Human hand radiography using X-ray differential phase contrast combined with dark-field imaging

Feasibility of Dark-Field Radiography to Enhance Detection of Nondisplaced Fractures

Background Many clinically relevant fractures are occult on conventional radiographs and therefore challenging to diagnose reliably. X-ray dark-field radiography is a developing method that uses x-ray scattering as an additional signal source. Purpose To investigate whether x-ray dark-field radiography enhances the depiction of radiographically occult fractures in an experimental model compared with attenuation-based radiography alone and whether the directional dependence of dark-field signal impacts observer ratings. Materials and Methods Four porcine loin ribs had nondisplaced fractures experimentally introduced. Microstructural changes were visually verified using high-spatial-resolution three-dimensional micro-CT. X-ray dark-field radiographs were obtained before and after fracture, with the before-fracture scans serving as control images. The presence of a fracture was scored by three observers using a six-point scale (6, surely; 5, very likely; 4, likely; 3, unlikely; 2, very unlikely; and 1, certainly not). Differences between scores based on attenuation radiographs alone (n = 96) and based on combined attenuation and dark-field radiographs (n = 96) were evaluated by using the DeLong method to compare areas under the receiver operating characteristic curve. The impact of the dark-field signal directional sensitivity on observer ratings was evaluated using the Wilcoxon test. The dark-field data were split into four groups (24 images per group) according to their sensitivity orientation and tested against each other. Musculoskeletal dark-field radiography was further demonstrated on human finger and foot specimens. Results The addition of dark-field radiographs was found to increase the area under the receiver operating characteristic curve to 1 compared with an area under the receiver operating characteristic curve of 0.87 (95% CI: 0.80, 0.94) using attenuation-based radiographs alone (P < .001). There were similar observer ratings for the four different dark-field sensitivity orientations (P = .16-.65 between the groups). Conclusion These results suggested that the inclusion of dark-field radiography has the potential to help enhance the detection of nondisplaced fractures compared with attenuation-based radiography alone. © RSNA, 2024 See also the editorial by Rubin in this issue.

Dark-field computed tomography reaches the human scale

X-ray computed tomography (CT) is one of the most commonly used diagnostic three-dimensional imaging modalities today. Conventionally, this noninvasive technique generates contrast by measuring the X-ray attenuation properties of different tissues. Considering the wave nature of X-rays, complementary contrast can be achieved by further measuring their small-angle scattering (dark-field) properties. This provides additional valuable diagnostic information on otherwise unresolved tissue microstructure. In our work, we have translated this wave-optical mechanism from the optical bench to a human-sized prototype CT system. This involved the integration of an interferometer into a clinical CT gantry and overcoming several associated challenges regarding vibrations, continuous gantry rotation, and large field of view. This development puts complementary X-ray contrast within reach for real-word medical applications.

X-ray computed tomography (CT) is one of the most commonly used three-dimensional medical imaging modalities today. It has been refined over several decades, with the most recent innovations including dual-energy and spectral photon-counting technologies. Nevertheless, it has been discovered that wave-optical contrast mechanisms—beyond the presently used X-ray attenuation—offer the potential of complementary information, particularly on otherwise unresolved tissue microstructure. One such approach is dark-field imaging, which has recently been introduced and already demonstrated significantly improved radiological benefit in small-animal models, especially for lung diseases. Until now, however, dark-field CT could not yet be translated to the human scale and has been restricted to benchtop and small-animal systems, with scan durations of several minutes or more. This is mainly because the adaption and upscaling to the mechanical complexity, speed, and size of a human CT scanner so far remained an unsolved challenge. Here, we now report the successful integration of a Talbot–Lau interferometer into a clinical CT gantry and present dark-field CT results of a human-sized anthropomorphic body phantom, reconstructed from a single rotation scan performed in 1 s. Moreover, we present our key hardware and software solutions to the previously unsolved roadblocks, which so far have kept dark-field CT from being translated from the optical bench into a rapidly rotating CT gantry, with all its associated challenges like vibrations, continuous rotation, and large field of view. This development enables clinical dark-field CT studies with human patients in the near future.

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.

X-ray Dark-Field Radiography: Potential for Visualization of Monosodium Urate Deposition

OBJECTIVE

The aim of this study was to evaluate the potential of x-ray dark-field radiography for the noninvasive detection of monosodium urate (MSU) crystals as a novel diagnostic tool for gout.

