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Phase recovery is a well-known inverse problem prevalent across science disciplines and attracts active research interests to develop a number of theoretical and experimental methods. Recent developments in artificial intelligence have further prompted research activities in processing the experimentally collected imperfect data, but applications have been limited to slow-varying data such as real images. Experimental noise present in largely fluctuating diffraction data, in particular, adds practical challenges to hamper consistent phase recovery. Here, we introduce a convolutional neural-network assisted $k$-space denoising method that can directly manage noisy diffraction signals. It showed superior performance on denoising the diffraction data, which promote improved phase recovery from noise-buried single-pulse diffraction signals obtained by the x-ray free-electron laser. Adapting our method to general diffraction data can expand boundaries of interpretable data and enhance observability of faint objects with weak signals.

DNA molecules are atomic-scale information storage molecules that promote reliable information transfer via fault-free repetitions of replications and transcriptions. Remarkable accuracy of compacting a few-meters-long DNA into a micrometer-scale object, and the reverse, makes the chromosome one of the most intriguing structures from both physical and biological viewpoints. However, its three-dimensional (3D) structure remains elusive with challenges in observing native structures of specimens at tens-of-nanometers resolution. Here, using cryogenic coherent X-ray diffraction imaging, we succeeded in obtaining nanoscale 3D structures of metaphase chromosomes that exhibited a random distribution of electron density without characteristics of high-order folding structures. Scaling analysis of the chromosomes, compared with a model structure having the same density profile as the experimental results, has discovered the fractal nature of density distributions. Quantitative 3D density maps, corroborated by molecular dynamics simulations, reveal that internal structures of chromosomes conform to diffusion-limited aggregation behavior, which indicates that 3D chromatin packing occurs via stochastic processes.

With each single X-ray pulse having its own characteristics, understanding the individual property of each X-ray free-electron laser (XFEL) pulse is essential for its applications in probing and manipulating specimens as well as in diagnosing the lasing performance. Intensive research using XFEL radiation over the last several years has introduced techniques to characterize the femtosecond XFEL pulses, but a simple characterization scheme, while not requiring ad hoc assumptions, to address multiple aspects of XFEL radiation via a single data collection process is scant. Here, it is shown that single-particle diffraction patterns collected using single XFEL pulses can provide information about the incident photon flux and coherence property simultaneously, and the X-ray beam profile is inferred. The proposed scheme is highly adaptable to most experimental configurations, and will become an essential approach to understanding single X-ray pulses.

Three-dimensional structures of Ni nanoparticles undergoing significant morphological changes on oxidation were observed non-destructively using coherent X-ray diffraction imaging. The Ni particles were oxidized into Ni1O1 while forming pores of various sizes internally. For each Ni nanoparticle, one large void was identified at a lower corner near the interface with the substrate. The porosity of the internal region of the agglomerated Ni oxide was about 38.4%. Regions of high NiO density were mostly observed at the outer crust of the oxide or at the boundary with the large voids. This research expands our understanding of general catalytic reactions with direct observation of oxidation-induced nanoscale morphological changes.

Interest in atomic scale structures of individual specimens has invigorated developments of high-resolution probes, which include single-particle imaging using x-ray free-electron lasers (XFELs). The demonstrated spatial resolution, however, remains at tens of nanometers with difficulty in collecting diffraction signals at high frequency distinguished from noises. As such, various resolution-enhancement methods have been introduced, but few experimental verifications are available. Here, by carrying out XFEL single-pulse diffraction experiments, we explicitly unveil the dependence of SNRs on incident x-ray flux, data averaging, or multiparticle interference. We further propose a data-accumulation method of resolution-shell averaging as a robust scheme to improve the SNR. This study establishes a roadmap with which high-resolution XFEL single-pulse experiments can be contrived.

Unraveling nanoscale spin structures has long been an important activity addressing various scientific interests, that are also readily adaptable to technological applications. This has invigorated the development of versatile nanoprobes suitable for imaging specimens under native conditions. Here we have demonstrated the resonant coherent diffraction of an artificial quasicrystal magnet with circularly polarized X-rays. The nanoscale magnetic structure was revealed from X-ray speckle patterns by comparing with micromagnetic simulations, as a step toward understanding the intricate relationship between the chemical and spin structures in an aperiodic quasicrystal lattice. Femtosecond X-ray pulses from free electron lasers are expected to immediately extend the current work to nanoscale structure investigations of ultrafast spin dynamics, surpassing the present spatio-temporal resolution.