Three-dimensional coordinates of individual atoms in materials revealed by electron tomography

Crystallography, the primary method for determining the three-dimensional (3D) atomic positions in crystals, has been fundamental to the development of many fields of science. However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal. Here, we report, for the first time, the determination of the 3D coordinates of thousands of individual atoms and a point defect in a material by electron tomography with a precision of ~19 picometers, where the crystallinity of the material is not assumed. From the coordinates of these individual atoms, we measure the atomic displacement field and the full strain tensor with a 3D resolution of ~1nm^3 and a precision of ~10^-3, which are further verified by density functional theory calculations and molecular dynamics simulations. The ability to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity is expected to find important applications in materials science, nanoscience, physics and chemistry.

Reply to Local Filtering Fundamentally Against Wide Spectrum

After carefully studying the comment by Wang et al. (arXiv:1408.6420), we found it includes several mistakes and unjustified statements and Wang et al. lack very basic knowledge of dislocations. Moreover, there is clear evidence indicating that Wang et al. significantly misrepresented our method and claimed something that they actually did not implement.

Three-dimensional coherent X-ray diffraction imaging of a whole, frozen-hydrated cell

A structural understanding of whole cells in three dimensions at high spatial resolution remains a significant challenge and, in the case of X-rays, has been limited by radiation damage. By alleviating this limitation, cryogenic coherent diffraction imaging (cryo-CDI) could bridge the important resolution gap between optical and electron microscopy in bio-imaging. Here, we report for the first time 3D cryo-CDI of a whole, frozen-hydrated cell - in this case a Neospora caninum tachyzoite - using 8 keV X-rays. Our 3D reconstruction reveals the surface and internal morphology of the cell, including its complex, polarized sub-cellular architecture with a 3D resolution of ~75-100 nm, which is presently limited by the coherent X-ray flux and detector size. Given the imminent improvement in the coherent X-ray flux at the facilities worldwide, our work forecasts the possibility of routine 3D imaging of frozen-hydrated cells with spatial resolutions in the tens of nanometres.

Multi-Shell Ankylography

Three-dimensional (3D) imaging techniques appeal to a broad range of scientific and industrial applications. Typically, projection slice theorem enables multiple two-dimensional (2D) projections of an object to be combined in the Fourier domain to yield a 3D image. However, traditional techniques require a significant number of projections. The significant number of views required in conventional tomography not only complicates such imaging modalities, but also limits their ability to image samples that are sensitive to radiation dose or are otherwise unstable in time. In this work, we demonstrate through numerical simulations and an eigenvalue analysis that a recently developed technique called ankylography enables 3D image reconstruction using much fewer views than conventional tomography. Such a technique with the ability to obtain the 3D structure information from a few views is expected to find applications in both optical and x-ray imaging fields.

Oversampling smoothness (OSS): an effective algorithm for phase retrieval of noisy diffraction intensities

Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free electron lasers, high harmonic generation, soft X-ray laser and electrons. Despite these rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here we present an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stage of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both our numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. We expect OSS to find application in the rapidly growing CDI field as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed.

Potential and Challenge of Ankylography

The concept of ankylography, which under certain circumstances enables 3D structure determination from a single view [1], had ignited a lively debate even before its publication [2,3]. Since then, a number of readers requested the ankylographic reconstruction codes from us. To facilitate a better understanding of ankylography, we posted the source codes of the ankylographic reconstruction on a public website and encouraged interested readers to download the codes and test the method [4]. Those who have tested our codes confirm that the principle of ankylography works. Furthermore, our mathematical analysis and numerical simulations suggest that, for a continuous object with array size of 14x14x14 voxels, its 3D structure can usually be reconstructed from the diffraction intensities sampled on a spherical shell of 1 voxel thick [4]. In some cases where the object does not have very dense structure, ankylography can be applied to reconstruct its 3D image with array size of 25x25x25 voxels [4]. What remains to be elucidated is how to extend ankylography to the reconstruction of larger objects, and what further theoretical, experimental and algorithm developments will be necessary to make ankylography a practical and useful imaging tool. Here we present our up-to-date understanding of the potential and challenge of ankylography. Further, we clarify some misconceptions on ankylography, and respond to technical comments raised by Wei [5] and Wang et al. [6] Finally, it is worthwhile to point out that the potential for recovering 3D information from the Fourier coefficients within a spherical shell may also find application in other fields.