EBSD

Electron Backscatter Diffraction

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Standard reconstruction benchmark — forward model perfectly known, no calibration needed. Score = 0.5 × clip((PSNR−15)/30, 0, 1) + 0.5 × SSIM

#	Method	Score	PSNR (dB)	SSIM	Source
🥇	DiffEBSD DiffEBSD Gao et al. 2024 39.1 dB SSIM 0.954 Checkpoint unavailable	0.879	39.1	0.954	✓ Certified	Gao et al. 2024
🥈	PhysEBSD PhysEBSD Chen et al. 2024 37.8 dB SSIM 0.943 Checkpoint unavailable	0.851	37.8	0.943	✓ Certified	Chen et al. 2024
🥉	SwinEBSD SwinEBSD Li et al. 2023 36.5 dB SSIM 0.931 Checkpoint unavailable	0.824	36.5	0.931	✓ Certified	Li et al. 2023
4	TransEBSD TransEBSD Wang et al. 2022 34.9 dB SSIM 0.913 Checkpoint unavailable	0.788	34.9	0.913	✓ Certified	Wang et al. 2022
5	PointEBSD PointEBSD Foden et al. 2022 32.3 dB SSIM 0.874 Checkpoint unavailable	0.725	32.3	0.874	✓ Certified	Foden et al. 2022
6	DnCNN-EBSD DnCNN-EBSD Kaufmann et al. 2020 29.6 dB SSIM 0.834 Checkpoint unavailable	0.660	29.6	0.834	✓ Certified	Kaufmann et al. 2020
7	TV-EBSD TV-EBSD Wilkinson et al. 2006 26.8 dB SSIM 0.779 Try in SpecLab →	0.586	26.8	0.779	✓ Certified	Wilkinson et al. 2006
8	DI-EBSD DI-EBSD Chen et al. 2015 24.2 dB SSIM 0.741 Try in SpecLab →	0.524	24.2	0.741	✓ Certified	Chen et al. 2015
9	Hough-EBSD Hough-EBSD Krieger Lassen 1994 21.5 dB SSIM 0.698 Try in SpecLab →	0.457	21.5	0.698	✓ Certified	Krieger Lassen 1994

Dataset: PWM Benchmark (9 algorithms)

Blind Reconstruction Challenge — forward model has unknown mismatch, must calibrate from data. Score = 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

#	Method	Overall Score	Public PSNR / SSIM	Dev PSNR / SSIM	Hidden PSNR / SSIM	Trust	Source
🥇	PhysEBSD + gradient PhysEBSD + gradient Chen et al., Acta Mater. 2024 Score 0.770 Correct & Reconstruct →	0.770	0.819 35.0 dB / 0.968	0.766 32.05 dB / 0.943	0.725 30.26 dB / 0.921	✓ Certified	Chen et al., Acta Mater. 2024
🥈	SwinEBSD + gradient SwinEBSD + gradient Li et al., npj Comput. Mater. 2023 Score 0.745 Correct & Reconstruct →	0.745	0.803 33.87 dB / 0.960	0.745 29.91 dB / 0.915	0.686 27.04 dB / 0.859	✓ Certified	Li et al., npj Comput. Mater. 2023
🥉	DiffEBSD + gradient DiffEBSD + gradient Gao et al., NeurIPS 2024 Score 0.742 Correct & Reconstruct →	0.742	0.835 36.11 dB / 0.974	0.716 28.32 dB / 0.887	0.676 26.93 dB / 0.856	✓ Certified	Gao et al., NeurIPS 2024
4	TransEBSD + gradient TransEBSD + gradient Wang et al., Acta Mater. 2022 Score 0.706 Correct & Reconstruct →	0.706	0.780 32.36 dB / 0.946	0.721 28.47 dB / 0.890	0.618 24.02 dB / 0.769	✓ Certified	Wang et al., Acta Mater. 2022
5	PointEBSD + gradient PointEBSD + gradient Foden et al., Ultramicroscopy 2022 Score 0.601 Correct & Reconstruct →	0.601	0.767 30.92 dB / 0.930	0.565 21.59 dB / 0.672	0.471 18.82 dB / 0.541	✓ Certified	Foden et al., Ultramicroscopy 2022
6	DnCNN-EBSD + gradient DnCNN-EBSD + gradient Kaufmann et al., npj Comput. Mater. 2020 Score 0.589 Correct & Reconstruct →	0.589	0.721 27.94 dB / 0.880	0.555 21.32 dB / 0.660	0.492 19.34 dB / 0.567	✓ Certified	Kaufmann et al., npj Comput. Mater. 2020
7	DI-EBSD + gradient DI-EBSD + gradient Chen et al., Ultramicroscopy 2015 Score 0.556 Correct & Reconstruct →	0.556	0.578 22.32 dB / 0.703	0.545 21.18 dB / 0.654	0.546 21.15 dB / 0.652	✓ Certified	Chen et al., Ultramicroscopy 2015
8	TV-EBSD + gradient TV-EBSD + gradient Wilkinson et al., Mater. Charact. 2006 Score 0.520 Correct & Reconstruct →	0.520	0.637 24.56 dB / 0.788	0.493 19.37 dB / 0.568	0.430 18.08 dB / 0.504	✓ Certified	Wilkinson et al., Mater. Charact. 2006
9	Hough-EBSD + gradient Hough-EBSD + gradient Krieger Lassen, J. Microsc. 1994 Score 0.480 Correct & Reconstruct →	0.480	0.537 20.46 dB / 0.621	0.462 18.27 dB / 0.513	0.440 17.67 dB / 0.484	✓ Certified	Krieger Lassen, J. Microsc. 1994

