Quantitative Phase Imaging Using Hard X Rays

Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates `unreasonable' effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification of photon shot noise. Here, it is shown that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the real decrement to the imaginary part of the refractive index of the imaged object. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper.

Characterization of Pharmaceutical Tablets by X-ray Tomography

Solid dosage forms such as tablets are extensively used in drug administration for their simplicity and large-scale manufacturing capabilities. High-resolution X-ray tomography is one of the most valuable non-destructive techniques to investigate the internal structure of the tablets for drug product development as well as for a cost effective production process. In this work, we review the recent developments in high-resolution X-ray microtomography and its application towards different tablet characterizations. The increased availability of powerful laboratory instrumentation, as well as the advent of high brilliance and coherent 3rd generation synchrotron light sources, combined with advanced data processing techniques, are driving the application of X-ray microtomography forward as an indispensable tool in the pharmaceutical industry.

Tomographic phase and attenuation extraction for a sample composed of unknown materials using x-ray propagation-based phase-contrast imaging

Propagation-based phase-contrast x-ray imaging (PB-PCXI) generates image contrast by utilizing sample-imposed phase-shifts. This has proven useful when imaging weakly attenuating samples, as conventional attenuation-based imaging does not always provide adequate contrast. We present a PB-PCXI algorithm capable of extracting the x-ray attenuation  β and refraction  δ, components of the complex refractive index of distinct materials within an unknown sample. The method involves curve fitting an error-function-based model to a phase-retrieved interface in a PB-PCXI tomographic reconstruction, which is obtained when Paganin-type phase retrieval is applied with incorrect values of δ and β. The fit parameters can then be used to calculate true δ and β values for composite materials. This approach requires no a priori sample information, making it broadly applicable. Our PB-PCXI reconstruction is single-distance, requiring only one exposure per tomographic angle, which is important for radiosensitive samples. We apply this approach to a breast-tissue sample, recovering the refraction component  δ, with 0.6-2.4% accuracy compared with theoretical values.

Real-Time Phase Retrieval Based on Cube-Corner Prisms Single Exposure

The phase retrieval method based on the Transport of Intensity Equation needs to record the light intensity information on two or more planes perpendicular to the optical axis propagating along the optical axis. Usually, a single CCD camera is moved back and forth for recording, which not only brings the corresponding mechanical errors, but also has a certain time difference between the collected intensity images, which cannot meet the real-time requirements. In this paper, a single phase retrieval technique based on cube-corner prisms is proposed. This method can simultaneously collect the required initial intensity image in a single exposure, and then calculate the phase after registration and repair, so as to obtain high-precision results. According to the parallel reflection characteristics of the cube-corner prisms, the experimental system designed correspondingly can not only stagger the two beams separated by the beam splitter, but also ensure that the upper and lower propagation distances of a single beam are equal. Finally, the accuracy and effectiveness of the proposed method are fully verified by simulation experiments and experimental measurements.

Two-dimensional monitoring of a laser-solid x-ray source spot via penumbral coded aperture imaging technique

The uncertainties of spot size and position need to be clarified for x-ray sources as they can affect the detecting precision of the x-ray probe beam in applications such as radiography. In particular, for laser-driven x-ray sources, they would be more significant as they influence the inevitable fluctuation of the driving laser pulses. Here, we have employed the penumberal coded aperture imaging technique to diagnose the two-dimensional spatial distribution of an x-ray emission source spot generated from a Cu solid target irradiated by an intense laser pulse. Taking advantage of the high detection efficiency and high spatial resolution of this technique, the x-ray source spot is characterized with a relative error of ∼5% in the full width at half maximum of the intensity profile in a single-shot mode for general laser parameters, which makes it possible to reveal the information of the unfixed spot size and position precisely. Our results show the necessity and feasibility of monitoring the spot of these novel laser-driven x-ray sources via the penumbral coded aperture imaging technique.

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.

Advanced X-ray imaging at beamline 07 of the SAGA Light Source

The SAGA Light Source provides X-ray imaging resources based on high-intensity synchrotron radiation (SR) emitted from the superconducting wiggler at beamline 07 (BL07). By combining quasi-monochromatic SR obtained by the newly installed water-cooled metal filter and monochromatic SR selected by a Ge double-crystal monochromator (DCM) with high-resolution lens-coupled X-ray imagers, fast and low-dose micro-computed tomography (CT), fast phase-contrast CT using grating-based X-ray interferometry, and 2D micro-X-ray absorption fine structure analysis can be performed. In addition, by combining monochromatic SR obtained by a Si DCM with large-area fiber-coupled X-ray imagers, high-sensitivity phase-contrast CT using crystal-based X-ray interferometry can be performed. Low-temperature CT can be performed using the newly installed cryogenic system, and time-resolved analysis of the crystallinity of semiconductor devices in operation can be performed using a time-resolved topography system. The details of each instrument and imaging method, together with exemplary measurements, are presented.

