Correcting for probe wandering by precession path segmentation

Precession electron diffraction has in the past few decades become a powerful technique for structure solving, strain analysis, and orientation mapping, to name a few. One of the benefits of precessing the electron beam, is increased reciprocal space resolution, albeit at a loss of spatial resolution due to an effect referred to as ‘probe wandering’. Here, a new methodology of precession path segmentation is presented to counteract this effect and increase the resolution in reconstructed virtual images from scanning precession electron diffraction data. By utilizing fast pixelated electron detector technology, multiple frames are recorded for each azimuthal rotation of the beam, allowing for the probe wandering to be corrected in post-acquisition processing. Not only is there an apparent increase in the resolution of the reconstructed images, but probe wandering due to instrument misalignment is reduced, potentially easing an already difficult alignment procedure.

💡 Research Summary

Precession electron diffraction (PED) has become a cornerstone technique for crystallographic structure determination, strain mapping, and orientation analysis because it samples a larger volume of reciprocal space and yields quasi‑kinematic intensities. However, as the precession angle increases, the electron probe follows a circular trajectory on the aberration surface, leading to a periodic displacement known as “probe wandering.” This displacement, driven primarily by spherical aberration and any misalignment of the precession pivot, effectively enlarges the probe size and blurs virtual bright‑field (VBF) reconstructions derived from scanning PED (SPED) data. Traditional approaches mitigate the effect by limiting the precession angle or by painstakingly optimizing instrument alignment, but a comprehensive correction has remained elusive.

In this work, Nordahl et al. introduce “precession path segmentation,” a methodology that leverages fast pixelated detectors to record multiple frames during each azimuthal rotation of the precessing beam. By dividing a full precession cycle into a series of n = 8 temporal segments, each segment captures a distinct portion of the probe’s trajectory. The authors employed a JEOL JEM‑2100F operating at 200 kV equipped with a NanoMEGAS DigiSTAR precession generator and a Quantum Detectors MerlinEM direct‑electron detector. The precession angle was set to 1.0° (≈17.5 mrad) with a rotation frequency of 100 Hz. Two SPED datasets were acquired: one with a well‑aligned scan (step size = 5.6 nm) and another deliberately misaligned by 0.1 % of the scan coil amplitudes (step size = 10.2 nm) to generate a larger probe shift (up to ~13 nm).

Data processing began by slicing the 2048 × 256 × 256 × 256 4D‑STEM stack into eight 256 × 256 sub‑stacks, each representing a single precession segment. For each sub‑stack, a VBF image was reconstructed. Because probe wandering causes the same structural features to appear at different lateral positions in each segment, the set of eight VBF images exhibits a circular motion. The authors imported the image stack into the SmartAlign plugin of Gatan Microscopy Suite, which first up‑samples the images by a factor of two (made possible by the relatively large scan step relative to probe size) and then performs rigid (translation‑only) alignment. After alignment, the eight corrected VBF images are summed to produce a final 256 × 256 VBF reconstruction.

The corrected images demonstrate a marked improvement in contrast and edge definition. In the deliberately misaligned dataset, the edge steepness parameter k (derived from an arctangent fit) increased from 0.15 ± 0.01 (uncorrected) to 0.38 ± 0.03 (corrected), a 2.5‑fold enhancement. The blur in the uncorrected image is quantitatively equivalent to convolution with a Gaussian kernel of σ ≈ 7 pixels. Line profiles extracted from identical regions show a broader intensity range and sharper transitions after correction. In the well‑aligned dataset, where probe wandering was estimated at ~7 nm, the correction still yielded noticeable gains: edge contrast was higher, subtle intensity variations within crystalline domains became visible, and the overall image appeared less smeared.

The authors discuss the theoretical limit of segmentation: for a probe semi‑convergence angle α ≈ 1.2 mrad and precession angle φ ≈ 17.5 mrad, achieving a “single‑probe” segment would require roughly 2π φ/(2α) ≈ 46 segments. While this would provide a true φ‑tilt series captured instantaneously, the per‑segment signal would drop dramatically unless the precession frequency is reduced, increasing total acquisition time. Nonetheless, the study demonstrates that even modest segmentation (n = 8) substantially mitigates probe wandering, especially when the dominant contribution arises from spherical aberration (≈1 nm shifts on aberration‑corrected instruments).

Beyond VBF reconstruction, the authors note that the same segmentation framework could be applied directly to diffraction patterns: by shifting each segment’s pattern by the estimated probe displacement before summation, one could recover higher‑quality diffraction data for indexing or quantitative analysis. However, this requires precise knowledge of the probe trajectory, which may be derived from experimental parameters, aberration coefficients, or iterative fitting of feature motion.

In conclusion, precession path segmentation combined with post‑acquisition rigid alignment offers a practical, data‑driven solution to probe wandering in SPED. It reduces image blur, enhances spatial resolution, and relaxes the stringent alignment requirements that traditionally limit PED throughput. The authors provide open‑access datasets and processing scripts (Zenodo DOI: 10.5281/zenodo.7319130), facilitating reproducibility and encouraging broader adoption of the technique within the electron microscopy community.