Focus on X-ray Beams with High Coherence

This editorial serves as the preface to a special issue of New Journal of Physics, which collects together solicited papers on a common subject, x-ray beams with high coherence. We summarize the issue's content, and explain why there is so much current interest both in the sources themselves and in the applications to the study of the structure of matter and its fluctuations (both spontaneous and driven). As this collection demonstrates, the field brings together accelerator physics in the design of new sources, particle physics in the design of detectors, and chemical and materials scientists who make use of the coherent beams produced. Focus on X-ray Beams with High Coherence Contents Femtosecond pulse x-ray imaging with a large field of view B Pfau, C M Günther, S Schaffert, R Mitzner, B Siemer, S Roling, H Zacharias, O Kutz, I Rudolph, R Treusch and S Eisebitt The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications E Allaria, C Callegari, D Cocco, W M Fawley, M Kiskinova, C Masciovecchio and F Parmigiani Beyond simple exponential correlation functions and equilibrium dynamics in x-ray photon correlation spectroscopy Anders Madsen, Robert L Leheny, Hongyu Guo, Michael Sprung and Orsolya Czakkel The Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS) Sébastien Boutet and Garth J Williams Dynamics and rheology under continuous shear flow studied by x-ray photon correlation spectroscopy Andrei Fluerasu, Pawel Kwasniewski, Chiara Caronna, Fanny Destremaut, Jean-Baptiste Salmon and Anders Madsen Exploration of crystal strains using coherent x-ray diffraction Wonsuk Cha, Sanghoon Song, Nak Cheon Jeong, Ross Harder, Kyung Byung Yoon, Ian K Robinson and Hyunjung Kim Coherence properties of the European XFEL G Geloni, E Saldin, L Samoylova, E Schneidmiller, H Sinn, Th Tschentscher and M Yurkov Fresnel coherent diffractive imaging: treatment and analysis of data G J Williams, H M Quiney, A G Peele and K A Nugent Imaging of complex density in silver nanocubes by coherent x-ray diffraction R Harder, M Liang, Y Sun, Y Xia and I K Robinson Methodology for studying strain inhomogeneities in polycrystalline thin films during in situ thermal loading using coherent x-ray diffraction N Vaxelaire, H Proudhon, S Labat, C Kirchlechner, J Keckes, V Jacques, S Ravy, S Forest and O Thomas Ptychographic coherent diffractive imaging of weakly scattering specimens Martin Dierolf, Pierre Thibault, Andreas Menzel, Cameron M Kewish, Konstantins Jefimovs, Ilme Schlichting, Konstanze von König, Oliver Bunk and Franz Pfeiffer Dose requirements for resolving a given feature in an object by coherent x-ray diffraction imaging Andreas Schropp and Christian G Schroer FLASH: new opportunities for (time-resolved) coherent imaging of nanostructures R Treusch and J Feldhaus Structure of a single particle from scattering by many particles randomly oriented about an axis: toward structure solution without crystallization? D K Saldin, V L Shneerson, M R Howells, S Marchesini, H N Chapman, M Bogan, D Shapiro, R A Kirian, U Weierstall, K E Schmidt and J C H Spence Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging V Favre-Nicolin, F Mastropietro, J Eymery, D Camacho, Y M Niquet, B M Borg, M E Messing, L-E Wernersson, R E Algra, E P A M Bakkers, T H Metzger, R Harder and I K Robinson Coherent science at the SwissFEL x-ray laser B D Patterson, R Abela, H-H Braun, U Flechsig, R Ganter, Y Kim, E Kirk, A Oppelt, M Pedrozzi, S Reiche, L Rivkin, Th Schmidt, B Schmitt, V N Strocov, S Tsujino and A F Wrulich Energy recovery linac (ERL) coherent hard x-ray sources Donald H Bilderback, Joel D Brock, Darren S Dale, Kenneth D Finkelstein, Mark A Pfeifer and Sol M Gruner Statistical and coherence properties of radiation from x-ray free-electron lasers E L Saldin, E A Schneidmiller and M V Yurkov Microscopic return point memory in Co/Pd multilayer films K A Seu, R Su, S Roy, D Parks, E Shipton, E E Fullerton and S D Kevan Holographic and diffractive x-ray imaging using waveguides as quasi-point sources K Giewekemeyer, H Neubauer, S Kalbfleisch, S P Krüger and T Salditt Mapping the conformations of biological assemblies P Schwander, R Fung, G N Phillips Jr and A Ourmazd Imaging the displacement field within epitaxial nanostructures by coherent diffraction: a feasibility study Ana Diaz, Virginie Chamard, Cristian Mocuta, Rogerio Magalhães-Paniago, Julian Stangl, Dina Carbone, Till H Metzger and Günther Bauer The potential for two-dimensional crystallography of membrane proteins at future x-ray free-electron laser sources Cameron M Kewish, Pierre Thibault, Oliver Bunk and Franz Pfeiffer Coherence properties of hard x-ray synchrotron sources and x-ray free-electron lasers I A Vartanyants and A Singer Coherent imaging of biological samples with femtosecond pulses at the free-electron laser FLASH A P Mancuso, Th Gorniak, F Staier, O M Yefanov, R Barth, C Christophis, B Reime, J Gulden, A Singer, M E Pettit, Th Nisius, Th Wilhein, C Gutt, G Grübel, N Guerassimova, R Treusch, J Feldhaus, S Eisebitt, E Weckert, M Grunze, A Rosenhahn and I A Vartanyants

