Young's double-slit interference with single hard X-ray photons.

Double-slit interference experiments using monochromatic hard X-rays with the energy of 25 keV are presented. The experiments were performed at a synchrotron source with a distance of 110 m between the interferometer and the detector to produce an interference pattern with a sufficiently broad period that could be adequately sampled by a photon-counting detector with 75 micrometre pixels. In the single-particle version of the experiment, over one million image frames with a single registered photon in each one were collected. The sum of these frames showed a clear presence of the interference pattern with the expected period. Subsequent analysis provided an objective estimation of the minimal number of detected photons required to determine, in accordance with the Rose criterion, the presence of the photon interference. Apart from a general theoretical interest, these investigations were aimed at exploring the possibility of medical X-ray phase-contrast imaging in photon-counting regime at minimal radiation doses.

Three-dimensional contrast-transfer-function approach in phase-contrast tomography.

A new method is developed for 3D reconstruction of multimaterial objects using propagation-based x-ray phase-contrast tomography (PB-CT) with phase retrieval via contrast-transfer-function (CTF) formalism. The approach differs from conventional PB-CT algorithms, which apply phase retrieval to individual 2D projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D. The CTF formalism is further extended to the cases of partially coherent illumination and strongly absorbing samples. Simulated results demonstrate that the proposed post-reconstruction CTF method provides fast and stable phase retrieval, producing results equivalent to conventional pre-reconstruction 2D CTF phase retrieval. Moreover, it is shown that application can be highly localized to isolated objects of interest, without a significant loss of quality, thus leading to increased computational efficiency. Combined with the extended validity of the CTF to greater propagation distances, this method provides additional advantages over approaches based on the transport-of-intensity equation.

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.

Dark-field tomography of an attenuating object using intrinsic x-ray speckle tracking.

Purpose: We investigate how an intrinsic speckle tracking approach to speckle-based x-ray imaging is used to extract an object's effective dark-field (DF) signal, which is capable of providing object information in three dimensions. Approach: The effective DF signal was extracted using a Fokker-Planck type formalism, which models the deformations of illuminating reference beam speckles due to both coherent and diffusive scatter from the sample. Here, we assumed that (a) small-angle scattering fans at the exit surface of the sample are rotationally symmetric and (b) the object has both attenuating and refractive properties. The associated inverse problem of extracting the effective DF signal was numerically stabilized using a "weighted determinants" approach. Results: Effective DF projection images, as well as the DF tomographic reconstructions of the wood sample, are presented. DF tomography was performed using a filtered back projection reconstruction algorithm. The DF tomographic reconstructions of the wood sample provided complementary, and otherwise inaccessible, information to augment the phase contrast reconstructions, which were also computed. Conclusions: An intrinsic speckle tracking approach to speckle-based imaging can tomographically reconstruct an object's DF signal at a low sample exposure and with a simple experimental setup. The obtained DF reconstructions have an image quality comparable to alternative x-ray DF techniques.

Effect of x-ray energy on the radiological image quality in propagation-based phase-contrast computed tomography of the breast.

Purpose: Breast cancer is the most common cancer in women in developing and developed countries and is responsible for 15% of women's cancer deaths worldwide. Conventional absorption-based breast imaging techniques lack sufficient contrast for comprehensive diagnosis. Propagation-based phase-contrast computed tomography (PB-CT) is a developing technique that exploits a more contrast-sensitive property of x-rays: x-ray refraction. X-ray absorption, refraction, and contrast-to-noise in the corresponding images depend on the x-ray energy used, for the same/fixed radiation dose. The aim of this paper is to explore the relationship between x-ray energy and radiological image quality in PB-CT imaging. Approach: Thirty-nine mastectomy samples were scanned at the imaging and medical beamline at the Australian Synchrotron. Samples were scanned at various x-ray energies of 26, 28, 30, 32, 34, and 60 keV using a Hamamatsu Flat Panel detector at the same object-to-detector distance of 6 m and mean glandular dose of 4 mGy. A total of 132 image sets were produced for analysis. Seven observers rated PB-CT images against absorption-based CT (AB-CT) images of the same samples on a five-point scale. A visual grading characteristics (VGC) study was used to determine the difference in image quality. Results: PB-CT images produced at 28, 30, 32, and 34 keV x-ray energies demonstrated statistically significant higher image quality than reference AB-CT images. The optimum x-ray energy, 30 keV, displayed the largest area under the curve ( AUC VGC ) of 0.754 ( p = 0.009 ). This was followed by 32 keV ( AUC VGC = 0.731 , p ≤ 0.001 ), 34 keV ( AUC VGC = 0.723 , p ≤ 0.001 ), and 28 keV ( AUC VGC = 0.654 , p = 0.015 ). Conclusions: An optimum energy range (around 30 keV) in the PB-CT technique allows for higher image quality at a dose comparable to conventional mammographic techniques. This results in improved radiological image quality compared with conventional techniques, which may ultimately lead to higher diagnostic efficacy and a reduction in breast cancer mortalities.

