Physics World Model — Modality Catalog
5 imaging modalities with descriptions, experimental setups, and reconstruction guidance.
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.
Coherent Diffractive Imaging / Phase Retrieval
Description
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.
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 — Signal Chain
Experimental Setup — Details
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.)
Digital Holographic Microscopy
Digital holographic microscopy (DHM) records the interference pattern between an object wave (scattered by the sample) and a reference wave on a digital sensor. The hologram encodes both amplitude and phase of the object wavefield. In off-axis configuration, the object spectrum is separated from the zero-order and twin-image terms in Fourier space. Numerical propagation (angular spectrum method) refocuses the wavefield at any desired plane, enabling quantitative phase imaging (QPI) with nanometer path-length sensitivity. Applications include label-free cell imaging and topography measurement.
Digital Holographic Microscopy
Description
Digital holographic microscopy (DHM) records the interference pattern between an object wave (scattered by the sample) and a reference wave on a digital sensor. The hologram encodes both amplitude and phase of the object wavefield. In off-axis configuration, the object spectrum is separated from the zero-order and twin-image terms in Fourier space. Numerical propagation (angular spectrum method) refocuses the wavefield at any desired plane, enabling quantitative phase imaging (QPI) with nanometer path-length sensitivity. Applications include label-free cell imaging and topography measurement.
Principle
Digital holographic microscopy records the interference pattern (hologram) between a reference wave and the wave scattered by the sample. The complex field (amplitude and phase) is recovered by numerical propagation of the recorded hologram to the object plane. Phase imaging reveals optical path length changes caused by refractive index or thickness variations, providing quantitative phase contrast without staining.
How to Build the System
Build an off-axis Mach-Zehnder interferometer: split a coherent source (He-Ne laser, 633 nm, or laser diode) into object and reference beams. The object beam passes through the sample via a microscope objective. The reference beam tilts at a small angle (off-axis) to create carrier fringes. Both beams interfere on a CMOS camera. The carrier frequency must be high enough to separate the twin image in Fourier space. Vibration isolation is essential.
Common Reconstruction Algorithms
- Fourier filtering (off-axis hologram: spatial filtering of +1 order)
- Angular spectrum propagation method
- Phase unwrapping (Goldstein, quality-guided, or least-squares)
- Numerical autofocusing (Tamura coefficient, Brenner gradient)
- Deep-learning phase retrieval (PhaseNet, holographic reconstruction CNN)
Common Mistakes
- Vibration causing fringe instability and phase noise
- Twin image and DC term not properly separated in on-axis holography
- Phase wrapping artifacts not resolved in thick or rapidly varying samples
- Coherence noise (speckle) from high temporal coherence of the laser source
- Incorrect propagation distance causing defocused reconstruction
How to Avoid Mistakes
- Use an optical table with active vibration isolation; enclose the setup
- Use off-axis geometry with sufficient carrier frequency for clean Fourier separation
- Apply robust phase unwrapping algorithms; use multi-wavelength for large OPD
- Use a low-coherence source (LED or SLD) for speckle reduction in off-axis DHM
- Implement numerical autofocusing or calibrate propagation distance precisely
Forward-Model Mismatch Cases
- The widefield fallback produces real-valued output, but holography records complex-valued interference between object and reference waves — the phase information encoding 3D depth and optical path length is completely lost
- The interference fringe pattern (I = |E_ref + E_obj|^2) encodes both amplitude and phase of the object wave, enabling numerical refocusing — the Gaussian blur destroys the fringe structure and all quantitative phase information
How to Correct the Mismatch
- Use the holography operator that models the coherent interference between object wave (after propagation) and reference wave, producing complex-valued holographic data
- Reconstruct amplitude and phase by digital holographic processing: Fourier filtering to isolate the sideband, numerical back-propagation using the angular spectrum method or Fresnel transform
Experimental Setup — Signal Chain
Experimental Setup — Details
Key References
- Cuche et al., 'Digital holography for quantitative phase-contrast imaging', Optics Letters 24, 291-293 (1999)
- Kim, 'Principles and techniques of digital holographic microscopy', SPIE Reviews 1, 018005 (2010)
Canonical Datasets
- Lyncee Tec DHM application datasets
- HoloGAN benchmark (simulated holograms)
Optical Diffraction Tomography (ODT)
Optical Diffraction Tomography (ODT)
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 Imaging
Description
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.
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 — Signal Chain
Experimental Setup — Details
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