Introduction
This article covers everything you need to know to simulate measurements for transmission electron microscopy (TEM) and scanning TEM (STEM) experiments Pennycook & Nellist, 2011Carter & Williams, 2016. We focus on modern Python implementations centered around the numpy Harris et al., 2020 and cupy Nishino & Loomis, 2017 libraries, for CPU and GPU calculations respectively, as implemented in the open-source abTEM code.
This text is aimed at both beginner and intermediate users, though experts may also learn some new concepts. The goal of the text is to enable readers to have an understanding of both the theory and practical applications of STEM image simulation. After reading, you should feel comfortable in devising, preparing and running STEM image simulations, and be able to critically assess simulated images in literature. To that end, this text contains interactive figures, with the hope that these may aide the reader in understanding/visualising the described concepts, as well as familiarising them with the associated code, which is provided in the text. While there are no formal pre-requisites and the text aims to be self-contained, a basic understanding of the Python programming language, linear algebra, and condensed matter physics will enhance the understanding of the text.
The text can be broken into three sections:
- Basic introduction to Python as well as crucial mathematical concepts.
- Theory of STEM simulations.
- Practical implementations and considerations for simulation.
The first section consists of a brief overview to the Python programming language and instructions on how to run the interactive figures. This is followed by a primer on the mathematical concepts that underpin image simulations. The second section addresses the theory of STEM image simulation, beginning with a discussion on the underlying physics of electron-atom interactions, after which the algorithms used to simulate images are detailed. Finally, wave aberrations that are vital for understanding contrast formation are briefly described. In the final section the practicalities of image simulation are discussed, covering creating simulation inputs before turning to TEM simulations and STEM simulations in turn, including some helpful tips on how to save computational effort while creating more experimentally realistic images. Finally we conclude with an outlook for simulations of this kind, which play an increasingly important role in modern research.
- Pennycook, S. J., & Nellist, P. D. (2011). Scanning transmission electron microscopy: imaging and analysis. Springer Science & Business Media.
- Carter, C. B., & Williams, D. B. (2016). Transmission electron microscopy: Diffraction, imaging, and spectrometry. Springer.
- Harris, C. R., Millman, K. J., Van Der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., & others. (2020). Array programming with NumPy. Nature, 585(7825), 357–362.
- Nishino, R., & Loomis, S. H. C. (2017). Cupy: A numpy-compatible library for nvidia gpu calculations. 31st Confernce on Neural Information Processing Systems, 151(7).
