4D-STEM

4D-STEM Electron 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
🥇 DiffED 0.878 39.1 0.953 ✓ Certified Gao et al. 2024
🥈 PhysED 0.849 37.7 0.941 ✓ Certified Chen et al. 2024
🥉 SwinED 0.822 36.4 0.930 ✓ Certified Wang et al. 2023
4 TransED 0.786 34.8 0.912 ✓ Certified Li et al. 2022
5 PhaseGAN-ED 0.725 32.3 0.873 ✓ Certified Zimmermann et al. 2021
6 DnCNN-ED 0.658 29.5 0.833 ✓ Certified Cherukara et al. 2018
7 MicroED 0.586 26.7 0.781 ✓ Certified Shi et al. 2013
8 PEDT 0.517 23.9 0.738 ✓ Certified Kolb et al. 2007
9 Direct-Methods 0.450 21.2 0.694 ✓ Certified Hauptman & Karle 1985

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
🥇 DiffED + gradient 0.767
0.837
36.95 dB / 0.978
0.742
31.09 dB / 0.932
0.723
29.78 dB / 0.913
✓ Certified Gao et al., NeurIPS 2024
🥈 PhysED + gradient 0.752
0.839
36.32 dB / 0.975
0.732
30.43 dB / 0.923
0.684
27.13 dB / 0.861
✓ Certified Chen et al., Nat. Commun. 2024
🥉 SwinED + gradient 0.747
0.801
33.87 dB / 0.960
0.755
30.61 dB / 0.926
0.684
27.17 dB / 0.862
✓ Certified Wang et al., npj Comput. Mater. 2023
4 TransED + gradient 0.702
0.780
32.33 dB / 0.946
0.713
28.13 dB / 0.883
0.612
23.77 dB / 0.760
✓ Certified Li et al., Nat. Commun. 2022
5 PhaseGAN-ED + gradient 0.641
0.767
30.77 dB / 0.928
0.621
24.33 dB / 0.780
0.536
20.8 dB / 0.636
✓ Certified Zimmermann et al., Sci. Adv. 2021
6 MicroED + gradient 0.617
0.641
24.91 dB / 0.799
0.609
23.56 dB / 0.753
0.602
24.04 dB / 0.770
✓ Certified Shi et al., eLife 2013
7 DnCNN-ED + gradient 0.558
0.721
28.14 dB / 0.884
0.522
20.29 dB / 0.613
0.430
17.91 dB / 0.496
✓ Certified Cherukara et al., npj Comput. Mater. 2018
8 PEDT + gradient 0.511
0.566
21.76 dB / 0.680
0.512
20.43 dB / 0.619
0.456
18.92 dB / 0.546
✓ Certified Kolb et al., Ultramicroscopy 2007
9 Direct-Methods + gradient 0.470
0.518
19.67 dB / 0.583
0.454
18.46 dB / 0.523
0.437
17.37 dB / 0.469
✓ Certified Hauptman & Karle, Nobel Prize 1985

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

Join the competition →
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 PhysED + gradient 0.839 36.32 0.975
2 DiffED + gradient 0.837 36.95 0.978
3 SwinED + gradient 0.801 33.87 0.96
4 TransED + gradient 0.780 32.33 0.946
5 PhaseGAN-ED + gradient 0.767 30.77 0.928
6 DnCNN-ED + gradient 0.721 28.14 0.884
7 MicroED + gradient 0.641 24.91 0.799
8 PEDT + gradient 0.566 21.76 0.68
9 Direct-Methods + gradient 0.518 19.67 0.583
Spec Ranges (3 parameters)
Parameter Min Max Unit
camera_length -2.0 4.0 %
center_offset -1.0 2.0 pixels
elliptical_distortion -0.005 0.01
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 SwinED + gradient 0.755 30.61 0.926
2 DiffED + gradient 0.742 31.09 0.932
3 PhysED + gradient 0.732 30.43 0.923
4 TransED + gradient 0.713 28.13 0.883
5 PhaseGAN-ED + gradient 0.621 24.33 0.78
6 MicroED + gradient 0.609 23.56 0.753
7 DnCNN-ED + gradient 0.522 20.29 0.613
8 PEDT + gradient 0.512 20.43 0.619
9 Direct-Methods + gradient 0.454 18.46 0.523
Spec Ranges (3 parameters)
Parameter Min Max Unit
camera_length -2.4 3.6 %
center_offset -1.2 1.8 pixels
elliptical_distortion -0.006 0.009
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 DiffED + gradient 0.723 29.78 0.913
2 PhysED + gradient 0.684 27.13 0.861
3 SwinED + gradient 0.684 27.17 0.862
4 TransED + gradient 0.612 23.77 0.76
5 MicroED + gradient 0.602 24.04 0.77
6 PhaseGAN-ED + gradient 0.536 20.8 0.636
7 PEDT + gradient 0.456 18.92 0.546
8 Direct-Methods + gradient 0.437 17.37 0.469
9 DnCNN-ED + gradient 0.430 17.91 0.496
Spec Ranges (3 parameters)
Parameter Min Max Unit
camera_length -1.4 4.6 %
center_offset -0.7 2.3 pixels
elliptical_distortion -0.0035 0.0115
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

