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

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. We also report the newly developed OpenMP version of the code, that, together with the berthmod Python module, provides a significant leap forward in terms of usability and applicability of the BERTHA software. Some applications of the recently developed natural orbitals for chemical valence/charge displacement bonding analysis and the real-time time dependent DKS implementation are also reported. [ABSTRACT FROM AUTHOR]

The variational determination of the two-fermion reduced density matrix (2-RDM) is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a semi-definite program, with the 2-RDM being subject to well-known N -representability conditions. The ground-state energies, as well as the density, pair-correlation function, and lower-order eigenvalues of the 2-RDM of various fermionic systems are found by utilising an augmented Lagrangian method for semi-definite programming. The ground-state energies are found to match well to those determined by full-configuration interaction and coupled-cluster calculations and the density, pair-correlation function, and eigenvalue results demonstrate that the salient features of these systems are well-described by this method. These results collectively demonstrate the utility of the reduced density matrix method firstly in describing strong correlation arising from short-range interactions, suggesting that the well-known N -representability conditions are sufficient to model ultracold fermionic systems, and secondly in illustrating the prospect of treating larger systems currently out of the reach of established methods. [ABSTRACT FROM AUTHOR]

We investigate coherent dynamics in the cryptophyte light-harvesting complex Phycocyanin-645 (PC-645). A two-colour four-wave mixing experiment allows us to isolate a coherence pathway and observe its evolution in the absence of other signals. We measured a decoherence time of 540fs for the coherence [1]. Additionally oscillations in the signal pathway give evidence for the coherent excitation of states outside the bandwidth of the laser pulse. This suggests strong coupling between the excited states and phonon modes [1].

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Not only do speckle‐tracking techniques give the potential for high‐resolution imaging, but they also provide rapid and robust characterization of aberrations of X‐ray optical elements, focal spot profiles, and sample position and transmission properties. In order to realize these capabilities, software implementations are required that are equally rapid and robust. To address this need, a software suite has been developed for the ptychographic X‐ray speckle‐tracking technique, an X‐ray speckle‐based method suitable for highly divergent wavefields. The software suite is written in Python 3, with an OpenCL back end for GPU and multi‐CPU core processing. It is accessible as a Python module, through the command line or through a graphical user interface, and is available as source code under Version 3 or later of the GNU General Public License. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X‐ray speckle tracking methods, it is robust to low‐coherence X‐ray sources, making it suitable for laboratory‐based X‐ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X‐ray free‐electron laser facilities, where beam‐pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second‐order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field. [ABSTRACT FROM AUTHOR]

A new approach to diffractive imaging using polychromatic diffraction data is described. The method is tested using simulated and experimental data and is shown to yield high-quality reconstructions. Diffraction data produced using a high-harmonic generation source are considered explicitly here. The formalism can be readily adapted, however, to any short-wavelength source producing a discrete spectrum and possessing sufficient spatial coherence. [ABSTRACT FROM AUTHOR]

We present recent developments in the implementation of the density fitting approach for the Coulomb interaction within the four-component formulation of relativistic density functional theory [Belpassi et al., J. Chem. Phys. 124, 124104 (2006)]. In particular, we make use of the Poisson equation to generate suitable auxiliary basis sets and simplify the electron repulsion integrals [Manby and Knowles, Phys. Rev. Lett. 87, 163001 (2001)]. We propose a particularly simple and efficient method for the generation of accurate Poisson auxiliary basis sets, based on already available standard Coulomb fitting sets. Just as is found in the nonrelativistic case, we show that the number of standard auxiliary fitting functions that need to be added to the Poisson-generated functions in order to achieve a fitting accuracy equal or, in some cases, better than that of the standard procedure is remarkably small. The efficiency of the present implementation is demonstrated in a detailed study of the spectroscopic properties and energetics of several gold containing systems, including the Au dimer and the CsAu molecule. The extraction reaction of a H2O molecule from a Au(H2O)9+ cluster is also calculated as an example of mixed heavy-light-atom molecular systems. The scaling behavior of the algorithm implemented is illustrated for some closed shell gold clusters up to Au5+. The increased sparsity of the Coulomb matrices involved in the Poisson fitting is identified, as are potential computational applications and the use of the Poisson fitting for the relativistic exchange-correlation problem. [ABSTRACT FROM AUTHOR]

