[Paper Review] Near-real-time diagnosis of electron optical phase aberrations in scanning transmission electron microscopy using an artificial neural network

Giovanni Bertoni, Enzo Rotunno+5 more|arXiv (Cornell University)|Jun 13, 2022

Electron and X-Ray Spectroscopy Techniques4 citations

TL;DR

This paper presents an artificial neural network (ANN) that enables near-real-time diagnosis of electron optical phase aberrations in scanning transmission electron microscopy (STEM) using single Ronchigram images. By training on synthetic Ronchigrams derived from Fourier transforms of diffractograms, the ANN accurately predicts 8 key aberration coefficients with mean absolute errors below 5% of their dynamic range, enabling rapid feedback for aberration correction in real-time applications including MEMS-based optics.

ABSTRACT

The key to optimizing spatial resolution in a state-of-the-art scanning transmission electron microscope is the ability to precisely measure and correct for electron optical aberrations of the probe-forming lenses. Several diagnostic methods for aberration measurement and correction with maximum precision and accuracy have been proposed, albeit often at the cost of relatively long acquisition times. Here, we illustrate how artificial intelligence can be used to provide near-realtime diagnosis of aberrations from individual Ronchigrams. The demonstrated speed of aberration measurement is important as microscope conditions can change rapidly, as well as for the operation of MEMS-based hardware correction elements that have less intrinsic stability than conventional electromagnetic lenses.

Motivation & Objective

• To develop a fast, automated method for diagnosing electron optical phase aberrations in STEM to overcome the slow acquisition times of conventional methods.
• To enable real-time feedback for aberration correction, especially critical for unstable MEMS-based optics.
• To leverage artificial intelligence to extract precise aberration parameters directly from a single Ronchigram without relying on multi-tilt or semi-analytical fitting.
• To validate the ANN's performance against established Zemlin tableau methods used in commercial aberration correctors.

Proposed method

• The method uses synthetic Ronchigrams generated from a physical model of electron scattering through a phase object, incorporating Zernike polynomial-based aberration terms.
• The Ronchigrams are segmented into 5×5 tiles, and the Fast Fourier Transform (FFT) of each tile is computed to extract local diffraction patterns.
• An artificial neural network (ANN) architecture with 4 blocks of 2D convolutional layers, pooling layers, dropout layers, and fully connected dense layers is trained to map the 25 FFT patterns to the corresponding aberration coefficients.
• The network is trained on 100,000 synthetic datasets with randomly generated aberration values within defined ranges for defocus, spherical aberration, astigmatism, and coma.
• The ANN outputs the coefficients (𝐶𝑛,𝑚,𝑎, 𝐶𝑛,𝑚,𝑏) for 8 principal aberrations, which are then converted to standard Zernike form using trigonometric relations.
• The trained model is validated on experimental Ronchigrams from a CTEM, comparing predictions with values obtained from the microscope’s Zemlin tableau-based correction software.

Experimental results

Research questions

• RQ1 Can a deep neural network accurately infer electron optical phase aberrations from a single Ronchigram with high precision and speed?
• RQ2 How does the performance of the ANN compare to conventional Zemlin tableau-based methods in terms of accuracy and error margins?
• RQ3 To what extent can the ANN generalize across different aberration types, including higher-order terms like 3-fold astigmatism and coma?
• RQ4 Can the ANN provide reliable sign detection for all aberration coefficients, which is essential for corrector feedback?
• RQ5 What is the achievable real-time performance of the ANN for dynamic aberration diagnosis in operational STEM environments?

Key findings

• The ANN achieved a mean absolute error (MAE) of 15 nm for defocus (C1,0), representing 0.8% relative error, due to the strong sensitivity of the first diffraction minimum to defocus.
• For spherical aberration (C3,0), the MAE was 3.49 µm, corresponding to a 3.5% relative error, demonstrating high precision in a critical aberration term.
• The ANN achieved MAEs of 4.7 nm and 4.8 nm for 2-fold astigmatism (A1), with relative errors of 4.8% and 4.9%, respectively, indicating strong performance for low-order astigmatism.
• For coma (B2), the MAE was 49 nm (4.9% error), and for 3-fold astigmatism (A2), it was 37 nm (3.7% error), showing consistent performance across higher-order aberrations.
• The ANN correctly determined the sign of all aberrations in every tested case, which is essential for effective correction in real-time systems.
• Experimental validation showed strong agreement between ANN predictions and Zemlin tableau measurements, with R² > 0.95 for all aberration types, confirming robustness and reliability.