This master´s thesis provides basic properties and measurement of optical beams. In the first chapter is shown division of light on ray, wave and beam optics. Atmospheric optics and properties associated with propagation of light through the earth's atmosphere is presented in the second chapter. In the third part are shown basic techniques for Gaussian beam shaping. The last chapter deals with measurement of optical beam after propagating through a turbulent medium. In this section is shown distribution of relative variance of optical intensity in Gaussian and Top-Hat beam. There is also measured spatial coherence of laser beam in the turbulent atmospheric transmission media. Finally effect of the beam wander is investigated.

Le sujet de cette thèse est l'interférométrie X à réseaux: une technique d’imagerie développée pour la première fois il y a quelques années et qui donne des images de phase et de diffusion (small angle X-ray scattering) de haute sensibilité. Cette technique a un potentiel considérable pour la visualisation du structures qui absorbent faiblement les rayons X, et pour la détection de détails plus petits que la résolution du détecteur, par exemple les fissures et les fibres. Des structures de ce type ne peuvent pas être visualisées avec l’imagerie conventionnelle à rayons X en absorption. Dans le cadre des travaux sur cette thèse, un interféromètre à réseau à rayons X pour radiographie et tomographie multimodale a été installé à la ligne de lumière ID19 de l‘European Synchrotron Radiation Facility à Grenoble, France. L’excellente performance de cet instrument a été démontrée sur une grande variété d'échantillons de tissus biologiques mous, sur des échantillons paléontologiques, et sur des tissus osseux. Une autre partie des ce travail porte sur des améliorations de la technique d’imagerie elle-même. La première des ces améliorations consiste en un développement de méthodes avancées pour la tomographie avec réseaux. Ces méthodes peuvent réduire considérablement la dose livrée à l’échantillon durant les mesures nécessaires pour la reconstruction tomographique tout en préservant la qualité d’image. Un autre résultat majeur dans le cadre de ce travail est la conception, la mise en oeuvre et la démonstration d’un interféromètre à réseau à deux dimensions (2D). Cet appareil utilise des réseaux bidimentionnels au lieu de réseaux linéaires. L’interféromètre 2D produit des cartes d'angles de réfraction et des images de type champ sombre dans plusieurs directions du plan d’image et améliore considérablement la qualité des radiographies à réseau. Le champ d’application de l’interféromètre 2D n’est pas limité à l'imagerie par rayons X, puisque le nouveau dispositif peut aussi être particulièrement utile pour la caractérisation de composantes optiques de haute précision, tel que démontré par des expériences de métrologie à la longueur d'onde d'utilisationsur des lentilles réfractives pour rayons X. / The subject of this thesis is X-ray grating interferometry: an imaging technique first demonstrated a few years ago, which yields high-sensitivity phase and dark-field (small angle X-ray scattering) images of the investigated specimen. It bears tremendous potential for the visualization of low-absorbing features, and for the detection of details smaller than the resolution of the imaging system, such as cracks and fibers. Structures of this type cannot be visualized with conventional absorption X-ray imaging. As a part of this thesis work, an X-ray grating interferometer for multimodal radiography and tomography was installed at the beamline ID19 of the European Synchrotron Radiation Facility in Grenoble, France. The excellent performance of this instrument has been demonstrated on a large variety of soft-tissue biological samples, on paleontological specimens, and on osseous tissues. Another part of the present work concerns improvements of the imaging technique itself. The first of these improvements consists in the development of advanced schemes for grating-based tomography. These schemes can substantially reduce the dose delivered to the sample during a grating-based tomography scan, while preserving the image quality. Another major achievement of this thesis is the design, implementation and demonstration of a two-dimensional (2D) grating interferometer. This device uses gratings structured in two dimensions rather than line gratings. The 2D interferometer gives refraction angle and dark-field signals in multiple directions of the image plane and significantly improves the quality of the grating-based radiographies. The application range of the 2D interferometer is not restricted to X-ray imaging; the new device may also be particularly useful for high-precision optics characterization, as is shown by in-situ at-wavelength investigations of X-ray refractive lenses.

