Periodic Artifact Reduction in Fourier transforms of Full Field Atomic Resolution Images

TL;DR

This paper introduces a simple and efficient method using Periodic Plus Smooth Decomposition to remove edge artifacts in Fourier transforms of atomic resolution images, preserving lattice peaks for better analysis.

Contribution

The paper presents a novel application of Periodic Plus Smooth Decomposition for artifact removal in Fourier transforms of high-resolution images, improving analysis accuracy.

Findings

Effective removal of edge artifacts demonstrated.

Preservation of sharp reciprocal lattice peaks.

Compatible with existing Fourier analysis workflows.

Abstract

The discrete Fourier transform is among the most routine tools used in high-resolution scanning / transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp discontinuities between the edges of an image cause a cross patterned artifact along the reciprocal space axes. This artifact can interfere with the analysis of reciprocal lattice peaks of an atomic resolution image. Here we demonstrate that the recently developed Periodic Plus Smooth Decomposition technique provides a simple, efficient method for reliable removal of artifacts caused by edge discontinuities. In this method, edge artifacts are reduced by subtracting a smooth background that solves Poisson's equation with boundary conditions set by the image's edges. Unlike the traditional windowed Fourier transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal lattice peaks from the image's entire field of view.