The nuclear quadrupole moment for 197Au has been determined on the base of the state-of-art relativistic molecular calculations. The experimental shifts in the nuclear coupling constants in the series of molecules AuF, XeAuF, KrAuF, ArAuF, (OC)AuF, and AuH have been combined with highly accurate determinations of the electric field gradient (EFG) at the gold nucleus, obtained by molecular relativistic Dirac-Coulomb-Gaunt Hartree-Fock calculations. The electronic correlation contribution to the EFG is included with the CCSD(T) and CCSD-T approaches, also in the four-component framework, using a finite-difference method. In order to estimate the accuracy of their approach the authors have thoroughly investigated the convergence of the results with respect to the basis set employed and the size of the correlated orbital space. The effect of the full Breit electron-electron interaction on the nuclear quadrupole moment of gold has also been considered explicitly for the AuF molecule. They obtain for 197Au a nuclear quadrupole moment of 510±15 mb, which deviates by about 7% from the currently accepted muonic value. [ABSTRACT FROM AUTHOR]

A density fitting approach for the Coulomb matrix representation within the four-component formulation of relativistic density-functional theory is presented. Our implementation, which uses G-spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closed-shell gold clusters (Au2,Au3+,Au4,Au5+). The algorithm is found to scale as O(N3), just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for Au2 and up to 1% in the case of Au5+. [ABSTRACT FROM AUTHOR]

An implementation of the generalized gradient approximation within the four-component formulation of relativistic density-functional theory using G-spinor basis sets is presented. This approach is based on the direct evaluation of the relativistic density and its gradient from the G-spinor amplitudes and gradients without explicit reference to the total density matrix. This proves to be a particularly efficient scheme, with an intrinsic computational cost that scales linearly with the number of G-spinor basis functions. In order to validate this new implementation, incorporated in the parallel version of the program BERTHA, a detailed study of the diatomic system CsAu is also reported. The spectroscopic constants De,re,ωe, and xeωe and the dipole moment μ have been calculated and compared with the best available theoretical and experimental data. The sensitivity of our results to the details of the numerical schemes used to evaluate the matrix elements is analyzed in detail. Also presented is a comparative study of molecular properties in the alkali auride series which have been obtained using several standard nonrelativistic density functionals. [ABSTRACT FROM AUTHOR]

The four-component formulation of relativistic density functional theory was employed to calculate spectroscopic constants, including dissociation energies, harmonic and anharmonic vibrational frequencies and dipole movements for alkali auride series. The comparative study reveal that, on the basis of several topological properties and the variation in bond lengths, the gold atom behaves similarly to a halogen intermediate between Br and I.

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. [ABSTRACT FROM AUTHOR]

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. To interpret these differences two possibilities are considered: structural differences between the nanocrystal and larger crystalline forms of β-hematin, and radiation damage. Simulation studies show that structural inhomogeneity appears at present to provide a better fit to the experimental data. If confirmed, these observations will have implications for designing compounds that inhibit hemozoin formation and suggest that, for some systems at least, additional information may be gained by comparing structures obtained from nanocrystals and macroscopic crystals of the same molecule. [ABSTRACT FROM AUTHOR]

Developments in experimental techniques in micro electron diffraction and serial X-ray crystallography provide the opportunity to collect diffraction data from protein nanocrystals. Incomplete unit cells on the surfaces of protein crystals can affect the distribution of diffracted intensities for crystals with very high surface-to-volume ratios. The extraction of structure factors from diffraction data for such finite protein crystals sizes is considered here. A theoretical model for the continuous diffracted intensity distribution for data merged from finite crystals with two symmetry-related sub-units of the conventional unit cell is presented. This is used to extend a whole-pattern fitting technique to account for incomplete unit cells in the extraction of structure factor amplitudes. The accuracy of structure factor amplitudes found from this whole-pattern fitting technique and from an integration approach are evaluated. [ABSTRACT FROM AUTHOR]

