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A method for three-dimensional reconstruction of objects from defocused images collected at multiple illumination directions in high-resolution transmission electron microscopy is presented. The method effectively corrects for the Ewald sphere curvature by taking into account the in-particle propagation of the electron beam. Numerical simulations demonstrate that the proposed method is capable of accurately reconstructing biological molecules or nanoparticles from high-resolution defocused images under conditions achievable in single-particle electron cryo-microscopy or electron tomography with realistic radiation doses, non-trivial aberrations, multiple scattering, and other experimentally relevant factors. The physics of the method is based on the well-known Diffraction Tomography formalism, but with the phase-retrieval step modified to include a conjugation of the phase (i.e., multiplication of the phase by a negative constant). At each illumination direction, numerically backpropagating the beam with the conjugated phase produces maximum contrast at the location of individual atoms in the molecule or nanoparticle. The resultant algorithm, Conjugated Holographic Reconstruction, can potentially be incorporated into established software tools for single-particle analysis, such as, for example, RELION or FREALIGN, in place of the conventional contrast transfer function correction procedure, in order to account for the Ewald sphere curvature and improve the spatial resolution of the three-dimensional reconstruction.

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based, phase-contrast, or diffraction imaging using x rays, electrons, and other forms of penetrating radiation or matter waves. Both the phase retrieval (also known as contrast transfer function correction) and the effect of Ewald sphere curvature (in the cases with a shallow depth of field and significant in-object diffraction) are incorporated in the proposed algorithm and can be taken into account. Multiple scattering is not treated explicitly but can be mitigated as a result of angular averaging that constitutes an essential feature of the method. The corresponding numerical algorithm is based on three-dimensional gridding which allows for fast computational implementation, including a straightforward parallelization. The algorithm can be used with any scanning geometry involving plane-wave illumination. A software code implementing the proposed algorithm has been developed, tested on simulated and experimental image data, and made publicly available.

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.

A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle, provided that the depth of field is smaller than the thickness of the sample. The physical optics basis for the method is elucidated and the reconstruction algorithm is presented in detail. A simulated example demonstrates an application of the method to three-dimensional electron transmission imaging of a nanoparticle under realistic radiation dose and spatial resolution constraints. It is envisaged that the method can be applicable in high-resolution transmission electron microscopy, soft X-ray microscopy, ultrasound imaging and other areas., 20 pages, 5 figures

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.

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed., 32 pages, 8 figures, version 5c (a few typos have been found in the previous version and fixed in the current version)

Propagation-based phase-contrast CT (PB-CT) is a novel imaging technique that visualises variations in both X-ray attenuation and refraction. This study aimed to compare the clinical image quality of breast PB-CT using synchrotron radiation with conventional absorption-based CT (AB-CT), at the same radiation dose. Seven breast mastectomy specimens were scanned and evaluated by a group of 14 radiologists and medical imaging experts who assessed the images based on seven radiological image quality criteria. Visual grading characteristics (VGC) were used to analyse the results and the area under the VGC curve was obtained to measure the differences between the two techniques. For six image quality criteria (overall quality, perceptible contrast, lesion sharpness, normal tissue interfaces, calcification visibility and image noise), PB-CT images were superior to AB-CT images of the same dose (AUCVGC: 0.704 to 0.914, P≤.05). For the seventh criteria (artefacts), PB-CT images were also rated better than AB-CT images (AUCVGC: 0.647) but the difference was not significant. The results of this study provide a solid basis for future experimental and clinical protocols of breast PB-CT.

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.

The deterioration of both the signal-to-noise ratio and the spatial resolution in the electron-density distribution reconstructed from diffraction intensities collected at different orientations of a sample is analysed theoretically with respect to the radiation damage to the sample and the variations in the X-ray intensities illuminating different copies of the sample. The simple analytical expressions and numerical estimates obtained for models of radiation damage and incident X-ray pulses may be helpful in planning X-ray free-electron laser (XFEL) imaging experiments and in analysis of experimental data. This approach to the analysis of partially coherent X-ray imaging configurations can potentially be used for analysis of other forms of imaging where the temporal behaviour of the sample and the incident intensity during exposure may affect the inverse problem of sample reconstruction.

