Polarization-sensitive coherent diffractive imaging using HHG

High harmonic generation (HHG) from lasers have attractive properties for probing ultrafast dynamics at the nanoscale. The spectral range of high harmonics at the extreme-UV and soft-X-rays (λ∼ 100 nm–1 nm, ℏω∼ 10 eV–1 keV) enables element specificity, the short wavelengths combined with high spatial coherence allows for imaging with nanometric spatial resolution, the extremely short pulse durations provide access to dynamics faster than a femtosecond (1 fs=10−15 s), and all that, on a compact system. In this chapter, we focus on experimental aspects of imaging with high harmonics. First, we present the experimental system and the image reconstruction procedure. Second, we show experimental results from the various configurations that were used throughout this project. Finally, we discuss mechanisms that played an important role in this imaging effort, and would contribute to the advancement of nanoscale imaging

Tomography of a Cryo-immobilized Yeast Cell Using Ptychographic Coherent X-Ray Diffractive Imaging

The structural investigation of noncrystalline, soft biological matter using x-rays is of rapidly increasing interest. Large-scale x-ray sources, such as synchrotrons and x-ray free electron lasers, are becoming ever brighter and make the study of such weakly scattering materials more feasible. Variants of coherent diffractive imaging (CDI) are particularly attractive, as the absence of an objective lens between sample and detector ensures that no x-ray photons scattered by a sample are lost in a limited-efficiency imaging system. Furthermore, the reconstructed complex image contains quantitative density information, most directly accessible through its phase, which is proportional to the projected electron density of the sample. If applied in three dimensions, CDI can thus recover the sample's electron density distribution. As the extension to three dimensions is accompanied by a considerable dose applied to the sample, cryogenic cooling is necessary to optimize the structural preservation of a unique sample in the beam. This, however, imposes considerable technical challenges on the experimental realization. Here, we show a route toward the solution of these challenges using ptychographic CDI (PCDI), a scanning variant of coherent imaging. We present an experimental demonstration of the combination of three-dimensional structure determination through PCDI with a cryogenically cooled biological sample—a budding yeast cell (Saccharomyces cerevisiae)—using hard (7.9 keV) synchrotron x-rays. This proof-of-principle demonstration in particular illustrates the potential of PCDI for highly sensitive, quantitative three-dimensional density determination of cryogenically cooled, hydrated, and unstained biological matter and paves the way to future studies of unique, nonreproducible biological cells at higher resolution

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

Multi-slice ptychographic tomography

Ptychography is a form of Coherent Diffractive Imaging, where diffraction patterns are processed by iterative algorithms to recover an image of a specimen. Although mostly applied in two dimensions, ptychography can be extended to produce three dimensional images in two ways: via multi-slice ptychography or ptychographic tomography. Ptychographic tomography relies on 2D ptychography to supply projections to conventional tomographic algorithms, whilst multi-slice ptychography uses the redundancy in ptychographic data to split the reconstruction into a series of axial slices. Whilst multi-slice ptychography can handle multiple-scattering thick specimens and has a much smaller data requirement than ptychographic tomography, its depth resolution is relatively poor. Here we propose an imaging modality that combines the benefits of the two approaches, enabling isotropic 3D resolution imaging of thick specimens with a small number of angular measurements. Optical experiments validate our proposed method

Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging

Diffractive imaging, in which image-forming optics are replaced by an inverse computation using scattered intensity data, could, in principle, realize wavelength-scale resolution in a transmission electron microscope. However, to date all implementations of this approach have suffered from various experimental restrictions. Here we demonstrate a form of diffractive imaging that unshackles the image formation process from the constraints of electron optics, improving resolution over that of the lens used by a factor of five and showing for the first time that it is possible to recover the complex exit wave (in modulus and phase) at atomic resolution, over an unlimited field of view, using low-energy (30 keV) electrons. Our method, called electron ptychography, has no fundamental experimental boundaries: further development of this proof-of-principle could revolutionize sub-atomic scale transmission imaging

