Sub-Pixel Electron Beam Alignment for Machine Learning Characterization of Hybrid Pixel Detectors

TL;DR

This work addresses the limited spatial resolution of hybrid pixel detectors by enabling sub-pixel localization of electron hits through experimentally labeled training data. It introduces two data-generation methods—a narrowly focused $2\,\mu$m beam scanned across the detector and aperture-mask-based sub-pixel labeling—to produce detector-specific ground-truth data across $60$–$200\,\mathrm{keV}$. Ground-truth data are preprocessed and used to train CNN-based models, revealing that experimental training achieves $0.60$ px RMSE at $200\,\mathrm{keV}$ (about a $3\times$ improvement over centroid methods) and that synthetic data alone can yield $0.47$ px on synthetic data but transfers less effectively to real measurements. Overall, the study demonstrates two robust, transferable calibration strategies that enable sub-pixel resolution enhancements for hybrid pixel detectors, paving the way for universal, experimentally calibrated ML-based reconstruction in both diffraction and imaging modes.

Abstract

Due to their radiation hardness, kilohertz frame rates, and high dynamic range, hybrid pixel detectors have recently expanded their application range to electron diffraction and recently also electron imaging. However, these detectors typically have pixel sizes about ten times larger than those of direct electron detectors commonly used for imaging and more prominent electron multiple scattering effects. To overcome these limitations, machine learning approaches can be utilized to reconstruct the electron entrance point and achieve super-resolution. As this process is inherently stochastic, and machine learning relies on suitable training data, high-quality, representative training data are essential for developing models that achieve the best possible resolution. In this work, we present two novel experimental methods for generating such training data. The first method employs precise microscope alignment to scan the detector plane using a finely focused electron beam of 2 μm diameter, enabling controlled sub-pixel mapping. The second method utilizes specially designed aperture masks with sub-pixel-sized holes to accurately localize electron entry points. We developed and validated two experimental strategies for collecting training data at acceleration voltages of 60, 80, 120, and 200 keV, which enable sub-pixel labeling for hybrid pixel detectors. Notably, our methodology is broadly applicable to a wide range of hybrid pixel detectors.

Figures (6)

• Figure 1: Schematic representation of the detector characterization strategies projection of the real space image of a narrow beam onto the detector (a–b) and the aperture mask setup on the MÖNCH sensor (c). For measurements at 200 keV, a narrow, semi-parallel beam with a diameter around 2 $\mu$m was used (a). For a more universal method, an aperture mask with holes of varying diameters between 2 and 5 $\mu$m was designed (b). The mask can be mounted above the sensor using fixation clamps on a support frame, as illustrated in (c).
• Figure 2: Manufacturing of holes (a, c, and d) and the knife edge (b) was performed using Ga and plasma FIB/SEM respectively. Two types of holes were tested. One hole geometry shown in (a) featuring a groove with a height of approximately 4 $\mu$m. The other type were just straight holes, penetrating the whole W-foil with as little change in diameter as possible (c). The holes are arranged as a regular 2D array (d).
• Figure 3: Graphic representation of mask aperture evolution (a – c) and a photograph of the final mask (d) with an overlay positions of the holes, mounted on a silicon frame support for FIB/SEM. Mask 1 featured two corners of different sizes (a) to aid in determining the distance to the holes after mounting above the detector. Mask 2 had a single open corner and an additional position marker next to the knife edge (b), along with a greater number of holes. Note that the diagrams show rather the positioning than actual number of holes. For mask 3 the W-foil covered a larger surface area and contained an even higher number of hole (c). All masks were mounted on an aluminum plate with an opening of approximately 12 × 12 mm; Masks 2 and 3 were first glued to a silicon support. The foil shape is outlined in yellow, with holes marked as red circles (3 $\mu$m) or blue (5 $\mu$m). Blue rectangles around certain holes in Mask 1 indicate additional wells milled around the respective holes.
• Figure 4: Example of detector signal at 200 and 80 keV obtained from two different training data acquisition strategies. (a) Overlay of scanning points acquired using focused beam-based detector calibration at 200 keV, where each scanning point represents thousand of electron events. (b) Aperture Mask 2 array under parallel beam illumination at 80 keV, used to fit grid coordinates and label electron events according to their corresponding aperture positions, indicating the entrance positions of electron tracks.
• Figure S1: Schematic diagram of the hole geometries used in this work. Panels I, II and III show the holes included in the first mask geometry, where wells of different depths were first milled before the actual hole was cut into the W-foil. Hole geometry III was used for masks two and three, since the holes in the first mask had confirmed that despite the large thickness of the W-foil it was possible to drill a hole through the full thickness of the membrane with the FIB. For simplicity, the drawing represents the hole as a cylinder, whereas in reality, due to the beam shape, it more closely resembles a trapezoid with some narrowing at the bottom, as indicated with a dashed lines.