The recent development of X-ray free-electron laser sources has created new opportunities for the structural analysis of protein nanocrystals. The extremely small sizes of the crystals, as well as imperfections of the crystal structure, result in an interference phenomenon in the diffraction pattern. With decreasing crystallite size the structural imperfections play a role in the formation of the diffraction pattern that is comparable in importance to the size effects and should be taken into account during the data analysis and structure reconstruction processes. There now exists a need to develop new methods of protein structure determination that do not depend on the availability of good-quality crystals and that can treat proteins under conditions close to the active form. This paper demonstrates an approach that is specifically tailored to nanocrystalline samples and offers a unique crystallographic solution. [ABSTRACT FROM AUTHOR]

High-resolution X-ray imaging techniques using optical elements such as zone plates are widely used for viewing the internal structure of samples in exquisite detail. The resolution attainable is ultimately limited by the manufacturing tolerances for the optics. Combining ideas from crystallography and holography, this limit may be surpassed by the method of coherent diffractive imaging (CDI). Although CDI shows particular promise in applications involving X-ray free-electron lasers, it is also emerging as an important new technique for imaging at third-generation synchrotrons. The limited coherent output of these sources, however, is a significant barrier to obtaining shorter exposure times. A fundamental assumption of coherent diffractive imaging is that the incident light is well-approximated by a single optical frequency. In this Letter, we demonstrate the first experimental realization of 'polyCDI', using a broadband source to achieve a factor of 60 reduction in the exposure time over quasi-monochromatic coherent diffractive imaging. [ABSTRACT FROM AUTHOR]

We review recent theoretical and computational advances in the full relativistic four-component Dirac–Kohn–Sham (DKS) approach and its application to the calculation of the electronic structure of chemical systems containing many heavy atoms. We describe our implementation of an all-electron DKS approach based on the use of G-spinor basis sets, Hermite Gaussian functions, state-of-the-art density-fitting techniques and memory distributed parallelism. This approach has enormously extended the applicability of the DKS method, including for example large clusters of heavy atoms, and opens the way for future key developments. We examine the current limitations and future possible applications of the DKS approach, including the implementation of four-current density functionals and real-time propagation schemes. This would make possible to describe molecules in strong fields, accurately accounting for relativistic kinematic effects and spin–orbit coupling. [ABSTRACT FROM AUTHOR]

The challenges involved in determining the structures of molecules to atomic resolution in non-crystalline samples using X-ray free-electron laser pulses are formidable. Proposals to determine biomolecular structures from diffraction experiments using femtosecond X-ray free-electron laser pulses involve a conflict between the incident brightness required to achieve diffraction-limited atomic resolution and the electronic and structural damage induced by the illumination. Significant advances have already been made, however, in the design and preparation of experiments using fourth-generation sources and the corresponding structural analysis of diffraction data. Here we show that previous estimates of the conditions under which biomolecular structures may be obtained in this manner are unduly restrictive, because they are based on a coherent diffraction model that is not appropriate to the proposed interaction conditions. A more detailed imaging model derived from optical coherence theory and quantum electrodynamics is shown to be far more tolerant of electronic damage. The nuclear density is employed as the principal descriptor of molecular structure. The foundations of the approach may also be used to characterize electrodynamical processes by carrying out scattering experiments on complex molecules of known structure. [ABSTRACT FROM AUTHOR]