To evaluate and compare the image quality of propagation-based phase-contrast computed tomography (PB-CT) using synchrotron radiation and conventional cone-beam breast computed tomography (CBBCT) based on various radiological image quality criteria. Eight excised breast tissue samples of various sizes and containing different lesion types were scanned using PB-CT at a synchrotron facility and using CBBCT at a university-affiliated breast imaging centre. PB-CT scans were performed at two different mean glandular dose (MGD) levels: standard (5.8 mGy) and low (1.5 mGy), for comparison with CBBCT scans at the standard MGD (5.8 mGy). Image quality assessment was carried out using six quality criteria and six independent medical imaging experts in a reading room with mammography workstations. The interobserver agreement between readers was evaluated using intraclass correlation coefficient (ICC), and image quality was compared between the two breast imaging modalities using the area under the visual grading characteristic curve (AUCVGC). Interobserver agreement between the readers showed moderate reliability for five image criteria (ICC: ranging from 0.488 to 0.633) and low reliability for one criterion (image noise) (ICC 0.307). For five image quality criteria (overall quality, perceptible contrast, lesion sharpness, normal tissue interfaces, and calcification visibility), both standard-dose PB-CT images (AUCVGC 0.958 to 1, p ≤ .05) and low dose PB-CT images (AUCVGC 0.785 to 0.834, p ≤ .05) were of significantly higher image quality than standard-dose CBBCT images. Synchrotron-based PB-CT can achieve a significantly higher radiological image quality at a substantially lower radiation dose compared with conventional CBBCT. • PB-CT using synchrotron radiation results in higher image quality than conventional CBBCT for breast imaging. • PB-CT using synchrotron radiation requires a lower radiation dose than conventional CBBCT for breast imaging. • PB-CT can help clinicians diagnose patients with breast cancer.

IUCrJ 7(6), 1114 - 1123 (2020). doi:10.1107/S2052252520013019, Resolving the electronic structure of single biological molecules in their native state was among the primary motivations behind X-ray free-electron lasers. The ultra-short pulses they produce can outrun the atomic motion induced by radiation damage, but the electronic structure of the sample is still significantly modified from its original state. This paper explores the decoherence of the scattered signal induced by temporal evolution of the electronic structure in the sample molecule. It is shown that the undamaged electron density of a single-molecule sample can often be retrieved using only the two most occupied modes from the coherent mode decomposition of the partially coherent diffraction fluence., Published by Chester

Histopathological analysis is the current gold standard in breast cancer diagnosis and management, however, as imaging technology improves, the amount of potential diagnostic information that may be demonstrable radiologically should also increase. We aimed to evaluate the potential clinical usefulness of 3-D phase-contrast micro-computed tomography (micro-CT) imaging at high spatial resolutions as an adjunct to conventional histological microscopy. Ten breast tissue specimens, 2 mm in diameter, were scanned at the SYRMEP beamline of the Elettra Synchrotron using the propagation-based phase-contrast micro-tomography method. We obtained $1.2~\mu \text{m}$ pixel size images, which were analyzed and compared with corresponding histological sections examined under light microscopy. To evaluate the effect of spatial resolution on breast cancer diagnosis, scans with four different pixel sizes were also performed. Our comparative analysis revealed that high-resolution images can enable, at a near-histological level, detailed architectural assessment of tissue that may permit increased breast cancer diagnostic sensitivity and specificity when compared with current imaging practices. The potential clinical applications of this method are also discussed.

Signal-to-noise ratio, spatial resolution and information capacity of tomographic coherent diffractive imaging are investigated; the results are expected to be useful for the design and analysis of synchrotron and XFEL-based diffractive imaging experiments., It is shown that the average signal-to-noise ratio (SNR) in the three-dimensional electron-density distribution of a sample reconstructed by coherent diffractive imaging cannot exceed twice the square root of the ratio of the mean total number of scattered photons detected during the scan and the number of spatially resolved voxels in the reconstructed volume. This result leads to an upper bound on Shannon’s information capacity of this imaging method by specifying the maximum number of distinguishable density distributions within the reconstructed volume when the radiation dose delivered to the sample and the spatial resolution are both fixed. If the spatially averaged SNR in the reconstructed electron density is fixed instead, the radiation dose is shown to be proportional to the third or fourth power of the spatial resolution, depending on the sampling of the three-dimensional diffraction space and the scattering power of the sample.

The purpose of this article is to review different x-ray phase-contrast breast imaging techniques and their potential application in clinical settings.Phase-contrast imaging depicts not only the absorption contrast but also the refraction contrast of the transmitted x-ray beam. Early data suggest that this new modality may overcome some of the diagnostic limitations associated with current clinically available mammography systems and that it has potential for improving breast cancer detection.

