Indexing a selected-area electron diffraction (SAED) pattern means assigning Miller indices (hkl) to the diffraction spots and identifying the zone axis [uvw]: the crystallographic direction along which the electron beam travels through the crystal. It is one of the most common tasks in transmission electron microscopy (TEM), and one of the most error-prone to do by hand with a ruler and a table of d-spacings.
Click the transmitted beam and the two shortest independent spots. The tool measures R₁, R₂ and the angle between them.
The ratio R₂/R₁ and the angle do not depend on the camera constant, so no camera-length calibration is needed.
Superlattice, twin and double-diffraction spots can sit closer to 000 than the true fundamentals. Pick two short, strong spots of the innermost net.
Matching zone axes are ranked, and a predicted net is drawn on your image so you can check the answer against the actual spots.
This tool automates the classic ratio method. You upload a diffraction pattern, click the transmitted (central) beam and the two shortest independent spots, and it measures the two reciprocal distances R₁ and R₂ and the angle between them. Because the analysis uses the ratio R₂/R₁ together with the inter-spot angle, the camera constant cancels out. No camera-length calibration is needed. One habit keeps the method honest: pick two short, strong spots that clearly belong to the innermost net. The nearest spots are not automatically the right pair; superlattice reflections, twins and double diffraction can plant fainter spots closer to 000 than the true fundamentals, which is exactly what the extra-spot checks below are for. The measured ratio and angle are compared against every allowed reflection pair for the chosen structure, and matching zone axes are ranked. A predicted diffraction net is then overlaid on your image so you can verify the assignment against the actual spots rather than trusting a table.
Built-in structure-factor rules cover FCC (e.g. Al, Cu, Ni, austenitic steels), BCC (e.g. ferrite, W, Mo), simple cubic, diamond cubic (Si, Ge), and HCP (e.g. Ti, Zn, Mg), plus a custom-lattice mode where you supply your own lattice parameters.
Real patterns are rarely clean. The illumination is uneven, the transmitted beam is clipped and blooming, spots are streaked or all elongated along one axis because the stigmators are off, the camera has hot pixels and a dead column, a beamstop covers 000, and a twin or a precipitate has planted a second net on top of the first. Auto-detect is built for that case, and every stage is there to defeat one of those problems.
Auto-detect will also say that it cannot fit a net rather than invent one. That is the correct answer for a pattern that is polycrystalline, badly overlapped, or too far gone, and it is the answer you want from a tool you are about to quote in a thesis.
Elliptical distortion of the projector system turns a circle into an ellipse. The same {hkl} family then measures a different d-spacing at different azimuths.
Reported values run from 0.38% on a well-characterised machine to a 2% installation specification. At 1%, a reflection 500 px out moves 5 px.
A net gives two shape numbers, a length ratio and an angle. The distortion adds two unknowns, an amplitude and an axis.
It ranks candidates by the stretch each one needs, checks which nodes of the net are occupied, and says so in the Pattern quality panel when the leaders are too close to call.
Elliptical distortion of the projector system is the geometric artifact that defeats calibration-free indexing, and no amount of algorithm will remove it from a single spot pattern. The recorded net is the true net carried through a linear map, so a circle images as an ellipse and the same {hkl} family measures a different d-spacing at different azimuths. Reported magnitudes are 1.6–1.9% across camera lengths on one instrument (Capitani et al. 2006), a 2% installation specification with 1.6% as-installed falling to 0.3% after stigmator optimisation (Mitchell 2022), and 0.38–0.39% on a well-characterised machine (Brázda et al. 2022). At 1% and a reflection 500 px out, that is a 5 px radial displacement, two orders of magnitude above the sub-pixel precision of the peak finder.
The reason it cannot be solved from one pattern is a counting argument: a two-dimensional net gives you two shape observables, a length ratio and an included angle, and the distortion adds two unknowns, an amplitude and an axis. Brázda et al. state the same conclusion, that elliptical distortion is the one distortion that cannot be separated from the lattice parameters without external information. So this tool does three things instead of pretending otherwise. It ranks candidates by how much anisotropic stretch each one needs rather than by ratio and angle separately, so the correct zone axis stays in contention instead of falling out of tolerance. It checks each candidate against which nodes of the net are actually occupied, since a wrong candidate that happens to match the distorted shape rarely also predicts the right extinctions. And when the leading candidates are separated by less than the distortion a real instrument carries, it says so in the Pattern quality panel instead of letting rank 1 look decisive.
If you have calibrated your instrument, enter the ellipticity and its axis in the Crystal panel, or press Load saved calibration to pull them from the distortion calibrator, and the distortion is removed before anything is measured. Entering a camera constant so absolute d-spacings can discriminate, or tilting to a second zone axis, are the other two ways out.
A clean, symmetric single-crystal net. Not rings or overlapping grains.
It fits the net to every spot at once. If you click, zoom in first and keep snap to spot centroid ticked.
A correct index reproduces all spots of the net, not just the two you used.
It tells you whether 000 was seen or reconstructed, whether spots are clipped, and whether an elongation is really your stigmators.
Use an on-axis single-crystal pattern (a clean symmetric net, not rings or overlapping grains). Prefer Auto-detect over clicking: it fits the net to every spot at once, so it does not carry the error of two hand-placed centroids, and at high-symmetry zones such as ⟨100⟩ and ⟨112⟩ that error is the whole ballgame (with no camera constant entered, those zones show genuine ratio and angle ties between different families, and a fraction of a pixel decides which one is ranked first). If you do click, zoom in first and leave snap to spot centroid ticked. Always check the overlay: a correct index reproduces all spots of the net, not just the two you used. Read the Pattern quality panel before you believe the answer: it tells you whether 000 was actually seen or reconstructed, whether spots are clipped, and whether the elongation you are about to call a relrod is really your stigmators.
The tool runs entirely in your browser; your image is never uploaded to any server.
More TEM guides on this site: the back focal plane & diffraction focus · CBED & lamella thickness from K–M fringes · about the author
@misc{tripathy2026saedzoneaxisindexer,
author = {Tripathy, Manisha},
title = {SAED Zone-Axis Indexer},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/saed-zone-axis-indexer}},
note = {Interactive teaching resource}
}