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

Purpose: Breast cancer is the most common cancer in women in developing and developed countries and is responsible for 15% of women's cancer deaths worldwide. Conventional absorption-based breast imaging techniques lack sufficient contrast for comprehensive diagnosis. Propagation-based phase-contrast computed tomography (PB-CT) is a developing technique that exploits a more contrast-sensitive property of x-rays: x-ray refraction. X-ray absorption, refraction, and contrast-to-noise in the corresponding images depend on the x-ray energy used, for the same/fixed radiation dose. The aim of this paper is to explore the relationship between x-ray energy and radiological image quality in PB-CT imaging. Approach: Thirty-nine mastectomy samples were scanned at the imaging and medical beamline at the Australian Synchrotron. Samples were scanned at various x-ray energies of 26, 28, 30, 32, 34, and 60 keV using a Hamamatsu Flat Panel detector at the same object-to-detector distance of 6 m and mean glandular dose of 4 mGy. A total of 132 image sets were produced for analysis. Seven observers rated PB-CT images against absorption-based CT (AB-CT) images of the same samples on a five-point scale. A visual grading characteristics (VGC) study was used to determine the difference in image quality. Results: PB-CT images produced at 28, 30, 32, and 34 keV x-ray energies demonstrated statistically significant higher image quality than reference AB-CT images. The optimum x-ray energy, 30 keV, displayed the largest area under the curve ( AUC VGC ) of 0.754 ( p = 0.009 ). This was followed by 32 keV ( AUC VGC = 0.731 , p ≤ 0.001 ), 34 keV ( AUC VGC = 0.723 , p ≤ 0.001 ), and 28 keV ( AUC VGC = 0.654 , p = 0.015 ). Conclusions: An optimum energy range (around 30 keV) in the PB-CT technique allows for higher image quality at a dose comparable to conventional mammographic techniques. This results in improved radiological image quality compared with conventional techniques, which may ultimately lead to higher diagnostic efficacy and a reduction in breast cancer mortalities., (© 2021 Society of Photo-Optical Instrumentation Engineers (SPIE).)

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 (AUC VGC  = 0.901, p = 0.001 and AUC VGC  = 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., (Crown Copyright © 2020. Published by Elsevier Inc. All rights reserved.)

We show that the width of an arbitrary 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 then 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. This 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 optics and imaging.

Objectives: 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., Methods: 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 (AUC VGC )., Results: 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 (AUC VGC 0.958 to 1, p ≤ .05) and low dose PB-CT images (AUC VGC 0.785 to 0.834, p ≤ .05) were of significantly higher image quality than standard-dose CBBCT images., Conclusions: Synchrotron-based PB-CT can achieve a significantly higher radiological image quality at a substantially lower radiation dose compared with conventional CBBCT., Key Points: • 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.

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

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 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.

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 aim of this study was to highlight the advantages that propagation-based phase-contrast computed tomography (PB-CT) with synchrotron radiation can provide in breast cancer diagnostics. For the first time, a fresh and intact mastectomy sample from a 60 year old patient was scanned on the IMBL beamline at the Australian Synchrotron in PB-CT mode and reconstructed. The clinical picture was described and characterized by an experienced breast radiologist, who underlined the advantages of providing diagnosis on a PB-CT volume rather than conventional two-dimensional modalities. Subsequently, the image quality was assessed by 11 breast radiologists and medical imaging experts using a radiological scoring system. The results indicate that, with the radiation dose delivered to the sample being equal, the accuracy of a diagnosis made on PB-CT images is significantly higher than one using conventional techniques.

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 behavior by analyzing the propagation of noise in typical in-line holography experiments. This analysis indicates that novel imaging techniques may be designed that produce high signal-to-noise images at low radiation doses without sacrificing spatial resolution.