MATERIALS AND METHODS

Contrast-to-noise ratios of MSU crystals in conventional radiography and dark-field radiography have been compared in a proof of principle measurement. Monosodium urate crystals have been injected into mouse legs in an ex vivo experimental gout setup. Three radiologists independently evaluated the images for the occurrence of crystal deposits in a blinded study for attenuation images only, dark-field images only, and with both images available for a comprehensive diagnosis. All imaging experiments have been performed at an experimental x-ray dark-field setup with a 3-grating interferometer, a rotating anode tube (50 kVp), and a photon-counting detector (effective pixel size, 166 μm).

RESULTS

X-ray dark-field radiography provided a strong signal increase for MSU crystals in a physiological buffer solution compared with conventional attenuation radiography with a contrast-to-noise ratio increase from 0.8 to 19.3. Based on conventional attenuation images only, the reader study revealed insufficient diagnostic performance (sensitivity, 11%; specificity, 92%) with poor interrater agreement (Cohen's coefficient κ = 0.031). Based on dark-field images, the sensitivity increased to 100%, specificity remained at 92%, and the interrater agreement increased to κ = 0.904. Combined diagnosis based on both image modalities maximized both sensitivity and specificity to 100% with absolute interrater agreement (κ = 1.000).

CONCLUSIONS

X-ray dark-field radiography enables the detection of MSU crystals in a mouse-based gout model. The simultaneous avaliability of a conventional attenuation image together with the dark-field image provides excellent detection rates of gout deposits with high specificity.

Discrimination analysis of breast calcifications using x-ray dark-field radiography

BACKGROUND

X-ray dark-field radiography could enhance mammography by providing more information on imaged tissue and microcalcifications. The dark field signal is a measure of small angle scattering and can thus provide additional information on the imaged materials. This information can be useful for material distinction of calcifications and the diagnosis of breast cancer by classifying benign and malign association of these calcifications.

METHODS

For this study, institutional review board approval was obtained. We present the evaluation of images acquired with interferometric grating-based x-ray imaging of 323 microcalcifications (166 malign and 157 benign associated) in freshly dissected breast tissue and compare the results to the information extracted in follow-up pathological evaluation. The number of imaged calcifications is sufficiently higher than in similar previous studies. Fourteen calcification properties were extracted from the digital images and used as predictors in three different models common in discrimination analysis namely a simple threshold model, a naive Bayes model and a linear regression model, which classify the calcifications as associated with a benign or suspicious finding. Three of these fourteen predictors have been newly defined in this work and are independent from the tissue background surrounding the microcalcifications. Using these predictors no background correction is needed, as in previous works in this field. The new predictors are the length of the first and second principle component of the absorption and dark-field data, as well as the angle between the first principle component and the dark-field axis. We called these predictors data length, data width, and data orientation.

RESULTS

In fourfold cross-validation malignancy of the imaged tissue was predicted. Models that take only classical absorption predictors into account reached a sensitivity of 53.3% at a specificity of 81.1%. For a combination of predictors that also include dark field information, a sensitivity of 63.2% and specificity of 80.8% were obtained. The included dark field information consisted of the newly introduced parameters, data orientation and data width.

CONCLUSIONS

While remaining at a similar specificity, the sensitivity, with which a trained model was able to distinguish malign from benign associated calcifications, was increased by 10% on including dark-field information. This suggests grating-based x-ray imaging as a promising clinical imaging method in the field of mammography.

Quantitative characterization of ex vivo breast tissue via x-ray phase-contrast tomography

BACKGROUND

Grating-based X-ray phase-contrast imaging (GPCI) has received growing interests in recent years due to its high capability of visualizing soft tissue. Breast imaging is one of the most promising candidates for the first clinical application of this imaging modality.

OBJECTIVE

In this work, quantitative breast tissue characterization based on GPCI computed tomography (CT) is investigated with a laboratory X-ray tube through a comparison between attenuation-based CT images and phase-contrast CT images.

METHODS

The Hounsfield units (HU) scale was introduced to phase-contrast images due to its wide application in clinical medicine. In this work, instead of water, plastic cylinders composed of polyethylene terephthalate (PET) was treated as the calibration material. An alternative test-retest reliability (TRR) was presented to evaluate the repeatability of GPCI. Comparison between attenuation-based CT imaging and GPCI CT imaging was operated with the use of statistical analysis methods like histograms and receiver operating characteristic (ROC) curves.