In this paper, we evaluate the performance of block sparse Bayesian learning BSBL method for EEG source localization. By exploiting the internal block structure, the BSBL method solves the ill-posed inverse problem more efficiently than other methods that do not consider block structure. Simulation experiments were conducted on a realistic head model obtained by segmentation of MRI images of the head. Two definitions of blocks were considered: Brodmann areas and automated anatomical labeling AAL. The experiments were performed both with and without the presence of noise. Six different noise levels were considered having SNR values from 5 dB to 30 dB with 5dB increment. The evaluation reveals several potential findings-first, BSBL is more likely to produce better source localization than sparse Bayesian learning SBL, however, this is true up until a limited number of simultaneously active areas only. Experimental results show that for 71-channel electrodes setup BSBL outperforms SBL for up to three simultaneously active blocks. From four simultaneously active blocks SBL turns out to be marginally better and the difference between them is statistically insignificant. Second, different anatomical block structures such as Brodmann areas or AAL does not seem to produce any significant difference in EEG source localization relying on BSBL. Third, even when the block partitions are not known exactly BSBL ensures better localization than SBL as soon as block structure persists in the signal. © 2017 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 27, 46-56, 2017

The relative roles of multiple electron scattering and in-molecule Fresnel diffraction in atomic-resolution transmission electron microscopy of small molecules are discussed. It is argued that, while multiple scattering tends to have only a moderate effect, the in-molecule Fresnel diffraction can be significant due to the shallow depth of focus in high-resolution electron microscopy. When the depth of focus is smaller than the size of molecule along the trajectory of the electrons, the projection approximation breaks down and pairs of images at orientations of the molecule rotated by 180 degrees are not the same. Put another way, it matters which way the electrons traverse the specimen. In such cases, diffraction tomography based on the first Born or first Rytov approximation represents a more suitable method for the reconstruction of the three-dimensional distribution of the electrostatic potential, compared to conventional computed tomography which intrinsically relies on the validity of the projection approximation. A simplified method for diffraction tomography based on the approximation of Fresnel diffraction by the transport of intensity equation is proposed and tested on numerically simulated examples.

PURPOSE Propagation-based phase-contrast computed tomography (PB-CT) is a method for three-dimensional x-ray imaging that utilizes refraction, as well as absorption, of x rays in the tissues to increase the signal-to-noise ratio (SNR) in the resultant images, in comparison with equivalent conventional absorption-only x-ray tomography (CT). Importantly, the higher SNR is achieved without sacrificing spatial resolution or increasing the radiation dose delivered to the imaged tissues. The present work has been carried out in the context of the current development of a breast CT imaging facility at the Australian Synchrotron. METHODS Seven unfixed complete mastectomy samples with and without breast cancer lesions have been imaged using absorption-only CT and PB-CT techniques under controlled experimental conditions. The radiation doses delivered to the mastectomy samples during the scans were comparable to those approved for mammographic screening. Physical characteristics of the reconstructed images, such as spatial resolution and SNR, have been measured and compared with the results of the radiological quality assessment of the complete absorption CT and PB-CT image stacks. RESULTS Despite the presence of some image artefacts, the PB-CT images have outperformed comparable absorption CT images collected at the same radiation dose, in terms of both the measured objective image characteristics and the radiological image scores. The outcomes of these experiments are shown to be consistent with predictions of the theory of PB-CT imaging and previous reported experimental studies of this imaging modality. CONCLUSIONS The results presented in this paper demonstrate that PB-CT holds a high potential for improving on the quality and diagnostic value of images obtained using existing medical x-ray technologies, such as mammography and digital breast tomosynthesis (DBT). If implemented at suitable synchrotron imaging facilities, PB-CT can be used to complement existing imaging modalities, leading to more accurate breast cancer diagnosis.

The notions of spatial resolution and signal-to-noise are central to most forms of imaging. However, it appears that rigorous definitions of these quantities, which would be general enough to be useful in a broad range of imaging problems, while being also sufficiently specific to enable precise quantitative evaluation of the relevant properties of imaging systems, have been somewhat lacking. This is particularly true in respect to many modern forms of imaging that include digital processing of the acquired imaging data as an integral step leading to final images presented to the enduser. In the present paper, both the well-known historical definitions of spatial resolution and some more recent approaches suitable for many modern computational imaging techniques are discussed. An intrinsic duality of the spatial resolution and signal-to-noise exists in almost all types of imaging, with the related uncertainty relationship determining the inevitable trade-offs between the two quantities. Examples are presented with applications to some forms of X-ray imaging. Relations to Shannon and Fisher information capacity of imaging systems and super-resolution are also briefly discussed.