Dual-energy phase retrieval algorithm for inline phase sensitive x-ray imaging system

Phase retrieval is vital for quantitative x-ray phase contrast imaging. This work presents an iterative method to simultaneously retrieve the x-ray absorption and phase images from a single x-ray exposure. The proposed approach uses the photon-counting detectors' energy-resolving capability in providing multiple spectrally resolved phase contrast images from a single x-ray exposure. The retrieval method is derived, presented, and experimentally tested with a multi-material phantom in an inline phase contrast imaging setup. By separating the contributions of photoelectric absorption and Compton scattering to the attenuation, the authors divide the phase contrast image into two portions, the attenuation map arises from photoelectric absorption and a pseudo phase contrast image generated by electron density. This way one can apply the Phase Attenuation Dualiby (PAD) algorithm and Fresnel propagation for the iteration. The retrieval results from the experimental images show that this iterative method is fast, accurate, robust against noise, and thus yields noticeable enhancement in contrast to noise ratios.

Quantitative hyperspectral coherent diffractive imaging spectroscopy of a solid-state phase transition in vanadium dioxide

Solid-state systems can host a variety of thermodynamic phases that can be controlled with magnetic fields, strain, or laser excitation. Many phases that are believed to exhibit exotic properties only exist on the nanoscale, coexisting with other phases that make them challenging to study, as measurements require both nanometer spatial resolution and spectroscopic information, which are not easily accessible with traditional x-ray spectromicroscopy techniques. Here, we use coherent diffractive imaging spectroscopy (CDIS) to acquire quantitative hyperspectral images of the prototypical quantum material vanadium oxide across the vanadium L 2,3 and oxygen K x-ray absorption edges with nanometer-scale resolution. We extract the full complex refractive indices of the monoclinic insulating and rutile conducting phases of VO2 from a single sample and find no evidence for correlation-driven phase transitions. CDIS will enable quantitative full-field x-ray spectromicroscopy for studying phase separation in time-resolved experiments and other extreme sample environments where other methods cannot operate.

Comparison of microstructural imaging of the root canal isthmus using propagation-based X-ray phase-contrast and absorption micro-computed tomography

Clear and complete microstructural imaging of the root canal isthmus is an important part of pathological investigations in research and clinical practice. X-ray micro-computed tomography (μCT) is a widely used non-destructive imaging technique, which allows for distortion-free three-dimensional (3D) visualisation. While absorption μCT typically has poor contrast resolution for observing the root canal isthmus, especially for weak-absorbing tissues, propagation-based X-ray phase-contrast imaging (PBI) is a powerful imaging method, which in its combination with μCT (PB-PCμCT) enables high-resolution and high-contrast microstructural imaging of the weak-absorbing tissues in samples. To investigate the feasibility and ability of PB-PCμCT in microstructural imaging of the root canal isthmus, conventional absorption μCT and PB-PCμCT experiments were performed. The two-dimensional (2D) and 3D comparison results demonstrated that, compared to absorption μCT, PB-PCμCT has the ability to image the root canal isthmus more clearly and completely, and thus, it has great potential to serve as a valuable tool for biomedical and preclinical studies on the root canal isthmus.

Sparse-domain regularized stripe decomposition combined with guided-image filtering for ring artifact removal in propagation-based x-ray phase-contrast CT

Propagation-based x-ray phase-contrast computed tomography (PB-PCCT) images often suffer from severe ring artifacts. Ring artifacts are mainly caused by the nonuniform response of detector elements, and they can degrade image quality and affect the subsequent image processing and quantitative analyses. To remove ring artifacts in PB-PCCT images, a novel method combined sparse-domain regularized stripe decomposition (SDRSD) method with guided image filtering (GIF) was proposed. In this method, polar coordinate transformation was utilized to convert the ring artifacts to stripe artifacts. And then considering the directional and sparse properties of the stripe artifacts and the continuity characteristics of the sample, the SDRSD method was designed to remove stripe artifacts. However, for the SDRSD method, the presence of noise may destroy the edges of the stripe artifacts and lead to incomplete decomposition. Hence, a simple and efficient smoothing technique, namely GIF, was employed to overcome this issue. The simulations and real experiments demonstrated that the proposed method could effectively remove ring artifacts as well as preserve the structures and edges of the samples. In conclusion, the proposed method can serve as an effective tool to remove ring artifacts in PB-PCCT images, and it has high potential for promoting the biomedical and preclinical applications of PB-PCCT.

