The linac coherent light source single particle imaging road map.

Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.

Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns.

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. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.

Searching with iterated maps.

In many problems that require extensive searching, the solution can be described as satisfying two competing constraints, where satisfying each independently does not pose a challenge. As an alternative to tree-based and stochastic searching, for these problems we propose using an iterated map built from the projections to the two constraint sets. Algorithms of this kind have been the method of choice in a large variety of signal-processing applications; we show here that the scope of these algorithms is surprisingly broad, with applications as diverse as protein folding and Sudoku.

Solving the crystallographic phase problem in i(AlPdMn).

We apply a new technique for ab initio phase determination [Acta Crystallogr. Sect. A 55, 48 (1999)] to solve for the average structure of the icosahedral ( i) phase of AlPdMn. After an introduction to the crystallographic phase problem and a description of the method, we present a brief report of our findings for the structure of i(AlPdMn). Despite the use of data from extremely high quality samples, we find strong evidence of disorder in the structure, lending support to the random tiling model of quasicrystal stabilization.

X-ray phase determination by the principle of minimum charge.

When the electron density in a crystal or a quasicrystal is reconstructed from its Fourier modes, the global minimum value of the density is sensitively dependent on the relative phases of the modes. The set of phases that maximizes the value of the global minimum corresponds, by positivity of the density, to the density having the minimum total charge that is consistent with the measured Fourier amplitudes. Phases that minimize the total electronic charge (i.e. the average electron density) have the additional property that the lowest minima of the electron density become exactly degenerate and proliferate within the unit cell. The large number of degenerate minima have the effect that density maxima are forced to occupy ever smaller regions of the unit cell. Thus, by minimization of the electronic charge, the atomicity of the electron density is enhanced as well. Charge minimization applied to simulated crystalline and quasicrystalline diffraction data successfully reproduces the correct phases starting from random initial phases.