The high intensity of free-electron X-ray light sources may enable structure determinations of viruses or even individual proteins without the encumbrance of first forming crystals. This note compares two schemes of non-crystalline diffraction data collection that have been proposed: serial single-shot data from individual particles, and averaged cross-correlation data from particle ensembles. The information content of these schemes is easily compared and we show that the single-shot approach, although experimentally more challenging, is always superior in this respect.

We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all the way to the sphere. Thus, we also connect the two well-studied problems of sphere packing and tetrahedron packing on a single axis. Our numerical results uncover a rich optimal-packing behavior, compared to that of other continuous families of particles previously studied.

Previous criteria for the feasibility of reconstructing phase information from intensity measurements, both in x-ray crystallography and more recently in coherent x-ray imaging, have been based on the Maxwell constraint counting principle. We propose a new criterion, based on Shannon's utual information, that is better suited for noisy data or contrast that has strong priors not well modeled by continuous variables.

We study, using simulated experiments inspired by thin-film magnetic domain patterns, the feasibility of phase retrieval in x-ray diffractive imaging in the presence of intrinsic charge scattering given only photon-shot-noise limited diffraction data. We detail a reconstruction algorithm to recover the sample's magnetization distribution under such conditions and compare its performance with that of Fourier transform holography.

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting de novo (from-scratch) searches for dense packings becomes crucial. In this paper, we use the divide and concur framework to develop a general search method for the solution of periodic constraint problems, and we apply it to the discovery of dense periodic packings.

The problem of optimizing antenna locations in a radio telescope with a large number of antennas is addressed. An algorithm is developed that first optimizes the probability density function of the antenna positions and this distribution is subsequently sampled. This approach avoids the large number of variables with many antennas. The density function is optimized subject to terrain constraints and the distribution of visibility samples. The optimization is solved by mapping the problem to a phase retrieval problem which is solved using an iterative projection algorithm. © 2010 IEEE.

We present a one-parameter family of periodic packings of regular tetrahedra, with the packing fraction 100/117≈0.8547, that are simple in the sense that they are transitive and their repeating units involve only four tetrahedra. The construction of the packings was inspired from results of a numerical search that yielded a similar packing. We present an analytic construction of the packings and a description of their properties. We also present a transitive packing with a repeating unit of two tetrahedra and a packing fraction. © 2010 Springer Science+Business Media, LLC.

X-ray diffraction phenomena have been used for decades to study matter at the nanometer and subnanometer scales. X-ray diffraction microscopy uses the far-field scattering of coherent X-rays to form the 2D or 3D image of a scattering object in a way that resembles crystallography. In this review, we describe the main principles, benefits, and limitations of diffraction microscopy. After sampling some of the milestones of this young technique and its close variants, we conclude with a short assessment of the current state of the field. Copyright © 2010 by Annual Reviews.

We reconstructed the 3D Fourier intensity distribution of monodisperse prolate nanoparticles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast x-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the expansion-maximization-compression framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter.