Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval

Coherent diffraction imaging (CDI) allows the retrieval of the structure of an isolated object, such as a macromolecule, from its diffraction pattern. CDI requires the fulfilment of two conditions: the imaging radiation must be coherent and the object must be isolated. We discuss that it is possible to directly retrieve the molecular structure from its diffraction pattern which was acquired neither with coherent radiation nor from an individual molecule, provided the molecule exhibits periodicity in one direction, as in the case of fiber diffraction. We demonstrate that by applying iterative phase retrieval methods to a fiber diffraction pattern, the repeating unit, that is, the molecule structure, can directly be reconstructed without any prior modeling. As an example, we recover the structure of the DNA double helix in three-dimensions from its two-dimensional X-ray fiber diffraction pattern, Photograph 51, acquired in the famous experiment by Raymond Gosling and Rosalind Franklin, at a resolution of 3.4 Angstrom

Electron tomography at 2.4 {\AA} resolution

Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial resolution and image quality in TEM have been significantly improved(4,5) and resolution below 0.5 {\AA} has been demonstrated(6). To reveal the 3D structure of thin samples, electron tomography is the method of choice(7-11), with resolutions of ~1 nm^3 currently achievable(10,11). Recently, discrete tomography has been used to generate a 3D atomic reconstruction of a silver nanoparticle 2-3 nm in diameter(12), but this statistical method assumes prior knowledge of the particle's lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of a ~10 nm gold nanoparticle at 2.4 {\AA} resolution. While we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified at three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply-twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic scale resolution(13-15), but also to improve the spatial resolution and image quality in other tomography fields(7,9,16-20).Comment: 27 pages, 17 figure

Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy

Image symmetrization is an effective strategy to correct symmetry distortion in experimental data for which symmetry is essential in the subsequent analysis. In the process, a coordinate transform, the symmetrization transform, is required to undo the distortion. The transform may be determined by image registration (i.e. alignment) with symmetry constraints imposed in the registration target and in the iterative parameter tuning, which we call symmetry-guided registration. An example use case of image symmetrization is found in electronic band structure mapping by multidimensional photoemission spectroscopy, which employs a 3D time-of-flight detector to measure electrons sorted into the momentum ($k_x$, $k_y$) and energy ($E$) coordinates. In reality, imperfect instrument design, sample geometry and experimental settings cause distortion of the photoelectron trajectories and, therefore, the symmetry in the measured band structure, which hinders the full understanding and use of the volumetric datasets. We demonstrate that symmetry-guided registration can correct the symmetry distortion in the momentum-resolved photoemission patterns. Using proposed symmetry metrics, we show quantitatively that the iterative approach to symmetrization outperforms its non-iterative counterpart in the restored symmetry of the outcome while preserving the average shape of the photoemission pattern. Our approach is generalizable to distortion corrections in different types of symmetries and should also find applications in other experimental methods that produce images with similar features

Common Arc Method for Diffraction Pattern Orientation

Very short pulses of x-ray free-electron lasers opened the way to obtain diffraction signal from single particles beyond the radiation dose limit. For 3D structure reconstruction many patterns are recorded in the object's unknown orientation. We describe a method for orientation of continuous diffraction patterns of non-periodic objects, utilizing intensity correlations in the curved intersections of the corresponding Ewald spheres, hence named Common Arc orientation. Present implementation of the algorithm optionally takes into account the Friedel law, handles missing data and is capable to determine the point group of symmetric objects. Its performance is demonstrated on simulated diffraction datasets and verification of the results indicates high orientation accuracy even at low signal levels. The Common Arc method fills a gap in the wide palette of the orientation methods.Comment: 16 pages, 10 figure

Fast tomographic inspection of cylindrical objects

This paper presents a method for improved analysis of objects with an axial symmetry using X-ray Computed Tomography (CT). Cylindrical coordinates about an axis fixed to the object form the most natural base to check certain characteristics of objects that contain such symmetry, as often occurs with industrial parts. The sampling grid corresponds with the object, allowing for down-sampling hence reducing the reconstruction time. This is necessary for in-line applications and fast quality inspection. With algebraic reconstruction it permits the use of a pre-computed initial volume perfectly suited to fit a series of scans where same-type objects can have different positions and orientations, as often encountered in an industrial setting. Weighted back-projection can also be included when some regions are more likely subject to change, to improve stability. Building on a Cartesian grid reconstruction code, the feasibility of reusing the existing ray-tracers is checked against other researches in the same field.Comment: 13 pages, 13 figures. submitted to Journal Of Nondestructive Evaluation (https://www.springer.com/journal/10921

Improved success rate and stability for phase retrieval by including randomized overrelaxation in the hybrid input output algorithm

In this paper, we study the success rate of the reconstruction of objects of finite extent given the magnitude of its Fourier transform and its geometrical shape. We demonstrate that the commonly used combination of the hybrid input output and error reduction algorithm is significantly outperformed by an extension of this algorithm based on randomized overrelaxation. In most cases, this extension tremendously enhances the success rate of reconstructions for a fixed number of iterations as compared to reconstructions solely based on the traditional algorithm. The good scaling properties in terms of computational time and memory requirements of the original algorithm are not influenced by this extension.Comment: 14 pages, 8 figure

A Parallel Iterative Method for Computing Molecular Absorption Spectra

We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table