4D-STEM acquires a full 2D convergent-beam electron diffraction (CBED) pattern at each probe position during a 2D STEM scan, yielding a 4D dataset (2 real-space + 2 reciprocal-space dimensions). This enables simultaneous mapping of strain, orientation, electric fields, and thickness with nanometer spatial resolution. Phase retrieval from the 4D dataset (electron ptychography) can achieve sub-angstrom resolution. High data rates (>1 GB/s) from fast pixelated detectors create computational challenges.

Principle

4D-STEM electron diffraction scans a convergent electron beam across the specimen and records a full 2-D diffraction pattern (convergent beam electron diffraction, CBED) at each scan position. The resulting 4-D dataset (2-D scan × 2-D diffraction) enables mapping of crystal structure, orientation, strain, electric fields, and charge density with nanometer spatial resolution.

How to Build the System

Use a STEM equipped with a fast pixelated detector (Medipix3, EMPAD, or Dectris ARINA) capable of recording diffraction patterns at >1000 fps. Set a small convergence semi-angle (1-5 mrad) for nanobeam diffraction or large (20-30 mrad) for CBED. The scan step should be comparable to the probe size. Data volumes are large (tens of GB per scan), requiring efficient data pipeline and storage.

Common Reconstruction Algorithms

  • Virtual detector imaging (synthesized BF, DF, iDPC from 4D data)
  • Center-of-mass (COM) analysis for electric field mapping
  • Ptychographic reconstruction from 4D-STEM data
  • Orientation mapping (template matching against simulated patterns)
  • Strain mapping via disk position analysis

Common Mistakes

  • Detector dynamic range insufficient for simultaneous central beam and weak diffraction
  • Scan step too large relative to probe size, under-sampling the specimen
  • Not accounting for specimen thickness variation in diffraction pattern interpretation
  • Excessive electron dose for beam-sensitive materials (organics, 2D materials)
  • Misindexing diffraction patterns due to double diffraction or overlapping grains

How to Avoid Mistakes

  • Use counting-mode detectors (Medipix) with high dynamic range or electron counting
  • Match scan step to probe size for complete spatial sampling
  • Simulate diffraction patterns at the measured thickness for accurate interpretation
  • Use low-dose 4D-STEM protocols with fast detectors to minimize beam damage
  • Carefully index patterns considering multiple scattering; compare with simulations

Forward-Model Mismatch Cases

  • The widefield fallback produces a real-space blurred image, but electron diffraction records the far-field diffraction pattern (reciprocal space) — Bragg spots encode crystal structure, lattice spacings, and symmetry, which bear no resemblance to a blurred image
  • The diffraction pattern intensity I(k) = |F{V(r) * P(r)}|^2 encodes the Fourier transform of the projected crystal potential — the widefield real-space blur cannot access reciprocal-space crystallographic information

How to Correct the Mismatch

  • Use the electron diffraction operator that models kinematic or dynamical scattering from the crystal lattice, producing far-field diffraction patterns with Bragg peaks at reciprocal lattice positions
  • Index diffraction patterns to determine crystal structure and orientation; use dynamical simulation (Bloch wave or multislice) for accurate intensity matching and structure refinement

Experimental Setup — Signal Chain

Experimental setup diagram for 4D-STEM Electron Diffraction

Experimental Setup

Instrument: Thermo Fisher Titan with Medipix3 / JEOL ARM with EMPAD
Accelerating Voltage Kv: 200
Convergence Angle Mrad: 1.5
Step Size Nm: 1.0
Detector: Medipix3 / Merlin (256x256 px)
Exposure Ms: 1
Camera Length Mm: 580
Reconstruction: ptychographic phase retrieval / WDD

Key References

  • Ophus, 'Four-dimensional scanning transmission electron microscopy', Microscopy & Microanalysis 25, 563 (2019)
  • Jiang et al., 'Electron ptychography of 2D materials to deep sub-angstrom resolution', Nature 559, 343 (2018)

Canonical Datasets

  • 4D-STEM benchmark datasets (Ophus group, NCEM)

Spec DAG — Forward Model Pipeline

P(e⁻) → F(diffraction) → D(g, η₁)

P Convergent Beam (e⁻)
F Diffraction Pattern (diffraction)
D Pixelated Detector (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
ΔL camera_length Camera length error (%) 0 2.0
Δc center_offset Diffraction center offset (pixels) 0 1.0
ε elliptical_distortion Elliptical distortion 0 0.005

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.