State of the Art of X-ray Speckle-Based Phase-Contrast and Dark-Field Imaging

Speckle-Based Transmission and Dark-Field Imaging for Material Analysis with a Laboratory X-Ray Source

Multimodal imaging is valuable because it can provide additional information beyond that obtained from a conventional bright-field (BF) image and can be implemented with a widely available device. In this paper, we investigate the implementation of speckle-based transmission (T) and dark-field (DF) imaging in a laboratory X-ray setup to confirm its usefulness for material analysis. Three methods for recovering T and DF images were applied to a sample composed of six materials: plastic, nylon, cardboard, cork, expanded polystyrene and foam with different absorption and scattering properties. Contrast-to-noise ratio (CNR) and linear attenuation, absorption and diffusion coefficients obtained from BF, T and DF images are studied for two object-to-detector distances (ODDs). Two analysis windows are evaluated to determine the impact of noise on the image contrast of T and DF images and the ability to retrieve material characteristics. The unified modulated pattern analysis method proves to be the most reliable among the three studied speckle-based methods. The results showed that the CNR of T and DF images increases with larger analysis windows, while linear absorption and diffusion coefficients remain constant. The CNR of T images decreases with increasing ODD due to noise, whereas the CNR of DF images exhibits more complex behaviour, due to the material-dependent reduction in DF signal with increasing ODD. The experimental results on the ODD dependence of T and DF signals are consistent with recently reported numerical simulation results of these signals. The absorption coefficients derived from T images are largely independent of the ODD and the speckle-based method used, making them a universal parameter for material discrimination. In contrast, the linear diffusion coefficients vary with the ODD, limiting their applicability to specific experimental configurations despite their notable advantages in distinguishing materials. These findings highlight that T and DF images obtained from a laboratory X-ray setup offer complementary insights, enhancing their value for material analysis.

Separating edges from microstructure in X-ray dark-field imaging: evolving and devolving perspectives via the X-ray Fokker-Planck equation

A key contribution to X-ray dark-field (XDF) contrast is the diffusion of X-rays by sample structures smaller than the imaging system's spatial resolution; this is related to position-dependent small-angle X-ray scattering. However, some experimental XDF techniques have reported that XDF contrast is also generated by resolvable sample edges. Speckle-based X-ray imaging (SBXI) extracts the XDF by analyzing sample-imposed changes to a reference speckle pattern's visibility. We present an algorithm for SBXI (a variant of our previously developed multimodal intrinsic speckle-tracking (MIST) algorithm) capable of separating these two physically different XDF contrast mechanisms. The algorithm uses what we call the devolving Fokker-Planck equation for paraxial X-ray imaging as its forward model and then solves the associated multimodal inverse problem to retrieve the attenuation, phase, and XDF properties of the sample. Previous MIST variants were based on the evolving Fokker-Planck equation, which considers how a reference-speckle image is modified by the introduction of a sample. The devolving perspective instead considers how the image collected in the presence of the sample and the speckle membrane optically flows in reverse to generate the reference-speckle image when the sample is removed from the system. We compare single- and multiple-exposure multimodal retrieval algorithms from the two Fokker-Planck perspectives. We demonstrate that the devolving perspective can distinguish between two physically different XDF contrast mechanisms, namely, unresolved microstructure- and sharp-edge-induced XDF. This was verified by applying the different retrieval algorithms to two experimental data sets - one phantom sample and one organic sample. We anticipate that this work will be useful in (1) yielding a pair of complementary XDF images that separate sharp-edge diffuse scatter from diffuse scatter due to spatially random unresolved microstructure, (2) XDF computed tomography, where the strong edge XDF signal can lead to strong contaminating streaking artefacts, and (3) sample preparation, as samples will not need to be embedded since the strong XDF edge signal seen between the sample and air can be separated out.

High-resolution X-ray phase-contrast tomography of human placenta with different wavefront markers

Phase-contrast micro-tomography ([Formula: see text]CT) with synchrotron radiation can aid in the differentiation of subtle density variations in weakly absorbing soft tissue specimens. Modulation-based imaging (MBI) extracts phase information from the distortion of reference patterns, generated by periodic or randomly structured wavefront markers (e.g., gratings or sandpaper). The two approaches have already found application for the virtual inspection of biological samples. Here, we perform high-resolution [Formula: see text]CT scans of an unstained human placenta specimen, using MBI with both a 2D grating and sandpaper as modulators, as well as conventional propagation-based imaging (PBI). The 3D virtual representation of placenta offers a valuable tool for analysing its intricate branching villous network and vascular structure, providing new insights into its complex architecture. Within this study, we assess reconstruction quality achieved with all three evaluated phase-contrast methods. Both MBI datasets are processed with the Unified Modulated Pattern Analysis (UMPA) model, a pattern-matching algorithm. In order to evaluate the benefits and suitability of MBI for virtual histology, we discuss how the complexities of the technique influence image quality and correlate the obtained volumes to 2D techniques, such as conventional histology and X-ray fluorescence (XRF) elemental maps.

Review and experimental comparison of speckle-tracking algorithms for X-ray phase contrast imaging

X-ray speckles have been used in a wide range of experiments, including imaging (and tomography), wavefront sensing, spatial coherence measurements, X-ray photon correlation spectroscopy and ptychography. In this review and experimental comparison, we focus on using X-ray near-field speckle grains as wavefront markers and numerical methods for retrieving the phase information they contain. We present the most common tracking methods, introducing the existing algorithms with their specifications and comparing their performances under various experimental conditions. This comparison includes applications to different types of samples: phantoms for quantitative analysis and complex samples for assessing image quality. Our goal is to unify concepts from several speckle tracking methods using consistent terminology and equation formalism, while keeping the discussion didactic and accessible to a broad audience.

Correcting directional dark field x-ray imaging artefacts using position dependent image deblurring and attenuation removal

In recent years, a novel x-ray imaging modality has emerged that reveals unresolved sample microstructure via a "dark-field image", which provides complementary information to conventional "bright-field" images, such as attenuation and phase-contrast modalities. This x-ray dark-field signal is produced by unresolved microstructures scattering the x-ray beam resulting in localised image blur. Dark-field retrieval techniques extract this blur to reconstruct a dark-field image. Unfortunately, the presence of non-dark-field blur such as source-size blur or the detector point-spread-function can affect the dark-field retrieval as they also blur the experimental image. In addition, dark-field images can be degraded by the artefacts induced by large intensity gradients from attenuation and propagation-based phase contrast, particularly around sample edges. By measuring any non-dark-field blurring across the image plane and removing it from experimental images, as well as removing attenuation and propagation-based phase contrast, we show that a directional dark-field image can be retrieved with fewer artefacts and more consistent quantitative measures. We present the details of these corrections and provide "before and after" directional dark-field images of samples imaged at a synchrotron source. This paper utilises single-grid directional dark-field imaging, but these corrections have the potential to be broadly applied to other x-ray imaging techniques.