X-ray Phase-Contrast Computed Tomography for Soft Tissue Imaging at the Imaging and Medical Beamline (IMBL) of the Australian Synchrotron

The Imaging and Medical Beamline (IMBL) is a superconducting multipole wiggler-based beamline at the 3 GeV Australian Synchrotron operated by the Australian Nuclear Science and Technology Organisation (ANSTO). The beamline delivers hard X-rays in the 25–120 keV energy range and offers the potential for a range of biomedical X-ray applications, including radiotherapy and medical imaging experiments. One of the imaging modalities available at IMBL is propagation-based X-ray phase-contrast computed tomography (PCT). PCT produces superior results when imaging low-density materials such as soft tissue (e.g., breast mastectomies) and has the potential to be developed into a valuable medical imaging tool. We anticipate that PCT will be utilized for medical breast imaging in the near future with the advantage that it could provide better contrast than conventional X-ray absorption imaging. The unique properties of synchrotron X-ray sources such as high coherence, energy tunability, and high brightness are particularly well-suited for generating PCT data using very short exposure times on the order of less than 1 min. The coherence of synchrotron radiation allows for phase-contrast imaging with superior sensitivity to small differences in soft-tissue density. Here we also compare the results of PCT using two different detectors, as these unique source characteristics need to be complemented with a highly efficient detector. Moreover, the application of phase retrieval for PCT image reconstruction enables the use of noisier images, potentially significantly reducing the total dose received by patients during acquisition. This work is part of ongoing research into innovative tomographic methods aimed at the introduction of 3D X-ray medical imaging at the IMBL to improve the detection and diagnosis of breast cancer. Major progress in this area at the IMBL includes the characterization of a large number of mastectomy samples, both normal and cancerous, which have been scanned at clinically acceptable radiation dose levels and evaluated by expert radiologists with respect to both image quality and cancer diagnosis.

Visualization Ability of Phase-Contrast Synchrotron-Based X-Ray Imaging Using an X-Ray Interferometer in Soft Tissue Tumors

Phase-contrast synchrotron-based X-ray imaging using an X-ray interferometer provides high sensitivity and high spatial resolution, and it has the ability to depict the fine morphological structures of biological soft tissues, including tumors. In this study, we quantitatively compared phase-contrast synchrotron-based X-ray computed tomography images and images of histopathological hematoxylin-eosin-stained sections of spontaneously occurring rat testicular tumors that contained different types of cells. The absolute densities measured on the phase-contrast synchrotron-based X-ray computed tomography images correlated well with the densities of the nuclear chromatin in the histological images, thereby demonstrating the ability of phase-contrast synchrotron-based X-ray imaging using an X-ray interferometer to reliably identify the characteristics of cancer cells within solid soft tissue tumors. In addition, 3-dimensional synchrotron-based phase-contrast X-ray computed tomography enables screening for different structures within tumors, such as solid, cystic, and fibrous tissues, and blood clots, from any direction and with a spatial resolution down to 26 μm. Thus, phase-contrast synchrotron-based X-ray imaging using an X-ray interferometer shows potential for being useful in preclinical cancer research by providing the ability to depict the characteristics of tumor cells and by offering 3-dimensional information capabilities.

Performance analysis of phase retrieval using transport of intensity with digital holography [Invited]

The performance of direct and unwrapped phase retrieval, which combines digital holography with the transport of intensity, is examined in detail in this paper. In this technique, digital holography is used to numerically reconstruct the intensities at different planes around the image plane, and phase retrieval is achieved by the transport of intensity. Digital holography with transport of intensity is examined for inline and off-axis geometries. The effect of twin images in the inline case is evaluated. Phase-shifting digital holography with transport of intensity is introduced. The performance of digital holography with transport of intensity is compared with traditional off-axis single- and dual-wavelength techniques, which employ standard phase unwrapping algorithms. Simulations and experiments are performed to determine and compare the accuracy of phase retrieval through a mean-squared-error figure of merit as well as the computational speeds of the various methods.

High sensitivity X-ray phase contrast imaging by laboratory grating-based interferometry at high Talbot order geometry

X-ray phase contrast imaging is a powerful analysis technique for materials science and biomedicine. Here, we report on laboratory grating-based X-ray interferometry employing a microfocus X-ray source and a high Talbot order (35th) asymmetric geometry to achieve high angular sensitivity and high spatial resolution X-ray phase contrast imaging in a compact system (total length <1 m). The detection of very small refractive angles (∼50 nrad) at an interferometer design energy of 19 keV was enabled by combining small period X-ray gratings (1.0, 1.5 and 3.0 µm) and a single-photon counting X-ray detector (75 µm pixel size). The performance of the X-ray interferometer was fully characterized in terms of angular sensitivity and spatial resolution. Finally, the potential of laboratory X-ray phase contrast for biomedical imaging is demonstrated by obtaining high resolution X-ray phase tomographies of a mouse embryo embedded in solid paraffin and a formalin-fixed full-thickness sample of human left ventricle in water with a spatial resolution of 21.5 µm.

Dark-field signal extraction in propagation-based phase-contrast imaging

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real decrement to the imaginary part of the complex refractive index, the proposed method requires a single image for extraction of the dark-field signal in two-dimensional projection imaging. In the case of three-dimensional tomographic imaging, the method needs only one image to be collected at each projection angle. Initial examples using simulated and experimental data indicate that this method can improve visualization of small sharp features inside a larger object, e.g. the visualization of microcalcifications in propagation-based x-ray breast cancer imaging. It is suggested that the proposed approach may be useful in other forms of biomedical imaging, where it can help one to obtain additional small-angle scattering information without increasing the radiation dose to the sample.

