Key Findings
The implementation of a physics-informed Bayesian optimization (BO) framework has significantly reduced the time required for quantitative high-resolution transmission electron microscopy (HRTEM). In a model system using a BaTiO 3 single crystal containing heavy, medium, and light elements, the framework determined the three-dimensional crystal structure from a single HRTEM image. This process achieved a time efficiency improvement of three to four orders of magnitude compared to conventional methods.
Technical Details
The framework utilizes a stepwise strategy and a probabilistic engine to refine high-dimensional parameter spaces. The quantification process involves a physics-informed model where parameters are categorized into two groups:
- Imaging-related parameters: These include image spread σ and residual aberrations of the imaging lens system, such as defocus C 1, twofold astigmatism A 1, threefold astigmatism A 2, axial coma B 2, spherical aberration C 3, fourfold astigmatism A 3, and star aberration S 3.
- Structure parameters: These include atomic positions, atomic occupancies, and the electron absorption factor AF.
The system compares simulated images with experimental images using criteria such as image contrast (standard deviation of intensity distribution), image similarity (normalized cross-correlation coefficient or structural similarity index metric), and goodness of fit (χ 2 statistic or R-factor).
Background & Context
HRTEM allows for the direct atomic resolution observation of crystal lattices, defects, and interfaces. However, essential structural information is often distorted by imaging imperfections, residual aberrations, sample orientation misalignment, and noise, including magnetic Johnson noise. While model-based iterative image simulation has been used for quantification, the high number of parameters typically makes the process time-consuming and dependent on experienced users, limiting its application to small sample areas.
Significance & Outlook
By moving toward full automation, this BO framework overcomes the limitations of user-supervised iterative approaches. This capability opens new avenues for the analysis of larger sample volumes and provides a promising pathway for in-situ applications, such as observing phase transformations and catalysis processes in real-time.
Source: https://www.nature.com/articles/s41524-026-02364-8
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