In this study we demonstrate the first direct comparison between synchrotron x-ray propagation-based CT (PB-CT) and cone-beam breast-CT (CB-CT) on human mastectomy specimens (N = 12) including different benign and malignant lesions. The image quality and diagnostic power of the obtained data sets were compared and judged by two independent expert radiologists. Two cases are presented in detail in this paper including a comparison with the corresponding histological evaluation. Results indicate that with PB-CT it is possible to increase the level of contrast-to-noise ratio (CNR) keeping the same level of dose used for the CB-CT or achieve the same level of CNR reached by CB-CT at a lower level of dose. In other words, PB-CT can achieve a higher diagnostic potential compared to the commercial breast-CT system while also delivering a considerably lower mean glandular dose. Therefore, we believe that PB-CT technique, if translated to a clinical setting, could have a significant impact in improving breast cancer diagnosis.

The following paper describes a method for three-dimensional (3D) reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogenous 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 localised region of the CT-reconstructed volume. We demonstrate via numerical simulations the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it to both conventional absorption tomography and two-dimensional (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 localised 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., 23 pages, 8 figures

A generic computational imaging setup is considered which assumes sequential illumination of a semitransparent object by an arbitrary set of structured coherent illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the square of the spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the square of the mean signal to the noise variance is proportional to the ratio of the mean number of registered photons to the number of illumination patterns. The signal-to-noise ratio in a reconstructed transmission distribution is always lower if the illumination patterns are nonorthogonal, because of spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging, and computed tomography.

X-ray computed tomography (XCT) is an important clinical diagnostic tool which is also used in a range of biological imaging applications in research. The increasing prevalence of metallic implants in medical and dental radiography and tomography has driven the demand for new approaches to solving the issue of metal artefacts in XCT. Metal artefacts occur when a highly absorbing material is imaged which is in boundary contact with one or more weakly absorbing components, such as soft-tissue. The resulting ‘streaking’ in the reconstructed images creates significant challenges for X-ray analysis due to the non-linear dependence on the absorption properties of the sample. In this paper we introduce a new approach to removing metal artefacts which exploits the capabilities of the recently available, photon-counting PiXirad detector. Our approach works for standard lab-based polychromatic X-ray tubes and does not rely on any postprocessing of the data. The method is demonstrated using both simulated data from a test phantom and experimental data collected from a cochlear implant. The results show that by combining the individual images, which are simultaneously generated for each different energy threshold, artefact -free segmentation of the implant from the surrounding biological tissue is achieved.

In this paper, we use optical coherence theory to define the limit for the spatial coherence length with respect to the degree of overlap between adjacent probe positions in ptychography. The influence of the degree of curvature of the probe in relation to partial coherence in the Fresnel geometry for a fixed overlap is also considered. This work has implications for the application of ptychographic coherent imaging using partially coherent sources. We validate these results through a simulation study of coherence versus overlap parameter and curvature.

Rationale and Objectives This study employs clinical/radiological evaluation in establishing the optimum imaging conditions for breast cancer imaging using the X-ray propagation-based phase-contrast tomography. Materials and Methods Two series of experiments were conducted and in total 161 synchrotron-based computed tomography (CT) reconstructions of one breast mastectomy specimen were produced at different imaging conditions. Imaging factors include sample-to-detector distance, X-ray energy, CT reconstruction method, phase retrieval algorithm applied to the CT projection images and maximum intensity projection. Observers including breast radiologists and medical imaging experts compared the quality of the reconstructed images with reference images approximating the conventional (absorption) CT. Various radiological image quality attributes in a visual grading analysis design were used for the radiological assessments. Results The results show that the application of the longest achievable sample-to-detector distance (9.31 m), the lowest employed X-ray energy (32 keV), the full phase retrieval, and the maximum intensity projection can significantly improve the radiological quality of the image. Several combinations of imaging variables resulted in images with very high-quality scores. Conclusion The results of the present study will support future experimental and clinical attempts to further optimize this innovative approach to breast cancer imaging.

