Reconstruction of 3D Phase Contrast Atomic Electron Tomography

John MelonakosArrayFire, Case Studies Leave a Comment

Researchers from UC Berkeley and Lawrence Berkeley National Laboratory credit ArrayFire in a paper published in the 2020 IEEE High-Performance Extreme Computing Conference (HPEC). The paper is titled “GPU Accelerated Anomaly Detection of Large Scale Light Curves.” In this work, the authors present a new algorithm for reconstructing the three-dimensional (3D) electrostatic potential of a sample at atomic resolution from phase contrast imaging using high-resolution transmission electron microscopy.


Transmission electron microscopy (TEM) offers various imaging modes, allowing for quantitative 3D estimations of local structure, electrostatic and magnetic potentials, and local chemistry, significantly impacting biology and materials science. It is now possible to measure the 3D position of individual atoms with high precision and even determine both the 3D position and species of every atom in a nanoscale sample with high reliability. These atomic electron tomographic (AET) studies used a TEM imaging mode called annular dark field (ADF) scanning transmission electron microscopy (STEM). ADF-STEM imaging offers monotonic contrast that is close to a linear 2D projection of the 3D electrostatic potential of the sample. This feature allows for both traditional tomographic reconstruction algorithms and advanced algorithms that allow for some deviation from linearity. However, this imaging mode requires large electron doses, as it is much less efficient than phase contrast imaging modes. Additionally, because the electron probe is focused on a small spot and scanned over the sample surface, sample motion during the experiment can cause artifacts.

This paper presents a new method for 3D tomographic reconstruction from a tilt series of one or more intensity-only images at different defocus values. The algorithm models the multiple scattering of the electron beam and the strong phase shifts induced by individual atoms at atomic resolution and includes efficient regularization to recover a physically accurate structure even with a very low signal-to-noise ratio (SNR). The authors also implemented an atom-tracing algorithm to identify individual atoms and estimate their sub-voxel 3D positions and chemical species. The method allows for AET experiments to be performed on samples that contain weakly scattering elements, such as carbon, oxygen, or even lithium, with either crystalline or amorphous structures or a mix of both. Additionally, it allows for the reconstruction of samples that cannot withstand the required electron dose for existing atomic resolution reconstruction methods. Biological cryo-EM studies may also benefit if they are performed on very large volumes (where the projection assumption breaks down) or contain multiple scattering regions.

Figure 1 shows the experimental layout of the paper, including the tilt series at different defocus values.


Figure 4 shows the effect of different electron doses on the results. Reducing electron dose is helpful in many applications.

Figure 6 shows the impact of varying tilt angles and defocus planes.

The forward simulation and reconstruction algorithms are implemented in Python, using ArrayFire for GPU calculations.


This paper shows that the method is robust to low electron dose measurements, works for a small number of defocused images or even a single image per tilt angle, and can handle a missing wedge in the tilt angles of up to 60◦. The method enables atomic-resolution tomographic reconstruction of nanoscale samples containing both strongly and weakly scattering elements, with either crystalline or amorphous structures. All source codes have been opened to encourage researchers to perform phase-contrast atomic electron tomography experiments to solve structures on the smallest length scales.

Thanks to these researchers for sharing their great work with us!

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