Complete score requires all 3 tiers (Public + Dev + Hidden).

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Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%

Public 3 scenes

Full-access development tier with all data visible.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), spec ranges, ground truth (x_true), and true mismatch spec.

How to use: Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

What to submit: Reconstructed signals (x_hat) and corrected spec as HDF5.

Public Leaderboard

#	Method	Score	PSNR	SSIM
1	DiffEBSD + gradient	0.835	36.11	0.974
2	PhysEBSD + gradient	0.819	35.0	0.968
3	SwinEBSD + gradient	0.803	33.87	0.96
4	TransEBSD + gradient	0.780	32.36	0.946
5	PointEBSD + gradient	0.767	30.92	0.93
6	DnCNN-EBSD + gradient	0.721	27.94	0.88
7	TV-EBSD + gradient	0.637	24.56	0.788
8	DI-EBSD + gradient	0.578	22.32	0.703
9	Hough-EBSD + gradient	0.537	20.46	0.621

Spec Ranges (3 parameters)

Parameter	Min	Max	Unit
pattern_center	-2.0	4.0	pixels
sample_tilt	69.5	71.0	deg
detector_distance	-0.5	1.0	mm

View Details →

Dev 3 scenes

Blind evaluation tier — no ground truth available.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), and spec ranges only.

How to use: Apply your pipeline from the Public tier. Use consistency as self-check.

What to submit: Reconstructed signals and corrected spec. Scored server-side.

Dev Leaderboard

#	Method	Score	PSNR	SSIM
1	PhysEBSD + gradient	0.766	32.05	0.943
2	SwinEBSD + gradient	0.745	29.91	0.915
3	TransEBSD + gradient	0.721	28.47	0.89
4	DiffEBSD + gradient	0.716	28.32	0.887
5	PointEBSD + gradient	0.565	21.59	0.672
6	DnCNN-EBSD + gradient	0.555	21.32	0.66
7	DI-EBSD + gradient	0.545	21.18	0.654
8	TV-EBSD + gradient	0.493	19.37	0.568
9	Hough-EBSD + gradient	0.462	18.27	0.513

Spec Ranges (3 parameters)

Parameter	Min	Max	Unit
pattern_center	-2.4	3.6	pixels
sample_tilt	69.4	70.9	deg
detector_distance	-0.6	0.9	mm

Submit Reconstruction View Details →

Hidden 3 scenes

Fully blind server-side evaluation — no data download.

What you get & how to use

What you get: No data downloadable. Algorithm runs server-side on hidden measurements.

How to use: Package algorithm as Docker container / Python script. Submit via link.

What to submit: Containerized algorithm accepting y + H, outputting x_hat + corrected spec.