Speckle tracking phase-contrast computed tomography at an inverse Compton X-ray source

Speckle-based X-ray imaging (SBI) is a phase-contrast method developed at and for highly coherent X-ray sources, such as synchrotrons, to increase the contrast of weakly absorbing objects. Consequently, it complements the conventional attenuation-based X-ray imaging. Meanwhile, attempts to establish SBI at less coherent laboratory sources have been performed, ranging from liquid metal-jet X-ray sources to microfocus X-ray tubes. However, their lack of coherence results in interference fringes not being resolved. Therefore, algorithms were developed which neglect the interference effects. Here, we demonstrate phase-contrast computed tomography employing SBI in a laboratory-setting with an inverse Compton X-ray source. In this context, we investigate and compare also the performance of the at synchrotron conventionally used phase-retrieval algorithms for SBI, unified modulated pattern analysis (UMPA) with a phase-retrieval method developed for low coherence systems (LCS). We successfully retrieve a full computed tomography in a phantom as well as in biological specimens, such as larvae of the greater wax moth (Galleria mellonella), a model system for studies of pathogens and infections. In this context, we additionally demonstrate quantitative phase-contrast computed tomography using SBI at a low coherent set-up.

Multimodal 2D and 3D microscopic mapping of growth cartilage by computational imaging techniques - a short review including new research

Being able to image the microstructure of growth cartilage is important for understanding the onset and progression of diseases such as osteochondrosis and osteoarthritis, as well as for developing new treatments and implants. Studies of cartilage using conventional optical brightfield microscopy rely heavily on histological staining, where the added chemicals provide tissue-specific colours. Other microscopy contrast mechanisms include polarization, phase- and scattering contrast, enabling non-stained or 'label-free' imaging that significantly simplifies the sample preparation, thereby also reducing the risk of artefacts. Traditional high-performance microscopes tend to be both bulky and expensive.Computational imagingdenotes a range of techniques where computers with dedicated algorithms are used as an integral part of the image formation process. Computational imaging offers many advantages like 3D measurements, aberration correction and quantitative phase contrast, often combined with comparably cheap and compact hardware. X-ray microscopy is also progressing rapidly, in certain ways trailing the development of optical microscopy. In this study, we first briefly review the structures of growth cartilage and relevant microscopy characterization techniques, with an emphasis on Fourier ptychographic microscopy (FPM) and advanced x-ray microscopies. We next demonstrate with our own results computational imaging through FPM and compare the images with hematoxylin eosin and saffron (HES)-stained histology. Zernike phase contrast, and the nonlinear optical microscopy techniques of second harmonic generation (SHG) and two-photon excitation fluorescence (TPEF) are explored. Furthermore, X-ray attenuation-, phase- and diffraction-contrast computed tomography (CT) images of the very same sample are presented for comparisons. Future perspectives on the links to artificial intelligence, dynamic studies andin vivopossibilities conclude the article.

X-ray phase and dark-field computed tomography without optical elements

X-ray diffusive dark-field imaging, which allows spatially unresolved microstructure to be mapped across a sample, is an increasingly popular tool in an array of settings. Here, we present a new algorithm for phase and dark-field computed tomography based on the x-ray Fokker-Planck equation. Needing only a coherent x-ray source, sample, and detector, our propagation-based algorithm can map the sample density and dark-field/diffusion properties of the sample in 3D. Importantly, incorporating dark-field information in the density reconstruction process enables a higher spatial resolution reconstruction than possible with previous propagation-based approaches. Two sample exposures at each projection angle are sufficient for the successful reconstruction of both the sample density and dark-field Fokker-Planck diffusion coefficients. We anticipate that the proposed algorithm may be of benefit in biomedical imaging and industrial settings.

Multi-resolution X-ray phase-contrast and dark-field tomography of human cerebellum with near-field speckles

In this study, we use synchrotron-based multi-modal X-ray tomography to examine human cerebellar tissue in three dimensions at two levels of spatial resolution (2.3 µm and 11.9 µm). We show that speckle-based imaging (SBI) produces results that are comparable to propagation-based imaging (PBI), a well-established phase-sensitive imaging method. The different SBI signals provide complementary information, which improves tissue differentiation. In particular, the dark-field signal aids in distinguishing tissues with similar average electron density but different microstructural variations. The setup's high resolution and the imaging technique's excellent phase sensitivity enabled the identification of different cellular layers and additionally, different cell types within these layers. We also correlated this high-resolution phase-contrast information with measured dark-field signal levels. These findings demonstrate the viability of SBI and the potential benefit of the dark-field modality for virtual histology of brain tissue.

Clinical boundary conditions for propagation-based X-ray phase contrast imaging: from bio-sample models targeting to clinical applications

BACKGROUND

Typical propagation-based X-ray phase contrast imaging (PB-PCI) experiments using polyenergetic sources are tested in very ideal conditions: low-energy spectrum (mainly characteristic X-rays), small thickness and homogeneous materials considered weakly absorbing objects, large object-to-detector distance, long exposure times and non-clinical detector.

OBJECTIVE

Explore PB-PCI features using boundary conditions imposed by a low power polychromatic X-ray source (X-ray spectrum without characteristic X-rays), thick and heterogenous materials and a small area imaging detector with high low-detection radiation threshold, elements commonly found in a clinical scenario.

METHODS

A PB-PCI setup implemented using a microfocus X-ray source and a dental imaging detector was characterized in terms of different spectra and geometric parameters on the acquired images. Test phantoms containing fibers and homogeneous materials with close attenuation characteristics and animal bone and mixed soft tissues (bio-sample models) were analyzed. Contrast to Noise Ratio (CNR), system spatial resolution and Kerma values were obtained for all images.

RESULTS

Phase contrast images showed CNR up to 15% higher than conventional contact images. Moreover, it is better seen when large magnifications (>3) and object-to-detector distances (>13 cm) were used. The influence of the spectrum was not appreciable due to the low efficiency of the detector (thin scintillator screen) at high energies.

CONCLUSIONS

Despite the clinical boundary condition used in this work, regarding the X-ray spectrum, thick samples, and detection system, it was possible to acquire phase contrast images of biological samples.

