EBSD · Indexing
EBSD indexing methods compared: Hough, dictionary, refinement and spherical indexing
The pattern is the same. The method decides which mistakes end up in your map.
Indexing is the step that turns each Kikuchi pattern into a crystal orientation. This page simulates one EBSD map (the truth is known at every point), indexes it four ways, and puts the maps side by side: IPF, the method's own score, the error against the truth, KAM and grain boundaries. Pick a case, then click any point to see its pattern and what each method did with it.
Patterns
Hough
Dictionary and refinement
Spherical
Maps
Material and microstructure come with each case.
How does each indexing method find an orientation?
Hough (triplet voting)
Background removed, the pattern goes through a Hough (Radon) transform: every straight line in the pattern becomes a point, so a bright band becomes a bright spot. The strongest spots are the bands. Every band is a lattice plane, so the angles between bands are angles between planes. Three bands at a time are compared with a table of plane angles; each consistent set votes for an orientation. The confidence index (CI) is the winner's lead over the runner-up, as a share of all triplets.
Dictionary indexing
A computer simulates a pattern for every orientation on a grid (the cubochoric grid, about 30,000 orientations 3° apart for a cubic crystal). Each measured pattern is compared with all of them. The score is the normalised cross-correlation (NCC): 1 is a perfect match, 0 no match. The best score wins. The answer is always one of the grid orientations, so it is never closer than about half the grid spacing.
Refinement
Start from the dictionary answer (or any other). Simulate the pattern at that orientation, then at slightly turned ones, and keep moving towards a higher NCC until it stops improving (a Nelder-Mead search). The answer can now fall between grid points. It needs about a hundred simulations per point, so it is the slowest step here.
Spherical indexing
Every pixel of the screen is a direction in space, so the pattern can be put back on a sphere. There it is written as a sum of spherical harmonics up to a degree B, the bandwidth. The master pattern is written the same way. The match for every possible rotation then comes out of one set of Fourier transforms. The highest peak is the orientation. B sets the finest detail it uses.
Which indexing method should I use?
| Your situation | What tends to work | Why | Case to try |
|---|---|---|---|
| Clean patterns, you want a map quickly | Hough | Fast and precise enough (a few tenths of a degree here). Every method finds the same grains. | 1 |
| Noisy patterns from fast mapping or a low beam current | Dictionary or spherical indexing, then refinement | They compare the whole pattern, so they keep working after the Hough step can no longer pick out the bands. | 2 |
| You must use Hough on noisy data | Neighbour averaging (NPAR) first | Averaging raises the signal. It also mixes grains at boundaries, so check boundary points. | 3 |
| You need small misorientations (KAM, GND, subgrains) | Refinement after dictionary or spherical indexing | A grid answer adds steps; refinement removes them and gives the lowest noise floor here. | 4 |
| Grains near the size of the beam spot | Any method, then use the score map to flag boundary points | A mixed pattern is mostly indexed as the grain with the larger share; its score drops, so boundaries show up in the score map. | 5 |
| A pseudosymmetric phase (γ-TiAl, tetragonal ZrO2, many martensites) | A whole-pattern method, then refine every pseudosymmetric variant and keep the best match | The variants differ in weak bands and band intensities, which Hough does not use. A coarse dictionary grid can hide that difference; comparing refined variants does not (Pang et al. 2020). | 6 |
| Orientations drift slowly across a large map, or the fit is poor everywhere | Calibrate the pattern centre, or refine it with the orientations | No method fixes the geometry it is given. | 7 |
Indexing an EBSD map: seven steps
| Step | What you do | Knob on this page | What goes wrong |
|---|---|---|---|
| 1 Collect | Choose pattern size (binning) and exposure. Keep the raw patterns: every method below can be rerun on them later. | pattern size, electrons per pattern | Too few electrons: Hough fails first. Saving only orientations locks you into one method. |