RESULTS

The determined mean TRR related to cylinders is slightly larger in phase-contrast imaging (0.93) than that in attenuation-based imaging (0.89). With respect to distinguishing breast tissues, the AUC (area under curve) values of ROC curves of phase-contrast images are higher than that of attenuation-based images.

CONCLUSIONS

An ex vivo study of GPCI shows that it is a stable imaging modality for visualizing the breast tissue with good repeatability, and that it could be of potential for the diagnosis of breast cancer as well.

Implementation of a Talbot-Lau interferometer in a clinical-like c-arm setup: A feasibility study

X-ray grating-based phase-contrast imaging has raised interest regarding a variety of potential clinical applications, whereas the method is feasible using a medical x-ray tube. Yet, the transition towards a clinical setup remains challenging due to the requirement of mechanical robustness of the interferometer and high demands applying to medical equipment in clinical use. We demonstrate the successful implementation of a Talbot-Lau interferometer in an interventional c-arm setup. The consequence of vibrations induced by the rotating anode of the tube is discussed and the prototype is shown to provide a visibility of 21.4% at a tube voltage of 60 kV despite the vibrations. Regarding clinical application, the prototype is mainly set back due to the limited size of the field of view covering an area of 17 mm × 46 mm. A c-arm offers the possibility to change the optical axis according to the requirements of the medical examination. We provide a method to correct for artifacts that result from the angulation of the c-arm. Finally, the images of a series of measurements with the c-arm in different angulated positions are shown. Thereby, it is sufficient to perform a single reference measurement in parking position that is valid for the complete series despite angulation.

Simultaneous wood and metal particle detection on dark-field radiography

Background

Currently, the detection of retained wood is a frequent but challenging task in emergency care. The purpose of this study is to demonstrate improved foreign-body detection with the novel approach of preclinical X-ray dark-field radiography.

Methods

At a preclinical dark-field x-ray radiography, setup resolution and sensitivity for simultaneous detection of wooden and metallic particles have been evaluated in a phantom study. A clinical setting has been simulated with a formalin fixated human hand where different typical foreign-body materials have been inserted. Signal-to-noise ratios (SNR) have been determined for all test objects.

Results

On the phantom, the SNR value for wood in the dark-field channel was strongly improved by a factor 6 compared to conventional radiography and even compared to the SNR of an aluminium structure of the same size in conventional radiography. Splinters of wood < 300 μm in diameter were clearly detected on the dark-field radiography. Dark-field radiography of the formalin-fixated human hand showed a clear signal for wooden particles that could not be identified on conventional radiography.

Conclusions

x-ray dark-field radiography enables the simultaneous detection of wooden and metallic particles in the extremities. It has the potential to improve and simplify the current state-of-the-art foreign-body detection.

K-edge energy-based calibration method for photon counting detectors

In recent years, potential applications of energy-resolved photon counting detectors (PCDs) in the x-ray medical imaging field have been actively investigated. Unlike conventional x-ray energy integration detectors, PCDs count the number of incident x-ray photons within certain energy windows. For PCDs, the interactions between x-ray photons and photoconductor generate electronic voltage pulse signals. The pulse height of each signal is proportional to the energy of the incident photons. By comparing the pulse height with the preset energy threshold values, x-ray photons with specific energies are recorded and sorted into different energy bins. To quantitatively understand the meaning of the energy threshold values, and thus to assign an absolute energy value to each energy bin, energy calibration is needed to establish the quantitative relationship between the threshold values and the corresponding effective photon energies. In practice, the energy calibration is not always easy, due to the lack of well-calibrated energy references for the working energy range of the PCDs. In this paper, a new method was developed to use the precise knowledge of the characteristic K-edge energy of materials to perform energy calibration. The proposed method was demonstrated using experimental data acquired from three K-edge materials (viz., iodine, gadolinium, and gold) on two different PCDs (Hydra and Flite, XCounter, Sweden). Finally, the proposed energy calibration method was further validated using a radioactive isotope (Am-241) with a known decay energy spectrum.