Dynamic X-ray speckle-tracking imaging with high-accuracy phase retrieval based on deep learning

Speckle-tracking X-ray imaging is an attractive candidate for dynamic X-ray imaging owing to its flexible setup and simultaneous yields of phase, transmission and scattering images. However, traditional speckle-tracking imaging methods suffer from phase distortion at locations with abrupt changes in density, which is always the case for real samples, limiting the applications of the speckle-tracking X-ray imaging method. In this paper, we report a deep-learning based method which can achieve dynamic X-ray speckle-tracking imaging with high-accuracy phase retrieval. The calibration results of a phantom show that the profile of the retrieved phase is highly consistent with the theoretical one. Experiments of polyurethane foaming demonstrated that the proposed method revealed the evolution of the complicated microstructure of the bubbles accurately. The proposed method is a promising solution for dynamic X-ray imaging with high-accuracy phase retrieval, and has extensive applications in metrology and quantitative analysis of dynamics in material science, physics, chemistry and biomedicine.

Tri-directional x-ray phase contrast multimodal imaging using one hexagonal mesh modulator

Objective. X-ray phase contrast imaging is a promising technique for future clinical diagnostic as it can provide enhanced contrast in soft tissues compared to traditional x-ray attenuation-contrast imaging. However, the strict requirements on the x-ray coherence and the precise alignment of optical elements limit its applications towards clinical use. To solve this problem, mesh-based x-ray phase contrast imaging method with one hexagonal mesh is proposed for easy alignment and better image visualization.Approach. The mesh produces structured illuminations and the detector captures its distortions to reconstruct the absorption, differential phase contrast (DPC) and dark-field (DF) images of the sample. In this work, we fabricated a hexagonal mesh to simultaneously retrieve DPC and DF signals in three different directions with single shot. A phase retrieval algorithm to obtain artifacts-free phase from DPC images with three different directions is put forward and false color dark-field image is also reconstructed with tri-directional images. Mesh-shifting method based on this hexagonal mesh modulator is also proposed to reconstruct images with better image quality at the expense of increased dose.Main results. In numerical simulations, the proposed hexagonal mesh outperforms the traditional square mesh in image evaluation metrics performance and false color visualization with the same radiation dose. The experimental results demonstrate its feasiblity in real imaging systems and its advantages in quantitive imaging and better visualization. The proposed hexagonal mesh is easy to fabricate and can be successfully applied to x-ray source with it spot size up to 300μm.Significance. This work opens new possibilities for quantitative x-ray non-destructive imaging and may also be instructive for research fields such as x-ray structured illumination microscopy (SIM), x-ray spectral imaging and x-ray phase contrast and dark-field computed tomography (CT).

Mask design, fabrication, and experimental ghost imaging applications for patterned X-ray illumination

A set of non-configurable transversely-displaced masks has been designed and fabricated to generate high-quality X-ray illumination patterns for use in imaging techniques such as ghost imaging (GI), ghost projection, and speckle tracking. The designs include a range of random binary and orthogonal patterns, fabricated through a combination of photolithography and gold electroplating techniques. We experimentally demonstrated that a single wafer can be used as an illumination mask for GI, employing individual illumination patterns and also a mixture of patterns, using a laboratory X-ray source. The quality of the reconstructed X-ray ghost images has been characterized and evaluated through a range of metrics.

Multimodal intrinsic speckle-tracking (MIST) to extract images of rapidly-varying diffuse X-ray dark-field

Speckle-based phase-contrast X-ray imaging (SB-PCXI) can reconstruct high-resolution images of weakly-attenuating materials that would otherwise be indistinguishable in conventional attenuation-based X-ray imaging. The experimental setup of SB-PCXI requires only a sufficiently coherent X-ray source and spatially random mask, positioned between the source and detector. The technique can extract sample information at length scales smaller than the imaging system's spatial resolution; this enables multimodal signal reconstruction. "Multimodal Intrinsic Speckle-Tracking" (MIST) is a rapid and deterministic formalism derived from the paraxial-optics form of the Fokker-Planck equation. MIST simultaneously extracts attenuation, refraction, and small-angle scattering (diffusive dark-field) signals from a sample and is more computationally efficient compared to alternative speckle-tracking approaches. Hitherto, variants of MIST have assumed the diffusive dark-field signal to be spatially slowly varying. Although successful, these approaches have been unable to well-describe unresolved sample microstructure whose statistical form is not spatially slowly varying. Here, we extend the MIST formalism such that this restriction is removed, in terms of a sample's rotationally-isotropic diffusive dark-field signal. We reconstruct multimodal signals of two samples, each with distinct X-ray attenuation and scattering properties. The reconstructed diffusive dark-field signals have superior image quality-as measured by the naturalness image quality evaluator, signal-to-noise ratio, and azimuthally averaged power-spectrum-compared to our previous approaches which assume the diffusive dark-field to be a slowly varying function of transverse position. Our generalisation may assist increased adoption of SB-PCXI in applications such as engineering and biomedical disciplines, forestry, and palaeontology, and is anticipated to aid the development of speckle-based diffusive dark-field tensor tomography.

Directional dark-field retrieval with single-grid x-ray imaging

Directional dark-field imaging is an emerging x-ray modality that is sensitive to unresolved anisotropic scattering from sub-pixel sample microstructures. A single-grid imaging setup can be used to capture dark-field images by looking at changes in a grid pattern projected upon the sample. By creating analytical models for the experiment, we have developed a single-grid directional dark-field retrieval algorithm that can extract dark-field parameters such as the dominant scattering direction, and the semi-major and -minor scattering angles. We show that this method is effective even in the presence of high image noise, allowing for low-dose and time-sequence imaging.

High-speed processing of X-ray wavefront marking data with the Unified Modulated Pattern Analysis (UMPA) model

Wavefront-marking X-ray imaging techniques use e.g., sandpaper or a grating to generate intensity fluctuations, and analyze their distortion by the sample in order to retrieve attenuation, phase-contrast, and dark-field information. Phase contrast yields an improved visibility of soft-tissue specimens, while dark-field reveals small-angle scatter from sub-resolution structures. Both have found many biomedical and engineering applications. The previously developed Unified Modulated Pattern Analysis (UMPA) model extracts these modalities from wavefront-marking data. We here present a new UMPA implementation, capable of rapidly processing large datasets and featuring capabilities to greatly extend the field of view. We also discuss possible artifacts and additional new features.

