Numerical methods for low-dose EDS tomography

Abstract

Energy-dispersive X-ray spectroscopic (EDS) tomography is a powerful three-dimensional (3D) imaging technique for characterizing the chemical composition and structure of nanomaterials. However, the accuracy and resolution are typically hampered by the limited number of tilt images that can be measured and the low signal-to-noise ratios (SNRs) of the energy-resolved tilt images. Various sophisticated reconstruction algorithms have been proposed for specific types of samples and imaging conditions, yet deciding on which algorithm to use for each new case remains a complex problem. In this paper, we propose to tailor the reconstruction algorithm for EDS tomography in three aspects: (1) model the reconstruction problem based on an accurate assumption of the data statistics; (2) regularize the reconstruction to incorporate prior knowledge; (3) apply bimodal tomography to augment the EDS data with a high-SNR modality. Methods for the three aspects can be combined in one reconstruction procedure as three modules. Therefore, a reconstruction algorithm can be constructed as a 'recipe'. We also provide guidelines for preparing the recipe based on conditions and assumptions for the data. We investigate the effects of different recipes on both simulated data and real experimental data. The results show that the preferred recipe depends on both acquisition conditions and sample properties, and that the image quality can be enhanced using a properly tailored recipe.

Machine learning in electron microscopy for advanced nanocharacterization: current developments, available tools and future outlook

“…On the other hand, EDX, EELS and even Energy-Filtered TEM (EFTEM) tomography skyrocketed its progress in the last two decades. 301–307 Both qualitatively and quantitatively. 308–311 Even though its major advances in reconstruction algorithmics were not CS/ML-based, classic data processing established a starting point to which apply these new methodologies for refinement (majorly for EDX and EELS).…”

Applications of Transmission Electron Microscopy in Phase Engineering of Nanomaterials

“…However, this method currently cannot achieve atomic-resolution EDX tomography, primarily because of the low SNR in the EDX spectra at relatively low electron doses. The introduction of advanced reconstruction strategies, such as incorporating prior knowledge and applying bimodal tomography, may address this issue . Given the rapid development of high-performance EDX detectors and tomographic reconstruction algorithms, we expect that atomic-resolution 3D reconstructions of the structure and composition using this method will become possible in the near future.…”

Extraction of 3D quantitative maps using EDS-STEM tomography and HAADF-EDS bimodal tomography

“…It is worth noticing that HEBT can be applied only when two conditions are satisfied: first, both the HAADF and EDS data fulfill the projection requirement, that the signal is a monotonic function of the thickness and composition [30], and secondly, the HAADF signals are the weighted sum of the EDS signals for all the elements present [31].…”