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

High-resolution quantitative phase imaging based on a spatial light modulator and incremental binary random sampling

We propose a single-beam high-resolution quantitative phase imaging method based on a spatial light modulator (SLM) and an incremental binary random sampling (IBRS) algorithm. In this method, the image of the test object presents on the image sensor through an optical microscopy system composed of an objective lens and a collimating lens. A transmittance SLM displaying a group of well-designed IBRS patterns is inserted in the optical microscopy system to modulate the object wavefront. The phase information of the object image can be quantitatively retrieved from the recorded intensities using the IBRS algorithm and the amplitude obtained directly from the diffraction intensity. The IBRS algorithm employed in our method has higher accuracy for phase retrieval compared with our previously proposed complementary random sampling algorithm, which is confirmed by simulations. Further, we demonstrate experimentally the feasibility of our method through several examples: phase imaging of immersion oil droplets with a diffraction-limited lateral resolution of 1.54 µm and a few microbiological specimens with 0.70 µm. Experimental results reveal that our proposed method provides a feasible single-beam technique for quantitative phase imaging with a high spatial resolution.

On a universal solution to the transport-of-intensity equation

The transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a non-interferometric, deterministic manner. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive pre-knowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions. In this Letter, we propose a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily shaped regions, and simplified implementation and computation. With the "maximum intensity assumption," we first simplify TIE as a standard Poisson equation to get an initial guess of the solution. Then the initial solution is further refined iteratively by solving the same Poisson equation, and thus the instability associated with the division by zero/small intensity values and large intensity variations can be effectively bypassed. Simulations and experiments with arbitrary phase, arbitrary aperture shapes, and nonuniform intensity distributions verify the effectiveness and universality of the proposed method.

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.

Multi-resolution convolutional neural networks for inverse problems

Inverse problems in image processing, phase imaging, and computer vision often share the same structure of mapping input image(s) to output image(s) but are usually solved by different application-specific algorithms. Deep convolutional neural networks have shown great potential for highly variable tasks across many image-based domains, but sometimes can be challenging to train due to their internal non-linearity. We propose a novel, fast-converging neural network architecture capable of solving generic image(s)-to-image(s) inverse problems relevant to a diverse set of domains. We show this approach is useful in recovering wavefronts from direct intensity measurements, imaging objects from diffusely reflected images, and denoising scanning transmission electron microscopy images, just by using different training datasets. These successful applications demonstrate the proposed network to be an ideal candidate solving general inverse problems falling into the category of image(s)-to-image(s) translation.

Fast diffraction-enhanced imaging using continuous sample rotation and analyzer crystal scanning

Diffraction-enhanced imaging (DEI) has high sensitivity and a wide dynamic range of density and thus can be used for fine imaging of biological and organic samples that include large differences in density. A fast DEI method composed of continuous fast sample rotations and slow analyzer crystal scanning was developed to shorten the measurement period. Fine sectional images of a biological sample were successfully obtained within a half measurement period of the conventional step-scanning method while keeping the same exposure time. In addition, a fine three-dimensional image of a rat tail was obtained with a 375 s measurement period.

Recent Progress in X-ray and Neutron Phase Imaging with Gratings

Under the JST-ERATO project in progress to develop X-ray and neutron phase-imaging methods together, recent achievements have been selected and reviewed after describing the merit and the principle of the phase imaging method. For X-ray phase imaging, recent developments of four-dimensional phase tomography and phase microscopy at SPring-8, Japan are mainly presented. For neutron phase imaging, an approach in combination with the time-of-flight method developed at J-PARC, Japan is described with the description of new Gd grating fabrication.

Three-dimensional visualization of microvasculature from few-projection data using a novel CT reconstruction algorithm for propagation-based X-ray phase-contrast imaging

Propagation-based X-ray phase-contrast imaging (PBI) is a powerful nondestructive imaging technique that can reveal the internal detailed structures in weakly absorbing samples. Extending PBI to CT (PBCT) enables high-resolution and high-contrast 3D visualization of microvasculature, which can be used for the understanding, diagnosis and therapy of diseases involving vasculopathy, such as cardiovascular disease, stroke and tumor. However, the long scan time for PBCT impedes its wider use in biomedical and preclinical microvascular studies. To address this issue, a novel CT reconstruction algorithm for PBCT is presented that aims at shortening the scan time for microvascular samples by reducing the number of projections while maintaining the high quality of reconstructed images. The proposed algorithm combines the filtered backprojection method into the iterative reconstruction framework, and a weighted guided image filtering approach (WGIF) is utilized to optimize the intermediate reconstructed images. Notably, the homogeneity assumption on the microvasculature sample is adopted as prior knowledge, and therefore, a prior image of microvasculature structures can be acquired by a k-means clustering approach. Then, the prior image is used as the guided image in the WGIF procedure to effectively suppress streaking artifacts and preserve microvasculature structures. To evaluate the effectiveness and capability of the proposed algorithm, simulation experiments on 3D microvasculature numerical phantom and real experiments with CT reconstruction on the microvasculature sample are performed. The results demonstrate that the proposed algorithm can, under noise-free and noisy conditions, significantly reduce the artifacts and effectively preserve the microvasculature structures on the reconstructed images and thus enables it to be used for clear and accurate 3D visualization of microvasculature from few-projection data. Therefore, for 3D visualization of microvasculature, the proposed algorithm can be considered an effective approach for reducing the scan time required by PBCT.