Propagation-Based Phase-Contrast CT of the Breast Demonstrates Higher Quality Than Conventional Absorption-Based CT Even at Lower Radiation Dose.

RATIONALE AND OBJECTIVES: Propagation-based phase-contrast CT (PB-CT) is an advanced X-ray imaging technology that exploits both refraction and absorption of the transmitted X-ray beam. This study was aimed at optimizing the experimental conditions of PB-CT for breast cancer imaging and examined its performance relative to conventional absorption-based CT (AB-CT) in terms of image quality and radiation dose. MATERIALS AND METHODS: Surgically excised breast mastectomy specimens (n = 12) were scanned using both PB-CT and AB-CT techniques under varying imaging conditions. To evaluate the radiological image quality, visual grading characteristics (VGC) analysis was used in which 11 breast specialist radiologists compared the overall image quality of PB-CT images with respect to the corresponding AB-CT images. The area under the VGC curve was calculated to measure the differences between PB-CT and AB-CT images. RESULTS: The highest radiological quality was obtained for PB-CT images using a 32 keV energy X-ray beam and by applying the Homogeneous Transport of Intensity Equation phase retrieval with the value of its parameter γ set to one-half of the theoretically optimal value for the given materials. Using these optimized conditions, the image quality of PB-CT images obtained at 4 mGy and 2 mGy mean glandular dose was significantly higher than AB-CT images at 4 mGy (AUCVGC = 0.901, p = 0.001 and AUCVGC = 0.819, p = 0.011, respectively). CONCLUSION: PB-CT achieves a higher radiological image quality compared to AB-CT even at a considerably lower mean glandular dose. Successful translation of the PB-CT technique for breast cancer imaging can potentially result in improved breast cancer diagnosis.

Fast three-dimensional phase retrieval in propagation-based X-ray tomography.

The following article describes a method for 3D reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogeneous form of the transport of intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localized region of the CT-reconstructed volume. This work demonstrates, via numerical simulations, the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it with both conventional absorption tomography and 2D TIE-Hom phase retrieval applied to projection images. The results indicate that the 3D post-reconstruction method generally achieves a modest improvement in noise suppression over existing PB-CT methods. It is also shown that potentially large computational gains over projection-based phase retrieval for multi-material samples are possible. In particular, constraining phase retrieval to a localized 3D region of interest reduces the overall computational cost and eliminates the need for multiple CT reconstructions and global 2D phase retrieval operations for each material within the sample.

Deterministic Bragg Coherent Diffraction Imaging.

A deterministic variant of Bragg Coherent Diffraction Imaging is introduced in its kinematical approximation, for X-ray scattering from an imperfect crystal whose imperfections span no more than half of the volume of the crystal. This approach provides a unique analytical reconstruction of the object's structure factor and displacement fields from the 3D diffracted intensity distribution centred around any particular reciprocal lattice vector. The simple closed-form reconstruction algorithm, which requires only one multiplication and one Fourier transformation, is not restricted by assumptions of smallness of the displacement field. The algorithm performs well in simulations incorporating a variety of conditions, including both realistic levels of noise and departures from ideality in the reference (i.e. imperfection-free) part of the crystal.

A feasibility study of X-ray phase-contrast mammographic tomography at the Imaging and Medical beamline of the Australian Synchrotron.

Results are presented of a recent experiment at the Imaging and Medical beamline of the Australian Synchrotron intended to contribute to the implementation of low-dose high-sensitivity three-dimensional mammographic phase-contrast imaging, initially at synchrotrons and subsequently in hospitals and medical imaging clinics. The effect of such imaging parameters as X-ray energy, source size, detector resolution, sample-to-detector distance, scanning and data processing strategies in the case of propagation-based phase-contrast computed tomography (CT) have been tested, quantified, evaluated and optimized using a plastic phantom simulating relevant breast-tissue characteristics. Analysis of the data collected using a Hamamatsu CMOS Flat Panel Sensor, with a pixel size of 100 µm, revealed the presence of propagation-based phase contrast and demonstrated significant improvement of the quality of phase-contrast CT imaging compared with conventional (absorption-based) CT, at medically acceptable radiation doses.

Darwin's approach to X-ray diffraction on lateral crystalline structures.

Darwin's dynamical theory of X-ray diffraction is extended to the case of lateral (i.e., having a finite length in the lateral direction) crystalline structures. This approach allows one to calculate rocking curves as well as reciprocal-space maps for lateral crystalline structures having a rectangular cross section. Numerical modelling is performed for these structures with different lateral sizes. It is shown that the kinematical approximation is valid for thick crystalline structures having a small length in the lateral direction.