traditional field of optics to the shorter wavelength range. This allows access to the nanometre and even the atomic length scale in many cases. The papers included here can generally be identified with one of three topics, 'sources', 'structure' and 'fluctuations', although there is considerable overlap between these.

Sources
Much of the excitement concerning 'coherence-based' experiments stems from the unprecedented properties of free-electron laser (FEL) sources. These Linac-based machines can produce ultrashort photon pulses of well below 100 femtoseconds' (fs) duration, while providing pulse intensities in excess of 10 12 photons pulse −1 . The corresponding peak brilliance of such a source thus supersedes modern third-generation synchrotron sources by 10 orders of magnitude. This is illustrated in figure 1. The number of photons per mode (usually referred to as the degeneracy parameter δ) can reach values of 10 9 or higher, thus underlining the laser-like nature of FEL radiation.
The coherence properties of FEL radiation can be described within the framework of statistical optics, with the help of field correlation functions. As shown by Saldin et al [11] and Geloni et al [21], the spectrum of self-amplified spontaneous emission (SASE)-type FELs may contain up to hundreds of spikes indicative of the limited temporal coherence of these machines. The coherence times are typically about 1 fs. The degree of transverse coherence is generally high, with values close to unity. The high gain of the amplification process, and the exceptionally bright electron beams, give rise to the exceptional peak brilliance and the degeneracy parameter of x-ray FELs. The first SASE-type FEL, in operation since 2005 in the vacuum ultraviolet (VUV) and soft x-ray regimes, is FLASH at DESY/Hamburg. An overview of coherence-based experiments carried out there is given by Treusch et al [12]. The linac coherent light source (LCLS) started user operation in 2009, producing for the first time 1.5 Å FEL radiation. In this issue, Boutet et al [19] describes the coherent x-ray imaging (CXI) instrument at the LCLS. Worldwide, there are quite a number of FEL projects in the planning, construction or commissioning phase, as summarized in table 1. Two FEL projects, the FERMI FEL at Elettra and the SwissFEL X-Ray Laser, and their related science programmes are described in more detail by Allaria et al [18] and Patterson et al, respectively.
Low repetition rate is a characteristic feature of FEL sources (120 Hz for LCLS or up to 30 000 pulses s −1 sorted into 10-30 macropulses for the European XFEL). This can be a disadvantage for certain classes of experiment, but will eventually be overcome by energyrecovery linac (ERL) machines. The Cornell project described by Bilderback et al [13] comprises a 5 GeV ERL with GHz repetition rates, typically 2 ps long pulses available simultaneously to all x-ray beamlines at the ERL. This will allow the whole portfolio of coherence-based techniques to be used.

