Deep Learning-Assisted Weak Beam Identification in Dark-Field X-ray Microscopy

TL;DR

A deep learning framework is introduced that automates the reliable identification of weak- versus strong-beam conditions using a lightweight convolutional neural network trained on small, hand-labeled datasets, and supports scalable DFXM analysis.

Abstract

Dislocations control the mechanical behavior of crystalline materials, yet their quantitative characterization in bulk has remained elusive. Transmission Electron Microscopy provides atomic-scale resolution but is restricted to thin foils, limiting relevance to structural performance. Dark-field X-ray microscopy (DFXM) has recently opened access to three-dimensional, non-destructive imaging of dislocations in macroscopic crystals. A critical bottleneck, however, is the reliable identification of weak- versus strong-beam conditions. Weak-beam imaging enhances dislocation contrast, while strong-beam conditions are dominated by multiple scattering and obscure interpretation. Current practice depends on manual classification by specialists, which is subjective, slow, and incompatible with the scale of modern experiments. Here, we introduce a deep learning framework that automates this task using a lightweight convolutional neural network trained on small, hand-labeled datasets. By enabling robust, rapid, and scalable identification of imaging conditions, this approach supports scalable DFXM analysis, unlocking statistically significant studies of dislocation dynamics in bulk material

Figures (5)

• Figure 1: Schematic of a Dark-Field X-ray Microscopy (DFXM) experiment. (A) A line-focused X-ray beam (approximately 500 nm in height in $z$ direction and a couple of hundreds of microns wide in $y$ direction, illuminates a layer of the crystal. The diffracted beam at the scattering angle $2\theta$ is selected by a compound refractive lens (CRL) system and imaged onto a 2D detector Isern2024. Rotating the sample around the $\phi$-axis left handed rotation around y axis enables collection of a rocking curve, capturing lattice distortions and rotations about the scattering vector $\mathbf{Q}$. (B) A representative rocking curve obtained from fine angular steps. Each point corresponds to an image recorded at a discrete ($\phi$) angle. The curve's tails reflect WB conditions, sensitive to dislocations and strain, while the peak corresponds to SB conditions, often showing dynamical diffraction fringes.
• Figure 2: Deep learning architecture for DFXM image patch classification. Raw DFXM images are divided into smaller patches that are independently analyzed using a lightweight convolutional neural network. Each patch is passed through a sequence of depthwise and pointwise separable convolution layers with ReLU activation functions, enabling efficient feature extraction. The resulting features are then fed into a fully connected (FC) layer that classifies each patch as corresponding to either a weak-beam or strong-beam diffraction condition.
• Figure 3: Performance metrics of the classification model. From left to right: (1) Training and test loss plotted over 50 epochs, showing a decreasing trend and convergence, indicating effective learning and minimal overfitting. (2) Accuracy curves for both training and test sets, demonstrating stable and high performance throughout training. (3) Confusion matrix summarizing the validation dataset classification results, highlighting the model’s ability to distinguish between weak-beam and strong-beam conditions.
• Figure 4: Classification of weak- and strong-beam conditions using LCNN. (A) and (B) show diffraction contrast maps from the training dataset, automatically classified by our lightweight model as WB and SB conditions, respectively. In both cases, dislocation boundaries and branching structures are visible, and individual dislocations can be resolved. (C) and (D) show predictions on an independent experimental dataset that is different from the training dataset (annealed Al, probed at the $(111)$ reflection, 17 keV), where the model correctly identifies weak-beam and strong-beam conditions, respectively Borgi2025. Training data are from Ref. Yildirim2023. The scale bar in (A) applies also to (B), and the scale bar in (C) applies also to (D).
• Figure 5: Comparison of dislocation structure reconstruction using automated and manual methods. (A) 3D reconstruction of individual dislocations and dislocation boundaries using our fully automated machine learning workflow based on weak-beam identification. (B) Corresponding 3D reconstruction using manual intensity thresholding from the published experimental dataset Yildirim2023. (C) Distribution of symmetric nearest-neighbor distances between the automated and manually reconstructed dislocation networks, quantifying the spatial agreement between the two approaches. (D) Representative dislocation boundaries ROIs from the reconstructed volumes (automated: green; manual: orange), demonstrating close structural correspondence across multiple Despite relying on significantly less data and requiring no human intervention.