Phase-retrieval method for measuring small contact angles of pentane on water

Pentane drops on a water surface are predicted to have contact angles of the order of 1 degree or less in the phase of frustrated complete wetting. We have developed an optical method of measuring such small contact angles, applicable to cases where the refractive indices of the substrate and adsorbate are very similar and the fluid dynamics do not allow delay between image acquisitions, by using phase retrieval to map the surface profile of the drops. It is empirically shown that, with our method, a difference of nanometer order can be achieved for the phase-retrieved dimensions relative to their expected value. Results agree with numerical predictions by Weiss and Widom [Physica A292, 137 (2001)PHYADX0378-437110.1016/S0378-4371(00)00619-1].

A Deep Learning Reconstruction Framework for Differential Phase-Contrast Computed Tomography With Incomplete Data

Differential phase-contrast computed tomography (DPC-CT) is a powerful analysis tool for soft-tissue and low-atomic-number samples. Limited by the implementation conditions, DPC-CT with incomplete projections happens quite often. Conventional reconstruction algorithms face difficulty when given incomplete data. They usually involve complicated parameter selection operations, which are also sensitive to noise and are time-consuming. In this paper, we report a new deep learning reconstruction framework for incomplete data DPC-CT. It involves the tight coupling of the deep learning neural network and DPC-CT reconstruction algorithm in the domain of DPC projection sinograms. The estimated result is not an artifact caused by the incomplete data, but a complete phase-contrast projection sinogram. After training, this framework is determined and can be used to reconstruct the final DPC-CT images for a given incomplete projection sinogram. Taking the sparse-view, limited-view and missing-view DPC-CT as examples, this framework is validated and demonstrated with synthetic and experimental data sets. Compared with other methods, our framework can achieve the best imaging quality at a faster speed and with fewer parameters. This work supports the application of the state-of-the-art deep learning theory in the field of DPC-CT.

Quantitative Phase and Intensity Microscopy Using Snapshot White Light Wavefront Sensing

Phase imaging techniques are an invaluable tool in microscopy for quickly examining thin transparent specimens. Existing methods are limited to either simple and inexpensive methods that produce only qualitative phase information (e.g. phase contrast microscopy, DIC), or significantly more elaborate and expensive quantitative methods. Here we demonstrate a low-cost, easy to implement microscopy setup for quantitative imaging of phase and bright field amplitude using collimated white light illumination.

Quantification of the Whole Lymph Node Vasculature Based on Tomography of the Vessel Corrosion Casts

Lymph nodes (LN) are crucial for immune function, and comprise an important interface between the blood and lymphatic systems. Blood vessels (BV) in LN are highly specialized, featuring high endothelial venules across which most of the resident lymphocytes crossed. Previous measurements of overall lymph and BV flow rates demonstrated that fluid also crosses BV walls, and that this is important for immune function. However, the spatial distribution of the BV in LN has not been quantified to the degree necessary to analyse the distribution of transmural fluid movement. In this study, we seek to quantify the spatial localization of LNBV, and to predict fluid movement across BV walls. MicroCT imaging of murine popliteal LN showed that capillaries were responsible for approximately 75% of the BV wall surface area, and that this was mostly distributed around the periphery of the node. We then modelled blood flow through the BV to obtain spatially resolved hydrostatic pressures, which were then combined with Starling’s law to predict transmural flow. Much of the total 10 nL/min transmural flow (under normal conditions) was concentrated in the periphery, corresponding closely with surface area distribution. These results provide important insights into the inner workings of LN, and provide a basis for further exploration of the role of LN flow patterns in normal and pathological functions.

Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage

Holographic data storage (HDS), in which both the amplitude and the phase of a signal beam are modulated, has been extensively studied with the goal of increasing its storage capacity. To detect such modulation during data retrieval, it is necessary to acquire the complex amplitude of the signal beam. In this study, we focus on the transport of intensity equation (TIE) method, which allows us to detect the phase distribution of the light wave quantitatively without using interferometry, contributing to miniaturization of the optical system and improvement of the vibration tolerance of HDS. We discuss the conditions of the modulation phase distribution of the signal beam required for accurate phase detection and propose a method to estimate and eliminate the noise that frequently appears in the phase distribution detected by the TIE method.

