Holographic X-ray Phase Contrast Imaging with Partial Coherence: Uniqueness and Reconstructions from Intensity Correlations
For researchers in X-ray imaging, this work provides a theoretical foundation and practical algorithm for phase retrieval with partially coherent beams, which is a known bottleneck in nanoscale biological imaging.
The paper addresses the problem of recovering phase and absorption contrast in holographic X-ray imaging under partial coherence. It analytically proves uniqueness of reconstruction from intensity correlations under a symmetry-breaking condition, and proposes a low-rank method that avoids explicit correlation computation, achieving accurate simultaneous reconstructions in numerical experiments.
Holographic coherent X-ray imaging enables nanoscale imaging of biological cells and tissues, rendering both phase and absorption contrast, i.e. real and imaginary parts of the refractive index. Unlike the standard model, which assumes a perfectly coherent incident beam, we consider partial coherence characterized by a known covariance operator. In addition, we assume time-resolved intensity measurements, granting access not only to expected intensities but also to their correlations. We investigate the information content of these correlations and analytically demonstrate that, under a symmetry-breaking condition on the sample and the illumination area, both phase and absorption contrast can be uniquely recovered in both the full and the linearized models. A key challenge in numerical reconstruction is the substantial increase in data dimensionality caused by computing intensity correlations during preprocessing. We propose a novel approach that leverages a low-rank assumption on the incident beam covariance operator, bypassing explicit correlation computation while still exploiting its full information. Numerical experiments demonstrate its feasibility, yielding accurate simultaneous reconstructions of phase and absorption contrast.