Deposition of nanoscale thickness films is ubiquitous in micro- and nano-scale device manufacturing. Current techniques such as spin-coating and chemical vapor deposition are designed to create only uniform thin films, and can be wasteful in material consumption. They lack the ability to adaptively prescribe desired film thickness profiles. This dissertation presents a novel inkjet-based zero-waste polymer deposition process referred to as Jet and Coat of Adaptive Sustainable Thin Films or J-CAST. The core of this process is built on an experimentally validated multi-scale fluid evolution model, based on extensions of lubrication theory. This model involves a nano-scale fluid film sandwiched between two flat plates: a compliant superstrate and a rigid substrate, with spatial topography on both surfaces. Accounting for the flexural elasticity of the compliant superstrate, and describing the temporal evolution of the fluid film in the presence of different boundary conditions reveals that instead of seeking process equilibrium, non-equilibrium transients should be exploited to guide film deposition. This forms the first core concept behind the process. This concept also enables robust full-wafer processes for creation of uniform films as well as nanoscale films with prescribed variation of thickness at mm-scale spatial wavelengths. The use of inkjets enables zero-waste adaptive material deposition with the preferred drop volumes and locations obtained from an inverse optimization formulation. This forms the second core concept behind the process. The optimization is based on the prescribed film thickness profile and typically involves >100,000 integer parameters. Using simplifying approximations for the same, three specific applications have been discussed - gradient surfaces in combinatorial materials science and research, elliptical profiles with ~10km radius of curvature for X-ray nanoscopy applications and polishing of starting wafer surfaces for mitigation of existing nanotopography. In addition, the potential of extending the demonstrated process to high throughput roll-roll systems has also been mentioned by modifying the model to incorporate the compliance of the substrate along with that of the superstrate. / text

Early detection is vital to successfully treating breast cancer, and mammography screening is the most efficient and wide-spread method to reach this goal. Imaging low-contrast targets, while minimizing the radiation exposure to a large population is, however, a major challenge. Optimizing the image quality per unit radiation dose is therefore essential. In this thesis, two optimization schemes with respect to x-ray photon energy have been investigated: filtering the incident spectrum with refractive x-ray optics (spectral shaping), and utilizing the transmitted spectrum with energy-resolved photon-counting detectors (spectral imaging). Two types of x-ray lenses were experimentally characterized, and modeled using ray tracing, field propagation, and geometrical optics. Spectral shaping reduced dose approximately 20% compared to an absorption-filtered reference system with the same signal-to-noise ratio, scan time, and spatial resolution. In addition, a focusing pre-object collimator based on the same type of optics reduced divergence of the radiation and improved photon economy by about 50%. A photon-counting silicon detector was investigated in terms of energy resolution and its feasibility for spectral imaging. Contrast-enhanced tumor imaging with a system based on the detector was characterized and optimized with a model that took anatomical noise into account. Improvement in an ideal-observer detectability index by a factor of 2 to 8 over that obtained by conventional absorption imaging was found for different levels of anatomical noise and breast density. Increased conspicuity was confirmed by experiment. Further, the model was extended to include imaging of unenhanced lesions. Detectability of microcalcifications increased no more than a few percent, whereas the ability to detect large tumors might improve on the order of 50% despite the low attenuation difference between glandular and cancerous tissue. It is clear that inclusion of anatomical noise and imaging task in spectral optimization may yield completely different results than an analysis based solely on quantum noise. / QC 20100714

The exploitation of the soft x-ray/extreme ultra-violet (EUV) region of the electromagnetic spectrum is possible mainly due to the development of multilayer (ML) mirrors. This region of the electromagnetic spectrum offers great opportunities in both science and technology. The shorter wavelength allows one to see smaller features in microscopy and write finer features in lithography. High reflectivity with moderate spectral bandwidth at normal/near-normal incidence can be achieved in soft x-ray/ EUV spectral range using these ML mirrors, where natural crystals with the required large periodicity are not available. These MLs are generally artificial Bragg’s reflectors, which consist of alternative high and low density materials with periodicity in the nanometer range. The main advantages of ML optics stem from the tunability of layer thickness, composition, lateral gradient, and the gradient along the normal to the substrate; these can be tailored according to the desired wavelength regime. They have the great advantage of being adaptable to figured surfaces, enabling their use as reflective optics in these spectral regions, for focusing and imaging applications. Broadband reflectivity and wavelength tunability are also possible by using MLs with normal and lateral gradient, respectively. However, fabrication of these ML mirrors requires the capability to deposit uniform, ultra-thin (a few angstroms-thick) films of different materials with thickness control on the atomic scale. Thus, one requires a proper understanding of substrate surfaces, individual layers, chemical reactivity at interfaces and, finally, of the ML structures required for particular applications. The performance of these