Technical Design Considerations of a Human-Scale Talbot-Lau Interferometer for Dark-Field CT

Computed tomography (CT) as an important clinical diagnostics method can profit from extension with dark-field imaging, as it is currently restricted to X-rays' attenuation contrast only. Dark-field imaging allows access to more tissue properties, such as micro-structural texture or porosity. The up-scaling process to clinical scale is complex because several design constraints must be considered. The two most important ones are that the finest grating is limited by current manufacturing technology to a [Formula: see text] period and that the interferometer should fit into the CT gantry with minimal modifications only. In this work we discuss why an inverse interferometer and a triangular G1 profile are advantageous and make a compact and sensitive interferometer implementation feasible. Our evaluation of the triangular grating profile reveals a deviation in the interference pattern compared to standard grating profiles, which must be considered in the subsequent data processing. An analysis of the grating orientation demonstrates that currently only a vertical layout can be combined with cylindrical bending of the gratings. We also provide an in-depth discussion, including a new simulation approach, of the impact of the extended X-ray source spot which can lead to large performance loss and present supporting experimental results. This analysis reveals a vastly increased sensitivity to geometry and grating period deviations, which must be considered early in the system design process.

Physics-informed neural network for phase imaging based on transport of intensity equation

Non-interferometric quantitative phase imaging based on Transport of Intensity Equation (TIE) has been widely used in bio-medical imaging. However, analytic TIE phase retrieval is prone to low-spatial frequency noise amplification, which is caused by the illposedness of inversion at the origin of the spectrum. There are also retrieval ambiguities resulting from the lack of sensitivity to the curl component of the Poynting vector occurring with strong absorption. Here, we establish a physics-informed neural network (PINN) to address these issues, by integrating the forward and inverse physics models into a cascaded deep neural network. We demonstrate that the proposed PINN is efficiently trained using a small set of sample data, enabling the conversion of noise-corrupted 2-shot TIE phase retrievals to high quality phase images under partially coherent LED illumination. The efficacy of the proposed approach is demonstrated by both simulation using a standard image database and experiment using human buccal epitehlial cells. In particular, high image quality (SSIM = 0.919) is achieved experimentally using a reduced size of labeled data (140 image pairs). We discuss the robustness of the proposed approach against insufficient training data, and demonstrate that the parallel architecture of PINN is efficient for transfer learning.

Two-dimensional speckle technique for slope error measurements of weakly focusing reflective X-ray optics

Speckle-based at-wavelength metrology techniques now play an important role in X-ray wavefront measurements. However, for reflective X-ray optics, the majority of existing speckle-based methods fail to provide reliable 2D information about the optical surface being characterized. Compared with the 1D information typically output from speckled-based methods, a 2D map is more informative for understanding the overall quality of the optic being tested. In this paper, we propose a method for in situ 2D absolute metrology of weakly focusing X-ray mirrors. Importantly, the angular misalignment of the mirror can be easily corrected with the proposed 2D processing procedure. We hope the speckle pattern data processing method presented here will help to extend this technique to wider applications in the synchrotron radiation and X-ray free-electron laser communities.

X-ray directional dark-field imaging using Unified Modulated Pattern Analysis

X-ray directional dark-field imaging is a recent technique that can reveal a sample’s small-scale structural properties which are otherwise invisible in a conventional imaging system. In particular, directional dark-field can detect and quantify the orientation of anisotropic structures. Here, we present an algorithm that allows for the extraction of a directional dark-field signal from X-ray speckle-based imaging data. The experimental setup is simple, as it requires only the addition of a diffuser to a full-field microscope setup. Sandpaper is an appropriate diffuser material in the hard x-ray regime. We propose an approach to extract the mean scattering width, directionality, and orientation from the recorded speckle images acquired with the technique. We demonstrate that our method can detect and quantify the orientation of fibres inside a carbon fibre reinforced polymer (CFRP) sample within one degree of accuracy and show how the accuracy depends on the number of included measurements. We show that the reconstruction parameters can be tuned to increase or decrease accuracy at the expense of spatial resolution.

Robust ptychographic X-ray speckle tracking with multilayer Laue lenses

In recent years, X-ray speckle tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications, and have been actively developed for use at synchrotron light sources. Speckle techniques can recover an image free of aberrations and can be used to measure wavefronts with a high angular sensitivity. Since they are compatible with low-coherence sources they can be also used with laboratory X-ray sources. A new implementation of the ptychographic X-ray speckle tracking method, suitable for the metrology of highly divergent wavefields, such as those created by multilayer Laue lenses, is presented here. This new program incorporates machine learning techniques such as Huber and non-parametric regression and enables robust and quick wavefield measurements and data evaluation even for low brilliance X-ray beams, and the imaging of low-contrast samples. To realize this, a software suite was written in Python 3, with a C back-end capable of concurrent calculations for high performance. It is accessible as a Python module and is available as source code under Version 3 or later of the GNU General Public License.

Grating-free quantitative phase retrieval for x-ray phase-contrast imaging with conventional sources

X-ray phase-contrast imaging can display subtle differences in low-density materials (e.g., soft tissues) more readily than conventional x-ray imaging. However, producing x-ray phase images requires significant spatial coherence of the beam which requires highly specialized sources such as synchrotrons, small and low power microfocus sources, or complex procedures, such as multiple exposures with several carefully stepped precision gratings. To find appropriate approaches for producing x-ray phase-contrast imaging in a clinically meaningful way, we employed a grating-free method that utilized a low-cost, coarse wire mesh and simple processing. This method relaxes the spatial coherence constraint and allows quantitative phase retrieval for not only monochromatic but also polychromatic beams. We also combined the mesh-based system with polycapillary optics to significantly improve the accuracy of quantitative phase retrieval.

Functional and multiscale 3D structural investigation of brain tissue through correlative in vivo physiology, synchrotron microtomography and volume electron microscopy

Understanding the function of biological tissues requires a coordinated study of physiology and structure, exploring volumes that contain complete functional units at a detail that resolves the relevant features. Here, we introduce an approach to address this challenge: Mouse brain tissue sections containing a region where function was recorded using in vivo 2-photon calcium imaging were stained, dehydrated, resin-embedded and imaged with synchrotron X-ray computed tomography with propagation-based phase contrast (SXRT). SXRT provided context at subcellular detail, and could be followed by targeted acquisition of multiple volumes using serial block-face electron microscopy (SBEM). In the olfactory bulb, combining SXRT and SBEM enabled disambiguation of in vivo-assigned regions of interest. In the hippocampus, we found that superficial pyramidal neurons in CA1a displayed a larger density of spine apparati than deeper ones. Altogether, this approach can enable a functional and structural investigation of subcellular features in the context of cells and tissues.