Structure
Coherent x-ray diffraction (CXD) is the name given to the application of coherent x-ray beams when they are used to solve structure in the general sense. Traditionally, the field has been limited to crystal structure determination of the position of atoms within a unit cell, the basis of x-ray crystallography. The limitation to crystals was always attributed to the need to solve the 'phase problem', for which decades of progress has led to many elegant solutions.
Coherence offers a new general solution to the phase problem, which was first stated in a short paper by Sayre in 1952 [25], closely following the conclusions of Shannon in the field of communication theory [26]. Sayre pointed out that the continuous diffraction pattern from a non-crystallographic object was overdetermined, and so could be inverted to a structure. This result has been confirmed by subsequent mathematical analysis of the problem in a number of 4 different contexts. It was not well appreciated at the time that there was an implicit assumption of coherence behind these results. With hard x-rays, we had to wait until the turn of the 21st century for the first demonstration that the methods worked in practice [27]. The delay was partly due to the need to wait for the development of suitably bright x-ray sources to provide the necessary coherence.
Because CXD methods are distinguished from the crystallographic case by the need for a non-crystalline sample, there is a strong overlap with the fields of imaging, microscopy and holography. There is also a strong synergy with the current interest in nanotechnology. This comes about because nanoparticles are not really crystalline in the mathematical sense, but contain inherent strains associated with their facets, vertices and edges. Many of the useful applications of nanoparticles can be attributed to their structure in this way.
In this issue, there are three papers devoted to methodological developments of the experiments and algorithms needed to invert the diffraction patterns. There is a paper on Fresnel coherent diffractive imaging concerning the treatment and analysis of data by Williams et al [17], and one concerning the imaging of complex density in silver nanocubes by Harder et al [15]. A variation of a method called Ptychography [28] has been applied to coherent diffractive imaging of weakly scattering specimens by Dierolf et al [14]. Lastly, there is a paper on holographic and diffractive x-ray imaging using waveguides as quasi-point sources by Giewekemeyer et al [9].
There are several papers concerning the application of CXD methods to strain mapping. There is a general study of crystal strains using CXD with examples of zeolites by Cha et al [20]. There is also an analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging by Favre-Nicolin et al [10]; this paper illustrates the technological application of nanocrystals for the development of new semiconductor devices. Diaz et al [5] have carried out a feasibility study for imaging the displacement field within epitaxial nanostructures by coherent diffraction. Application to polycrystalline thin films is investigated by Vaxelaire et al [16] in a paper on the methodology for studying strain inhomogeneities during in situ thermal loading.
The appearance of x-ray free-electron lasers (XFELs) has led to exciting new developments such as the single-shot 'diffract and destroy' approach that promises to prevent radiation damage. The structure of a single particle from scattering by many particles, randomly oriented about an axis, is discussed by Saldin et al [6] because it promises a structure solution without crystallization. Coherent imaging of biological samples with femtosecond pulses at the FEL FLASH is presented by Mancuso et al [2]. The dose requirements for resolving a given feature in an object by CXD imaging is then addressed by Schropp et al [8]. These methods have quite promising applications in biology, such as the mapping of the conformations of biological assemblies by Schwander et al [4] and the potential for 2D crystallography of membrane proteins at future xFEL sources, which is discussed by Kewish et al [1].

Fluctuations
It was realized before the application of coherence for determining structure that the intensity at each point in a specked coherent diffraction pattern would change when the structure fluctuates. This allows a systematic measurement of the relaxation times of fluctuations as a function of their length scale. Photon correlation spectroscopy (PCS) [29] was well established using lasers 5 for this purpose long before x-ray beams with sufficient coherence came along. The advantage of using x-rays, of course, is that shorter distances can be probed, possibly reaching the atomic length scale.
In this issue, there is a paper about microscopic return point memory in magnetic Co/Pd multilayer films by Seu et al [24], where the need to invert the data to get real space images is avoided using a clever trick. In their paper, Madsen et al [22] take us beyond the commonly used simple exponential correlation functions in the study of equilibrium dynamics to explain the stretched behaviour that is sometimes seen. Looking to the future, the paper by Fluerasu et al [23] describes some of the advances that have been made with the development of the x-ray PCS technique at the new National Synchrotron Light Source II, where a dedicated XPCS beamline is under construction. This machine has the second-highest coherent x-ray flux of all the synchrotron sources that are planned worldwide. XPCS with a steady state source is sensitive to spontaneous fluctuations arising from thermal excitation. The pulsed XFEL sources described above will also encourage the development of new techniques for the study of the susceptibility of matter through its impulse response, which provides the same information in a complementary way.