MLs is limited by (the lack of) contrast in optical constants of the two materials, interfacial roughness, the chemical reactivity of two materials and, finally, errors in the thickness of individual layers. Soft x-ray/extreme ultra-violet ML mirrors have found a wide range of applications in synchrotron radiation beam lines, materials science, astronomy, x-ray microscopy, x-ray laser, x-ray lithography, polarizers, and plasma diagnostics. The Indus–1 synchrotron radiation (SR) source is an operational 450 MeV machine, which produces radiation up to soft x-rays. Indus-2 is a 2.5 GeV machine, which has been commissioned recently to produce hard x-rays (E > 25 keV). The combination of Indus-1 and Indus-2 will cover a broad energy spectrum from IR to hard x-rays. Therefore, there is a significant need and opportunity to study MLs of different pairs of materials, with different parameters such as periodicity and optimum thickness of individual layers. The goal of the present thesis is to fabricate MLs for soft x-ray optics and to study their physics for application as polarizers in the wavelength range from 67 Å to 160 Å on the Indus-1 synchrotron source. To accomplish this task, a UHV electron beam evaporation system has been developed indigenously for the fabrication of MLs. Three different ML systems viz., Mo/Si, Fe/B4C and Mo/Y have been fabricated, and their surfaces and interfaces were investigated thoroughly for the polarizer application. X-ray reflectivity (XRR) has been used extensively in the investigations of these MLs. This is because XRR is a highly sensitive non-destructive technique for the characterization of buried interfaces, and gives microscopic information (at atomic resolution) over a macroscopic length scale (a few microns). Numerical analysis of XRR data has been carried out using computer programs. Depth-graded x-ray photoelectron spectroscopy (XPS) has been used for compositional analysis at interfaces for some of the ML structures, as a technique complementary to XRR. The performance of some of these MLs has been tested in the soft x-ray region, using the Indus-1 synchrotron radiation (SR) source. Prior to studying the MLs, a detailed study of the surfaces and interfaces of thin films, bi-layers, and tri-layers was carried out using XRR and the glancing incidence fluorescence technique. The discontinuous-to-continuous transition and the mode of film growth, which are vital to the optimization of layer thickness (basically for the high-atomic number or high-Z layer) in the ML structures, were also investigated using in situ sheet resistance measurement method. Indus-1 is a soft x-ray SR source that covers atomic absorption edges of many low-Z materials. The present work demonstrates the possibilities of characterizing low-Z thin films and multilayers using soft x-ray resonant reflectivity. In one case, we have shown for first time that soft x-ray resonant reflectivity can be employed as a non-destructive technique for the determination of interlayer composition. In a second study using the Indus-1 SR source, we have shown, by observing the effect of the anomalous optical constant on reflectivity pattern when photon energy is tuned across the atomic absorption edge of the constituent low-Z element, that soft x-ray resonant reflectivity is an element-specific technique. This thesis is organized into 7 chapters. A brief summary of individual chapters is presented below. Chapter 1 gives a brief general introduction to x-ray ML optics. This is followed by a discussion of the importance of the soft x-ray region of electromagnetic radiation. The optical properties of x-rays are reviewed and optical constants are calculated for some of the important materials used for x-ray MLs. The refractive index in the x-ray region being less than unity (except absorption edges), the consequent limitation of conventional transmission lenses is discussed. The limitation of glancing angle incidence optics is presented, motivating the need for ML optics, which is discussed along with a theoretically calculated reflectivity profile. The procedure for materials for the MLs for application in different spectral regions is discussed, along with a survey of literature related to the present thesis. The importance of the quality of surfaces and interfaces on the performance of ML structures has been shown through simulations. The applications of soft x-ray MLs are discussed with emphasis on polarization. This is followed by a review of different modes of growth of thin films. Finally, the scope of the present work is highlighted. Chapter 2 provides brief descriptions of the experimental techniques used in the present investigations and of the numerical methods employed for quantitative data analysis. The XRR technique is discussed elaborately because it has been used extensively. Detailed calculations of x-ray reflectivity from single surfaces, thin films and bi-layers are presented, along with simulated values. The effect of critical angle and Brewster’s angle is also discussed. Data analysis methods for computing x-ray reflectivity from multilayer structures, based on dynamical and kinematical models, have been discussed. The effect of roughness on XRR has been discussed based on the recursion formalism of dynamical theory. Simulations of XRR and experimental XRR data fitting are carried out using computer programs. The XRR experimental set up is also outlined. A theoretical background is given for the electrical measurements on thin films. This is followed by a brief overview of x-ray photoelectron spectroscopy (XPS) and interpretation of spectra. Finally, the glancing incidence x-ray fluorescence (GIXRF) technique is outlined. Chapter 3 describes in detail the ultra-high vacuum electron beam evaporation system developed in house especially for the fabrication of thin films and x-ray multilayer optics. At the outset, a brief overview of different deposition techniques commonly used for the fabrication of x-ray optical elements is presented. Design, fabrication, and assembly of different accessories