Multi-Modal X-ray Imaging and Analysis for Characterization of Urinary Stones

Backgound: The composition of stones formed in the urinary tract plays an important role in their management over time. The most common imaging method for the non-invasive evaluation of urinary stones is radiography and computed tomography (CT). However, CT is not very sensitive, and cannot differentiate between all critical stone types. In this study, we propose the application, and evaluate the potential, of a multi-modal (or multi-contrast) X-ray imaging technique called speckle-based imaging (SBI) to differentiate between various types of urinary stones. Methods: Three different stone samples were extracted from animal and human urinary tracts and examined in a laboratory-based speckle tracking setup. The results were discussed based on an X-ray diffraction analysis and a comparison with X-ray microtomography and grating-based interferometry. Results: The stones were classified through compositional analysis by X-ray diffraction. The multi-contrast images obtained using the SBI method provided detailed information about the composition of various urinary stone types, and could differentiate between them. X-ray SBI could provide highly sensitive and high-resolution characterizations of different urinary stones in the radiography mode, comparable to those by grating interferometry. Conclusions: This investigation demonstrated the capability of the SBI technique for the non-invasive classification of urinary stones through radiography in a simple and cost-effective laboratory setting. This opens the possibility for further studies concerning full-field in vivo SBI for the clinical imaging of urinary stones.

Quantifying the x-ray dark-field signal in single-grid imaging

X-ray dark-field imaging reveals the sample microstructure that is unresolved when using conventional methods of x-ray imaging. In this paper, we derive a new method to extract and quantify the x-ray dark-field signal collected using a single-grid imaging set-up, and relate the signal strength to the number of sample microstructures, N. This was achieved by modelling sample-induced changes to the shadow of the upstream grid, and fitting experimental data to this model. Our results suggested that the dark-field scattering angle from our spherical microstructures deviates slightly from the theoretical model of N, which was consistent with results from other experimental methods. We believe the approach outlined here can equip quantitative dark-field imaging of small samples, particularly in cases where only one sample exposure is possible, either due to sample movement or radiation dose limitations. Future directions include an extension into directional dark-field imaging.

A bibliometric and social network analysis perspective of X-ray phase-contrast imaging in medical imaging

INTRODUCTION

Phase-contrast imaging (PCI) is a novel technology that can visualise variations in X-ray refraction (phase contrast) in addition to differences in X-ray attenuation (absorption contrast). Compared to radiography using conventional methods (i.e. absorption-based imaging), PCI techniques can potentially produce images with higher contrast-to-noise ratio and superior spatial resolution at the same or lower radiation doses. This has led PCI to be explored for implementation in medical imaging. While interest in this research field is increasing, the whole body of PCI research in medical imaging has been under-investigated. This paper provides an overview of PCI literature and then focusses on evaluating its development within the scope of medical imaging.

METHODS

Bibliographic data between 1995 and 2018 were used to visualise collaboration networks between countries, institutions and authors. Social network analysis techniques were implemented to measure these networks in terms of centrality and cohesion. These techniques also assisted in the exploration of underlying research paradigms of clinical X-ray PCI investigations.

RESULTS

Forty-one countries, 592 institutions and 2073 authors contributed 796 investigations towards clinical PCI research. The most influential contributors and network collaboration characteristics were identified. Italy was the most influential country, with the European Synchrotron Radiation Facility being the most influential institution. At an author level, F. Pfeiffer was found to be the most influential researcher. Among various PCI techniques, grating interferometry was the most investigated, while computed tomography was the most frequently examined modality.

CONCLUSIONS

By gaining an understanding of collaborations and trends within clinical X-ray PCI research, the links between existing collaborators were identified, which can aid future collaborations between emerging and established collaborators. Moreover, exploring the paradigm of past investigations can shape future research - well-researched PCI techniques may be studied to bring X-ray PCI closer to clinical implementation, or the potential of seldom-investigated techniques may be explored.

An In-House Cone-Beam Tomographic Reconstruction Package for Laboratory X-ray Phase-Contrast Imaging

Phase-contrast, and in general, multi-modal, X-ray micro-tomography is proven to be very useful for low-density, low-attention samples enabling much better contrast than its attenuation-based pendant. Therefore, it is increasingly applied in bio- and life sciences primarily dealing with such samples. Although there is a plethora of literature regarding phase-retrieval algorithms, access to implementations of those algorithms is relatively limited and very few packages combining phase-retrieval methods with the full tomographic reconstruction pipeline are available. This is especially the case for laboratory-based phase-contrast imaging typically featuring cone-beam geometry. We present here an in-house cone-beam tomographic reconstruction package for laboratory X-ray phase-contrast imaging. It covers different phase-contrast techniques and phase retrieval methods. The paper explains their implementation and integration in the filtered back projection chain. Their functionality and efficiency will be demonstrated through applications on a few dedicated samples.

High-resolution and sensitivity bi-directional x-ray phase contrast imaging using 2D Talbot array illuminators

Two-dimensional (2D) Talbot array illuminators (TAIs) were designed, fabricated, and evaluated for high-resolution high-contrast x-ray phase imaging of soft tissue at 10-20 keV. The TAIs create intensity modulations with a high compression ratio on the micrometer scale at short propagation distances. Their performance was compared with various other wavefront markers in terms of period, visibility, flux efficiency, and flexibility to be adapted for limited beam coherence and detector resolution. Differential x-ray phase contrast and dark-field imaging were demonstrated with a one-dimensional, linear phase stepping approach yielding 2D phase sensitivity using unified modulated pattern analysis (UMPA) for phase retrieval. The method was employed for x-ray phase computed tomography reaching a resolution of 3 µm on an unstained murine artery. It opens new possibilities for three-dimensional, non-destructive, and quantitative imaging of soft matter such as virtual histology. The phase modulators can also be used for various other x-ray applications such as dynamic phase imaging, super-resolution structured illumination microscopy, or wavefront sensing.

Quantitative X-ray phase contrast computed tomography with grating interferometry : Biomedical applications of quantitative X-ray grating-based phase contrast computed tomography

The ability of biomedical imaging data to be of quantitative nature is getting increasingly important with the ongoing developments in data science. In contrast to conventional attenuation-based X-ray imaging, grating-based phase contrast computed tomography (GBPC-CT) is a phase contrast micro-CT imaging technique that can provide high soft tissue contrast at high spatial resolution. While there is a variety of different phase contrast imaging techniques, GBPC-CT can be applied with laboratory X-ray sources and enables quantitative determination of electron density and effective atomic number. In this review article, we present quantitative GBPC-CT with the focus on biomedical applications.

Dynamic Multicontrast X-Ray Imaging Method Applied to Additive Manufacturing

We present a dynamic implementation of the beam-tracking x-ray imaging method providing absorption, phase, and ultrasmall angle scattering signals with microscopic resolution and high frame rate. We demonstrate the method's ability to capture dynamic processes with 22-ms time resolution by investigating the melting of metals in laser additive manufacturing, which has so far been limited to single-modality synchrotron radiography. The simultaneous availability of three contrast channels enables earlier segmentation of droplets, tracking of powder dynamic, and estimation of unfused powder amounts, demonstrating that the method can provide additional information on melting processes.