| 2 Background | Subtract the static background (the average pattern of the map), then the dynamic one (a wide blur of each pattern). | always on here | A poor background leaves broad shading that the Hough transform reads as bands. |
| 3 Pattern centre | Calibrate where the beam spot sits relative to the screen (x*, y*, z*). | pattern-centre error | Every orientation is off, and the error changes across a large map. |
| 4 Index | Hough for clean patterns; dictionary or spherical indexing for noisy or pseudosymmetric ones. | bands, tolerance, grid spacing, bandwidth | A coarse dictionary grid with sharp patterns can pick a wrong neighbour; a low bandwidth blurs the detail. |
| 5 Refine | Refine the orientations (and the pattern centre) against simulated patterns. | the refinement row | Refinement polishes an answer; it does not fix a wrong grain. |
| 6 Check | Look at the score maps, not only IPF. Plot the score along boundaries. | score and error columns | A low score along a boundary is a mixed pattern, not a new phase. |
| 7 Report | Write down the method, its settings (bands, tolerance, grid, bandwidth, refinement), the pattern size and the threshold you used. | Numbers such as KAM and grain count depend on the method; without the settings nobody can repeat them. |
Do it on your own data
- Save the raw patterns (for example as an EDAX .up2, Oxford .h5oina or Bruker .h5 file), not just the orientations.
- Index once with your usual Hough settings. Keep the CI (or MAD) map.
- Calibrate the pattern centre on a few clean patterns. Open-source tools can do it (kikuchipy, PyEBSDIndex, EMsoft).
- Rerun the noisy regions with dictionary indexing, or the whole map with spherical indexing if your software has it.
- Refine the orientations. Compare the KAM map before and after: the floor you see inside a flat grain is your noise floor.
- For a pseudosymmetric phase, check a few points by eye: overlay the simulated pattern of each candidate and look at the weak bands.
- Report the method and its settings with every map.
Scope and limits
The patterns are simulated with the site's dynamical EBSD engine (a Monte Carlo of the beam and many-beam Bloch waves: EBSD pattern simulator) at 20 kV and 70° tilt, for nickel and γ-TiAl. The experimental patterns add three energy bins with their own depth and angle spread, the electrons that lose coherence (a smooth background), sub-pixel detector integration, beam-spot mixing and Poisson counting noise. The indexing model uses the energy-averaged master pattern, so it is close to the experiment but not identical, as in real work. Not included: detector gain, read noise and distortion, surface layers, sample drift, charging, pattern-centre variation across the map, and more than one phase. Hough follows the classic triplet method; modern implementations (for example PyEBSDIndex) weight bands and index some very noisy patterns that this one does not. The dictionary search uses a 3° grid on patterns binned 2 × 2, and spherical indexing a bandwidth of 63, so both run in a browser; commercial and research codes often use finer grids and higher bandwidths. Error, KAM and grain counts are measured against the known truth, which a real map never has.
On this site: From Kikuchi pattern to orientation · Pattern quality · KAM, GND and step size · Cleaning EBSD data honestly · Reference frames and conventions · EBSD pattern simulator
Questions people ask
Is dictionary indexing always better than Hough?
No. With clean patterns both find the same grains, and Hough is much faster. Dictionary indexing wins when the patterns are noisy, small or pseudosymmetric, because it uses the whole pattern. On its own it is less precise than Hough, because its answers sit on a grid; refinement fixes that.
What dictionary grid spacing should I use?
Fine enough that the nearest grid orientation still matches better than any wrong one. Sharp, large patterns need a finer grid. Try case 1 with 5°, 4° and 3° and watch the error column: at 5° some points pick a wrong neighbour. The kikuchipy tutorial uses 3° followed by refinement. A finer grid costs time: half the spacing means about eight times as many patterns.
What does the confidence index actually measure?
How far the winning orientation is ahead of the second one in the Hough vote, as a share of all band triplets. A low CI means the vote was close, not necessarily that the answer is wrong. De Vincentis and Field (2021) found about 90 % of solutions right at CI 0.1 or more when at least 8 bands were used, in silicon and zinc. The table on this page shows the same check for each run.
