Linear imaging theory for differential phase contrast and other phase imaging modes in scanning transmission electron microscopy

Takehito Seki; Kushagra Khare; Yoshiki O Murakami; Satoko Toyama; Gabriel Sánchez-Santolino; Hirokazu Sasaki; Scott D Findlay; Timothy C Petersen; Yuichi Ikuhara; Naoya Shibata

doi:10.1016/j.ultramic.2022.113580

Linear imaging theory for differential phase contrast and other phase imaging modes in scanning transmission electron microscopy

Ultramicroscopy. 2022 Oct:240:113580. doi: 10.1016/j.ultramic.2022.113580. Epub 2022 Jun 23.

Affiliations

¹ Institute of Engineering Innovation, School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan; PRESTO, Japan Science and Technology Agency, Kawaguchi, 332-0012, Japan. Electronic address: seki@sigma.t.u-tokyo.ac.jp.
² School of Physics and Astronomy, Monash University, Clayton, Victoria, 3800, Australia.
³ Institute of Engineering Innovation, School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan.
⁴ Analysis Technology Center, Furukawa Electric Co., Ltd., Yokohama, 220-0073, Japan.
⁵ Monash Centre for Electron Microscopy, Monash University, Clayton, Victoria, 3800, Australia.
⁶ Institute of Engineering Innovation, School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan; Nanostructures Research Laboratory, Japan Fine Ceramic Center, Atsuta-ku, Nagoya, 456-8587, Japan.
⁷ Institute of Engineering Innovation, School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan; Nanostructures Research Laboratory, Japan Fine Ceramic Center, Atsuta-ku, Nagoya, 456-8587, Japan. Electronic address: shibata@sigma.t.u-tokyo.ac.jp.

PMID: 35908324
DOI: 10.1016/j.ultramic.2022.113580

Abstract

We propose a linear imaging theory for differential phase contrast under the weak-phase-weak-amplitude object approximation. Contrast transfer functions are defined for thin and thick weak objects, and they successfully describe several imaging characteristics of differential phase contrast. We discuss the defocus dependence of the contrast for several examples: atomic resolution, a p-n junction, a heterointerface, and grain boundaries. Understanding the imaging characteristics helps in adjusting aberrations in DPC STEM.