Ptychographic Imaging
Ptychography is a scanning coherent diffractive imaging technique where a coherent beam (X-ray or electron) illuminates overlapping regions of the sample and far-field diffraction patterns are recorded at each scan position. The overlap between adjacent probe positions provides redundancy that enables simultaneous recovery of the complex-valued object transmission function and the illumination probe via iterative algorithms (ePIE, difference map). The forward model at each position is I_j = |F{P(r-r_j) * O(r)}|^2 where P is the probe and O is the object. Achievable resolution is limited by the detector NA, not the optics, reaching sub-10 nm for X-rays.
Ptychographic Forward
Poisson
epie
PHOTON_COUNTER
Forward-Model Signal Chain
Each primitive represents a physical operation in the measurement process. Arrows show signal flow left to right.
P(probe) → D(g, η₁)
Benchmark Variants & Leaderboards
Ptychography
Ptychographic Imaging
P(probe) → D(g, η₁)
Standard Leaderboard (Top 10)
| # | Method | Score | PSNR (dB) | SSIM | Trust | Source |
|---|---|---|---|---|---|---|
| 🥇 | AutoPhaseNN | 0.784 | 34.0 | 0.935 | ✓ Certified | Chan et al., 2024 |
| 🥈 | PtychoNN | 0.747 | 32.5 | 0.910 | ✓ Certified | Cherukara et al., 2020 |
| 🥉 | sDR | 0.635 | 28.5 | 0.820 | ✓ Certified | Wen et al., J. Opt. 2019 |
| 4 | ePIE | 0.522 | 25.0 | 0.710 | ✓ Certified | Maiden & Rodenburg, 2009 |
Mismatch Parameters (3) click to expand
| Name | Symbol | Description | Nominal | Perturbed |
|---|---|---|---|---|
| probe_error | ΔP | Probe function error (%) | 0 | 5.0 |
| position_error | Δr | Scan position error (nm) | 0 | 10.0 |
| partial_coherence | σ_c | Partial coherence width (nm) | 0 | 5.0 |
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: ptychographic forward — Mismatch modes: position error, partial coherence, probe drift, detector saturation
Noise: poisson — Typical SNR: 10.0–30.0 dB
Requires: probe function, scan positions, detector distance, wavelength, pixel size
Modality Deep Dive
Principle
Ptychography is a scanning coherent diffractive imaging technique where a coherent beam (visible, X-ray, or electron) illuminates overlapping regions of the sample. At each scan position, a far-field diffraction pattern is recorded. The redundancy from overlapping illumination positions constrains the phase-retrieval problem, enabling simultaneous recovery of both the complex sample transmittance and the illumination probe function.
How to Build the System
For X-ray ptychography at a synchrotron: focus the beam to a defined spot (0.1-1 μm) using a Fresnel zone plate or KB mirrors. Mount the sample on a precision piezo scanning stage. Place a photon-counting area detector (Eiger, Pilatus) in the far field (1-5 m downstream). Scan positions should overlap by 60-70 %. For visible-light or electron ptychography, adapt the geometry but maintain the overlap requirement.
Common Reconstruction Algorithms
- ePIE (extended Ptychographic Iterative Engine)
- Difference Map algorithm
- Maximum Likelihood refinement (MLR)
- PtychoShelves (modular framework for ptychographic reconstruction)
- Deep-learning ptychography (PtychoNN, learned phase retrieval)
Common Mistakes
- Insufficient overlap between adjacent scan positions (need ≥60 %)
- Position errors in the scanning stage causing reconstruction artifacts
- Partial coherence effects not modeled, degrading recovered phase
- Vibration or drift during the scan corrupting the diffraction data
- Detector saturation at the central beam stop region
How to Avoid Mistakes
- Maintain ≥65 % overlap; include position correction in the reconstruction algorithm
- Use position refinement (annealing) as part of the ptychographic reconstruction
- Include mixed-state (multi-mode) probe to model partial coherence
- Use interferometric position feedback and short dwell times per point
- Use a semi-transparent beam stop or high-dynamic-range detector modes
Forward-Model Mismatch Cases
- The widefield fallback produces a single (64,64) image, but ptychography acquires diffraction patterns at multiple overlapping scan positions — output shape (n_positions, det_x, det_y) is a set of far-field intensity measurements
- Ptychography is fundamentally nonlinear (y_j = |F{P * O_j}|^2, intensity of Fourier transform of probe times object) — the widefield linear blur cannot model coherent wave propagation, diffraction, or phase retrieval
How to Correct the Mismatch
- Use the ptychography operator that generates one far-field diffraction pattern per probe position, with overlapping illumination enabling redundant phase information for robust reconstruction
- Reconstruct using PIE (Ptychographic Iterative Engine), ePIE, or gradient-descent methods that alternate between real-space (overlap constraint) and Fourier-space (modulus constraint) using the coherent forward model
Experimental Setup
Diamond Light Source I13 / APS 2-ID / ESRF ID16A
12.4
0.1
Eiger 500K (512x512 px, 75 um pitch)
1.0
200
0.7
2.1
10
ePIE / difference map / Adam-based optimization
Signal Chain Diagram
Key References
- Rodenburg & Faulkner, 'A phase retrieval algorithm for shifting illumination (ePIE)', Appl. Phys. Lett. 85, 4795-4797 (2004)
- Thibault et al., 'High-resolution scanning X-ray diffraction microscopy', Science 321, 379-382 (2008)
Canonical Datasets
- PtychoNN benchmark datasets (Cherukara et al.)
- Diamond I13 ptychography test data