Why does my KAM map look speckled or stepped after dictionary indexing?
Neighbouring points jump between grid orientations, so the map shows the grid, not the crystal. Refine the orientations before you compute KAM or GND density.
Is spherical indexing the same as dictionary indexing?
They answer the same question: which orientation makes the simulated pattern look most like the measured one. Spherical indexing gets the answer for every rotation at once through spherical harmonics, instead of trying a list. Its detail is set by the bandwidth, the dictionary's by the grid spacing. Both are usually followed by refinement.
Can any indexing method fix pseudosymmetry?
Only a method that sees the difference. When the variants put the bands in almost the same places, the difference lies in weak bands and band intensities. Hough uses band positions, so it cannot. A dictionary can, but only if its grid is fine enough near the answer; the usual fix is to refine each variant and keep the best match. Case 6 shows both steps. Check a few points by eye as well.
References
Show the 14 references
- N. C. Krieger Lassen, Automated determination of crystal orientations from electron backscattering patterns, PhD thesis, Technical University of Denmark (1994).
- K. Kunze, S. I. Wright, B. L. Adams and D. J. Dingley, Advances in automatic EBSP single orientation measurements, Textures and Microstructures 20, 41 (1993).
- D. P. Field, Recent advances in the application of orientation imaging, Ultramicroscopy 67, 1 (1997). The confidence index.
- N. S. De Vincentis and D. P. Field, Factors affecting confidence index in EBSD analysis, Ultramicroscopy 225, 113269 (2021).
- Y. H. Chen, S. U. Park, D. Wei, G. Newstadt, M. A. Jackson, J. P. Simmons, M. De Graef and A. O. Hero, A dictionary approach to electron backscatter diffraction indexing, Microscopy and Microanalysis 21, 739 (2015).
- S. I. Wright, M. M. Nowell, S. P. Lindeman, P. P. Camus, M. De Graef and M. A. Jackson, Introduction and comparison of new EBSD post-processing methodologies, Ultramicroscopy 159, 81 (2015). Neighbour pattern averaging.
- F. Ram, S. Wright, S. Singh and M. De Graef, Error analysis of the crystal orientations obtained by the dictionary approach to EBSD indexing, Ultramicroscopy 181, 17 (2017).
- S. Singh, F. Ram and M. De Graef, Application of forward models to crystal orientation refinement, Journal of Applied Crystallography 50, 1664 (2017).
- W. C. Lenthe, S. Singh and M. De Graef, A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns, Ultramicroscopy 207, 112841 (2019).
- R. Hielscher, F. Bartel and T. B. Britton, Gazing at crystal balls: electron backscatter diffraction pattern analysis and cross correlation on the sphere, Ultramicroscopy 207, 112836 (2019).
- D. J. Rowenhorst, P. G. Callahan and H. W. Ånes, Fast Radon transforms for high-precision EBSD orientation determination using PyEBSDIndex, Journal of Applied Crystallography 57, 3 (2024).
- M. A. Jackson, E. Pascal and M. De Graef, Dictionary indexing of electron back-scatter diffraction patterns: a hands-on tutorial, Integrating Materials and Manufacturing Innovation 8, 226 (2019).
- P. G. Callahan and M. De Graef, Dynamical electron backscatter diffraction patterns. Part I: pattern simulations, Microscopy and Microanalysis 19, 1255 (2013).
- E. L. Pang, P. M. Larsen and C. A. Schuh, Resolving pseudosymmetry in tetragonal ZrO2 using electron backscatter diffraction with a modified dictionary indexing approach, Journal of Applied Crystallography 53, 1060 (2020).
BibTeX
@misc{tripathy2026ebsdindexing,
author = {Tripathy, Manisha},
title = {EBSD Indexing Methods Compared: Hough, Dictionary, Refinement and Spherical Indexing},
howpublished = {untethered atom},
year = {2026},
url = {https://untetheredatom.com/ebsd/ebsd-indexing-methods}
}