Coherent Diffractive Imaging / Phase Retrieval
Coherent diffractive imaging (CDI) recovers the complex-valued exit wave from a coherent scattering experiment where only the diffraction intensity |F{O}|^2 is measured (the phase is lost). Phase retrieval algorithms (HIO + ER, Fienup) iteratively enforce constraints in both real space (finite support, non-negativity) and reciprocal space (measured intensity). The oversampling condition (sampling at least 2x the Nyquist rate) ensures sufficient information for unique phase recovery. CDI achieves diffraction-limited resolution without imaging optics. Applications include imaging of nanocrystals, viruses, and materials at X-ray and electron wavelengths.
Fourier Magnitude
Poisson
hio
PHOTON_COUNTER
Forward-Model Signal Chain
Each primitive represents a physical operation in the measurement process. Arrows show signal flow left to right.
P(far-field) → D(g, η₁)
Benchmark Variants & Leaderboards
CDI
Coherent Diffractive Imaging
P(far-field) → D(g, η₁)
Standard Leaderboard (Top 10)
| # | Method | Score | PSNR (dB) | SSIM | Trust | Source |
|---|---|---|---|---|---|---|
| 🥇 | ScorePhase | 0.831 | 35.82 | 0.968 | ✓ Certified | Wei et al., ECCV 2025 |
| 🥈 | DiffusionPhase | 0.823 | 35.48 | 0.964 | ✓ Certified | Song et al., NeurIPS 2024 |
| 🥉 | HolographyViT | 0.816 | 35.18 | 0.960 | ✓ Certified | Wang et al., ICCV 2024 |
| 4 | AutoPhase++ | 0.811 | 34.92 | 0.958 | ✓ Certified | Rivenson et al., ECCV 2024 |
| 5 | PhaseFormer | 0.801 | 34.5 | 0.952 | ✓ Certified | Tian et al., ICCV 2024 |
| 6 | PhaseResNet | 0.773 | 33.15 | 0.942 | ✓ Certified | Baoqing et al., Optica 2023 |
| 7 | LRGS | 0.764 | 32.8 | 0.935 | ✓ Certified | Choi et al., 2023 |
| 8 | CyclePhase | 0.761 | 32.5 | 0.938 | ✓ Certified | Ge et al., IEEE Photonics 2023 |
| 9 | PhaseNet | 0.725 | 31.2 | 0.910 | ✓ Certified | Rivenson et al., LSA 2018 |
| 10 | prDeep | 0.617 | 27.45 | 0.820 | ✓ Certified | Metzler et al., ICML 2018 |
Showing top 10 of 14 methods. View all →
Mismatch Parameters (3) click to expand
| Name | Symbol | Description | Nominal | Perturbed |
|---|---|---|---|---|
| support | ΔS | Support constraint error (pixels) | 0 | 3.0 |
| saturation | I_sat | Detector saturation threshold error (%) | 0 | 5.0 |
| missing_center | r_0 | Missing center radius (pixels) | 0 | 3 |
Reconstruction Triad Diagnostics
The three diagnostic gates (G1, G2, G3) characterize how reconstruction quality degrades under different error sources. Each bar shows the relative attribution.
Model: fourier magnitude — Mismatch modes: support error, partial coherence, missing center, detector gap
Noise: poisson — Typical SNR: 5.0–25.0 dB
Requires: support mask, beam stop mask, wavelength, detector distance
Modality Deep Dive
Principle
Coherent Diffractive Imaging (CDI) records the far-field diffraction pattern of an isolated object illuminated by a coherent beam. Only intensity (not phase) is measured on the detector. Phase retrieval algorithms iteratively recover the lost phase by enforcing known constraints: the measured Fourier modulus and the finite support of the object in real space. CDI achieves diffraction-limited resolution without any imaging lens.
How to Build the System
Illuminate an isolated object (nanocrystal, cell, virus particle) with a coherent, quasi-plane-wave beam (X-ray from synchrotron or XFEL, or visible laser). Record the continuous diffraction pattern on a pixel detector (Eiger, Jungfrau for X-ray; CMOS for visible) placed far enough for adequate oversampling (oversampling ratio ≥ 2 in each dimension). Remove the direct beam with a beam stop. Ensure the object is isolated (no other scatterers in the beam).
Common Reconstruction Algorithms
- Hybrid Input-Output (HIO) algorithm
- Error Reduction (ER) algorithm
- Shrink-Wrap (adaptive support HIO)
- Relaxed Averaged Alternating Reflections (RAAR)
- Deep-learning phase retrieval (PhaseDNN, learned proximal operator)
Common Mistakes
- Insufficient oversampling (detector pixels too coarse or too close to sample)
- Object not truly isolated, violating the support constraint
- Missing low-frequency data due to beam stop causing artifacts
- Stagnation in reconstruction (trapped in local minimum) without proper initialization
- Ignoring partial coherence effects from finite source size or bandwidth
How to Avoid Mistakes
- Ensure oversampling ratio ≥ 2× (linear) in each dimension; use a large detector
- Isolate the object on a thin membrane or in free space; verify no neighbor scattering
- Use low-frequency intensity constraints or a semi-transparent beam stop
- Run multiple random starts and use HIO-ER hybrid strategies to escape local minima
- Model partial coherence in the forward model or select sufficiently coherent beams
Forward-Model Mismatch Cases
- The widefield fallback is a linear operator, but phase retrieval measures only the intensity of the Fourier transform: y = |F{x}|^2 — this is a fundamentally nonlinear (quadratic) measurement that makes reconstruction non-convex
- The fallback preserves the spatial structure of the input, but phase retrieval destroys the phase of the Fourier transform — recovering the original signal from magnitude-only Fourier measurements is a fundamentally different (and harder) inverse problem
How to Correct the Mismatch
- Use the phase retrieval operator implementing y = |FFT(x)|^2 (or |F{x * support}|^2 with known support constraint), producing real-valued intensity measurements of the Fourier magnitude
- Reconstruct using iterative phase retrieval algorithms (Gerchberg-Saxton, HIO, ER) or gradient descent on the non-convex loss, which require the correct quadratic forward model
Experimental Setup
LCLS XFEL / APS coherent scattering beamline
300
1.97
CSPAD / Jungfrau 4M (direct detection)
4
2
HIO + ER (hybrid input-output + error reduction)
Signal Chain Diagram
Key References
- Miao et al., 'Extending the methodology of X-ray crystallography to non-crystalline specimens', Nature 400, 342-344 (1999)
- Fienup, 'Phase retrieval algorithms: a comparison', Applied Optics 21, 2758-2769 (1982)
Canonical Datasets
- CXIDB (Coherent X-ray Imaging Data Bank)
- Simulated CDI benchmark (Marchesini et al.)