is moved point-by-point through a sequence of measurement locations rather than continuously scanned as in standard imaging.