Signal Retrieval from Non-Sinusoidal Intensity Modulations in X-ray and Neutron Interferometry Using Piecewise-Defined Polynomial Function

Grating-based phase-contrast and dark-field imaging systems create intensity modulations that are usually modeled with sinusoidal functions to extract transmission, differential-phase shift, and scatter information. Under certain system-related conditions, the modulations become non-sinusoidal and cause artifacts in conventional processing. To account for that, we introduce a piecewise-defined periodic polynomial function that resembles the physical signal formation process, modeling convolutions of binary periodic functions. Additionally, we extend the model with an iterative expectation-maximization algorithm that can account for imprecise grating positions during phase-stepping. We show that this approach can process a higher variety of simulated and experimentally acquired data, avoiding most artifacts.

Phase and dark-field imaging with mesh-based structured illumination and polycapillary optics

PURPOSE

X-ray phase and dark-field (DF) imaging have been shown to improve the diagnostic capabilities of X-ray systems. However, these methods have found limited clinical use due to the need for multiple precision gratings with limited field of view or requirements on X-ray coherence that may not be easily translated to clinical practice. This work aims to develop a practicable X-ray phase and DF imaging system that could be translated and practiced in the clinic.

METHODS

This work employs a conventional source to create structured illumination with a simple wire mesh. A mesh-shifting algorithm is used to allow wider Fourier windowing to enhance resolution. Deconvolution of the source spot width and camera resolution improves accuracy. Polycapillary optics are employed to enhance coherence. The effects of incorporating optics with two different focal lengths are compared. Information apparent in enhanced absorption images, phase images, and DF images of fat embedded phantoms were compared and subjected to a limited receiver operator characteristic (ROC) study. The DF images of the moist and dry porous object (sponges) were compared.

RESULTS

The mesh-based phase and DF imaging system constructs images with three different information types: scatter-free absorption images, differential phase images, and scatter magnitude/DF images, simultaneously from the same original image. The polycapillary optic enhances the coherence of the beam. The deblurring technique corrects the phase signal error due to geometrical blur and the limitation of the camera modulation transfer function (MTF) and removes image artifacts to improve the resolution in a single shot. The mesh-shifting method allows the use of a wider Fourier processing window, which gives even higher resolution, at the expense of an increased dose. The limited ROC study confirms the efficacy of the system over the conventional system. DF images of moist and dry porous object show the significance of the system in the imaging of lung infections.

CONCLUSION

The mesh-based X-ray phase and DF imaging system is an inexpensive and easy setup in terms of alignment and data acquisition and can produce phase and DF images in a single shot with wide field of view. The system shows significant potential for use in diagnostic imaging in a clinical setting.

Tunable X-ray dark-field imaging for sub-resolution feature size quantification in porous media

X-ray computed micro-tomography typically involves a trade-off between sample size and resolution, complicating the study at a micrometer scale of representative volumes of materials with broad feature size distributions (e.g. natural stones). X-ray dark-field tomography exploits scattering to probe sub-resolution features, promising to overcome this trade-off. In this work, we present a quantification method for sub-resolution feature sizes using dark-field tomograms obtained by tuning the autocorrelation length of a Talbot grating interferometer. Alumina particles with different nominal pore sizes (50 nm and 150 nm) were mixed and imaged at the TOMCAT beamline of the SLS synchrotron (PSI) at eighteen correlation lengths, covering the pore size range. The different particles cannot be distinguished by traditional absorption µCT due to their very similar density and the pores being unresolved at typical image resolutions. Nevertheless, by exploiting the scattering behavior of the samples, the proposed analysis method allowed to quantify the nominal pore sizes of individual particles. The robustness of this quantification was proven by reproducing the experiment with solid samples of alumina, and alumina particles that were kept separated. Our findings demonstrate the possibility to calibrate dark-field image analysis to quantify sub-resolution feature sizes, allowing multi-scale analyses of heterogeneous materials without subsampling.

Quantitative analysis of speckle-based X-ray dark-field imaging using numerical wave-optics simulations

The dark-field signal measures the small-angle scattering strength and provides complementary diagnostic information. This is of particular interest for lung imaging due to the pronounced small-angle scatter from the alveolar microstructure. However, most dark-field imaging techniques are relatively complex, dose-inefficient, and require sophisticated optics and highly coherent X-ray sources. Speckle-based imaging promises to overcome these limitations due to its simple and versatile setup, only requiring the addition of a random phase modulator to conventional X-ray equipment. We investigated quantitatively the influence of sample structure, setup geometry, and source energy on the dark-field signal in speckle-based X-ray imaging with wave-optics simulations for ensembles of micro-spheres. We show that the dark-field signal is accurately predicted via a model originally derived for grating interferometry when using the mean frequency of the speckle pattern power spectral density as the characteristic speckle size. The size directly reflects the correlation length of the diffuser surface and did not change with energy or propagation distance within the near-field. The dark-field signal had a distinct dependence on sample structure and setup geometry but was also affected by beam hardening-induced modifications of the visibility spectrum. This study quantitatively demonstrates the behavior of the dark-field signal in speckle-based X-ray imaging.

Data processing methods and data acquisition for samples larger than the field of view in parallel-beam tomography

Parallel-beam tomography systems at synchrotron facilities have limited field of view (FOV) determined by the available beam size and detector system coverage. Scanning the full size of samples bigger than the FOV requires various data acquisition schemes such as grid scan, 360-degree scan with offset center-of-rotation (COR), helical scan, or combinations of these schemes. Though straightforward to implement, these scanning techniques have not often been used due to the lack of software and methods to process such types of data in an easy and automated fashion. The ease of use and automation is critical at synchrotron facilities where using visual inspection in data processing steps such as image stitching, COR determination, or helical data conversion is impractical due to the large size of datasets. Here, we provide methods and their implementations in a Python package, named Algotom, for not only processing such data types but also with the highest quality possible. The efficiency and ease of use of these tools can help to extend applications of parallel-beam tomography systems.