A new in-line X-ray phase-contrast computed tomography reconstruction algorithm based on adaptive-weighted anisotropic TpV regularization for insufficient data

In-line X-ray phase-contrast computed tomography (IL-PCCT) is a valuable tool for revealing the internal detailed structures in weakly absorbing objects (e.g. biological soft tissues), and has a great potential to become clinically applicable. However, the long scanning time for IL-PCCT will result in a high radiation dose to biological samples, and thus impede the wider use of IL-PCCT in clinical and biomedical imaging. To alleviate this problem, a new iterative CT reconstruction algorithm is presented that aims to decrease the radiation dose by reducing the projection views, while maintaining the high quality of reconstructed images. The proposed algorithm combines the adaptive-weighted anisotropic total p-variation (AwaTpV, 0 < p < 1) regularization technique with projection onto convex sets (POCS) strategy. Noteworthy, the AwaTpV regularization term not only contains the horizontal and vertical image gradients but also adds the diagonal image gradients in order to enforce the directional continuity in the gradient domain. To evaluate the effectiveness and ability of the proposed algorithm, experiments with a numerical phantom and synchrotron IL-PCCT were performed, respectively. The results demonstrated that the proposed algorithm had the ability to significantly reduce the artefacts caused by insufficient data and effectively preserved the edge details under noise-free and noisy conditions, and thus could be used as an effective approach to decrease the radiation dose for IL-PCCT.

Synchrotron radiation biomedical imaging and radiotherapy: from the UK to the Antipodes

Although the general public might think of 'X-rays' as they are applied to imaging (radiography) and for the treatment of disease (radiotherapy), the use of synchrotron radiation (SR) X-ray beams in these areas of science was a minor activity 50 years ago. The largest gains in science from SR were seen to be in those areas where signals were weakest in laboratory instruments, such as X-ray diffraction and spectroscopy. As the qualities of SR X-rays were explored and more areas of science adopted SR-based methods, this situation changed. About 30 years ago, the clinical advantages of using SR X-ray beams for radiography, radiotherapy and clinical diagnostics started to be investigated. In the UK, a multi-disciplinary group, consisting of clinicians, medical physicists and other scientists working mainly with the Synchrotron Radiation Source (SRS) in Cheshire, started to investigate techniques for diagnosis and potentially a cure for certain cancers. This preliminary work influenced the design of new facilities being constructed around the world, in particular the Imaging and Medical Beam Line on the Australian Synchrotron in Melbourne. Two authors moved from the UK to Australia to participate in this exciting venture. The following is a personal view of some of the highlights of the early-year SRS work, following through to the current activities on the new facility in Australia. This article is part of the theme issue 'Fifty years of synchrotron science: achievements and opportunities'.

Contrast enhancement for visualizing neuronal cytoarchitecture by propagation-based x-ray phase-contrast tomography

Knowledge of the three-dimensional (3d) neuronal cytoarchitecture is an important factor in order to understand the connection between tissue structure and function or to visualize pathological changes in neurodegenerative diseases or tumor development. The gold standard in neuropathology is histology, a technique which provides insights into the cellular organization based on sectioning of the sample. Conventional histology, however, misses the complete 3d information as only individual two-dimensional slices through the object are available. In this work, we use propagation-based phase-contrast x-ray tomography to perform 3d virtual histology on cerebellar tissue from mice. This technique enables us to non-invasively visualize the entire 3d density distribution of the examined samples at isotropic (sub-)cellular resolution. One central challenge, however, of the technique is the fact that contrast for important structural features can be easily lost due to small electron density differences, notably between the cells and surrounding tissue. Here, we evaluate the influence of different embedding media, which are intermediate steps in sample preparation for classical histology, on contrast formation and examine the applicability of the different sample preparations both at a synchrotron-based holotomography setup as well as a laboratory source.

Unsupervised solution for in-line holography phase retrieval using Bayesian inference

In propagation based phase contrast imaging, intensity patterns are recorded on a x-ray detector at one or multiple propagation distances, called in-line holograms. They form the input of an inversion algorithm that aims at retrieving the phase shift induced by the object. The problem of phase retrieval in in-line holography is an ill-posed inverse problem. Consequently an adequate solution requires some form of regularization with the most commonly applied being the classical Tikhonov regularization. While generally satisfying this method suffers from a few issues such as the choice of the regularization parameter. Here, we offer an alternative to the established method by applying the principles of Bayesian inference. We construct an iterative optimization algorithm capable of both retrieving the unknown phase and determining a multi-dimensional regularization parameter. In the end, we highlight the advantages of the introduced algorithm, chief among them being the unsupervised determination of the regularization parameter(s). The proposed approach is tested on both simulated and experimental data and is found to provide robust solutions, with improved response to typical issues like low frequency noise and the twin-image problem.

