Laboratory-based x-ray microtomography with directional dark-field sensitivity

TL;DR

This work addresses the limitation of laboratory X-ray imaging in capturing sub-resolution microstructure over centimetre-scale samples by leveraging directional dark-field signals. It introduces a compact two-directional beam-tracking (2DBT) system that uses a single intensity modulator to simultaneously recover attenuation, phase, and directional dark-field signals in a single exposure, compatible with standard X-ray sources. The approach relies on a convolution model with a Gaussian scattering function, extracting line-integral maps of $μ$, $δ$, and $ε$, and uses a covariance matrix to derive the dominant scattering direction $θ$ and anisotropy $κ$ from beamlet variances $Δσ_x^2$, $Δσ_y^2$, and $Δσ_{xy}$. Demonstrations on a custom phantom, a carbon-fibre composite, and ex-vivo soft tissues show that dark-field contrast highlights sub-voxel fibre orientation and microstructure not visible in attenuation or phase, indicating strong potential for non-destructive 3D characterization in engineering and biomedicine.

Abstract

We demonstrate dark-field x-ray microtomography in a compact, laboratory-based system capable of resolving attenuation, phase, and anisotropic scattering signals with micrometer-scale resolution across centimetre-scale samples. The method is based on two-directional beam tracking (2DBT), which requires only a single optical element and is compatible with standard x-ray sources and detectors. We validate the system's capabilities through imaging of a custom-built phantom, a fibre-reinforced composite and ex-vivo biological tissues, including a bovine intervertebral disc, a rat heart, and a porcine meniscus. The results show that dark-field tomography provides complementary information to attenuation as well as to phase tomography, by revealing sub-resolution features such as fibre orientation and microstructural heterogeneity at length scales that are well below the voxel size. A key element of our system is its sensitivity to scattering along two orthogonal directions in the image plane, enabling the measurement of scattering anisotropy with a single exposure. As well as simple and robust, our approach is sensitive and precise. These findings demonstrate the potential of 2DBT for non-destructive and three-dimensional structural characterisation of samples and materials in engineering, materials science and biomedical applications.

Figures (9)

• Figure 1: Schematic of the laboratory set-up for dark field imaging. The system features a sealed microfocus x-ray tube, an intensity modulator, a sample stage, and an x-ray detector. The local scattering of the sample is described using a convolution model, where the intensity distribution of each probe, $I_s(x, y)$, is a result of the scattering function $s$ convolved with the probe distribution in the absence of the sample $I_0$. The two-dimensional sensitivity of the system allows retrieval of the variances ($\Delta\sigma^2_{x}$, $\Delta\sigma^2_{y}$) and the orientation of the scattering function $s(x,y)$. To illustrate the scattering effect, the probes shown here were modelled with high oversampling; in experimental conditions, each probe is sampled with 5 to 10 pixels, depending on the modulator used.
• Figure 2: Directional x-ray dark-field radiography with the compact laboratory system. HSV colour mapping of directional scattering analysis showing primary scattering direction (Hue), anisotropy (Saturation), and scattering magnitude (Value) for (a) custom-built carbon fibre loop phantom, with wood and paper insets and (b) bovine intervertebral disc.
• Figure 3: Directional dark-field signal characterisation. (a) Zoomed-in images of the ROI highlighted with the dashed square box of the phantom image in Figure \ref{['fig:directional_darkfield_2']}, showing directional dark field imaging of bamboo wood (left) and paper (right), at different exposure levels (columns) and for the two types of detectors we investigated (rows). The system's ability to retrieve the primary scattering orientation depends on the detector technology. This is qualitatively observed in the image noise and in the histograms of the hue component from the highlighted bamboo regions. The dispersion of the retrieved fibres' angles (hues in Figure \ref{['fig:directional_darkfield_2']}) appears substantially narrower when observed with a photon-counting detector (blue histogram) in comparison to a flat-panel (gray histogram). The trend of precision as a function of the exposure time for both detector technologies is shown in panel (b). A similar trend is observed in the two cases, however an improved performance is associated with the photon-counter.
• Figure 4: Multicontrast x-ray microtomography of fibre-reinforced composite. (a,d) Volume renderings of the reconstructed linear attenuation coefficient $\mu$ and directional dark field coefficient $\epsilon_x$. (b,e) Zoom-in slices: attenuation ($\mu$) and phase ($\delta$) vary smoothly with laminate banding, whereas directional scattering ($\epsilon_x$, $\epsilon_y$) shows localised sub-voxel heterogeneity within the laminate. In this view, features approximately perpendicular to the system’s sensitivity direction appear stronger in the corresponding map: horizontal in $\epsilon_y$, vertical in $\epsilon_x$ (panel e). (c,f) Two-dimensional histograms from selected normalised sub-volumes show a strong voxel-wise correlation between $\mu$ and $\delta$, and a markedly weaker correlation between $\mu$ and the magnitude $\sqrt{\epsilon_x^2+\epsilon_y^2}$, indicating complementarity between the two channels.
• Figure 5: X-ray attenuation and dark-field microtomography of murine heart (a–d) and porcine meniscus (e–h). (a,e) Volume renderings of the reconstructed dark-field magnitude $\sqrt{\epsilon_x^2 + \epsilon_y^2}$ with isotropic resolution show structural differences across tissue regions. (b,f) Axial slices of the dark-field channel show spatial variations in the reconstructed signal arising from microstructure differences within the tissue. (c,g) Corresponding axial reconstructions of the linear attenuation coefficient $\mu$ show comparatively uniform signal across the same regions. (d) Intensity profiles from the endocardium to the epicardium in the heart reveal a sub-surface layer visible primarily in the dark-field signal, linked to changes in fibre organization along this profile. We observe a transition in fibre density from the outer to the inner meniscus, which correlates with the contrast differences observed in the dark-field signal (f) between regions marked (I) and (II), not apparent in attenuation (g). (h) Multi-photon fluorescence microscopy of picrosirius red-stained tissue section of the meniscus after rehydration shows the collagen fibre organisation within the tissue.