Comparison of X-ray speckle-based imaging deflection retrieval algorithms for the optimization of radiation dose

X-ray phase contrast imaging can provide improved or complementary information to traditional attenuation-based X-ray imaging, making the field a vast and rapidly evolving research subject. X-ray speckle-based imaging (SBI) is one phase-contrast imaging approach that has shown significant potential in providing both high sensitivity and high resolution while using a very simple experimental setup. With the aim of transferring such phase-contrast-based imaging techniques from synchrotron to laboratory X-ray sources, the issue of the deposited radiation dose still remains to be addressed. In this work, we experimentally and quantitatively compare the results from three different SBI phase retrieval algorithms using both phantoms and biological samples in order to infer the optimal configuration. The results obtained using a synchrotron beam suggest that the technique based on optical flow conservation achieves the most accurate retrieval from the lowest number of sample exposures. This constitutes an important step toward the possibility of transferring SBI into the clinic.

Investigation of the stripe patterns from X-ray reflection optics

X-ray beams reflected from a single layer or multilayer coating are widely used for X-ray tomography, holography, and X-ray phase contrast imaging. However, the observed irregular stripe patterns from either unfocused or defocused beams often cause disturbing artifacts and seriously deteriorate the image quality. In this work, we investigate the origin of these irregular fine structures using the wave optics theory. The connection to similar results obtained by the geometric optics theory is also presented. The proposed relation between the second derivative of the wavefront and the irregular structures was then verified by conducting at-wavelength metrology with the speckle-based wavefront sensing technique. This work will not only help to understand the formation of these irregular structures but also provide the basis for manufacturing future 'stripe-free' refection optics.

speckle-tracking: a software suite for ptychographic X-ray speckle tracking

The program speckle-tracking is described, an open-source software suite for performing wavefront metrology and sample imaging from projection in-line holograms of a sample.

In recent years, X-ray speckle-tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications. These methods are based on the measurement of near-field images. Thanks to their simple experimental setup, high angular sensitivity and compatibility with low-coherence sources, these methods have been actively developed for use with synchrotron and laboratory light sources. Not only do speckle-tracking techniques give the potential for high-resolution imaging, but they also provide rapid and robust characterization of aberrations of X-ray optical elements, focal spot profiles, and sample position and transmission properties. In order to realize these capabilities, software implementations are required that are equally rapid and robust. To address this need, a software suite has been developed for the ptychographic X-ray speckle-tracking technique, an X-ray speckle-based method suitable for highly divergent wavefields. The software suite is written in Python 3, with an OpenCL back end for GPU and multi-CPU core processing. It is accessible as a Python module, through the command line or through a graphical user interface, and is available as source code under Version 3 or later of the GNU General Public License.

Review and experimental verification of x-ray dark-field signal interpretations with respect to quantitative isotropic and anisotropic dark-field computed tomography

Talbot(-Lau) interferometric x-ray and neutron dark-field imaging has, over the past decade, gained substantial interest for its ability to provide insights into a sample's microstructure below the imaging resolution by means of ultra small angle scattering effects. Quantitative interpretations of such images depend on models of the signal origination process that relate the observable image contrast to underlying physical processes. A review of such models is given here and their relation to the wave optical derivations by Yashiro et al and Lynch et al as well as to small angle scattering is discussed. Fresnel scaling is introduced to explain the characteristic distance dependence observed in cone beam geometries. Moreover, a model describing the anisotropic signals of fibrous objects is derived. The Yashiro-Lynch model is experimentally verified both in radiographic and tomographic imaging in a monochromatic synchrotron setting, considering both the effects of material and positional dependence of the resulting dark-field contrast. The effect of varying sample-detector distance on the dark-field signal is shown to be non-negligible for tomographic imaging, yet can be largely compensated for by symmetric acquisition trajectories. The derived orientation dependence of the dark-field contrast of fibrous materials both with respect to variations in autocorrelation width and scattering cross section is experimentally validated using carbon fiber reinforced rods.

Quantitative X-ray Channel-Cut Crystal Diffraction Wavefront Metrology Using the Speckle Scanning Technique

A speckle-based method for the X-ray crystal diffraction wavefront measurement is implemented, and the slope errors of channel-cut crystals with different surface characteristics are measured. The method uses a speckle scanning technique generated by a scattering membrane translated using a piezo motor to infer the deflection of X-rays from the crystals. The method provides a high angular sensitivity of the channel-cut crystal slopes in both the tangential and sagittal directions. The experimental results show that the slope error of different cutting and etching processes ranges from 0.25 to 2.98 μrad. Furthermore, the results of wavefront deformation are brought into the beamline for simulation. This method opens up possibilities for new high-resolution applications for X-ray crystal diffraction wavefront measurement and provides feedback to crystal manufacturers to improve channel-cut fabrication.

High-precision speckle-tracking X-ray imaging with adaptive subset size choices

Speckle-tracking imaging has the advantages of simple setup and high-sensitivity to slowly varying phase gradients. Subset size choice is regarded as a trade-off problem for speckle-tracking X-ray imaging where one needs to balance the spatial resolution and accuracy, where the subset was defined as the region of interest of windowing choice for digital image correlation algorithm. An adaptive subset size choice method based on a Fourier transform for effectively detecting sample phase information without foreknowledge of the sample structure is presented in this study. The speckle-tracking phase-contrast and the form of dark-field imaging based on this method have the advantages of (i) high resolution and time saving compared to large subset choice and (ii) partially improvement the influence from experimental noises, background fluctuations, and false signals compared to small subset choice at the same time. This method has proven to be particularly robust in the experimental condition of poor signal-to-noise ratio. The proposed method may be expanded to all speckle-based imaging methods and other imaging techniques based on the subset or window matching.

Ptychographic X-ray speckle tracking with multi-layer Laue lens systems

The ever-increasing brightness of synchrotron radiation sources demands improved X-ray optics to utilize their capability for imaging and probing biological cells, nano-devices and functional matter on the nanometre scale with chemical sensitivity. Hard X-rays are ideal for high-resolution imaging and spectroscopic applications owing to their short wavelength, high penetrating power and chemical sensitivity. The penetrating power that makes X-rays useful for imaging also makes focusing them technologically challenging. Recent developments in layer deposition techniques have enabled the fabrication of a series of highly focusing X-ray lenses, known as wedged multi-layer Laue lenses. Improvements to the lens design and fabrication technique demand an accurate, robust, in situ and at-wavelength characterization method. To this end, a modified form of the speckle tracking wavefront metrology method has been developed. The ptychographic X-ray speckle tracking method is capable of operating with highly divergent wavefields. A useful by-product of this method is that it also provides high-resolution and aberration-free projection images of extended specimens. Three separate experiments using this method are reported, where the ray path angles have been resolved to within 4 nrad with an imaging resolution of 45 nm (full period). This method does not require a high degree of coherence, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology.

Ptychographic X-ray speckle tracking

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X-ray speckle tracking methods, it is robust to low-coherence X-ray sources, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second-order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.