An iterative image reconstruction algorithm combined with forward and backward diffusion filtering for in-line X-ray phase-contrast computed tomography

In-line X-ray phase-contrast computed tomography (IL-PCCT) can reveal fine inner structures for low-Z materials (e.g. biological soft tissues), and shows high potential to become clinically applicable. Typically, IL-PCCT utilizes filtered back-projection (FBP) as the standard reconstruction algorithm. However, the FBP algorithm requires a large amount of projection data, and subsequently a large radiation dose is needed to reconstruct a high-quality image, which hampers its clinical application in IL-PCCT. In this study, an iterative reconstruction algorithm for IL-PCCT was proposed by combining the simultaneous algebraic reconstruction technique (SART) with eight-neighbour forward and backward (FAB8) diffusion filtering, and the reconstruction was performed using the Shepp-Logan phantom simulation and a real synchrotron IL-PCCT experiment. The results showed that the proposed algorithm was able to produce high-quality computed tomography images from few-view projections while improving the convergence rate of the computed tomography reconstruction, indicating that the proposed algorithm is an effective method of dose reduction for IL-PCCT.

Direct information retrieval after 3D reconstruction in grating-based X-ray phase-contrast computed tomography

Grating-based X-ray differential phase-contrast imaging has attracted a great amount of attention and has been considered as a potential imaging method in clinical medicine because of its compatibility with the traditional X-ray tube source and the possibility of a large field of view. Moreover, phase-contrast computed tomography provides three-dimensional phase-contrast visualization. Generally, two-dimensional information retrieval performed on every projection is required prior to three-dimensional reconstruction in phase-contrast computed tomography. In this paper, a three-dimensional information retrieval method to separate absorption and phase information directly from two reconstructed images is derived. Theoretical derivations together with numerical simulations have been performed to confirm the feasibility and veracity of the proposed method. The advantages and limitations compared with the reverse projection method are also discussed. Owing to the reduced data size and the absence of a logarithm operation, the computational time for information retrieval is shortened by the proposed method. In addition, the hybrid three-dimensional images of absorption and phase information were reconstructed using an absorption reconstruction algorithm, hence the existing data pre-processing methods and iterative reconstruction algorithms in absorption reconstruction may be utilized in phase reconstruction immediately.

Amplitude and phase retrieval with simultaneous diversity estimation using expectation maximization

Iterative amplitude and phase retrieval algorithms have been proven to accurately reconstruct arbitrary wavefronts from multiple intensity measurements when system parameters are known exactly, given the ability to induce phase diversity between images. Such sets of intensity images with phase diversity can be generated by moving a lens in the optical system, but any position error on the lens will degenerate the reconstruction result. We demonstrate the use of an expectation-maximization algorithm with Kalman smoothing for recovering both the complex field and the lens position from a stack of intensity images. Our method successfully reduces the mean-squared-error of the estimated wavefront in comparison to an approach without position error estimation. We present and discuss the results of using a Kalman smoother and nonlinear least-squares optimization for the estimation of the moving lens position.

Optical convolution for quantitative phase retrieval using the transport of intensity equation

Propagation-based phase imaging using the transport of intensity equation (TIE) allows rapid, deterministic phase retrieval from defocused images. However, computational solutions to the TIE suffer from significant low-frequency noise artifacts and are unique up to the application of boundary conditions on the phase. We demonstrate that quantitative phase can be imaged directly at the detector for a class of pure-phase samples by appropriately patterning the illumination to solve the TIE through an optical convolution with the source. This can reduce noise artifacts, obviates the need for user-supplied boundary conditions and is demonstrated via simulation and experiment.

X-ray Fourier transform holography by amplitude-division-type Fresnel zone plate interferometer

A two-block X-ray Fresnel zone plate system forms two-beams - a plane wave and a spherical wave - which interfere at the focal distance of the virtual source of the spherical wave. An object placed in the path of the plane wave forms an object wave and the spherical wave is the reference wave. The recorded intensity distribution is the Fourier transform hologram of the object. Analytical and numerical calculations show the possibilities of this scheme to record the hologram and reconstruct the object image. Examples of recording holograms of a one-dimensional cosine-like grating and a two-dimensional grid object as well as reconstruction of the images are considered.

Fresnel diffractograms from pure-phase wave fields under perfect spatio-temporal coherence: Non-linear/non-local aspects and far-field behavior

Recently, the diffractogram, that is, the Fourier transform of the intensity contrast induced by Fresnel free-space propagation of a given (exit) wave field, was investigated non-perturbatively in the phase-scaling factor S (controlling the strength of phase variation) for the special case of a Gaussian phase of width [Formula: see text]. Surprisingly, an additional low-frequency zero σ_* = σ_*(S, F) >0 emerges critically at small Fresnel number F (σ proportional to square of 2D spatial frequency). Here, we study the S-scaling behavior of the entire diffractogram. We identify a valley of maximum S-scaling linearity in the F - σ plane corresponding to a nearly universal physical frequency ξml = (0:143 ± 0.001)w ^-1/2. Large values of F (near field) are shown to imply S-scaling linearity for low σ but nowhere else (overdamped non-oscillatory). In contrast, small F values (far field) entail distinct, sizable s-bands of good S-scaling linearity (damped oscillatory). These bands also occur in simulated diffractograms induced by a complex phase map (Lena). The transition from damped oscillatory to overdamped non-oscillatory diffractograms is shown to be a critical phenomenon for the Gaussian case. We also give evidence for the occurrence of this transition in an X-ray imaging experiment. Finally, we show that the extreme far-field limit generates a σ-universal diffractogram under certain requirements on the phase map: information on phase shape then is solely encoded in S-scaling behavior.