are discussed. The control of thickness and uniformity of the films deposited has been checked through the experiments, whose results are provided. The results obtained for ML test structures are presented to show the capability of system in carrying out fabrication of high quality x-ray ML structures. Finally, the versatility of evaporation system incorporating in situ characterization facilities such as -situ electrical measurements for different substrate temperatures is illustrated. Chapter 4 presents a study of the growth of ultra-thin Mo films at different substrate temperatures using in situ sheet resistance measurements. First, a theoretical background is given on the different stages of island growth and on factors affecting thin film growth, followed by a discussion of the possible electrical conduction phenomena in continuous and discontinuous metal films. The nature of thin film growth and a detailed microscopic picture at different growth stages are derived from a modeling of sheet resistance data obtained in situ. The various conduction mechanisms have been identified in different stages of growth. In the island growth stage, the isotropic and anisotropic growth of Mo islands is identified from the model. In the insulator-metal transition region, experimentally determined values of critical exponent of conductivity agrees well with theoretically predicted values for a two-dimensional (2D) percolating system, revealing that Mo films on float glass substrate is predominantly a 2D structure. The minimum thickness for which Mo films becomes continuous is obtained as 1.8 nm and 2.2 nm for Mo deposited at substrate temperatures 300 K and 100 K, respectively. An amorphous-to- crystalline transition is also observed, and discussed. Chapter 5 covers the detailed study of the surfaces and interfaces studies in three different ML structures viz., Mo/Si, Fe/B4C and Mo/Y, meant for the polarizer application in the wavelength range of 67 Å to 160 Å. Multilayers with varying periodicity, varying number of layer pairs, and different ratios of high-Z layer thickness to the period, were fabricated using the electron beam system. Initially, a brief overview of the design aspects of ML structures is given, along with the theoretically calculated reflectivity at Brewster’s angle from the best material combinations. In Mo/Si MLs, the interlayer formed at the interfaces due to interdiffusion of the two elements is asymmetric in thickness, i.e., Mo-on-Si interlayer is thicker than the Si-on-Mo interlayer. To take account of these interlayers in XRR data fitting, a four layer model is considered. The effect of interlayers on reflectivity pattern was studied using simulations, and differences with respect to roughness are also discussed. The mechanism of formation of asymmetric interlayers is also discussed. The interlayer composition has determined using depth-graded XPS. The results reveal the formation of the MoSi2 composition at both the interfaces. The experimental results agree well with theoretical calculations based on solid-state amorphization reaction, which is a result of large heat of mixing. The effective heat of formation model reveals the formation of MoSi2 as the first phase. The soft x-ray reflectivity performance of the Mo/Si ML structure at Brewster’s angle is tested using Indus-1 synchrotron radiation (SR). Using XRR and GIXFR, a study of the surfaces and interfaces of bilayers of B4C-on-Fe and Fe-on- B4C, and tri-layers of Fe-B4C-Fe was carried out, with a systematic variation of Fe and B4C layer thicknesses. A sharp interface was observed in Fe-on-B4C, whereas a low density (w.r.t. Fe) interlayer is observed at the B4C-on-Fe interface. The interlayer properties fluctuates w.r.t. the bottom Fe layer thickness and is independent of the top B4C layer thickness. The nature of fluctuations has been discussed in detail. A study of the surfaces and interfaces of Fe/B4C MLs is described. Finally, a study of the surfaces and interfaces of bilayers, tri-layers, and MLs of the Mo/Y system is discussed in detail. Chapter 6 describes the application of soft x-ray resonant reflectivity for the characterization of low-Z thin films and interfaces in multilayer structures. Initially, a discussion of the energy dependence of atomic scattering factors and hence of optical constants is provided with simulations, with emphasis on the atomic absorption edge. Then, a brief overview of synchrotron radiation, with particular emphasis on the parameters of the Indus-1 synchrotron source is given. The possibilities of determining the composition of the buried interlayer with sub-nanometer scale sensitivity using soft x-ray resonant reflectivity are discussed. The methodology has been applied to study the Mo/Si interface both by simulations and by experiments on the Indus-1 SR, by tuning the photon energy to the Si L-absorption edge. Finally, direct evidence of elemental specificity of soft x-ray resonant reflectivity through the observation of the effect of anomalous optical constants on the reflectivity pattern is discussed. We demonstrate the method through simulations and experiments on the B4C material in B4C thin films and Fe/ B4C bi-layers, using Indus-1 SR tuned to the boron Kedge. Chapter 7 summarizes the main findings of the present work, and provides an outlook for further investigations in the field.

