Modeling of beam hardening effects in a dual-phase X-ray grating interferometer for quantitative dark-field imaging

X-Ray Dark-Field Signal Reduction Due to Hardening of the Visibility Spectrum

X-ray dark-field imaging enables a spatially-resolved visualization of ultra-small-angle X-ray scattering. Using phantom measurements, we demonstrate that a material's effective dark-field signal may be reduced by modification of the visibility spectrum by other dark-field-active objects in the beam. This is the dark-field equivalent of conventional beam-hardening, and is distinct from related, known effects, where the dark-field signal is modified by attenuation or phase shifts. We present a theoretical model for this group of effects and verify it by comparison to the measurements. These findings have significant implications for the interpretation of dark-field signal strength in polychromatic measurements.

Implementation of a dual-phase grating interferometer for multi-scale characterization of building materials by tunable dark-field imaging

The multi-scale characterization of building materials is necessary to understand complex mechanical processes, with the goal of developing new more sustainable materials. To that end, imaging methods are often used in materials science to characterize the microscale. However, these methods compromise the volume of interest to achieve a higher resolution. Dark-field (DF) contrast imaging is being investigated to characterize building materials in length scales smaller than the resolution of the imaging system, allowing a direct comparison of features in the nano-scale range and overcoming the scale limitations of the established characterization methods. This work extends the implementation of a dual-phase X-ray grating interferometer (DP-XGI) for DF imaging in a lab-based setup. The interferometer was developed to operate at two different design energies of 22.0 keV and 40.8 keV and was designed to characterize nanoscale-size features in millimeter-sized material samples. The good performance of the interferometer in the low energy range (LER) is demonstrated by the DF retrieval of natural wood samples. In addition, a high energy range (HER) configuration is proposed, resulting in higher mean visibility and good sensitivity over a wider range of correlation lengths in the nanoscale range. Its potential for the characterization of mineral building materials is illustrated by the DF imaging of a Ketton limestone. Additionally, the capability of the DP-XGI to differentiate features in the nanoscale range is proven with the dark-field of Silica nanoparticles at different correlation lengths of calibrated sizes of 106 nm, 261 nm, and 507 nm.

Pixel-wise beam-hardening correction for dark-field signal in X-ray dual-phase grating interferometry

The dark-field signal provided by X-ray grating interferometry is an invaluable tool for providing structural information beyond the direct spatial resolution and their variations on a macroscopic scale. However, when using a polychromatic source, the beam-hardening effect in the dark-field signal makes the quantitative sub-resolution structural information inaccessible. Especially, the beam-hardening effect in dual-phase grating interferometry varies with spatial location, inter-grating distance, and diffraction order. In this work, we propose a beam-hardening correction algorithm, taking into account all these factors. The accuracy and robustness of the algorithm are then validated by experimental results. This work contributes a necessary step toward accessing small-angle scattering structural information in dual-phase grating interferometry.

On the quantification of sample microstructure using single-exposure x-ray dark-field imaging via a single-grid setup

The size of the smallest detectable sample feature in an x-ray imaging system is usually restricted by the spatial resolution of the system. This limitation can now be overcome using the diffusive dark-field signal, which is generated by unresolved phase effects or the ultra-small-angle x-ray scattering from unresolved sample microstructures. A quantitative measure of this dark-field signal can be useful in revealing the microstructure size or material for medical diagnosis, security screening and materials science. Recently, we derived a new method to quantify the diffusive dark-field signal in terms of a scattering angle using a single-exposure grid-based approach. In this manuscript, we look at the problem of quantifying the sample microstructure size from this single-exposure dark-field signal. We do this by quantifying the diffusive dark-field signal produced by 5 different sizes of polystyrene microspheres, ranging from 1.0 to 10.8 µm, to investigate how the strength of the extracted dark-field signal changes with the sample microstructure size, [Formula: see text]. We also explore the feasibility of performing single-exposure dark-field imaging with a simple equation for the optimal propagation distance, given microstructure with a specific size and thickness, and show consistency between this model and experimental data. Our theoretical model predicts that the dark-field scattering angle is inversely proportional to [Formula: see text], which is also consistent with our experimental data.

