Virtual dark field, digital dark field, and ML clustering

Because a 4D-STEM dataset contains the entire diffraction pattern at every probe position, any STEM detector geometry can be applied after the experiment: integrate the intensity inside a chosen region of the diffraction pattern at each probe position, and the result is an image. This is virtual imaging, and it is usually the first, and often the most informative, analysis applied to any 4D-STEM dataset. Virtual bright field and dark field reconstruction in this sense was popularized by Rauch and co-workers alongside scanning precession diffraction and ACOM VILADOT et al. (2013), Rauch & Véron (2014), and generalized to arbitrarily shaped virtual apertures by Gammer et al. Gammer et al. (2015).

Virtual bright field and dark field¶

A circular mask over the central beam gives a virtual bright field (BF) image; an annulus outside it gives a virtual annular dark field (ADF). The two are complementary: electrons scattered out of the BF disk land in the DF detector, so regions that darken in BF brighten in DF. Unlike physical detectors, virtual detectors are free: you can try any inner/outer radius, any shape, any position, and iterate until the contrast isolates the feature you care about Paterson et al. (2020):

• Detector design matters. The BF detector should capture the unscattered disk (slightly expanded to tolerate residual descan); the ADF annulus geometry controls whether contrast is dominated by diffraction (low angles) or thickness/Z (high angles).

• Selected-area diffraction in reverse: integrating diffraction patterns over a real-space region of interest gives a virtual selected-area pattern from exactly that region, ideal for identifying which reflections belong to which microstructural feature.

Digital dark field¶

Classical dark field TEM tilts the beam (or shifts the objective aperture) so one chosen Bragg reflection forms the image:

The 4D-STEM equivalent, digital dark field (DDF) MacLaren et al. (2024), places a virtual aperture over one (or several) specific Bragg reflections and maps where in real space that reflection is excited. Every reflection in the dataset is available simultaneously, from a single scan:

This is enormously powerful for microstructure:

• Grain and domain mapping: each grain lights up only in the reflections it produces, so DDF images segment grains, twins, and ferroelastic/ferroelectric domains, even when they are invisible in BF/ADF contrast MacLaren et al. (2020).

• Superlattice and ordered phases: placing the aperture on superlattice reflections maps ordered regions and antiphase domains directly:

• Tracking spots, not just masking them: in real datasets the reflections move (strain, rotation, descan), so robust DDF implementations follow the peak within a window rather than using a fixed mask; this is where Bragg-vector-based approaches and fast implementations (Kelvin_STEM, py4DSTEM, pyxem) come in.

• From the ensemble of DDF images, phase and domain maps of the whole field of view can be assembled, the manual counterpart of the machine-learning clustering approaches below.

Machine-learning clustering¶

A 4D-STEM dataset from a complex microstructure can contain thousands of distinct diffraction patterns: different phases, orientations, domains, and overlaps. Designing virtual detectors by hand (as in the previous section) works when you know what you are looking for; unsupervised machine learning lets the data tell you what distinct patterns exist and where they occur, with no prior assumptions about the structures present Martineau et al. (2019).

The idea¶

Treat each probe position as one observation (a vector of detector-pixel intensities) and ask: what small set of characteristic patterns, mixed in varying proportions, explains the whole dataset? Two families of methods are widely used:

• Matrix decomposition (PCA, non-negative matrix factorization): factorize the data into a set of component patterns and their real-space loading maps. NMF’s non-negativity constraint suits diffraction data, since patterns and mixing weights are both inherently non-negative. PCA is often used first for denoising and to estimate how many components the data supports (scree plot).

• Clustering: group similar observations, giving a hard segmentation of the field of view into phases/domains, with each cluster’s mean pattern available for crystallographic interpretation. Centroid methods (k-means, Gaussian mixtures) require choosing the number of clusters up front; density-based methods (DBSCAN and its relatives) instead take density threshold parameters and find as many clusters as the data supports arXiv:2606.23201. The observations need not be whole patterns: clustering the detected Bragg peaks themselves in combined real and diffraction space is the basis of the clustering-based digital dark field workflow in this session’s tutorial.

A typical workflow: preprocess (align the zero beam, mask the central disk or take a log/power scaling so weak reflections count, optionally bin) → reduce dimensionality → decompose or cluster → inspect the component patterns as diffraction patterns and interpret them crystallographically → refine.

Why this works so well for diffraction data¶

Unlike natural images, diffraction patterns from a given phase/orientation are highly reproducible; the “signal manifold” is low-dimensional. Clustering therefore tends to recover physically meaningful classes: distinct phases, orientation variants, ordered vs. disordered regions, and even subtle symmetry-breaking distortions that are hard to see by eye Kalinin et al. (2022). The output is a phase/domain map plus a library of representative patterns, obtained in minutes from datasets far too large to inspect manually:

Caveats¶

• Components are mathematical objects, not guaranteed physics: decomposition can mix or split physical phases (e.g., NMF components need not correspond one-to-one with real structures). Always validate components against the raw patterns and against crystallographic simulation.

• Intensity scaling choices (log, power, masking the direct beam) strongly affect what the algorithms consider “similar”; dynamical intensity variations within one grain can otherwise dominate over phase differences.

• Density-based clustering does not assign every point, and that is fine. The unclustered leftovers include very small diffracting objects, false detections, and poor detections shifted well off the true disk centroid. The density parameters set the smallest object you wish to see (e.g. min_samples = 20), and even without analysing every disk you get far more clusters than you would ever analyse manually.