Coherent hard x-ray beams with a flux exceeding 109 photons/second with a bandwidth of 0.1% will be provided by the undulator at the third generation synchrotron radiation sources such as APS, ESRF, and Spring-8. The availability of such high flux coherent x-ray beams offers excellent opportunities for extending the coherence-based techniques developed in the visible and soft x-ray part of the electromagnetic spectrum to the hard x-rays. These x-ray techniques (e.g., diffraction limited microfocusing, holography, interferometry, phase contrast imaging and signal enhancement), may offer substantial advantages over non-coherence-based x-ray techniques currently used. For example, the signal enhancement technique may be used to enhance an anomalous x-ray or magnetic x-ray scattering signal by several orders of magnitude. Coherent x-rays can be focused to a very small (diffraction-limited) spot size, thus allowing high spatial resolution microprobes to be constructed. The paper will discuss the feasibility of the extension of some coherence-based techniques to the hard x-ray range and the significant progress that has been made in the development of diffraction-limited focusing optics. Specific experimental results for a transmission Fresnel phase zone plate that can focus 8.2 keV x-rays to a spot size of about 2 microns will be briefly discussed. The comparison of measured focusing efficiency of the zone plate with that calculated will be made. Some specific applications of zone plates as coherent x-ray optics will be discussed. 17 refs., 4 figs.

X-ray microscopy is used to study the structure, dynamics and bulk properties of matter with high spatial resolutions. It is widely applied, from physics and chemistry to material and life sciences. In the past two decades, progress in X-ray microscopy was driven either by improvements in X-ray optics or by improvements in the image reconstruction by using algorithms as computational lenses. In this work both approaches are combined to exploit the advantages of X-ray imaging with a large numerical aperture and the advantages of coherent image reconstruction. It is shown that a combined X-ray microscope using both, advanced optics and algorithms, is neither limited by flawed optics nor by constraints imposed by reconstruction algorithms, which enables to go beyond current limits in resolution and applications. The thesis is structured in four parts. In the first part hard X-ray lenses, so called multilayer zone plates, are simulated to investigate volume diffraction effects within the multilayer structure, and to study the potential for smaller focus sizes and higher efficiencies. In the second part, the multilayer zone plates are characterized and implemented in an X-ray microscope. In the third part, a new imaging scheme is presented, which combines in-line holography and coherent diffractive imaging. This method overcomes the current resolution limit of in-line holography and can achieve super-resolution with respect to the numerical aperture of the illuminating beam. Finally, in the fourth part a multilayer zone plate is used as an objective lens with a known transfer function in a novel coherent full-field imaging experiment based on iterative phase retrieval, for high resolution and quantitative contrast.

The field of x-ray optics struggles to develop optical systems with the versatility and sophistication of their visible light counterparts. The advent of fourth-generation light sources will make the struggle even more difficult. Fourth-generation light sources include laser/plasma sources, x-ray Free Electron Lasers (FEL), inverse Compton scattering sources, and the National Ignition Facility. LCLS, (Linac Coherent Light Source), and its European cousin, will be the first of the x-ray FELs. The LCLS, to be built at the Stanford Linear Accelerator Center (SLAC), takes advantage of the existing SLAC linear accelerator to send intense, low emittance electron bunches through a 100 m long undulator structure. Through a process called SASE (Self Amplification of Spontaneous Emission) the electrons interact with the radiation fields they produce while in the undulator causing them to collect into micro bunches that emit coherent light. In the case of the LCLS the coherent radiation will have a wavelength in the x-ray regime, and will be tunable from 1.5 to 15 Å. The LCLS will deliver x-rays in individual coherent packages lasting

Hardly any other discovery of the nineteenth century did have such an impact on science and technology as Wilhelm Conrad Röntgen’s seminal find of the X-rays. X-ray tubes soon made their way as excellent instruments for numerous applications in medicine, biology, materials science and testing, chemistry and public security. Developing new radiation sources with higher brilliance and much extended spectral range resulted in stunning developments like the electron synchrotron and electron storage ring and the freeelectron laser. This handbook highlights these developments in fifty chapters. The reader is given not only an inside view of exciting science areas but also of design concepts for the most advanced light sources. The theory of synchrotron radiation and of the freeelectron laser, design examples and the technology basis are presented. The handbook presents advanced concepts like seeding and harmonic generation, the booming field of Terahertz radiation sources and upcoming brilliant light sources driven by laser-plasma accelerators. The applications of the most advanced light sources and the advent of nanobeams and fully coherent x-rays allow experiments from which scientists in the past could not even dream. Examples are the diffraction with nanometer resolution, imaging with a full 3D reconstruction of the object from a diffraction pattern, measuring the disorder in liquids with high spatial and temporal resolution. The 20th century was dedicated to the development and improvement of synchrotron light sources with an ever ongoing increase of brilliance. With ultrahigh brilliance sources, the 21st century will be the century of x-ray lasers and their applications. Thus, we are already close to the dream of condensed matter and biophysics: imaging single (macro)molecules and measuring their dynamics on the femtosecond timescale to produce movies with atomic resolution.

This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.