Hidden Leaderboard

#	Method	Score	PSNR	SSIM
1	PhysEBSD + gradient	0.725	30.26	0.921
2	SwinEBSD + gradient	0.686	27.04	0.859
3	DiffEBSD + gradient	0.676	26.93	0.856
4	TransEBSD + gradient	0.618	24.02	0.769
5	DI-EBSD + gradient	0.546	21.15	0.652
6	DnCNN-EBSD + gradient	0.492	19.34	0.567
7	PointEBSD + gradient	0.471	18.82	0.541
8	Hough-EBSD + gradient	0.440	17.67	0.484
9	TV-EBSD + gradient	0.430	18.08	0.504

Spec Ranges (3 parameters)

Parameter	Min	Max	Unit
pattern_center	-1.4	4.6	pixels
sample_tilt	69.65	71.15	deg
detector_distance	-0.35	1.15	mm

Submit Algorithm View Details →

Blind Reconstruction Challenge

Challenge

Given measurements with unknown mismatch and spec ranges (not exact params), reconstruct the original signal. A method must be evaluated on all three tiers for a complete score. Scored on a composite metric: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖).

Input

Measurements y, ideal forward model H, spec ranges

Output

Reconstructed signal x̂

About the Imaging Modality

EBSD maps crystallographic orientation by tilting a polished specimen to ~70 degrees in an SEM and recording Kikuchi diffraction patterns on a phosphor screen. Each pattern encodes the local crystal orientation, which is determined by automated indexing (Hough transform or dictionary indexing). Scanning the beam produces orientation maps (IPF), grain boundary maps, and texture information. Challenges include pattern quality degradation from surface damage, pseudosymmetry in indexing, and angular resolution limitations (~0.5 deg).

Principle

Electron Backscatter Diffraction (EBSD) maps the crystallographic orientation of polycrystalline materials at each surface point. A focused electron beam (15-30 keV) strikes a tilted (70°) polished specimen, generating backscattered electrons that form Kikuchi diffraction patterns on a phosphor screen/CMOS camera. Automated pattern indexing determines the crystal orientation at each point with ~0.5° angular resolution.

How to Build the System

Install an EBSD detector (phosphor screen + CCD/CMOS camera, e.g., Oxford Instruments Symmetry, EDAX Velocity) in an SEM chamber. Tilt the specimen to 70° toward the detector. Polish the sample surface to remove any deformation layer (final step: colloidal silica or ion milling). Set accelerating voltage 15-30 kV, high probe current (1-20 nA). Map with step sizes of 50 nm to 5 μm depending on grain size.

Common Reconstruction Algorithms

Hough transform band detection for Kikuchi pattern indexing
Dictionary indexing (template matching against simulated patterns)
Spherical indexing (GPU-accelerated orientation determination)
Neighbor pattern averaging and reindexing (NPAR) for noisy patterns
Deep-learning EBSD pattern indexing (faster and more robust than Hough)

Common Mistakes

Poor surface preparation leaving a deformed layer that degrades pattern quality
Camera settings (gain, exposure) not optimized, producing noisy or saturated patterns
Step size too large relative to the grain size, missing small grains or twin boundaries
Incorrect crystal structure or phase files used for indexing
Drift during long-duration EBSD maps distorting the scanned area

How to Avoid Mistakes

Use final polishing with colloidal silica (OPS) or broad Ar-ion milling
Optimize camera parameters with a reference crystal before mapping
Set step size ≤ 1/10 of the smallest grain dimension of interest
Verify crystal structure and lattice parameters in the phase file before indexing
Use beam shift or stage drift correction for maps longer than ~30 minutes

Forward-Model Mismatch Cases

The widefield fallback produces a blurred intensity image, but EBSD acquires Kikuchi diffraction patterns at each probe position — each pattern encodes the local crystal orientation (Euler angles) via characteristic Kikuchi bands
EBSD is fundamentally a crystallographic technique where the measurement is a diffraction pattern, not a spatial image — the widefield blur cannot produce orientation maps, grain boundaries, or texture information

How to Correct the Mismatch

Use the EBSD operator that models Kikuchi pattern generation from electron backscatter diffraction at each beam position, with pattern features determined by the local crystal orientation and structure
Index Kikuchi patterns using Hough transform (band detection) or dictionary-based matching to determine the crystal orientation (Euler angles) at each probe position, then assemble orientation maps

Experimental Setup — Signal Chain

$Experimental setup diagram for Electron Backscatter Diffraction$

Reconstruction Gallery — 4 Scenes × 3 Scenarios

Method: CPU_baseline | Mismatch: nominal (nominal=True, perturbed=False)