3D diffractive imaging of nanoparticle ensembles using an X-ray laser

We report the 3D structure determination of gold nanoparticles (AuNPs) by X-ray single particle imaging (SPI). Around 10 million diffraction patterns from gold nanoparticles were measured in less than 100 hours of beam time, more than 100 times the amount of data in any single prior SPI experiment, using the new capabilities of the European X-ray free electron laser which allow measurements of 1500 frames per second. A classification and structural sorting method was developed to disentangle the heterogeneity of the particles and to obtain a resolution of better than 3 nm. With these new experimental and analytical developments, we have entered a new era for the SPI method and the path towards close-to-atomic resolution imaging of biomolecules is apparent

Megahertz single-particle imaging at the European XFEL

The emergence of high repetition-rate X-ray free-electron lasers (XFELs) powered by superconducting accelerator technology enables the measurement of significantly more experimental data per day than was previously possible. The European XFEL is expected to provide 27,000 pulses per second, over two orders of magnitude more than any other XFEL. The increased pulse rate is a key enabling factor for single-particle X-ray diffractive imaging, which relies on averaging the weak diffraction signal from single biological particles. Taking full advantage of this new capability requires that all experimental steps, from sample preparation and delivery to the acquisition of diffraction patterns, are compatible with the increased pulse repetition rate. Here, we show that single-particle imaging can be performed using X-ray pulses at megahertz repetition rates. The results obtained pave the way towards exploiting high repetition-rate X-ray free-electron lasers for single-particle imaging at their full repetition rate.We acknowledge European XFEL in Schenefeld, Germany, for provision of X-ray free-electron laser beamtime at Scientific Instrument SPB/SFX and would like to thank the instrument group and facility staff for their assistance. We acknowledge the use of the XBI biological sample preparation laboratory, enabled by the XBI User Consortium. The results of the work were obtained using Maxwell computational resources operated at Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany, and computational resources of MCC NRC “Kurchatov Institute.” This research used resources of the National Synchrotron Light Source II, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704. We acknowledge the support of funding from: the Swedish Foundation for International Cooperation in Research and Higher Education (STINT); Helmholtz Associations Initiative and Networking Fund and the Russian Science Foundation grant HRSF-0002/18-41-0600; the Russian Science Foundation grant 18-14-00321; European Research Council, “Frontiers in Attosecond X-ray Science: Imaging and Spectroscopy (AXSIS),” ERC-2013-SyG 609920; Fellowship from the Joachim Herz Stiftung; Singapore National Research Foundation Grant number NRF-CRP16-2015-05; Ministry of Education, Science, Research and Sport of the Slovak Republic and by grant APVV-18-0104; the project CZ.02.1.01/0.0/0.0/16_019/0000789 (ADONIS) from European Regional Development Fund, Chalmers Area of Advance; Material Science and the Ministry of Education, Youth and Sports as part of targeted support from the National Programme of Sustainability II; US National Science Foundation (NSF) Science and Technology Center BioXFEL Award 1231306; Helmholtz Initiative and Networking Fund through the Young Investigators Group Program and Deutsche Forschungsgemeinschaft, project B03/SFB755; VR starting grant (2018-03387); FORMAS future research leader (2018-00421); KVA Biosciences 2018 (BS2018-0053); NSF 1231306; German Ministry for Education and Research, BMBF (grant No. 05K2016—Visavix); the Heinrich Pette Institute, Leibniz Institute for Experimental Virology is supported by the Free and Hanseatic City of Hamburg and the Federal Ministry of Health; NSF STC BioXFEL grant 1231306; The National Research Foundation (NRF) of Korea (Grant No. 2017K1A3A7A09016380); the Röntgen-Ångström Cluster; the Swedish Research Council; the Swedish Foundation for Strategic Research. We thank Arwen Pearson for critical reading of the manuscript. Open access funding provided by Uppsala University