A reciprocal relationship between the autocovariance of the light intensity in the source plane and in the far-field detector plane is presented in a form analogous to the classical van Cittert-Zernike theorem, but involving intensity correlation functions. A "classical" version of the reciprocity relationship is considered first, based on the assumption of circular Gaussian statistics of the complex amplitudes in the source plane. The result is consistent with the theory of Hanbury Brown-Twiss interferometry, but it is shown to be also applicable to estimation of the source size or the spatial resolution of the detector from the noise power spectrum of flat-field images. An alternative version of the van Cittert-Zernike theorem for intensity correlations is then derived for a quantized electromagnetic beam in a coherent state, which leads to Poisson statistics for the intrinsic intensity of the beam.

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.

A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the constraints of this model, the square of the signal-to-noise ratio is always proportional to the "volume" of the spatial resolution unit. In the case of Poisson statistics, the ratio of these two quantities divided by the incident density of the imaging particles (e.g. photons) represents a dimensionless invariant of the imaging system, which was previously termed the intrinsic imaging quality. The relationship of this invariant to the notion of information capacity of communication and imaging systems, which was previously considered by Shannon, Gabor and others, is investigated. The results are then applied to a simple generic model of quantitative imaging of weakly scattering objects, leading to an estimate of the upper limit for the amount of information about the sample that can be obtained in such experiments. It is shown that this limit depends only on the total number of imaging particles incident on the sample, the average scattering coefficient, the size of the sample and the number of spatial resolution units.

The contrast-transfer-function (CTF) approximation, widely used in various phase-contrast imaging techniques, is revisited. CTF validity conditions are extended to a wide class of strongly absorbing and refracting objects, as well as to nonuniform partially coherent incident illumination. Partially coherent free-space propagators, describing amplitude and phase in-line contrast, are introduced and their properties are investigated. The present results are relevant to the design of imaging experiments with partially coherent sources, as well as to the analysis and interpretation of the corresponding images.

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.

Statistical aspects of Young's double-slit diffraction experiment are analysed quantitatively. It is shown that the signal-to-noise ratio and the spatial resolution in the detected diffraction pattern satisfy a duality relationship which implies that both of them cannot be improved simultaneously beyond a certain limit if the total number of particles forming the image is fixed. As a consequence of this duality, it is possible to estimate the minimal number of particles that have to be detected in order for two slits separated by a given distance to be resolved with a confidence level corresponding to a pre-defined signal-to-noise ratio, e.g. according to the Rose criterion. These results are related to the recently introduced imaging system quality characteristic which combines the spatial resolution and the noise sensitivity, and allows one to estimate the efficiency with which imaging quanta are utilised in a system to deliver maximal amount of information about the imaged object. The presented results can be useful for applications where the imaging quanta are at a premium or where minimization of the radiation dose is important.

It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging. It is shown that in the latter case the spatial resolution and the noise can sometimes be decoupled, potentially leading to a substantial increase in the imaging quality.

In order to quantify the effect of phase contrast on X-ray image formation, the theory of statistical decision making has been applied to a binary classification task between two signals known exactly, namely, a phase-contrast image (that combines both the absorption and phase contrast) and the corresponding hypothetical pure absorption image that would be obtained under the same imaging conditions but without diffraction/refraction effects. The signal-to-noise ratio (SNR) for two widely used observers, including the ideal observer (also known as the prewhitening matched filter) and a non-ideal observer (the non-prewhitening matched filter) has been estimated in the case of in-line phase-contrast imaging, thus providing a figure-of-merit for the optimisation of the imaging conditions. A broad class of edge objects has been investigated and simple analytical expressions for the corresponding SNRs have been obtained and discussed.

The first monochromatic X-ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X-ray energies. In order to quantitatively account for the experimental values obtained for the Hounsfield (or CT) number, it was necessary to consider various issues including the point-spread function for the X-ray imaging system and harmonic contamination of the X-ray beam. The analysis and interpretation of the data includes detailed considerations of the resolution and efficiency of the CCD detector, calculations of the X-ray spectrum prior to monochromatization, allowance for the response of the double-crystal Si monochromator used (via X-ray dynamical theory), as well as a thorough assessment of the role of X-ray phase-contrast effects. Computer simulations relating to the tomography experiments also provide valuable insights into these important issues. It was found that a significant discrepancy between theory and experiment for the Cu wire could be largely resolved in terms of the effect of the point-spread function. The findings of this study are important in respect of any attempts to extract quantitative information from X-ray tomography data, across a wide range of disciplines, including materials and life sciences.