I Ideal II Mismatch (uncorrected) III Oracle correction

I — Ideal

Ground Truth

Measurement

Reconstruction

13.361718975877936 dB SSIM 0.012475920046010055

II — Mismatch

Ground Truth

Measurement

Reconstruction

13.355378863310248 dB SSIM 0.01188952431321307

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

17.660800558562674 dB SSIM 0.5449616747376919

I — Ideal

Ground Truth

Measurement

Reconstruction

14.602239047005954 dB SSIM 0.013106642314582598

II — Mismatch

Ground Truth

Measurement

Reconstruction

14.59613894925891 dB SSIM 0.012594004466623999

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

17.67274043078865 dB SSIM 0.39227201274836065

I — Ideal

Ground Truth

Measurement

Reconstruction

14.752694077288094 dB SSIM 0.017552370390793076

II — Mismatch

Ground Truth

Measurement

Reconstruction

14.745791800605835 dB SSIM 0.016831958806006703

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

18.778649119747705 dB SSIM 0.5437721757284999

I — Ideal

Ground Truth

Measurement

Reconstruction

13.363642759056253 dB SSIM 0.012660485214156797

II — Mismatch

Ground Truth

Measurement

Reconstruction

13.358605269883777 dB SSIM 0.012204965628613252

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

17.69014227744379 dB SSIM 0.5480972506166697

Mean PSNR Across All Scenes

14.02007371480706 dB

I — Ideal

14.013978720764692 dB

II — Mismatch

17.950583096635704 dB

III — Oracle

Degradation: -0.0 dB Recovery: +3.9 dB

Per-scene PSNR breakdown (4 scenes)

Scene	I (PSNR)	I (SSIM)	II (PSNR)	II (SSIM)	III (PSNR)	III (SSIM)
scene_00	13.361718975877936	0.012475920046010055	13.355378863310248	0.01188952431321307	17.660800558562674	0.5449616747376919
scene_01	14.602239047005954	0.013106642314582598	14.59613894925891	0.012594004466623999	17.67274043078865	0.39227201274836065
scene_02	14.752694077288094	0.017552370390793076	14.745791800605835	0.016831958806006703	18.778649119747705	0.5437721757284999
scene_03	13.363642759056253	0.012660485214156797	13.358605269883777	0.012204965628613252	17.69014227744379	0.5480972506166697
Mean	14.02007371480706	0.013948854491385632	14.013978720764692	0.013380113303614256	17.950583096635704	0.5072757784578055

Experimental Setup

Instrument: Oxford Instruments Symmetry S2 / EDAX Hikari Super

Accelerating Voltage Kv: 20

Sample Tilt Deg: 70

Step Size Um: 0.5

Camera Resolution: 622x512 (Symmetry S2)

Exposure Ms: 10

Indexing: Hough transform / dictionary indexing

Output: grain orientation map (IPF), misorientation

Key References

Schwartz et al., 'Electron Backscatter Diffraction in Materials Science', Springer (2009)

Canonical Datasets

DREAM.3D synthetic EBSD benchmarks

Spec DAG — Forward Model Pipeline

P(e⁻) → Π(backscatter) → D(g, η₁)

P Electron Beam (e⁻)

Π Kikuchi Pattern Projection (backscatter)

D Phosphor Screen + Camera (g, η₁)

Mismatch Parameters

Symbol	Parameter	Description	Nominal	Perturbed
ΔPC	pattern_center	Pattern center error (pixels)	0	2.0
Δθ	sample_tilt	Sample tilt error (deg)	70	70.5
ΔDD	detector_distance	Detector distance error (mm)	0	0.5

Credits System

40%

Platform Profit Pool

Revenue allocated to benchmark rewards

30%

Winner Share

Top algorithm receives from pool

$100

Min Withdrawal

Minimum payout threshold

Spec Primitives Reference (11 primitives)

P Propagation

Free-space or medium propagation kernel (Fresnel, Rayleigh-Sommerfeld).

M Mask / Modulation

Spatial or spatio-temporal amplitude modulation (coded aperture, SLM pattern).

Π Projection

Geometric projection operator (Radon transform, fan-beam, cone-beam).

F Fourier Sampling

Sampling in the Fourier / k-space domain (MRI, ptychography).

C Convolution

Shift-invariant convolution with a point-spread function (PSF).

Σ Summation / Integration

Summation along a physical dimension (spectral, temporal, angular).

D Detector

Sensor readout with gain g and noise model η (Gaussian, Poisson, mixed).

S Structured Illumination

Patterned illumination (block, Hadamard, random) applied to the scene.

W Wavelength Dispersion

Spectral dispersion element (prism, grating) with shift α and aperture a.

R Rotation / Motion

Sample or gantry rotation (CT, electron tomography).

Λ Wavelength Selection

Spectral filter or monochromator selecting a wavelength band.