Trabecular bone anisotropy imaging with a compact laser-undulator synchrotron x-ray source

Conventional x-ray radiography is a well-established standard in diagnostic imaging of human bones. It reveals typical bony anatomy with a strong surrounding cortical bone and trabecular structure of the inner part. However, due to limited spatial resolution, x-ray radiography cannot provide information on the microstructure of the trabecular bone. Thus, microfractures without dislocation are often missed in initial radiographs, resulting in a lack or delay of adequate therapy. Here we show that x-ray vector radiography (XVR) can overcome this limitation and allows for a deeper insight into the microstructure with a radiation exposure comparable to standard radiography. XVR senses x-ray ultrasmall-angle scattering in addition to the attenuation contrast and thereby reveals the mean scattering strength, its degree of anisotropy and the orientation of scattering structures. Corresponding to the structural characteristics of bones, there is a homogenous mean scattering signal of the trabecular bone but the degree of anisotropy is strongly affected by variations in the trabecular structure providing more detailed information on the bone microstructure. The measurements were performed at the Munich Compact Light Source, a novel type of x-ray source based on inverse Compton scattering. This laboratory-sized source produces highly brilliant quasi-monochromatic x-rays with a tunable energy.

Techniques to assess bone ultrastructure organization: orientation and arrangement of mineralized collagen fibrils

Bone's remarkable mechanical properties are a result of its hierarchical structure. The mineralized collagen fibrils, made up of collagen fibrils and crystal platelets, are bone's building blocks at an ultrastructural level. The organization of bone's ultrastructure with respect to the orientation and arrangement of mineralized collagen fibrils has been the matter of numerous studies based on a variety of imaging techniques in the past decades. These techniques either exploit physical principles, such as polarization, diffraction or scattering to examine bone ultrastructure orientation and arrangement, or directly image the fibrils at the sub-micrometre scale. They make use of diverse probes such as visible light, X-rays and electrons at different scales, from centimetres down to nanometres. They allow imaging of bone sections or surfaces in two dimensions or investigating bone tissue truly in three dimensions, in vivo or ex vivo, and sometimes in combination with in situ mechanical experiments. The purpose of this review is to summarize and discuss this broad range of imaging techniques and the different modalities of their use, in order to discuss their advantages and limitations for the assessment of bone ultrastructure organization with respect to the orientation and arrangement of mineralized collagen fibrils.

Three Dimensional Visualization of Human Cardiac Conduction Tissue in Whole Heart Specimens by High-Resolution Phase-Contrast CT Imaging Using Synchrotron Radiation

BACKGROUND

The feasibility of synchrotron radiation-based phase-contrast computed tomography (PCCT) for visualization of the atrioventricular (AV) conduction axis in human whole heart specimens was tested using four postmortem structurally normal newborn hearts obtained at autopsy.

METHODS

A PCCT imaging system at the beamline BL20B2 in a SPring-8 synchrotron radiation facility was used. The PCCT imaging of the conduction system was performed with "virtual" slicing of the three-dimensional reconstructed images. For histological verification, specimens were cut into planes similar to the PCCT images, then cut into 5-μm serial sections and stained with Masson's trichrome.

RESULTS

In PCCT images of all four of the whole hearts of newborns, the AV conduction axis was distinguished as a low-density structure, which was serially traceable from the compact node to the penetrating bundle within the central fibrous body, and to the branching bundle into the left and right bundle branches. This was verified by histological serial sectioning.

CONCLUSION

This is the first demonstration that visualization of the AV conduction axis within human whole heart specimens is feasible with PCCT.

A generalized quantitative interpretation of dark-field contrast for highly concentrated microsphere suspensions

In X-ray grating interferometry, dark-field contrast arises due to partial extinction of the detected interference fringes. This is also called visibility reduction and is attributed to small-angle scattering from unresolved structures in the imaged object. In recent years, analytical quantitative frameworks of dark-field contrast have been developed for highly diluted monodisperse microsphere suspensions with maximum 6% volume fraction. These frameworks assume that scattering particles are separated by large enough distances, which make any interparticle scattering interference negligible. In this paper, we start from the small-angle scattering intensity equation and, by linking Fourier and real-space, we introduce the structure factor and thus extend the analytical and experimental quantitative interpretation of dark-field contrast, for a range of suspensions with volume fractions reaching 40%. The structure factor accounts for interparticle scattering interference. Without introducing any additional fitting parameters, we successfully predict the experimental values measured at the TOMCAT beamline, Swiss Light Source. Finally, we apply this theoretical framework to an experiment probing a range of system correlation lengths by acquiring dark-field images at different energies. This proposed method has the potential to be applied in single-shot-mode using a polychromatic X-ray tube setup and a single-photon-counting energy-resolving detector.