Hard x rays come along with a variety of extraordinary properties which make them an excellent probe for investigation in science, technology and medicine. Their large attenuation length in matter opens up the possibility to use hard x-rays for non-destructive investigation of the inner structure of specimens. Medical radiography is one important example of exploiting this feature. Since their discovery by W. C. Röntgen in 1895, a large variety of x-ray analytical techniques have been developed and successfully applied, such as x-ray crystallography, reflectometry, fluorescence spectroscopy, x-ray absorption spectroscopy, small angle x-ray scattering, and many more. Each of those methods reveals information about certain physical properties, but usually, these properties are an average over the complete sample region illuminated by the x rays. In order to obtain the spatial distribution of those properties in inhomogeneous samples, scanning microscopy techniques have to be applied, screening the sample with a small x-ray beam. The spatial resolution is limited by the finite size of the beam. The availability of highly brilliant x-ray sources at third generation synchrotron radiation facilities together with the development of enhanced focusing x-ray optics made it possible to generate increasingly small high intense x-ray beams, pushing the spatial resolution down to the sub-100 nm range. During this thesis the prototype of a hard x-ray scanning microscope utilizing microstructured nanofocusing lenses was designed, built, and successfully tested. The nanofocusing x-ray lenses were developed by our research group of the Institute of Structural Physics at the Technische Universität Dresden. The prototype instrument was installed at the ESRF beamline ID 13. A wide range of experiments like fluorescence element mapping, fluorescence tomography, x-ray nano-diffraction, coherent x-ray diffraction imaging, and x-ray ptychography were performed as part of this thesis. The hard x-ray scanning microscope provides a stable x-ray beam with a full width at half maximum size of 50-100 nm near the focal plane. The nanoprobe was also used for characterization of nanofocusing lenses, crucial to further improve them. Based on the experiences with the prototype, an advanced version of a hard x-ray scanning microscope is under development and will be installed at the PETRA III beamline P06 dedicated as a user instrument for scanning microscopy. This document is organized as follows. A short introduction motivating the necessity for building a hard x-ray scanning microscope is followed by a brief review of the fundamentals of hard x-ray physics with an emphasis on free-space propagation and interaction with matter. After a discussion of the requirements on the x-ray source for the nanoprobe, the main features of synchrotron radiation from an undulator source are shown. The properties of the nanobeam generated by refractive x-ray lenses are treated as well as a two-stage focusing scheme for tailoring size, flux and the lateral coherence properties of the x-ray focus. The design and realization of the microscope setup is addressed, and a selection of experiments performed with the prototype version is presented, before this thesis is finished with a conclusion and an outlook on prospective plans for an improved microscope setup to be installed at PETRA III. / Aufgrund ihrer hervorragenden Eigenschaften kommt harte Röntgenstrahlung in vielfältiger Weise in der Wissenschaft, Industrie und Medizin zum Einsatz. Vor allem die Fähigkeit, makroskopische Gegenstände zu durchdringen, eröffnet die Möglichkeit, im Innern ausgedehnter Objekte verborgene Strukturen zum Vorschein zu bringen, ohne den Gegenstand zerstören zu müssen. Eine Vielzahl röntgenanalytischer Verfahren wie zum Beispiel Kristallographie, Reflektometrie, Fluoreszenzspektroskopie, Absorptionsspektroskopie oder Kleinwinkelstreuung sind entwickelt und erfolgreich angewendet worden. Jede dieser Methoden liefert gewisse strukturelle, chemische oder physikalische Eigenschaften der Probe zutage, allerdings gemittelt über den von der Röntgenstrahlung beleuchteten Bereich. Um eine ortsaufgelöste Verteilung der durch die Röntgenanalyse gewonnenen Information zu erhalten, bedarf es eines sogenannten Mikrostrahls, durch den die Probe lokal abgetastet werden kann. Die dadurch erreichbare räumliche Auflösung ist durch die Größe des Mikrostrahls begrenzt. Aufgrund der Verfügbarkeit hinreichend brillanter Röntgenquellen in Form von Undulatoren an Synchrotronstrahlungseinrichtungen und des Vorhandenseins verbesserter Röntgenoptiken ist es in den vergangen Jahren gelungen, immer kleinere intensive Röntgenfokusse zu erzeugen und somit das räumliche Auflösungsvermögen der Röntgenrastermikroskope auf unter 100 nm zu verbessern. Gegenstand dieser Arbeit ist der Prototyp eines Rastersondenmikroskops für harte Röntgenstrahlung unter Verwendung refraktiver nanofokussierender Röntgenlinsen, die von unserer Arbeitsgruppe am Institut für Strukturphysik entwickelt und hergestellt werden. Das Rastersondenmikroskop wurde im Rahmen dieser Promotion in Dresden konzipiert und gebaut sowie am Strahlrohr ID 13 des ESRF installiert und erfolgreich getestet. Das Gerät stellt einen hochintensiven Röntgenfokus der Größe 50-100 nm zur Verfügung, mit dem im Verlaufe dieser Doktorarbeit zahlreiche Experimente wie Fluoreszenztomographie, Röntgennanobeugung, Abbildung mittels kohärenter Röntgenbeugung sowie Röntgenptychographie erfolgreich durchgeführt wurden. Das Rastermikroskop dient unter anderem auch dem Charakterisieren der nanofokussierenden Linsen, wobei die dadurch gewonnenen Erkenntnisse in die Herstellung verbesserten Linsen einfließen. Diese Arbeit ist wie folgt strukturiert. Ein kurzes einleitendes Kapitel dient als Motivation für den Bau eines Rastersondenmikroskops für harte Röntgenstrahlung. Es folgt eine Einführung in die Grundlagen der Röntgenphysik mit Hauptaugenmerk auf die Ausbreitung von Röntgenstrahlung im Raum und die Wechselwirkungsmechanismen von Röntgenstrahlung mit Materie. Anschließend werden die Anforderungen an die Röntgenquelle besprochen und die Vorzüge eines Undulators herausgestellt. Wichtige Eigenschaften eines mittels refraktiver Röntgenlinsen erzeugten Röntgenfokus werden behandelt, und das Konzept einer Vorfokussierung zur gezielten Anpassung der transversalen Kohärenzeigenschaften an die Erfordernisse des Experiments wird besprochen. Das Design und die technische Realisierung des Rastermikroskops werden ebenso dargestellt wie eine Auswahl erfolgreicher Experimente, die am Gerät vollzogen wurden. Die Arbeit endet mit einem Ausblick, der mögliche Weiterentwicklungen in Aussicht stellt, unter anderem den Aufbau eines verbesserten Rastermikroskops am PETRA III-Strahlrohr P06.