"Advancement and research on phase retrieval techniques are in large part motivated by their application in high resolution lensless laser imaging and x- ray diffractive imaging. In the former a high resolution image can be obtained from measuring the intensity pattern of the propagated field without the use of any imaging optics, thus providing an imaging system that does not increase its thickness along the optical axis as the aperture diameter is increased. For x- ray coherent diffractive imaging, on the other hand, high-resolution conventional imaging is difficult to achieve at these wavelengths because of the difficulty of manufacturing and aligning x-ray focusing elements with sufficient numerical aperture and precision. Thus, in order to achieve resolutions on the order of a nanometer, a coherent x-ray beam is used to illuminate the object of interest and the object is reconstructed from a measurement of its far-field diffraction intensity without any imaging optics. Thus the advancement and application of lensless imaging techniques has become an increasingly important topic of research. X-ray diffractive imaging is set apart from other high-resolution imaging techniques (e.g. scanning electron or atomic force microscopy) for its high penetration depth, which enables tomographic 3D imaging of thick samples and buried structures. Furthermore, using short x-ray pulses, it enables the capability to take ultrafast snapshots, giving a unique opportunity to probe nanoscale dynamics at femtosecond time scales. In this thesis we present improvements to phase retrieval algorithms, assess their performance through numerical simulations, and develop new methods for both imaging and wavefront measurement. Using numerical simulations we identified and explained the origin of the twin-image problem in iterative transform phase retrieval with a centrosymmetric support constraint. We proposed and numerically demonstrated the effectiveness of a modified phase retrieval algorithm that uses Fourier weighted projections to increase the quality and resolution of the reconstructions by mitigating a problem arising from the finite measurement window and finite support constraint. Such an approach is particularly useful when the object presents large phase variations on a length- scale significantly smaller than the resolution, i.e. reconstruction of fully developed speckled images. In order to accurately and efficiently assess phase retrieval algorithm performance, we have developed algorithms for subpixel image registration. Despite being particularly well suited for comparing images from data collected in the Fourier domain (e.g., phase retrieval and holography), these algorithms have al- ready shown a substantial success in other applications as well. Building on the original work by Faulkner and Rodenburg, we developed an improved reconstruction algorithm for phase retrieval with transverse translations of the object relative to the illumination beam. Based on gradient-based non- linear optimization, this algorithm is capable of estimating the object, and at the same time refining the initial knowledge of the incident illumination and the object translations. The advantages of this algorithm over the original iterative transform approach are shown through numerical simulations. Phase retrieval has already shown substantial success in wavefront sensing at optical wavelengths. Although in principle the algorithms can be used at any wavelength, in practice the focus-diversity mechanism that makes optical phase retrieval robust is not practical to implement for x-rays. In this thesis we also describe the novel application of phase retrieval with transverse translations to the problem of x-ray wavefront sensing. This approach allows the characterization of the complex-valued x-ray field in-situ and at-wavelength and has several practical and algorithmic advantages over conventional focused beam measurement techniques. A few of these advantages include improved robustness through diverse measurements, reconstruction from far-field intensity measurements only, and significant relaxation of experimental requirements over other beam characterization approaches. Furthermore, we show that a one-dimensional version of this technique can be used to characterize an x-ray line focus produced by a cylindrical focusing element. We provide experimental demonstrations of the latter at hard x-ray wavelengths, where we have characterized the beams focused by a kinoform lens and an elliptical mirror. In both experiments the reconstructions exhibited good agreement with independent measurements, and in the latter a small mirror misalignment was inferred from the phase retrieval reconstruction. These experiments pave the way for the application of robust phase retrieval algorithms for in-situ alignment and performance characterization of x-ray optics for nanofocusing. We also present a study on how transverse translations help with the well-known uniqueness problem of one-dimensional phase retrieval. We also present a novel method for x-ray holography that is capable of reconstructing an image using an off-axis extended reference in a non-iterative computation, greatly generalizing an earlier approach by Podorov et.al. The approach, based on the numerical application of derivatives on the field autocorrelation, was developed from first mathematical principles. We conducted a thorough theoret- ical study to develop technical and intuitive understanding of this technique and derived sufficient separation conditions required for an artifact-free reconstruction. We studied the effects of missing information in the Fourier domain, and of an im- perfect reference, and we provide a signal-to-noise ratio comparison with the more traditional approach of Fourier transform holography. We demonstrated this new holographic approach through proof-of-principle optical experiments and later ex- perimentally at soft x-ray wavelengths, where we compared its performance to Fourier transform holography, iterative phase retrieval and state-of-the-art zone-plate x-ray imaging techniques (scanning and full-field). Finally, we present a demonstration of the technique using a single 20 fs pulse from a high-harmonic table-top source. Holography with an extended reference is shown to provide fast, good quality images that are robust to noise and artifacts that arise from missing information due to a beam stop."--Leaves viii-xi.

In this book, Carolyn A. MacDonald provides a comprehensive introduction to the physics of a wide range of x-ray applications, optics, and analysis tools. Theory is applied to practical considerations of optics and applications ranging from astronomy to medical imaging and materials analysis. Emphasizing common physical concepts that underpin diverse phenomena and applications of x-ray physics, the book opens with a look at nuclear medicine, motivating further investigations into scattering, detection, and noise statistics. The second section explores topics in x-ray generation, including characteristic emission, x-ray fluorescence analysis, bremsstrahlung emission, and synchrotron and laser sources. The third section details the main forms of interaction, including the physics of photoelectric absorption, coherent and Compton scattering, diffraction, and refractive, reflective, and diffractive optics. Applications in this section include x-ray spectroscopy, crystallography, and dose and contrast in radiography. A bibliography is included at the end of every chapter, and solutions to chapter problems are provided in the appendix. Based on a course for advanced undergraduates and graduate students in physics and related sciences and also intended for researchers, An Introduction to X-Ray Physics, Optics, and Applications offers a thorough survey of the physics of x-ray generation and of interaction with materials. Common aspects of diverse phenomena emphasized Theoretical development tied to practical applications Suitable for advanced undergraduate and graduate students in physics or related sciences, as well as researchers Examples and problems include applications drawn from medicine, astronomy, and materials analysis Detailed solutions are provided for all examples and problems