Directional Dark Field for Nanoscale Full-Field Transmission X-Ray Microscopy

Abstract

Dark-field X-ray imaging visualizes structural inhomogeneities through small-angle scattering, but existing directional methods are confined to the micrometer scale. While recent advances have extended dark-field capabilities to nanoscale transmission X-ray microscopy, directional scattering retrieval - critical for characterizing anisotropic nanostructures - has remained inaccessible for imaging resolutions in the sub-micrometer scale. Here, we demonstrate the first directional dark-field setup for nanoimaging, achieving orientation mapping of scattering features below the spatial resolution limit. Our method is experimentally simple to implement with existing transmission X-ray microscopy setups. We validate its performance by successfully resolving sub-resolution test structure orientations, cross-correlating orientational changes within hierarchical nanoporous materials, and mapping the directional arrangement of hydroxyapatite nanocrystals 30 - 70 nm within human tooth enamel. By utilizing shadow regions in the optical configuration, we further extend the detectable scattering vector range, demonstrating a pathway toward size-selective dark-field imaging. This advancement enables the quantitative structural characterization of anisotropic nanomaterials, which are critical to biomineralization, advanced materials, and nanotechnology applications.

Figures (9)

• Figure 1: Schematic of the normal dark-field TXM setup (A). The beam shaping condenser splits the beam into multiple deflected parallel beams, creating a ring of focused points in the back focal plane of the Fresnel zone plate (FZP), which can be blocked by dark-field apertures (DF-AP) to only let the scattered light pass to the detector. With an additional condenser aperture (C-AP), the setup can be extended to directional dark-field imaging (B). The C-AP blocks two-thirds of the condenser fields and only allows light from one direction to illuminate the sample. For non-uniform scattering structures, the focal spots are elongated (C). By successively closing the C-AP in the four directions (bottom, top, right, left), the orientation of the scattering can be retrieved. Here, visualized for scattering in the vertical direction. (A) is adapted with permission from Wirtensohn2024 © Optica Publishing Group.
• Figure 2: Extension of the maximal magnitude of the scattering vector $|\Vec{Q}_{\text{max, ext}}|$. By covering two-thirds of the condenser, the shadow area (gray) is elongated towards the opposite side. This allows further opening of the dark-field apertures in the back focal plane, extending $|\Vec{Q}_{\text{max, ext}}|$. The maximal scattering angle is achieved when the outermost beamlet from the condenser (orange solid line) gets scattered towards the edge of the shadow area (pink solid line). By using the additional shadow area, the scattering angle increases from the blue solid line to the pink solid line.
• Figure 3: Directional dark field of a Siemens star. The directional dark-field components in the x- and y- directions (A and B), originating from the C-AP being closed in left and right (A) and top and bottom (B), are used to calculate a scattering vector. The angle and magnitude of the resulting vector are used to create a color plot (C). The color corresponds to the scattering angle with respect to the vertical axis, and the luminance to the magnitude of the scattering vector. The different directions can be well separated (D), and works also for structure sizes below the spatial resolution of the setup, as visible for the line pairs with a pitch of 80nm (40nm feature size) and 60nm (30nm feature size) (E). The total exposure time of the directional dark-field image is $4 \times 300s = 20min$.
• Figure 4: SEM image of a highly porous hierarchical silicon pillar (A), which consists of 1µm to 8µm large, elongated pores. These pores consist of individual ligaments ranging from 50nm to 200nm in diameter. Their alignment along the major axis of the pores creates an anisotropic dark-field signal (B). The directional dark-field projection of the sample reveals directional changes in the internal structure of the pillar. The difference of the magnitude-weighted mean directional dark-field angle in the blue and red region of interest is $18.72° \pm 0.28°$ (C). A vertical slice through a Zernike phase contrast measurement validates an orientational change in the sample's pores of approximately 17.34°, visualized by the colored areas (D). The total exposure time of the directional dark-field image is $4 \times 250s = 16min \ 40s.$
• Figure 5: Directional dark-field projection of the enamel of a human permanent MIH-tooth. The enamel consists of hydroxyapatite crystals (30nm - 70nm), which are bundled into rods (around 6µm). These are visible as fish-scale-like structures. Due to the crystalline structure, the rods have a strong directional dependency, which can be visualized by the directional dark field. The difference in the magnitude-weighted angle of the directional dark-field image between the top right (red) and bottom left (turquoise) region of interest is $22.23° \pm 0.28°$. The total exposure time of the directional dark-field image is $4 \times 300s = 20min$.