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.

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.

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.

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.

: a software suite for ptychographic X-ray speckle tracking.

In recent years, X-ray speckle-tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications. These methods are based on the measurement of near-field images. Thanks to their simple experimental setup, high angular sensitivity and compatibility with low-coherence sources, these methods have been actively developed for use with synchrotron and laboratory light sources.

Recovery of undamaged electron-density maps in the presence of damage-induced partial coherence in single-particle imaging.

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.

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.

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.

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.

BERTHA: Implementation of a four-component Dirac-Kohn-Sham relativistic framework.

In this paper, we present and review the most recent computational advances in the BERTHA code. BERTHA can be regarded as the state of the art in fully relativistic four-component Dirac-Kohn-Sham (DKS) software. Thanks to the implementation of various parallelization and memory open-ended distribution schemes in combination with efficient "density fitting" algorithms, it greatly reduces the computational burden of four-component DKS calculations.

Structural dynamics in proteins induced by and probed with X-ray free-electron laser pulses.

X-ray free-electron lasers (XFELs) enable crystallographic structure determination beyond the limitations imposed upon synchrotron measurements by radiation damage. The need for very short XFEL pulses is relieved through gating of Bragg diffraction by loss of crystalline order as damage progresses, but not if ionization events are spatially non-uniform due to underlying elemental distributions, as in biological samples. Indeed, correlated movements of iron and sulfur ions were observed in XFEL-irradiated ferredoxin microcrystals using unusually long pulses of 80 fs.

PyBERTHART: A Relativistic Real-Time Four-Component TDDFT Implementation Using Prototyping Techniques Based on Python.

We present a real-time time-dependent four-component Dirac-Kohn-Sham (RT-TDDKS) implementation based on the BERTHA code. This new implementation takes advantage of modern software engineering, including the prototyping techniques. The software design follows a three step approach: (i) the prototype implementation of a time-propagation algorithm in nonrelativistic real-time TDDFT within the Psi4NumPy framework, which provides a suitable environment for the creation of a clear, readable, and easy to test reference code in Python, (ii) the design of an original Python application programming interface for the relativistic four-component code BERTHA (PyBERTHA), which has an efficient computational kernel for relativistic integrals written in FORTRAN, and (iii) the porting of the time-propagation scheme enveloped within the Psi4NumPy framework to PyBERTHA.

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.

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.

Charge-Displacement Analysis via Natural Orbitals for Chemical Valence in the Four-Component Relativistic Framework.

We have recently introduced a simple yet powerful tool for analyzing quantitatively the coordination bond in terms of the donation and back-donation constituents of the Dewar-Chatt-Duncanson model. Our approach is based on the decomposition, via natural orbitals for chemical valence (NOCV), of the so-called charge-displacement (CD) function into additive chemically meaningful components (Bistoni et al. J.

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.

On the van Cittert-Zernike theorem for intensity correlations and its applications.

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.

Nanocrystallography measurements of early stage synthetic malaria pigment.

The recent availability of extremely intense, femtosecond X-ray free-electron laser (XFEL) sources has spurred the development of serial femtosecond nanocrystallography (SFX). Here, SFX is used to analyze nanoscale crystals of β-hematin, the synthetic form of hemozoin which is a waste by-product of the malaria parasite. This analysis reveals significant differences in β-hematin data collected during SFX and synchrotron crystallography experiments.

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene.

The precise details of the interaction of intense X-ray pulses with matter are a topic of intense interest to researchers attempting to interpret the results of femtosecond X-ray free electron laser (XFEL) experiments. An increasing number of experimental observations have shown that although nuclear motion can be negligible, given a short enough incident pulse duration, electronic motion cannot be ignored. The current and widely accepted models assume that although electrons undergo dynamics driven by interaction with the pulse, their motion could largely be considered 'random'.

On noise-resolution uncertainty in quantum field theory.

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.

X-ray laser-induced electron dynamics observed by femtosecond diffraction from nanocrystals of Buckminsterfullerene.

X-ray free-electron lasers (XFELs) deliver x-ray pulses with a coherent flux that is approximately eight orders of magnitude greater than that available from a modern third-generation synchrotron source. The power density of an XFEL pulse may be so high that it can modify the electronic properties of a sample on a femtosecond time scale. Exploration of the interaction of intense coherent x-ray pulses and matter is both of intrinsic scientific interest and of critical importance to the interpretation of experiments that probe the structures of materials using high-brightness femtosecond XFEL pulses.