Mask-assisted deterministic phase-amplitude retrieval from a single far-field intensity diffraction pattern: two experimental proofs of principle using visible light.

We recently developed a simple closed-form algorithm, which allows one to reconstruct the complex scalar wavefield at the exit surface of a sample, from the intensity of its far-field coherent diffraction pattern which is obtained in the presence of a suitable object-plane mask. In the first variant of this algorithm, the sample is contained within a uniformly illuminated sharp rectangular aperture in which at least one transverse dimension is at least twice that of the object. In the second variant, the sample is uniformly illuminated and is transversely displaced from an opaque rectangular mask in the object plane. For both variants, the far-field diffraction pattern is first Fourier transformed and then differentiated with respect to both transverse coordinates, in order to deterministically yield a series of independent reconstructions of the sample. Here we give an experimental demonstration of each of these two variants of our technique, using visible light.

Phase contrast image segmentation using a Laue analyser crystal.

Dual-energy x-ray imaging is a powerful tool enabling two-component samples to be separated into their constituent objects from two-dimensional images. Phase contrast x-ray imaging can render the boundaries between media of differing refractive indices visible, despite them having similar attenuation properties; this is important for imaging biological soft tissues. We have used a Laue analyser crystal and a monochromatic x-ray source to combine the benefits of both techniques. The Laue analyser creates two distinct phase contrast images that can be simultaneously acquired on a high-resolution detector. These images can be combined to separate the effects of x-ray phase, absorption and scattering and, using the known complex refractive indices of the sample, to quantitatively segment its component materials. We have successfully validated this phase contrast image segmentation (PCIS) using a two-component phantom, containing an iodinated contrast agent, and have also separated the lungs and ribcage in images of a mouse thorax. Simultaneous image acquisition has enabled us to perform functional segmentation of the mouse thorax throughout the respiratory cycle during mechanical ventilation.

X-ray phase, absorption and scatter retrieval using two or more phase contrast images.

We have developed two phase-retrieval techniques for analyser-based phase contrast imaging that provide information about an object's X-ray absorption, refraction and scattering properties. The first requires rocking curves to be measured with and without the sample and improves upon existing techniques by accurately fitting the curves with Pearson type VII functions. The second employs an iterative approach using two simultaneously recorded images by exploiting the Laue crystal geometry. This technique provides a substantial reduction in X-ray dose and enables quantitative phase retrieval to be performed on images of moving objects.

Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging.

Analyser-based phase contrast X-ray imaging can provide high-contrast images of biological tissues with exquisite sensitivity to the boundaries between tissues. The phase and absorption information can be extracted by processing multiple images acquired at different analyser orientations. Recording both the transmitted and diffracted beams from a thin Laue analyser crystal can make phase retrieval possible for dynamic systems by allowing full field imaging. This technique was used to image the thorax of a mechanically ventilated newborn rabbit pup using a 25 keV beam from the SPring-8 synchrotron radiation facility. The diffracted image was produced from the (111) planes of a 50 mm x 40 mm, 100 microm thick Si analyser crystal in the Laue geometry. The beam and analyser were large enough to image the entire chest, making it possible to observe changes in anatomy with high contrast and spatial resolution.

Computed tomography with linear shift-invariant optical systems.

Optical systems capable of three-dimensional transmission imaging are considered; these systems employ a conventional tomographic setup with an added linear shift-invariant optical system between the sample and the detector. A theoretical analysis is presented of image formation and sample reconstruction in such systems, examples of which include diffraction tomography and phase-contrast tomography with the use of analyzer crystals. An example is introduced in which the image is obtained by scanning the beam along the line orthogonal to the optic axis and to the axis of rotation with a one-dimensional slit or grating parallel to the rotation axis. We show that under certain conditions the proposed system may allow quantitative local (region-of-interest) tomography.

Analyser-based mammography using single-image reconstruction.

We implement an algorithm that is able to decode a single analyser-based x-ray phase-contrast image of a sample, converting it into an equivalent conventional absorption-contrast radiograph. The algorithm assumes the projection approximation for x-ray propagation in a single-material object embedded in a substrate of approximately uniform thickness. Unlike the phase-contrast images, which have both directional bias and a bias towards edges present in the sample, the reconstructed images are directly interpretable in terms of the projected absorption coefficient of the sample. The technique was applied to a Leeds TOR[MAM] phantom, which is designed to test mammogram quality by the inclusion of simulated microcalcifications, filaments and circular discs. This phantom was imaged at varying doses using three modalities: analyser-based synchrotron phase-contrast images converted to equivalent absorption radiographs using our algorithm, slot-scanned synchrotron imaging and imaging using a conventional mammography unit. Features in the resulting images were then assigned a quality score by volunteers. The single-image reconstruction method achieved higher scores at equivalent and lower doses than the conventional mammography images, but no improvement of visualization of the simulated microcalcifications, and some degradation in image quality at reduced doses for filament features.