Characterization of source coherence requirements for laboratory x-ray diffraction imaging

Young's double-slit (YDS) fringe visibility provides a detector-accessible measure of spatial coherence, but implementing hard-X-ray YDS experiments with compact laboratory sources is fundamentally constrained by the coherence-flux trade-off imposed by spatial filtering. Here we present an end-to-end simulation framework that couples SHADOW3 ray statistics with WOFRY wave-optics propagation to evaluate detector-level interference patterns and feasibility metrics under partial coherence. Partial coherence is defined directly at the pinhole plane by discretizing the pinhole-filtered angular spectrum into a weighted angular-tilt ensemble, which is propagated through Fresnel (pinhole to slit) and Fraunhofer (slit to detector) operators with energy-conserving binning onto an oversampled detector grid. Across parameter sweeps of effective source size w (20-200 µm), source-pinhole distance S (3.0-4.7 m), pinhole diameter D (3-10 µm), pinhole-slit distance R (0.01-1.0 m), and Gaussian relative bandwidth σ_BW (0.1-5%), we evaluate Michelson visibility V, detector-ROI photon counts N_det, and a photon-statistics-aware figure of merit FOM = V²N_det. To capture bandwidth-driven degradation not reflected by global visibility alone, we additionally introduce a longitudinal-coherence wash-out metric LC_ratio. The resulting inverse-design maps reveal two distinct operating regimes. For larger sources (w∼200 µm), the feasible design space becomes visibility-limited, while smaller sources (w∼50 µm) operate primarily in a throughput-limited regime where performance improves monotonically with photon acceptance. Absolute photon statistics are anchored by calibrating the pinhole-transmitted flux to a published laboratory benchmark (≈5 × 10³ ph/s through a 5 µm pinhole at 0.1% σ_BW), enabling exposure-time interpretation of the design maps in experimentally meaningful units. The framework therefore provides a quantitative guideline for selecting source filtering and propagation geometry in compact laboratory YDS measurements under realistic coherence and photon-statistics constraints.