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Hard x rays come along with a variety of extraordinary properties which make them an excellent probe for investigation in science, technology and medicine. Their large attenuation length in matter opens up the possibility to use hard x-rays for non-destructive investigation of the inner structure of specimens. Medical radiography is one important example of exploiting this feature. Since their discovery by W. C. Röntgen in 1895, a large variety of x-ray analytical techniques have been developed and successfully applied, such as x-ray crystallography, reflectometry, fluorescence spectroscopy, x-ray absorption spectroscopy, small angle x-ray scattering, and many more. Each of those methods reveals information about certain physical properties, but usually, these properties are an average over the complete sample region illuminated by the x rays. In order to obtain the spatial distribution of those properties in inhomogeneous samples, scanning microscopy techniques have to be applied, screening the sample with a small x-ray beam. The spatial resolution is limited by the finite size of the beam. The availability of highly brilliant x-ray sources at third generation synchrotron radiation facilities together with the development of enhanced focusing x-ray optics made it possible to generate increasingly small high intense x-ray beams, pushing the spatial resolution down to the sub-100 nm range. During this thesis the prototype of a hard x-ray scanning microscope utilizing microstructured nanofocusing lenses was designed, built, and successfully tested. The nanofocusing x-ray lenses were developed by our research group of the Institute of Structural Physics at the Technische Universität Dresden. The prototype instrument was installed at the ESRF beamline ID 13. A wide range of experiments like fluorescence element mapping, fluorescence tomography, x-ray nano-diffraction, coherent x-ray diffraction imaging, and x-ray ptychography were performed as part of this thesis. The hard x-ray scanning microscope provides a stable x-ray beam with a full width at half maximum size of 50-100 nm near the focal plane. The nanoprobe was also used for characterization of nanofocusing lenses, crucial to further improve them. Based on the experiences with the prototype, an advanced version of a hard x-ray scanning microscope is under development and will be installed at the PETRA III beamline P06 dedicated as a user instrument for scanning microscopy. This document is organized as follows. A short introduction motivating the necessity for building a hard x-ray scanning microscope is followed by a brief review of the fundamentals of hard x-ray physics with an emphasis on free-space propagation and interaction with matter. After a discussion of the requirements on the x-ray source for the nanoprobe, the main features of synchrotron radiation from an undulator source are shown. The properties of the nanobeam generated by refractive x-ray lenses are treated as well as a two-stage focusing scheme for tailoring size, flux and the lateral coherence properties of the x-ray focus. The design and realization of the microscope setup is addressed, and a selection of experiments performed with the prototype version is presented, before this thesis is finished with a conclusion and an outlook on prospective plans for an improved microscope setup to be installed at PETRA III.:1 Introduction ............................................... 1 2 Basic Properties of Hard X Rays ............................ 3 2.1 Free Propagation of X Rays ............................... 3 2.1.1 The Helmholtz Equation ................................. 4 2.1.2 Integral Theorem of Helmholtz and Kirchhoff ............ 6 2.1.3 Fresnel-Kirchhoff's Diffraction Formula ................ 8 2.1.4 Fresnel-Kirchhoff Propagation .......................... 11 2.2 Interaction of X Rays with Matter ........................ 13 2.2.1 Complex Index of Refraction ............................ 13 2.2.2 Attenuation ............................................ 15 2.2.3 Refraction ............................................. 18 3 The X-Ray Source ........................................... 21 3.1 Requirements ............................................. 21 3.1.1 Energy and Energy Bandwidth ............................ 21 3.1.2 Source Size and Divergence ............................. 23 3.1.3 Brilliance ............................................. 23 3.2 Synchrotron Radiation .................................... 24 3.3 Layout of a Synchrotron Radiation Facility ............... 27 3.4 Liénard-Wiechert Fields .................................. 29 3.5 Dipole Magnets ........................................... 31 3.6 Insertion Devices ........................................ 36 3.6.1 Multipole Wigglers ..................................... 36 3.6.2 Undulators ............................................. 37 4 X-Ray Optics ............................................... 39 4.1 Refractive X-Ray Lenses .................................. 40 4.2 Compound Parabolic Refractive Lenses (CRLs) .............. 41 4.3 Nanofocusing Lenses (NFLs) ............................... 43 4.4 Adiabatically Focusing Lenses (AFLs) ..................... 45 4.5 Focal Distance ........................................... 46 4.6 Transverse Focus Size .................................... 50 4.7 Beam Caustic ............................................. 52 4.8 Depth of Focus ........................................... 53 4.9 Beam Divergence .......................................... 53 4.10 Chromaticity ............................................ 54 4.11 Transmission and Cross Section .......................... 55 4.12 Transverse Coherence .................................... 56 4.12.1 Mutual Intensity Function ............................. 57 4.12.2 Free Propagation of Mutual Intensity .................. 57 4.12.3 Mutual Intensity In The Focal Plane ................... 