1 Mark the two discs

Click the button, then click the disc centre on the image. Drag markers (or the ring handle ◆) to refine. Scroll = zoom, drag empty area = pan.

2 Fringe detection

averaging width px smoothing px sensitivity

Dark-fringe markers: drag to refine · alt-click the profile to add · double-click a marker to delete · drag the green s = 0 line onto the bright central fringe.

3 Physics inputs

HT kV λ = pm

d_hkl nm or a nm hkl

ξ_g (tabulated, optional) nm

4 Kelly–Allen fit

n₁ assignment:

5 Overlay style

Font

Font size (%) 100

Line thickness (%) 100

000 disc color

hkl disc color

Fringe marks color

s = 0 line color

bold labels disc labels disc rings

centreline fringe marks s = 0 line result stamp on export

Templates

Saved templates

New template name

The active style applies to the pattern view and the exported PNG, same as the SAED indexer. Download templates as a .json to reuse or share them; load the file in a future session to get them back.

Intensity profile along 000 → hkl (band-averaged)

Kelly–Allen extrapolation (s_i/n_i)² vs (1/n_i)²

What an ideal pattern looks like (for the easiest measurement)

Clean two-beam: only 000 and one strong hkl disc; everything else faint (tilt using Kikuchi bands until the bright band sits in the hkl disc).
Discs clearly separated: convergence α ≈ 0.3–0.7 θ_B; the gap between disc edges should be comparable to a disc radius. Overlap (Kossel regime) makes the profile unreadable.
Bright s = 0 band near the disc centre with dark fringes symmetric on both sides: that symmetry is your check that the tilt is right.
≥ 3 crisp dark fringes per side (t ≈ 2–5 ξ_g at that spot). Too few → move to a thicker area or a stronger (smaller-ξ_g) reflection; washed-out → thinner area or zero-loss filtering.
Straight, parallel fringes perpendicular to the 000→hkl line: probe on a flat, unbent, unstrained region.
Sharp disc edges (diffraction focus) and no saturation in either disc (a clipped 000 disc flattens the profile top and shifts detected minima).
Flat dark background: zero-loss energy filtering if available; short exposure sum beats one long saturated frame.
Checked on your pattern, clipping: pixels at the top or bottom of the file’s integer range in the part of the hkl disc that is read are counted, because a clipped pixel has lost its true value (a float file has no fixed range and is not checked).
Checked, different n values: R² can only test n₁ when the fringes give 3 or more different n, because a straight line always passes through two groups of points.
Checked, uncertainty: the 95% range of t from the scatter of the points, with the Student t factor for N − 2 spare points (NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.7.2); a range with no upper limit is flagged. It does not include errors in d, the voltage or n₁.
Checked, extinction distance: without a tabulated ξ_g, n₁ rests on the straightness of the line alone, so the t from the neighbouring n₁ is shown (Kelly et al. 1975; Allen 1981).
Fringe positions: fringes are found on the smoothed profile, then each one is placed by a weighted cubic fit to the unsmoothed profile across its dip. Smoothing alone moves an uneven dip outward by a fraction of a pixel, because the bright fringe outside each dark fringe is weaker than the one inside. A mark you add or drag by hand is not moved by this fit.
Automatic n₁: dark fringes come in mirror pairs about s = 0. So a mark within 3 px of s = 0, or one less than a third as far out as the next mark with no partner on the other side, is the dark centre and is left out. This keeps n counting the same fringes on both sides. Two marks within 3 px, one on each side at the same distance, are kept: they are the first pair of fringes. Then n₁ is the one whose fitted ξ_g is closest to the tabulated ξ_g (Kelly et al. 1975; Allen 1981), or, with none entered, the one with the straightest line, every mark’s position counted equally. n₁ from 1 to 20 is tried.
Checked, fit against marks: dark fringes sit where t·s_eff is a whole number, so the first one from s = 0 has the smallest whole n at or above t/ξ_g; a predicted fringe inside the first mark is flagged, unless a mark left out as the dark centre is there.
Checked, sampling: the fringe spacing the fit predicts at the edge of the disc; a repeat shorter than 2 pixels cannot be recorded.

Checked (October 2026). The built-in demo is a two-beam Al 200-type disc computed for t = 260 nm and ξ_g = 75 nm at 200 kV. The fringe finder and the Kelly-Allen fit return t = 260 ± 1 nm and ξ_g = 75 nm with R² = 1.0000 and n₁ = 4 picked automatically. The fit is the (s_i/n_i)² against (1/n_i)² line of Kelly et al. 1975 with the treatment of the first fringe order from Allen 1981.

Physics: dark fringes at t·s_eff = n with s_eff = √(s² + 1/ξ_g²); s_i = (x_i/X)·λ/d² (self-calibrating: camera length cancels); plot (s_i/n_i)² vs (1/n_i)²: intercept = 1/t², slope = −1/ξ_g². Companion pages: CBED & lamella thickness (the theory, interactive) · back focal plane & diffraction focus. References: P. M. Kelly et al., The determination of foil thickness by scanning transmission electron microscopy, Phys. Status Solidi A 31, 771–780 (1975); S. M. Allen, Foil thickness measurements from convergent-beam diffraction patterns, Philos. Mag. A 43, 325–335 (1981); D. B. Williams and C. B. Carter, Transmission Electron Microscopy, 2nd ed., Springer (2009), chapter 21 (thickness determination); NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.6.7.2 (Student t critical values). Decoders: UTIF.js (MIT), jsfive (BSD), pako (MIT), inlined; no network needed.