2D-Omnidirectional Hard-X-Ray Scattering Sensitivity in a Single Shot

X-ray scattering imaging can provide complementary information to conventional absorption based radiographic imaging about the unresolved microstructures of a sample. The scattering signal can be accessed with various methods based on coherent illumination, which span from self-imaging to speckle scanning. The directional sensitivity of the existing real space imaging methods is limited to a few directions on the imaging plane and requires scanning of the optical components, or the rotation of either the sample or the imaging setup, in order to cover the full range of possible scattering directions. In this Letter the authors propose a new method that allows the simultaneous acquisition of scattering images in all possible directions in a single shot. This is achieved by a specialized phase grating and a detector with sufficient spatial resolution to record the generated interference fringe. The structural length scale sensitivity of the system can be tuned by varying its geometry for a fixed grating design. Taking into account ongoing developments in the field of compact x-ray sources that allow high brightness and sufficient spatial coherence, the applicability of omnidirectional scattering imaging in industrial and medical settings is boosted significantly.

Note: Gratings on low absorbing substrates for x-ray phase contrast imaging

Grating based X-ray phase contrast imaging is on the verge of being applied in clinical settings. To achieve this goal, compact setups with high sensitivity and dose efficiency are necessary. Both can be increased by eliminating unwanted absorption in the beam path, which is mainly due to the grating substrates. Fabrication of gratings via deep X-ray lithography can address this issue by replacing the commonly used silicon substrate with materials with lower X-ray absorption that fulfill certain boundary conditions. Gratings were produced on both graphite and polymer substrates without compromising on structure quality. These gratings were tested in a three-grating setup with a source operated at 40 kVp and lead to an increase in the detector photon count rate of almost a factor of 4 compared to a set of gratings on silicon substrates. As the visibility was hardly affected, this corresponds to a significant increase in sensitivity and therefore dose efficiency.

Phase-Contrast Hounsfield Units of Fixated and Non-Fixated Soft-Tissue Samples

X-ray phase-contrast imaging is a novel technology that achieves high soft-tissue contrast. Although its clinical impact is still under investigation, the technique may potentially improve clinical diagnostics. In conventional attenuation-based X-ray computed tomography, radiological diagnostics are quantified by Hounsfield units. Corresponding Hounsfield units for phase-contrast imaging have been recently introduced, enabling a setup-independent comparison and standardized interpretation of imaging results. Thus far, the experimental values of few tissue types have been reported; these values have been determined from fixated tissue samples. This study presents phase-contrast Hounsfield units for various types of non-fixated human soft tissues. A large variety of tissue specimens ranging from adipose, muscle and connective tissues to liver, kidney and pancreas tissues were imaged by a grating interferometer with a rotating-anode X-ray tube and a photon-counting detector. Furthermore, we investigated the effects of formalin fixation on the quantitative phase-contrast imaging results.

Spline based iterative phase retrieval algorithm for X-ray differential phase contrast radiography

Differential phase contrast imaging using grating interferometer is a promising alternative to conventional X-ray radiographic methods. It provides the absorption, differential phase and scattering information of the underlying sample simultaneously. Phase retrieval from the differential phase signal is an essential problem for quantitative analysis in medical imaging. In this paper, we formalize the phase retrieval as a regularized inverse problem, and propose a novel discretization scheme for the derivative operator based on B-spline calculus. The inverse problem is then solved by a constrained regularized weighted-norm algorithm (CRWN) which adopts the properties of B-spline and ensures a fast implementation. The method is evaluated with a tomographic dataset and differential phase contrast mammography data. We demonstrate that the proposed method is able to produce phase image with enhanced and higher soft tissue contrast compared to conventional absorption-based approach, which can potentially provide useful information to mammographic investigations.

Alignment method combining interference lithography with anisotropic wet etch technique for fabrication of high aspect ratio silicon gratings

A method was developed for aligning interference fringes generated in interference lithography to the vertical {111} planes of <110> oriented silicon wafers. The alignment error is 0.036°. This high precision method makes it possible to combine interference lithography with anisotropic wet etch technique for the fabrication of high aspect ratio silicon gratings with extremely smooth sidewalls over a large sample area. With this alignment method, 320 nm and 2 μm period silicon gratings have been successfully fabricated. The highest aspect ratio is up to 100. The sample area is about 50 mm × 60 mm. The roughness (root mean square) of the sidewall is about 0.267 nm.

