  We introduce a structured illumination technique for dark-field x-ray
microscopy optimized for three-dimensional imaging of ordered materials at
sub-micrometer length scales. Our method utilizes a coded aperture to spatially
modulate the incident x-ray beam on the sample, enabling the reconstruction of
the sample's 3D structure from images captured at various aperture positions.
Unlike common volumetric imaging techniques such as tomography, our approach
casts a scanning x-ray silhouette of a coded aperture for depth resolution
along the axis of diffraction, eliminating any need for sample rotation or
rastering, leading to a highly stable imaging modality. This modification
provides robustness against geometric uncertainties during data acquisition,
particularly for achieving sub-micrometer resolutions where geometric
uncertainties typically limit resolution. We introduce the image reconstruction
model and validate our results with experimental data on an isolated twin
domain within a bulk single crystal of an iron pnictide obtained using a
dark-field x-ray microscope. This timely advancement aligns with the enhanced
brightness upgrade of the world's synchrotron radiation facilities, opening
unprecedented opportunities in imaging.