X-ray phase imaging with the unified modulated pattern analysis of near-field speckles at a laboratory source

X-ray phase-contrast techniques are powerful methods for discerning features with similar densities, which are normally indistinguishable with conventional absorption contrast. While these techniques are well-established tools at large-scale synchrotron facilities, efforts have increasingly focused on implementations at laboratory sources for widespread use. X-ray speckle-based imaging is one of the phase-contrast techniques with high potential for translation to conventional x-ray systems. It yields phase-contrast, transmission, and dark-field images with high sensitivity using a relatively simple and cost-effective setup tolerant to divergent and polychromatic beams. Recently, we have introduced the unified modulated pattern analysis (UMPA) [Phys. Rev. Lett.118, 203903 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.203903], which further simplifies the translation of x-ray speckle-based imaging to low-brilliance sources. Here, we present the proof-of-principle implementation of UMPA speckle-based imaging at a microfocus liquid-metal-jet x-ray laboratory source.

Single-shot, omni-directional x-ray scattering imaging with a laboratory source and single-photon localization

Omni-directional, ultra-small-angle x-ray scattering imaging provides a method to measure the orientation of micro-structures without having to resolve them. In this letter, we use single-photon localization with the Timepix3 chip to demonstrate, to the best of our knowledge, the first laboratory-based implementation of single-shot, omni-directional x-ray scattering imaging using the beam-tracking technique. The setup allows a fast and accurate retrieval of the scattering signal using a simple absorption mask. We suggest that our new approach may enable faster laboratory-based tensor tomography and could be used for energy-resolved x-ray scattering imaging.

X-ray Fokker-Planck equation for paraxial imaging

The Fokker-Planck equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity equation. The x-ray Fokker-Planck equation can simultaneously account for both propagation-based phase contrast, and the diffusive effects of sample-induced small-angle x-ray scattering, when forming an x-ray image of a thin sample. Two derivations are given for the Fokker-Planck equation associated with x-ray imaging, together with a Kramers-Moyal generalisation thereof. Both equations are underpinned by the concept of unresolved speckle due to unresolved sample micro-structure. These equations may be applied to the forward problem of modelling image formation in the presence of both coherent and diffusive energy transport. They may also be used to formulate associated inverse problems of retrieving the phase shifts due to a sample placed in an x-ray beam, together with the diffusive properties of the sample. The domain of applicability for the Fokker-Planck and Kramers-Moyal equations for paraxial imaging is at least as broad as that of the transport-of-intensity equation which they generalise, hence the technique is also expected to be useful for paraxial imaging using visible light, electrons and neutrons.

Applying the Fokker-Planck equation to grating-based x-ray phase and dark-field imaging

X-ray imaging has conventionally relied upon attenuation to provide contrast. In recent years, two complementary modalities have been added; (a) phase contrast, which can capture low-density samples that are difficult to see using attenuation, and (b) dark-field x-ray imaging, which reveals the presence of sub-pixel sample structures. These three modalities can be accessed using a crystal analyser, a grating interferometer or by looking at a directly-resolved grid, grating or speckle pattern. Grating and grid-based methods extract a differential phase signal by measuring how far a feature in the illumination has been shifted transversely due to the presence of a sample. The dark-field signal is extracted by measuring how the visibility of the structured illumination is decreased, typically due to the presence of sub-pixel structures in a sample. The strength of the dark-field signal may depend on the grating period, the pixel size and the set-up distances, and additional dark-field signal contributions may be seen as a result of strong phase effects or other factors. In this paper we show that the finite-difference form of the Fokker-Planck equation can be applied to describe the drift (phase signal) and diffusion (dark-field signal) of the periodic or structured illumination used in phase contrast x-ray imaging with gratings, in order to better understand any cross-talk between attenuation, phase and dark-field x-ray signals. In future work, this mathematical description could be used as a basis for new approaches to the inverse problem of recovering both phase and dark-field information.

Multilayer Laue lenses at high X-ray energies: performance and applications

X-ray microscopy at photon energies above 15 keV is very attractive for the investigation of atomic and nanoscale properties of technologically relevant structural and bio materials. This method is limited by the quality of X-ray optics. Multilayer Laue lenses (MLLs) have the potential to make a major impact in this field because, as compared to other X-ray optics, they become more efficient and effective with increasing photon energy. In this work, MLLs were utilized with hard X-rays at photon energies up to 34.5 keV. The design, fabrication, and performance of these lenses are presented, and their application in several imaging configurations is described. In particular, two "full field" modes of imaging were explored, which provide various contrast modalities that are useful for materials characterisation. These include point projection imaging (or Gabor holography) for phase contrast imaging and direct imaging with both bright-field and dark-field illumination. With high-efficiency MLLs, such modes offer rapid data collection as compared with scanning methods as well as a large field of views.

Phase-Contrast and Dark-Field Imaging

Very early, in 1896, Wilhelm Conrad Röntgen, the founding father of X-rays, attempted to measure diffraction and refraction by this new kind of radiation, in vain. Only 70 years later, these effects were measured by Ulrich Bonse and Michael Hart who used them to make full-field images of biological specimen, coining the term phase-contrast imaging. Yet, another 30 years passed until the Talbot effect was rediscovered for X-radiation, giving rise to a micrograting based interferometer, replacing the Bonse–Hart interferometer, which relied on a set of four Laue-crystals for beam splitting and interference. By merging the Lau-interferometer with this Talbot-interferometer, another ten years later, measuring X-ray refraction and X-ray scattering full-field and in cm-sized objects (as Röntgen had attempted 110 years earlier) became feasible in every X-ray laboratory around the world. Today, now that another twelve years have passed and we are approaching the 125th jubilee of Röntgen’s discovery, neither Laue-crystals nor microgratings are a necessity for sensing refraction and scattering by X-rays. Cardboard, steel wool, and sandpaper are sufficient for extracting these contrasts from transmission images, using the latest image reconstruction algorithms. This advancement and the ever rising number of applications for phase-contrast and dark-field imaging prove to what degree our understanding of imaging physics as well as signal processing have advanced since the advent of X-ray physics, in particular during the past two decades. The discovery of the electron, as well as the development of electron imaging technology, has accompanied X-ray physics closely along its path, both modalities exploring the applications of new dark-field contrast mechanisms these days. Materials science, life science, archeology, non-destructive testing, and medicine are the key faculties which have already integrated these new imaging devices, using their contrast mechanisms in full. This special issue “Phase-Contrast and Dark-field Imaging” gives us a broad yet very to-the-point glimpse of research and development which are currently taking place in this very active field. We find reviews, applications reports, and methodological papers of very high quality from various groups, most of which operate X-ray scanners which comprise these new imaging modalities.