Simple analytical expressions are derived for the spatial resolution, contrast and signal-to-noise in X-ray projection images of a generic phase edge. The obtained expressions take into account the maximum phase shift generated by the sample and the sharpness of the edge, as well as such parameters of the imaging set-up as the wavelength spectrum and the size of the incoherent source, the source-to-object and object-to-detector distances and the detector resolution. Different asymptotic behavior of the expressions in the cases of large and small Fresnel numbers is demonstrated. The analytical expressions are compared with the results of numerical simulations using Kirchhoff diffraction theory, as well as with experimental X-ray measurements.

We are developing and exploring the imaging performance of, an in vivo, in-line holography, x-ray phase-contrast, micro-CT system with an ultrafast laser-based x-ray (ULX) source. By testing and refining our system, and by performing computer simulations, we plan to improve system performance in terms of contrast resolution and multi-energy imaging to a level beyond what can be obtained using a conventional microfocal x-ray tube. Initial CT projection sets at single energy (Mo K(alpha) and K(beta) lines) were acquired in the Fresnel regime and reconstructed for phantoms and a euthanized mouse. We also performed computer simulations of phase-contrast micro-CT scans for low-contrast, soft-tissue, tumor imaging. We determined that, in order to perform a phase-contrast, complete micro-CT scan using ULX, the following conditions must be met: (i) the x-ray source needs to be stable during the scan; (ii) the laser focal spot size needs to be less than 10 mum for source-to-object distance greater than 30 cm; (iii) the laser light intensity on the target needs to be in the range of 5 x 10(17) to 5 x 10(19) W/cm(2); (iv) the ablation protection system needs to allow uninterrupted scans; (v) the laser light focusing on the target needs to remain accurate during the entire scan; (vi) a fresh surface of the target must be exposed to consecutive laser shots during the entire scan; (vii) the effective detector element size must be less than 12 mum. Based on the results obtained in this research project, we anticipate that the new 10 Hz, 200 TW laser with 50 W average power that is being commissioned at ALLS will allow us practical implementation of in vivo x-ray phase-contrast micro-CT.

To assess the feasibility of small soft tissue avascular tumor micro-CT imaging with x-ray phase-contrast in-line holography, we have studied micro-CT imaging with in-line geometry of small spheroidal avascular tumor models with quiescent cell core (< 250 mum) and various distributions of the proliferating cell density (PCD) forming the outer shell. We have simulated imaging with an ultrafast laser-based x-ray source with a Mo target. We observe phase-contrast enhancement of the tumor boundaries in the reconstructed transaxial images, resulting in improved detection of small soft tissue tumors, providing that the PCD density gradient is sufficiently large.

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

Effects of incident illumination on phase-contrast images obtained by means of free-space propagation are investigated under the "transport-of-intensity" approximation. Analytical expressions for image intensity distribution are derived in the cases of coherent quasi-plane and quasi-spherical incident waves, as well as for spatially incoherent and quasi-homogeneous sources and some other types of sources. Practical methods for measuring the relevant parameters of the incident radiation are discussed together with formulas allowing one to calculate the effect of these parameters on the image intensity distribution. The results are expected to be useful in quantitative in-line imaging, phase retrieval, and tomography with polychromatic and spatially partially coherent radiation. As an application we present a method for simultaneous "automatic" phase retrieval and spatial deconvolution in in-line imaging of homogeneous objects using extended polychromatic x-ray sources.

A new method for deconvolution of one-dimensional and multidimensional data is suggested. The proposed algorithm is local in the sense that the deconvolved data at a given point depend only on the value of the experimental data and their derivatives at the same point. In a regularized version of the algorithm the deconvolution is constructed iteratively with the help of an approximate deconvolution operator that requires only the low-order derivatives of the data and low-order integral moments of the point-spread function. This algorithm is expected to be particularly useful in applications in which only partial knowledge of the point-spread function is available. We tested and compared the proposed method with some of the popular deconvolution algorithms using simulated data with various levels of noise.