Localizing periodicity in near-field images

TL;DR

This paper introduces a Bayesian inference approach to improve the localization of periodic structures in near-field images, such as those from electron microscopy, by systematically constructing Fourier dark-field methods.

Contribution

It presents a novel Bayesian framework that guides the development of Fourier dark-field techniques for accurately localizing periodicity in near-field imaging.

Findings

Bayesian inference effectively predicts background phase in near-field images.

The method improves localization accuracy of periodic structures.

The approach is applicable to various near-field imaging modalities.

Abstract

We show that Bayesian inference, like that used in statistical mechanics, can guide the systematic construction of Fourier dark-field methods for localizing periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast) images. For crystals in an aperiodic field, the Fourier coefficient Ze^{i phi} combines with a prior estimate for background amplitude B to predict background phase (beta) values distributed with a probability p(beta - phi | Z,phi,B) inversely proportional to the amplitude P of the signal of interest, when this latter is treated as an unknown translation scaled to B.