58 4.12.4 Diffraction Limited Focus ............................. 59 4.13 Coherent Flux ........................................... 60 4.14 Two-Stage Focusing ...................................... 64 4.14.1 The Prefocusing Parameter ............................. 65 4.14.2 Required Refractive Power ............................. 67 4.14.3 Flux Considerations ................................... 70 4.14.4 Astigmatic Prefocusing ................................ 75 5 Nanoprobe Setup ............................................ 77 5.1 X-Ray Optics ............................................. 78 5.1.1 Nanofocusing Lenses .................................... 79 5.1.2 Entry Slits ............................................ 82 5.1.3 Pinhole ................................................ 82 5.1.4 Additional Shielding ................................... 83 5.1.5 Vacuum and Helium Tubes ................................ 83 5.2 Sample Stages ............................................ 84 5.2.1 High Resolution Scanner ................................ 84 5.2.2 High Precision Rotational Stage ........................ 85 5.2.3 Coarse Linear Stages ................................... 85 5.2.4 Goniometer Head ........................................ 85 5.3 Detectors ................................................ 86 5.3.1 High Resolution X-Ray Camera ........................... 86 5.3.2 Diffraction Cameras .................................... 89 5.3.3 Energy Dispersive Detectors ............................ 91 5.3.4 Photodiodes ............................................ 93 5.4 Control Software ......................................... 94 6 Experiments ................................................ 97 6.1 Lens Alignment ........................................... 97 6.2 Focus Characterization ................................... 99 6.2.1 Knife-Edge Scans ....................................... 100 6.2.2 Far-Field Measurements ................................. 102 6.2.3 X-Ray Ptychography ..................................... 103 6.3 Fluorescence Spectroscopy ................................ 105 6.3.1 Fluorescence Element Mapping ........................... 107 6.3.2 Fluorescence Tomography ................................ 110 6.4 Diffraction Experiments .................................. 111 6.4.1 Microdiffraction on Phase Change Media ................. 112 6.4.2 Microdiffraction on Stranski-Krastanow Islands ......... 113 6.4.3 Coherent X-Ray Diffraction Imaging of Gold Particles ... 115 6.4.4 X-Ray Ptychography of a Nano-Structured Microchip ...... 117 7 Conclusion and Outlook ..................................... 121 Bibliography ................................................. 125 List of Figures .............................................. 139 List of Publications ......................................... 141 Danksagung ................................................... 145 Curriculum Vitae ............................................. 149 Erklärung .................................................... 151 / Aufgrund ihrer hervorragenden Eigenschaften kommt harte Röntgenstrahlung in vielfältiger Weise in der Wissenschaft, Industrie und Medizin zum Einsatz. Vor allem die Fähigkeit, makroskopische Gegenstände zu durchdringen, eröffnet die Möglichkeit, im Innern ausgedehnter Objekte verborgene Strukturen zum Vorschein zu bringen, ohne den Gegenstand zerstören zu müssen. Eine Vielzahl röntgenanalytischer Verfahren wie zum Beispiel Kristallographie, Reflektometrie, Fluoreszenzspektroskopie, Absorptionsspektroskopie oder Kleinwinkelstreuung sind entwickelt und erfolgreich angewendet worden. Jede dieser Methoden liefert gewisse strukturelle, chemische oder physikalische Eigenschaften der Probe zutage, allerdings gemittelt über den von der Röntgenstrahlung beleuchteten Bereich. Um eine ortsaufgelöste Verteilung der durch die Röntgenanalyse gewonnenen Information zu erhalten, bedarf es eines sogenannten Mikrostrahls, durch den die Probe lokal abgetastet werden kann. Die dadurch erreichbare räumliche Auflösung ist durch die Größe des Mikrostrahls begrenzt. Aufgrund der Verfügbarkeit hinreichend brillanter Röntgenquellen in Form von Undulatoren an Synchrotronstrahlungseinrichtungen und des Vorhandenseins verbesserter Röntgenoptiken ist es in den vergangen Jahren gelungen, immer kleinere intensive Röntgenfokusse zu erzeugen und somit das räumliche Auflösungsvermögen der Röntgenrastermikroskope auf unter 100 nm zu verbessern. Gegenstand dieser Arbeit ist der Prototyp eines Rastersondenmikroskops für harte Röntgenstrahlung unter Verwendung refraktiver nanofokussierender Röntgenlinsen, die von unserer Arbeitsgruppe am Institut für Strukturphysik entwickelt und hergestellt werden. Das Rastersondenmikroskop wurde im Rahmen dieser Promotion in Dresden konzipiert und gebaut sowie am Strahlrohr ID 13 des ESRF installiert und erfolgreich getestet. Das Gerät stellt einen hochintensiven Röntgenfokus der Größe 50-100 nm zur Verfügung, mit dem im Verlaufe dieser Doktorarbeit zahlreiche Experimente wie Fluoreszenztomographie, Röntgennanobeugung, Abbildung mittels kohärenter Röntgenbeugung sowie Röntgenptychographie erfolgreich durchgeführt wurden. Das Rastermikroskop dient unter anderem auch dem Charakterisieren der nanofokussierenden Linsen, wobei die dadurch gewonnenen Erkenntnisse in die Herstellung verbesserten Linsen einfließen. Diese Arbeit ist wie folgt strukturiert. Ein kurzes einleitendes Kapitel dient als Motivation für den Bau eines Rastersondenmikroskops für harte Röntgenstrahlung. Es folgt eine Einführung in die Grundlagen der Röntgenphysik mit Hauptaugenmerk auf die Ausbreitung von Röntgenstrahlung im Raum und die Wechselwirkungsmechanismen von Röntgenstrahlung mit Materie. Anschließend werden die Anforderungen an die Röntgenquelle besprochen und die Vorzüge eines Undulators herausgestellt. Wichtige Eigenschaften eines mittels refraktiver Röntgenlinsen erzeugten Röntgenfokus werden behandelt, und das Konzept einer Vorfokussierung zur gezielten Anpassung der transversalen Kohärenzeigenschaften an die Erfordernisse des Experiments wird besprochen. Das Design und die technische Realisierung des Rastermikroskops werden ebenso dargestellt wie eine Auswahl erfolgreicher Experimente, die am Gerät vollzogen wurden. Die Arbeit endet mit einem Ausblick, der mögliche Weiterentwicklungen in Aussicht stellt, unter anderem den Aufbau eines verbesserten Rastermikroskops am PETRA III-Strahlrohr P06.:1 Introduction ............................................... 