The computational cost of ab initio molecular electronic structure calculations is dominated by the generation of electron–electron repulsion integrals, of which there are O(N4), where N is the dimension of the basis set. Even if allowance is made for integral economization schemes, the rapidity with which the computational cost grows as N increases is a problem for all ab initio calculations, particularly the intrinsically more laborious relativistic approaches. There is therefore a strong motive to search for accurate but inexpensive algorithms without having to simplify the equations. We report a preliminary assessment of a promising new scheme that scales much more slowly with N. The key idea is the equivalence of the conventional expression for the energy of an atom or molecule with the integral of the energy density of the related electromagnetic fields over all space. The electrostatic energy density can be constructed cheaply as the sum of scalar products of O(N2) pairs of electric fields Eij(r) generated by the overlap charge densities ρij(r). The integration of the total energy density over the whole molecule can be done by adapting a numerical integration scheme used in contemporary density functional (DFT) algorithms requiring only a relatively small number of cubature points. We explore the implications of this approach for calculations in quantum chemistry. In relativistic quantum theory the total energy can be expressed as the sum of scalar products of both electric Eij(r) fields and magnetic Bij(r) fields generated by the overlap charge and current densities. In the long‐wavelength approximation, in which retardation is neglected, this leads to a new interpretation of the Breit interaction energy as the energy of the associated magnetic fields. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 [ABSTRACT FROM AUTHOR]

The four-component formulation of the Dirac–Hartree–Fock (DHF) approximation is used to calculate the electronic g-tensors and nuclear hyperfine interaction A-tensors for a number of open-shell diatomic species. The four-component approach makes it possible to include all relativistic single-particle effects involving the calculated magnetic interactions within the spinor structure, using a compact computational formulation. Results for most of the molecules investigated here are in good agreement with experiment. [Copyright &y& Elsevier]

Relativistic energy corrections which arise from the use of the Dirac-Coulomb Hamiltonian, and the Gaunt and Breit interaction operators, plus Lamb-shift effects have been determined for the global minima of the ground electronic states of C[sub 2]H[sub 6], NH[sub 3], H[sub 2]O, [H,C,N], HNCO, HCOOH, SiC[sub 2], SiH[sub 3][sup -], and H[sub 2]S, and for barrier characteristics for these molecular systems (inversion barrier of NH[sub 3] and SiH[sub 3][sup -], barrier to linearity of H[sub 2]O, H[sub 2]S, and HNCO, rotational barrier of C[sub 2]H[sub 6], difference between conformations of HCOOH (Z/E) and SiC[sub 2] (linear/T-shaped), and isomerization barrier of HCN/HNC). The relativistic calculations performed at the Hartree-Fock and the highly correlated CCSD(T) levels employed a wide variety of basis sets. Comparison of the perturbational and the four-component fully variational results indicate that the Coulomb-Pauli Hamiltonian and the lowest order Hamiltonian of direct perturbation theory (DPT(2)) are highly successful for treating the relativistic energy effects in light molecular systems both at a single point on the potential energy hypersurface and along the surface. Electron correlation contributions to the relativistic corrections are relatively small for the systems studied, and are comparable with the 2-electron Darwin correction. Corrections beyond the Dirac-Coulomb treatment are usually rather small, but may become important for high accuracy ab initio calculations. [ABSTRACT FROM AUTHOR]

X-ray free-electron laser pulses initiate a complex series of changes to the electronic and nuclear structure of matter on femtosecond timescales. These damage processes include widespread ionization, the formation of a quasi-plasma state and the ultimate explosion of the sample due to Coulomb forces. The accurate simulation of these dynamical effects is critical in designing feasible XFEL experiments and interpreting the results. Current molecular dynamics simulations are, however, computationally intensive, particularly when they treat unbound electrons as classical point particles. On the other hand, plasma simulations are computationally efficient but do not model atomic motion. Here we present a hybrid approach to XFEL damage simulation that combines molecular dynamics for the nuclear motion and plasma models to describe the evolution of the low-energy electron continuum. The plasma properties of the unbound electron gas are used to define modified inter-ionic potentials for the molecular dynamics, including Debye screening and drag forces. The hybrid approach is significantly faster than damage simulations that treat unbound electrons as classical particles, enabling simulations to be performed on large sample volumes. [ABSTRACT FROM AUTHOR]

