Optimizing Resolution in a Scanning Tunneling Microscope: Mathematical Approaches and Experimental Results

This study is devoted to improving the process of processing and analyzing images obtained using a scanning probe microscope. Images obtained by this method are often subject to distortion owing to various factors, so this study proposes an approach to improve the quality of these images using various data processing methods. A mathematical model describing the image processing process is formulated with the aim of finding an optimal operator that maximizes the image processing quality score on a fixed dataset. For this purpose, various quality estimates are used, such as signal-to-noise ratio, averaged variance over rows, and averaged variance over windows. The research process included the following groups of methods: background subtraction, data alignment, filtering, row alignment, segmentation, and surface relief restoration.