Registration of phase-contrast images in propagation-based X-ray phase tomography

X-ray phase tomography aims at reconstructing the 3D electron density distribution of an object. It offers enhanced sensitivity compared to attenuation-based X-ray absorption tomography. In propagation-based methods, phase contrast is achieved by letting the beam propagate after interaction with the object. The phase shift is then retrieved at each projection angle, and subsequently used in tomographic reconstruction to obtain the refractive index decrement distribution, which is proportional to the electron density. Accurate phase retrieval is achieved by combining images at different propagation distances. For reconstructions of good quality, the phase-contrast images recorded at different distances need to be accurately aligned. In this work, we characterise the artefacts related to misalignment of the phase-contrast images, and investigate the use of different registration algorithms for aligning in-line phase-contrast images. The characterisation of artefacts is done by a simulation study and comparison with experimental data. Loss in resolution due to vibrations is found to be comparable to attenuation-based computed tomography. Further, it is shown that registration of phase-contrast images is nontrivial due to the difference in contrast between the different images, and the often periodical artefacts present in the phase-contrast images if multilayer X-ray optics are used. To address this, we compared two registration algorithms for aligning phase-contrast images acquired by magnified X-ray nanotomography: one based on cross-correlation and one based on mutual information. We found that the mutual information-based registration algorithm was more robust than a correlation-based method.

Identification of ginseng root using quantitative X-ray microtomography

BACKGROUND

The use of X-ray phase-contrast microtomography for the investigation of Chinese medicinal materials is advantageous for its nondestructive, in situ, and three-dimensional quantitative imaging properties.

METHODS

The X-ray phase-contrast microtomography quantitative imaging method was used to investigate the microstructure of ginseng, and the phase-retrieval method is also employed to process the experimental data. Four different ginseng samples were collected and investigated; these were classified according to their species, production area, and sample growth pattern.

RESULTS

The quantitative internal characteristic microstructures of ginseng were extracted successfully. The size and position distributions of the calcium oxalate cluster crystals (COCCs), important secondary metabolites that accumulate in ginseng, are revealed by the three-dimensional quantitative imaging method. The volume and amount of the COCCs in different species of the ginseng are obtained by a quantitative analysis of the three-dimensional microstructures, which shows obvious difference among the four species of ginseng.

CONCLUSION

This study is the first to provide evidence of the distribution characteristics of COCCs to identify four types of ginseng, with regard to species authentication and age identification, by X-ray phase-contrast microtomography quantitative imaging. This method is also expected to reveal important relationships between COCCs and the occurrence of the effective medicinal components of ginseng.

MHz frame rate hard X-ray phase-contrast imaging using synchrotron radiation

Third generation synchrotron light sources offer high photon flux, partial spatial coherence, and ~10^-10 s pulse widths. These enable hard X-ray phase-contrast imaging (XPCI) with single-bunch temporal resolutions. In this work, we exploited the MHz repetition rates of synchrotron X-ray pulses combined with indirect X-ray detection to demonstrate the potential of XPCI with millions of frames per second multiple-frame recording. This allows for the visualization of aperiodic or stochastic transient processes which are impossible to be realized using single-shot or stroboscopic XPCI. We present observations of various phenomena, such as crack tip propagation in glass, shock wave propagation in water and explosion during electric arc ignition, which evolve in the order of km/s (µm/ns).

Source diversity for transport of intensity phase imaging

The transport of intensity equation (TIE) is a phase retrieval method that relies on measurements of the intensity of a paraxial field under propagation between two or more closely spaced planes. A limitation of TIE is its susceptibility to low frequency noise artifacts in the reconstructed phase. Under Köhler illumination, when both illumination power and exposure time are limited, the use of larger sources can improve low-frequency performance although it introduces blurring. Appropriately combining intensity measurements taken with a diversity of source sizes can improve both low- and high-frequency performance in phase reconstruction.

Cardiac CT Imaging of Plaque Vulnerability: Hype or Hope?

Advances in cardiovascular computed tomography (CT) have resulted in an excellent ability to exclude coronary heart disease (CHD). Anatomical information, functional information, and spectral information can already be obtained with current CT technologies. Moreover, novel developments such as targeted nanoparticle contrast agents, photon-counting CT, and phase contrast CT will further enhance the diagnostic value of cardiovascular CT. This review provides an overview of current state of the art and future cardiovascular CT imaging.