It is proved that the width of a function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields. However, it is shown that, in the case of stochastic and quantum observables, certain non-classical states with sub-Poissonian statistics, such as for example photon number squeezed states in quantum optics, can overcome the "classical" noise-resolution uncertainty limit. The described uncertainty relationship, which is fundamentally different from the Heisenberg and related uncertainty principles, can define an upper limit for the information capacity of communication and imaging systems. It is expected to be useful in a variety of problems in classical and quantum physics., Comment: 12 pages, 1 figure, to be submitted to a journal

Phase-contrast X-ray imaging can improve the visibility of weakly absorbing objects (e.g. soft tissues) by an order of magnitude or more compared to conventional radiographs. Combining phase retrieval with computed tomography (CT) can increase the signal-to-noise ratio (SNR) by up to two orders of magnitude over conventional CT at the same radiation dose, without loss of image quality. Our experiments reveal that as the radiation dose decreases, the relative improvement in SNR increases. We show that this enhancement can be traded for a reduction in dose greater than the square of the gain in SNR. Upon reducing the dose 300 fold, the phase-retrieved SNR was still up to 9.6 ± 0.2 times larger than the absorption contrast data with spatial resolution in the tens of microns. We show that this theoretically reveals the potential for dose reduction factors in the tens of thousands without loss in image quality, which would have a profound impact on medical and industrial imaging applications.

The majority of current laboratory based X-ray sources are polychromatic and are not tuneable. This lack of monochromaticity limits the range of applications for these sources and in particular it reduces the elemental specificity of laboratory based X-ray imaging experiments. Here we present a solution to this problem based on the use of Ross filter pairs. Although such Ross filter arrangements have been applied in proof-of-principle spectroscopy experiments, to date there have been no reports of this approach used for full-field X-ray imaging. Here we report on the experimental demonstration of Ross filter pairs being used for quasi-monochromatic, full-field imaging. This arrangement has several important benefits for laboratory based X-ray imaging including, as we demonstrate, elemental contrast enhancement. The method is demonstrated both for two-dimensional radiography and for three-dimensional X-ray tomography.

The effectiveness of reconstructive imaging using the Homogeneous Transport of Intensity equation may be regarded as "unreasonable", because it has been shown to significantly increase signal-to-noise ratio while preserving spatial resolution, compared to equivalent conventional absorption-based imaging techniques at the same photon fluence. We reconcile this surprising behaviour by analysing the propagation of noise in typical in-line holography experiments. This analysis indicates that novel imaging techniques may be designed which produce high signal-to-noise images at low radiation doses without sacrificing spatial resolution.

Determining the specific spatial distributions of elements within compound samples is of critical importance to a range of applied research fields. The usual approaches to obtaining elemental contrast involve measurement of the characteristic peaks associated with x-ray fluorescence or measuring the x-ray transmission as a function of energy. In the laboratory these measurements are challenging due to the polychromaticity and lack of tunability of the source. Here we demonstrate how newly developed, high-resolution, energy-discriminating area detector technology can be exploited to enhance elemental contrast. The detector we employ here is the Pixirad area detector which can simultaneously have up to four separate colour channels. We also discuss the potential of this new technology in the context of tomographic imaging of soft tissue.

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck’s constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.

We present the outcomes of combined feasibility studies carried out at Elettra and Australian Synchrotron to evaluate novel protocols for threedimensional (3D) mammographic phase contrast imaging. A custom designed plastic phantom and some tissue samples have been studied at diverse resolution scales and experimental conditions. Several computed tomography (CT) reconstruction algorithms with different pre-processing and post-processing steps have been considered. Special attention was paid to the effect of phase retrieval on the diagnostic value of the reconstructed images. The images were quantitatively evaluated using objective quality indices in comparison with subjective assessments performed by three experienced radiologists and one pathologist. We show that the propagation-based phase-contrast imaging (PBI) leads to substantial improvement to the contrast-to-noise and to the intrinsic quality of the reconstructed CT images compared with conventional techniques as well as to an important reduction of the delivered doses, thus opening the way to clinical implementations.

Recently, the authors derived an uncertainty relationship between noise and spatial resolution in linear computational imaging systems that is similar to the Heisenberg uncertainty principle for conjugate variables in quantum mechanics. Specifically, for linear shift-invariant systems with a fixed incident photon density, the product of noise and spatial resolution has a positive absolute lower limit which can be evaluated with the aid of the inequality ‖ g ‖ p + 1 a ( p + 1 ) ‖ | x | a g ‖ 1 n p ‖ g ‖ 1 a ( p + 1 ) + n p ≥ C ( n , p , a ) , p > 0 ; a > 0 , where g ∈ L 1 ( R n ) ∩ L 1 ( R n , | x | a ) ∩ L p + 1 ( R n ) . This inequality, which is derived in this note, also has applications in data smoothing and in variations of Heisenberg’s inequality.

