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

Double-slit interference experiments using monochromatic hard X-rays with the energy of 25 keV are presented. The experiments were performed at a synchrotron source with a distance of 110 m between the interferometer and the detector to produce an interference pattern with a sufficiently broad period that could be adequately sampled by a photon-counting detector with 75 micrometre pixels. In the single-particle version of the experiment, over one million image frames with a single registered photon in each one were collected.

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.

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

A new method is developed for 3D reconstruction of multimaterial objects using propagation-based x-ray phase-contrast tomography (PB-CT) with phase retrieval via contrast-transfer-function (CTF) formalism. The approach differs from conventional PB-CT algorithms, which apply phase retrieval to individual 2D projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D.

Unified fast reconstruction algorithm for conventional, phase-contrast, and diffraction tomography.

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.

Method for virtual optical sectioning and tomography utilizing shallow depth of field.

A method is proposed for high-resolution, three-dimensional reconstruction of internal structures 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.

Imaging Breast Microcalcifications Using Dark-Field Signal in Propagation-Based Phase-Contrast Tomography.

Breast microcalcifications are an important primary radiological indicator of breast cancer. However, microcalcification classification and diagnosis may be still challenging for radiologists due to limitations of the standard 2D mammography technique, including spatial and contrast resolution. In this study, we propose an approach to improve the detection of microcalcifications in propagation-based phase-contrast X-ray computed tomography of breast tissues.

A Method for High-Resolution Three-Dimensional Reconstruction with Ewald Sphere Curvature Correction from Transmission Electron Images.

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.

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.

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

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.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons, Part II: Differential Holographic Tomography.

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.

Effect of radiation damage and illumination variability on signal-to-noise ratio in X-ray free-electron laser single-particle imaging.

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.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons.

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.

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.

Noise-resolution uncertainty principle in classical and quantum systems.

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.

Comparison of propagation-based CT using synchrotron radiation and conventional cone-beam CT for breast 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.

Propagation-based x-ray phase-contrast tomography of mastectomy samples using synchrotron radiation.

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.

Free propagation phase-contrast breast CT provides higher image quality than cone-beam breast-CT at low radiation doses: a feasibility study on human mastectomies.

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.

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

The following article describes a method for 3D reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogeneous form of the transport of intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localized region of the CT-reconstructed volume. This work demonstrates, via numerical simulations, the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it with both conventional absorption tomography and 2D TIE-Hom phase retrieval applied to projection images.

Signal-to-noise, spatial resolution and information capacity of coherent diffraction imaging.

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.

Toward Improving Breast Cancer Imaging: Radiological Assessment of Propagation-Based Phase-Contrast CT Technology.

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.

X-Ray Phase-Contrast Technology in Breast Imaging: Principles, Options, and Clinical Application.

Objective: The purpose of this article is to review different x-ray phase-contrast breast imaging techniques and their potential application in clinical settings.

Conclusion: 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.

On the "unreasonable" effectiveness of transport of intensity imaging and optical deconvolution.

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.

CT dose reduction factors in the thousands using X-ray phase contrast.

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.