The choice of an autocorrelation length in dark-field lung imaging

Respiratory diseases are one of the most common causes of death, and their early detection is crucial for prompt treatment. X-ray dark-field radiography (XDFR) is a promising tool to image objects with unresolved micro-structures such as lungs. Using Talbot-Lau XDFR, we imaged inflated porcine lungs together with Polymethylmethacrylat (PMMA) microspheres (in air) of diameter sizes between 20 and 500 [Formula: see text] over an autocorrelation range of 0.8-5.2 [Formula: see text]. The results indicate that the dark-field extinction coefficient of porcine lungs is similar to that of densely-packed PMMA spheres with diameter of [Formula: see text], which is approximately the mean alveolar structure size. We evaluated that, in our case, the autocorrelation length would have to be limited to [Formula: see text] in order to image [Formula: see text]-thick lung tissue without critical visibility reduction (signal saturation). We identify the autocorrelation length to be the critical parameter of an interferometer that allows to avoid signal saturation in clinical lung dark-field imaging.

Exploration of the X-ray Dark-Field Signal in Mineral Building Materials

Mineral building materials suffer from weathering processes such as salt efflorescence, freeze-thaw cycling, and microbial colonization. All of these processes are linked to water (liquid and vapor) in the pore space. The degree of damage following these processes is heavily influenced by pore space properties such as porosity, pore size distribution, and pore connectivity. X-ray computed micro-tomography (µCT) has proven to be a valuable tool to non-destructively investigate the pore space of stone samples in 3D. However, a trade-off between the resolution and field-of-view often impedes reliable conclusions on the material's properties. X-ray dark-field imaging (DFI) is based on the scattering of X-rays by sub-voxel-sized features, and as such, provides information on the sample complementary to that obtained using conventional µCT. In this manuscript, we apply X-ray dark-field tomography for the first time on four mineral building materials (quartzite, fired clay brick, fired clay roof tile, and carbonated mineral building material), and investigate which information the dark-field signal entails on the sub-resolution space of the sample. Dark-field tomography at multiple length scale sensitivities was performed at the TOMCAT beamline of the Swiss Light Source (Villigen, Switzerland) using a Talbot grating interferometer. The complementary information of the dark-field modality is most clear in the fired clay brick and roof tile; quartz grains that are almost indistinguishable in the conventional µCT scan are clearly visible in the dark-field owing to their low dark-field signal (homogenous sub-voxel structure), whereas the microporous bulk mass has a high dark-field signal. Large (resolved) pores on the other hand, which are clearly visible in the absorption dataset, are almost invisible in the dark-field modality because they are overprinted with dark-field signal originating from the bulk mass. The experiments also showed how the dark-field signal from a feature depends on the length scale sensitivity, which is set by moving the sample with respect to the grating interferometer.

Laboratory X-ray interferometry imaging with a fan-shaped source grating

The orientation mismatch between the cone beam of an X-ray tube and the grating lines in a flat substrate remains a big challenge for laboratory grating-based X-ray interferometry, since it severely limits the imaging field of view. Here, we fabricated fan-shaped G₀ source gratings by modulating the electric field during the deep reactive ion etching of silicon. The gold electroplated fan-shaped G₀ grating (3.0 µm pitch) in a 20 keV interferometer improves the uniformity of the field of view with an increase of average visibility from 16.2% to 18.5% and a better angular sensitivity (by a factor 5.8) at the edges.

Angular sensitivity of an x-ray differential phase contrast imaging system with real and virtual source images

In this work, a novel, to the best of our knowledge, approach based on an x-ray thin lens imaging theory is proposed to predict the angular sensitivity responses of dual-phase-grating differential phase contrast (DPC) interferometers. Experimental validations have been performed to demonstrate the high accuracy of theoretical predictions using two different setups: one with real source images and the other with virtual source images. This new sensitivity calculation method is helpful to optimize the DPC imaging performance of a dual-phase-grating system.

Sample phase gradient and fringe phase shift in triple phase grating X-ray interferometry

Triple phase grating X-ray interferometry is a promising new technique of grating based X-ray differential phase contrast imaging. Accurate retrieval of sample phase gradients from measured interference fringe shifts is a key task in X-ray interferometry. To fulfill this task in triple phase grating X-ray interferometry with monochromatic X-ray sources, the authors derived exact formulas relating sample phase gradient to fringe phase shift. These formulas not only provide a design optimization tool for triple phase grating interferometry, but also lay a foundation for quantitative phase contrast imaging.