Towards Self-Optimizing Electron Microscope: Robust Tuning of Aberration Coefficients via Physics-Aware Multi-Objective Bayesian Optimization

Technical Summary: Towards Self-Optimizing Electron Microscope via Physics-Aware Multi-Objective Bayesian Optimization

Problem Statement
High-throughput Scanning Transmission Electron Microscopy (STEM) is essential for atomic-resolution materials discovery, yet its practical throughput is severely bottlenecked by the manual, labor-intensive nature of instrument alignment. While modern aberration-corrected STEM enables sub-angstrom imaging, maintaining optimal probe conditions is fragile due to thermal drift, dose accumulation, and parameter coupling. Traditional automated alignment relies on serial, gradient-free searches (e.g., Nelder-Mead) or exhaustive grid sweeps. These methods are sample-inefficient, struggle to correct multiple interacting parameters simultaneously, and often optimize a single metric, leading to "reward hacking" where the system locks onto high-contrast artifacts rather than true resolution. Conversely, emerging deep learning methods offer speed but lack flexibility, requiring extensive retraining for varying sample conditions and often failing to adapt to novel imaging environments. Furthermore, the definition of "image quality" is ambiguous; optimizing for contrast may degrade resolution, and vice versa, creating a need for a framework that can navigate these competing physical objectives without collapsing them into a single, potentially misleading scalar.

Methodology
The authors introduce a Multi-Objective Bayesian Optimization (MOBO) framework designed to rapidly and robustly tune aberration coefficients. The core methodology involves:

1. Physics-Aware Reward Formulation: Instead of prescribing a single universal image quality metric, the framework utilizes user-defined, physically motivated reward functions. The study specifically implements two complementary metrics:
   • Normalized Image Variance (Contrast): Measures the standard deviation of pixel intensity normalized by the mean, decoupling contrast from beam current fluctuations.
   • FFT Spectral Power (Resolution): Quantifies crystallinity by applying a high-pass mask to the frequency domain to isolate Bragg peaks, eliminating DC background signals.
2. Multi-Objective Optimization: The tuning process is framed as a vector optimization problem $f(x) = [f_1(x), f_2(x)]$. Rather than scalarizing these rewards, the algorithm seeks to approximate the Pareto Front—the set of solutions where no single objective can be improved without degrading another. This approach exposes trade-offs between competing priorities (e.g., contrast vs. resolution) and prevents the optimizer from converging on "local optima" that satisfy only one metric.
3. Probabilistic Modeling: The system employs Gaussian Process (GP) regression to model the aberration landscape probabilistically. This allows the algorithm to actively select the most informative lens settings to evaluate next, rather than performing blind, exhaustive searches.
4. Sim-to-Real Strategy: The workflow was first validated using a physics-based simulator (built on abtem and pyTEMlib) simulating a Thermo Fisher Spectra 300 instrument. To bridge the gap to reality, the simulation included spatially correlated Gaussian noise and Poissonian shot noise to mimic environmental instability and detector stochasticity. The framework was subsequently deployed on a physical Thermo Fisher Spectra 300 microscope using CEOS and AutoScript APIs, controlling 1st and 2nd order aberrations (defocus and astigmatism) in a 7-dimensional search space.

Key Results

• Pareto Front Identification: In both simulated and experimental environments, the MOBO framework successfully identified the Pareto front, revealing that the optimal imaging state is not a broad basin but a sensitive manifold at the edge of the error landscape.
• Avoidance of Single-Metric Traps: The study demonstrated that single-objective optimization often leads to suboptimal states. For instance, maximizing contrast alone resulted in defocused, high-signal images that failed to resolve atomic lattices. The MOBO approach successfully navigated away from these "resolution traps" to find balanced states that simultaneously maximized contrast and spectral power.
• Convergence Efficiency: In the simulated environment, the agent converged to the optimal solution set within approximately 25 iterations. On the physical instrument, the framework robustly tuned defocus and astigmatism on gold (Au) nanoparticles, resolving sharp atomic lattices where single-metric approaches failed.
• Cost Analysis: A breakdown of optimization costs revealed that while hardware latency remains constant (~4 seconds), computational overhead (GP training and acquisition optimization) scales super-linearly with dimensionality. In high-dimensional searches (7 parameters), computation becomes the dominant bottleneck, suggesting a need for GPU acceleration in future iterations.

Significance and Claims
The paper claims that this MOBO framework enables "self-optimizing" microscopy by dynamically sustaining optimal performance during experiments. Its primary significance lies in:

• Robustness to Noise and Ambiguity: By treating alignment as a multi-objective problem, the framework acts as a "contaminant filter," preventing the system from locking onto artifacts (like dirt or beam blanker artifacts) that might satisfy a single metric.
• Human-in-the-Loop Capability: The explicit visualization of the Pareto front allows domain experts to intervene and select the optimal trade-off between competing objectives, rather than forcing a single, potentially arbitrary solution.
• Data Efficiency and FAIR Principles: Unlike manual tuning where suboptimal data is discarded, the MOBO engine logs every iteration, creating a persistent, reusable dataset that links aberration coefficients to image outcomes. This adheres to FAIR (Findable, Accessible, Interoperable, Reusable) data principles, building a cumulative knowledge base for future surrogate models.
• Foundation for Advanced Beam Engineering: The authors posit that this capability paves the way for intentionally shaping electron probes to break symmetry and enhance sensitivity to specific material properties (e.g., mapping lattice strains), moving beyond simple "round point" correction.

The work concludes that by replacing inefficient blind searches with sample-efficient, physics-aware active learning, this approach addresses the fundamental mismatch between idealized theoretical rewards and the non-idealities of physical instruments, offering a scalable path toward autonomous, high-throughput atomic-scale characterization.