Constraint-Free Coherent Diffraction Imaging via Physics-Guided Neural Fields

TL;DR

CDI phase retrieval is inherently ill-posed and historically constrained by handcrafted priors. The authors introduce CDIP, a constraint-free framework that uses an untrained coordinate-based neural field to model a 3D object and a physics-consistent forward operator to match measured diffraction intensities, with time encoded as an input coordinate for dynamics. Key innovations include progressive anchoring to suppress translational and twin-image ambiguities, the use of perceptual losses, and a 4D spatiotemporal representation that yields temporally coherent reconstructions without explicit temporal regularization. Empirically, CDIP outperforms classical iterative methods and untrained DL baselines on both static and dynamic CDI data, delivering high spatial resolution and robust temporal stability, with potential to generalize to ptychography, Bragg CDI, and other coherent imaging modalities.

Abstract

CDI is a lensless imaging technique that enables atomic-resolution imaging of non-crystalline specimens and their dynamics. However, its broader implementation has been hindered by the instability and ill-posedness of its reconstruction process, known as phase retrieval, which relies heavily on handcrafted, object-specific constraints. To overcome the key limitations, we propose CDIP, a robust phase-retrieval framework that eliminates the need for such constraints by combining untrained coordinate-based neural fields for static and dynamic reconstructions and a physics-consistent forward model. We evaluate CDIP on simulated and experimental datasets that involve both static samples and dynamic processes, demonstrating that it substantially outperforms classical iterative algorithms and deep-learning baselines in terms of fidelity and stability. These results highlight a paradigm shift in both static and time-resolved CDI reconstruction, providing a broadly applicable framework for coherent imaging modalities such as ptychography and holography, across X-ray, electron, and optical probes.

Figures (5)

• Figure 1: Schematic diagram of the CDIP concept. (a) Neural fields with a progressive anchoring strategy are used to generate a 3D volume. A differentiable forward operator, comprising a projection and a Fourier transform, is used to simulate predicted diffraction patterns. The neural field is optimized by minimizing the loss between predicted and measured intensities. (b) Illustration of the 2D view of the progressive anchoring strategy used in CDIP, where optimization begins from a small central region (red square) projected within the object area. (c) Illustration of the far-field CDI experiment setup. Coherent X-rays illuminate dynamic objects, and the resulting diffraction patterns are captured sequentially over time.
• Figure 2: Comparison of phase retrieval performance between PR and the proposed CDIP method. (a) Experimentally measured diffraction patterns from two samples. (b) Complex-valued fields reconstructed using the PR and CDIP methods, with both amplitude and phase components visualized for each sample. The accompanying color bar represents the phase values of each reconstruction. (c) PRTF curves for the two methods.
• Figure 3: Reconstruction results of the moving Ta test chart using different phase retrieval methods. (a) Reconstructed phase images at selected time frames (1, 400, 800, 1200) using four methods. (b) Phase profiles sampled along two circular arcs in the 400th frame, highlighting the ability of each method to resolve spatially varying patterns with known geometry. (c) PRTF analysis of the reconstructed phase maps. The dashed horizontal line indicates the resolution threshold at which the PRTF falls below $1/e$, marking the limit of reliable feature recovery. (d) Distribution of estimated sample velocities over the first 400 frames derived from each method. The dashed line represents the ground-truth velocity (340 nm/s), and the black lines within each box denote the median of the estimated velocities.
• Figure 4: Reconstruction of the dynamic AuNPs phase using different methods. (a) Phase reconstruction results at selected time frames (1, 50, 100, 150) obtained with different methods. The last column shows zoomed-in views (red boxes) of the highlighted regions at frame 100. (b) PRTF analysis of the reconstructed phase images. The dashed horizontal line indicates the $1/e$ threshold, marking the cutoff spatial frequency for reliable feature recovery. (c) Pixel intensity distributions within the particle region and the solution background in the reconstructed phase images. (d) Statistical distributions of pixel intensities from the reconstructed phase images, evaluated within the particle and the adjacent solution areas.
• Figure 5: Reconstruction of AuNPs phase information from experimentally captured diffraction patterns using different methods. (a) Reconstructed phase images at selected time frames (50, 500, 1000, 1500, 2000) using mf-PIE, PID3Net, CDIP-S, and CDIP. (b) PRTF analysis of the reconstructed phase images. The dashed horizontal line indicates the $1/e$ threshold, with the corresponding spatial frequency marked to estimate the resolution limit. (c) Distributions of pixel intensities in the reconstructed phase images for the particle and surrounding solution regions.