Tilted-grating approach for scanning-mode X-ray phase contrast imaging

Among the existent X-ray phase-contrast modalities, grating interferometry appears as a very promising technique for commercial applications, since it is compatible with conventional X-ray tubes and is robust from a mechanical point of view. However, since applications such as medical imaging and homeland security demand covering a considerable field of view, the fabrication of large-area gratings, which is known to be challenging and expensive, would be needed. A scanning setup is a good solution for this issue, because it uses cheaper line instead of large-area 2D detectors and, therefore, would require smaller gratings. In such a setup, the phase-retrieval using the conventional phase-stepping approach would be very slow, so having a faster method to record the signals becomes fundamental. To tackle this problem, we present a scanning-mode grating interferometer design, in which a grating is tilted to form Moiré fringes perpendicular to the grating lines. The sample is then translated along the fringes, so each line detector records a different phase step for each slice of the sample. This new approach was tested both in a simulated scenario and in an experimental setting, and its performance was quantitatively satisfactory compared to the traditional phase-stepping method and another existing scanning-mode technique.

Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings

Hard X-ray phase-contrast imaging characterizes the electron density distribution in an object without the need for radiation absorption. The power of phase contrast to resolve subtle changes, such as those in soft tissue structures, lies in its ability to detect minute refractive bending of X-rays. Here we report a far-field, two-arm interferometer based on the new nanometric phase gratings, which can detect X-ray refraction with subnanoradian sensitivity, and at the same time overcomes the fundamental limitation of ultra-narrow bandwidths (Δλ/λ~10⁻⁴) of the current, most sensitive methods based on crystal interferometers. On a 1.5% bandwidth synchrotron source, we demonstrate clear visualization of blood vessels in unstained mouse organs in simple projection views, with over an order-of-magnitude higher phase contrast than current near-field grating interferometers.

Phase-contrast imaging has become popular for medical diagnostic purposes because of the ability to see transparent structures at relatively small radiation energy dosed to samples. Wen et al. further develop this technique using nanometric phase gratings to achieve subnanoradian sensitivity.

Performance and optimization of X-ray grating interferometry

The monochromatic and polychromatic performance of a grating interferometer is theoretically analysed. The smallest detectable refraction angle is used as a metric for the efficiency in acquiring a differential phase-contrast image. Analytical formulae for the visibility and the smallest detectable refraction angle are derived for Talbot-type and Talbot-Lau-type interferometers, respectively, providing a framework for the optimization of the geometry. The polychromatic performance of a grating interferometer is investigated analytically by calculating the energy-dependent interference fringe visibility, the spectral acceptance and the polychromatic interference fringe visibility. The optimization of grating interferometry is a crucial step for the design of application-specific systems with maximum performance.

Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer

X-ray imaging using a Talbot-Lau interferometer, consisting of three binary gratings, is a well-established approach to acquire x-ray phase-contrast and dark-field images with a polychromatic source. However, challenges in the production of high aspect ratio gratings limit the construction of a compact setup for high x-ray energies. In this study we consider the use of phase gratings with triangular-shaped structures in an x-ray interferometer and show that such gratings can yield high visibilities for significantly shorter propagation distances than conventional gratings with binary structures. The findings are supported by simulation and experimental results for both cases of a monochromatic and a polychromatic source.

Flexible retrospective phase stepping in x-ray scatter correction and phase contrast imaging using structured illumination

The development of phase contrast methods for diagnostic x-ray imaging is inspired by the potential of seeing the internal structures of the human body without the need to deposit any harmful radiation. An efficient class of x-ray phase contrast imaging and scatter correction methods share the idea of using structured illumination in the form of a periodic fringe pattern created with gratings or grids. They measure the scatter and distortion of the x-ray wavefront through the attenuation and deformation of the fringe pattern via a phase stepping process. Phase stepping describes image acquisition at regular phase intervals by shifting a grating in uniform steps. However, in practical conditions the actual phase intervals can vary from step to step and also spatially. Particularly with the advent of electromagnetic phase stepping without physical movement of a grating, the phase intervals are dependent upon the focal plane of interest. We describe a demodulation algorithm for phase stepping at arbitrary and position-dependent (APD) phase intervals without assuming a priori knowledge of the phase steps. The algorithm retrospectively determines the spatial distribution of the phase intervals by a Fourier transform method. With this ability, grating-based x-ray imaging becomes more adaptable and robust for broader applications.