Relativistic corrections beyond the simple one-electron mass–velocity–Darwin (MVD1) approximation to the ground-state electronic energy of H2S are determined at over 250 geometries. The corrections considered include the two-electron Darwin, the Gaunt and Breit corrections, and the one-electron Lamb shift. Fitted correction surfaces are constructed and used with an accurate ab initio nonrelativistic Born–Oppenheimer potential, determined previously (J. Chem. Phys. 115 (2001) 1229), to calculate vibrational and rotational levels for H232S. The calculations suggest that one- and two-electron relativistic corrections have a noticable influence on the levels of H2S. As for water, the effects considered have markedly different characteristics for the stretching and bending states. [Copyright &y& Elsevier]

Coherent diffraction imaging (CDI) typically requires that the source should be highly coherent both laterally and longitudinally. In this paper, we demonstrate that lateral and longitudinal partial coherence can be successfully included in a CDI reconstruction algorithm simultaneously using experimental x-ray data. We study the interplay between lateral partial coherence and longitudinal partial coherence and their relative influence on CDI. We compare our results against the coherence criteria published by Spence et al. [Spence et at, Ultramicroscopy 101, 149 (2004)] and show, that for iterative ab initio phase-recovery algorithms based on those typically used in CDI and in cases where the coherence properties are known, we are able to relax the minimal coherence requirements by a factor of 2 both laterally and longitudinally, potentially yielding significant reduction in exposure time. [ABSTRACT FROM AUTHOR]

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. The sum of these frames showed a clear presence of the interference pattern with the expected period. Subsequent analysis provided an objective estimation of the minimal number of detected photons required to determine, in accordance with the Rose criterion, the presence of the photon interference. Apart from a general theoretical interest, these investigations were aimed at exploring the possibility of medical X-ray phase-contrast imaging in photon-counting regime at minimal radiation doses.

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.

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 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.

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., (© Alexander Kozlov et al. 2020.)

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. The propagation scheme consequently resides in a single readable Python computer code that is easy to maintain and in which the key quantities, such as the Dirac-Kohn-Sham and dipole matrices, can be accessed directly from the PyBERTHA module. For linear algebra operations (matrix-matrix multiplications and diagonalization) we use the highly optimized procedures implemented in the popular NumPy library. The overhead introduced by the Python interface to BERTHA is almost negligible (less than 1% evaluated on the SCF procedure), and the interoperability between different programming languages (FORTRAN, C, and Python) does not affect the numerical stability of the time-propagation scheme. Our new RT-TDDKS implementation has been employed to investigate the stability of the time-propagation procedure in combination with a density-fitting algorithm (both for the Coulomb and for the exchange-correlation matrix construction), which are employed in BERTHA to speed up the Dirac-Kohn-Sham matrix evaluation. On the basis of systematic calculations, employing several density-fitting basis sets of increasing accuracy, we showed that quantitative agreement can be achieved in combination with extended-fitting basis sets, with an error in the Coulomb energy below 1 μ-hartree. Convergence of the transition energies increasing of quality of the fitting basis sets has been also observed. Our data suggest that the error in the Coulomb energy may also represent a good estimate of the fitting basis set quality for real-time electron dynamics simulations. Further, we study the applicability of the RT-TDDKS method in combination with both weak- and extreme strong-field regime. Numerical results of excited-state transitions for the Group 12 atoms are reported and compared with a previous real-time Dirac-Kohn-Sham implementation (Repisky et al. J. Chem. Theory Comput. 2015, 11, 980-991). Finally, calculations of high harmonic generation in the hydrogen molecule and Au dimer have been also carried out. We were able to generate high harmonics with relatively well-defined peaks up to the 21st and 13th order in the case of H 2 and Au 2 , respectively. Our findings show that the four-component structure of the Dirac-Kohn-Sham Hamiltonian provides a suitable theoretical framework, with no intrinsic unfavorable features, to study molecules in the strong-field regime.

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.