Removing background and estimating a unit height of atomic steps from a scanning probe microscopy image using a statistical model

TL;DR

This paper introduces a statistical model-based method for removing background and estimating atomic step heights from scanning probe microscopy images, providing high precision and the ability to incorporate prior knowledge.

Contribution

The paper presents a novel statistical framework that simultaneously removes background and estimates atomic step heights, including the unit height, from microscopy images.

Findings

Background subtraction aligns terraces horizontally

Estimated atomic step height precision reaches picometer scale

Method successfully applied to Cu(111) surface images

Abstract

We present a statistical method to remove background and estimate a unit height of atomic steps of an image obtained using a scanning probe microscope. We adopt a mixture model consisting of multiple statistical distributions to describe an image. This statistical approach provides a comprehensive way to subtract a background surface even in the presence of atomic steps as well as to evaluate terrace heights in a single framework. Moreover, it also enables us to extract further quantitative information by introducing additional prior knowledge about the image. An example of this extension is estimating a unit height of atomic steps together with the terrace heights. We demonstrate the capability of our method for a topographic image of a Cu(111) surface taken using a scanning tunneling microscope. The background subtraction corrects all terraces to be parallel to a horizontal plane and the precision of the estimated unit height reaches the order of a picometer. An open-source implementation of our method is available on the web.