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Undersampling-based approaches in Atomic Force Microscopy (AFM) aim to reduce the time to acquire an image by reducing the number of measurements needed while still maintaining image quality. The approach consists of two components: data acquisition and image reconstruction. Successful practical implementation involves solving a variety of non-trivial problems. In this paper, we describe an implementation based on a collection of short scans known as µ-paths, and we demonstrate it on a commercial AFM using a grating sample. Reconstructions are made from the data using a new variant of basis pursuit designed to reduce artifacts arising from the sampling pattern. The quality of the resulting images is compared to images from standard raster scans of the same regions at comparable imaging rates using both the peak signal-to-noise ratio and the structured similarity index metric and a new metric we call the relative damage index. We also compare to simple subline sampling where only a subset of the rows of the image are acquired (followed by reconstruction). These experiments show that at low sampling densities and slow scan rates, µ-path scanning achieves better image quality in less time than subline sampling. Conversely, for faster scan rates subline sampling is faster and, for higher sampling densities, achieves comparable image quality.

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