Micro-CT scanners find applications in many areas ranging from biomedical research to material sciences. In order to provide spatial resolution on a micron scale, these scanners are usually equipped with micro-focus, low-power x-ray sources and hence require long scanning times to produce high resolution 3D images of the object with acceptable contrast-to-noise.Propagation-based phase-contrast tomography (PB-PCT) has the potential to significantly improve the contrast-to-noise ratio (CNR) or, alternatively, reduce the image acquisition time while preserving the CNR and the spatial resolution. We propose a general approach for the optimisation of the PB-PCT imaging system. When applied to an imaging system with fixed parameters of the source and detector this approach requires optimisation of only two independent geometrical parameters of the imaging system, i.e. the source-to-object distance R1 and geometrical magnification M, in order to produce the best spatial resolution and CNR. If, in addition to R1 and M, the system parameter space also includes the source size and the anode potential this approach allows one to find a unique configuration of the imaging system that produces the required spatial resolution and the best CNR.

A method for constructing the Green’s function for the Helmholtz equation in free space subject to Sommerfeld radiation conditions is presented. Unlike the methods found in many textbooks, the present technique allows us to obtain all of the possible Green’s functions before selecting the one that satisfies the choice of boundary conditions.

We treat the problems of phase-contrast image formation, deterministic phase retrieval and aberration balancing, in the imaging of weak objects using two-dimensional shift-invariant linear imaging systems. Three classes of model sample are considered: weak phase objects, weak phase-amplitude objects and single-material weak phase-amplitude objects. For each class of sample we show how the various aberration coefficients, which characterise a given imaging system, contribute to the structure of the associated phase-contrast image. The corresponding inverse problem, of obtaining a closed-form expression for the input wave-field given one or more aberrated phase-contrast images of the same, is then examined. Two sample applications are considered: analyser-crystal phase-contrast imaging of weak objects using hard X-rays, and Zernike-type phase-contrast imaging. We close with a discussion of how coherent and incoherent aberrations may be “balanced” against one another, briefly mentioning the applications of this idea to both “deblur by defocus” and proximity-corrected X-ray lithography.

Possibilities are investigated for quantitative computed tomography (CT) reconstruction of the spatial distribution of refractive index in a region of interest (ROI) inside an object which is larger than the field of view. The analysis is presented for the case of conventional (absorption) CT, as well as diffraction (phase-contrast) CT. It is shown that in both cases an accurate reconstruction can be achieved using the projection data corresponding to rays passing through a sufficiently wide vicinity of a ROI. Our analysis also indicates that X-ray phase-contrast CT can typically be localized to smaller regions compared to absorption CT. In particular, quasi-local hard X-ray micro-CT of regions of the order of 100 μm or even smaller in size, appears feasible with the use of propagation-based phase contrast. Numerical and experimental tests confirm the possibility of accurate quantitative CT reconstruction from truncated projections.

Over the past few years, results from the phase contrast imaging and tomography (PCIT) beamline at the Singapore Synchrotron Light Source (SSLS) have shown that high resolution (about 1 μm) 2-dimensional (2D) and 3-dimensional (3D) can be achieved in spite of the large emittance of the Helios 2 storage ring. Using white radiation the photon flux is high enough to perform real time radiology (100 ms per frame) at high lateral resolution as well as high-speed 2D imaging and 3D tomography. Refractive edge enhancement was also observed. PCIT is mostly used for materials and process characterization.

We show that an arbitrary spatial distribution of complex refractive index decrement inside an object can be exactly represented as a sum of two ``monomorphous'' complex distributions, i.e., distributions with the ratios of the real part to the imaginary part being constant throughout the object. A priori knowledge of constituent materials can be used to estimate the global lower and upper boundaries for this ratio. This ``monomorphous decomposition'' approach can be viewed as an extension of the successful phase-retrieval method, based on the transport of intensity equation, that was previously developed for monomorphous (homogeneous) objects, such as, e.g., objects consisting of a single material. We demonstrate that the monomorphous decomposition can lead to more stable methods for phase retrieval using the transport of intensity equation. Such methods may find application in quantitative in-line phase-contrast imaging and phase-contrast tomography.

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.