1 2 Basic Properties of Hard X Rays ............................ 3 2.1 Free Propagation of X Rays ............................... 3 2.1.1 The Helmholtz Equation ................................. 4 2.1.2 Integral Theorem of Helmholtz and Kirchhoff ............ 6 2.1.3 Fresnel-Kirchhoff's Diffraction Formula ................ 8 2.1.4 Fresnel-Kirchhoff Propagation .......................... 11 2.2 Interaction of X Rays with Matter ........................ 13 2.2.1 Complex Index of Refraction ............................ 13 2.2.2 Attenuation ............................................ 15 2.2.3 Refraction ............................................. 18 3 The X-Ray Source ........................................... 21 3.1 Requirements ............................................. 21 3.1.1 Energy and Energy Bandwidth ............................ 21 3.1.2 Source Size and Divergence ............................. 23 3.1.3 Brilliance ............................................. 23 3.2 Synchrotron Radiation .................................... 24 3.3 Layout of a Synchrotron Radiation Facility ............... 27 3.4 Liénard-Wiechert Fields .................................. 29 3.5 Dipole Magnets ........................................... 31 3.6 Insertion Devices ........................................ 36 3.6.1 Multipole Wigglers ..................................... 36 3.6.2 Undulators ............................................. 37 4 X-Ray Optics ............................................... 39 4.1 Refractive X-Ray Lenses .................................. 40 4.2 Compound Parabolic Refractive Lenses (CRLs) .............. 41 4.3 Nanofocusing Lenses (NFLs) ............................... 43 4.4 Adiabatically Focusing Lenses (AFLs) ..................... 45 4.5 Focal Distance ........................................... 46 4.6 Transverse Focus Size .................................... 50 4.7 Beam Caustic ............................................. 52 4.8 Depth of Focus ........................................... 53 4.9 Beam Divergence .......................................... 53 4.10 Chromaticity ............................................ 54 4.11 Transmission and Cross Section .......................... 55 4.12 Transverse Coherence .................................... 56 4.12.1 Mutual Intensity Function ............................. 57 4.12.2 Free Propagation of Mutual Intensity .................. 57 4.12.3 Mutual Intensity In The Focal Plane ................... 58 4.12.4 Diffraction Limited Focus ............................. 59 4.13 Coherent Flux ........................................... 60 4.14 Two-Stage Focusing ...................................... 64 4.14.1 The Prefocusing Parameter ............................. 65 4.14.2 Required Refractive Power ............................. 67 4.14.3 Flux Considerations ................................... 70 4.14.4 Astigmatic Prefocusing ................................ 75 5 Nanoprobe Setup ............................................ 77 5.1 X-Ray Optics ............................................. 78 5.1.1 Nanofocusing Lenses .................................... 79 5.1.2 Entry Slits ............................................ 82 5.1.3 Pinhole ................................................ 82 5.1.4 Additional Shielding ................................... 83 5.1.5 Vacuum and Helium Tubes ................................ 83 5.2 Sample Stages ............................................ 84 5.2.1 High Resolution Scanner ................................ 84 5.2.2 High Precision Rotational Stage ........................ 85 5.2.3 Coarse Linear Stages ................................... 85 5.2.4 Goniometer Head ........................................ 85 5.3 Detectors ................................................ 86 5.3.1 High Resolution X-Ray Camera ........................... 86 5.3.2 Diffraction Cameras .................................... 89 5.3.3 Energy Dispersive Detectors ............................ 91 5.3.4 Photodiodes ............................................ 93 5.4 Control Software ......................................... 94 6 Experiments ................................................ 97 6.1 Lens Alignment ........................................... 97 6.2 Focus Characterization ................................... 99 6.2.1 Knife-Edge Scans ....................................... 100 6.2.2 Far-Field Measurements ................................. 102 6.2.3 X-Ray Ptychography ..................................... 103 6.3 Fluorescence Spectroscopy ................................ 105 6.3.1 Fluorescence Element Mapping ........................... 107 6.3.2 Fluorescence Tomography ................................ 110 6.4 Diffraction Experiments .................................. 111 6.4.1 Microdiffraction on Phase Change Media ................. 112 6.4.2 Microdiffraction on Stranski-Krastanow Islands ......... 113 6.4.3 Coherent X-Ray Diffraction Imaging of Gold Particles ... 115 6.4.4 X-Ray Ptychography of a Nano-Structured Microchip ...... 117 7 Conclusion and Outlook ..................................... 121 Bibliography ................................................. 125 List of Figures .............................................. 139 List of Publications ......................................... 141 Danksagung ................................................... 145 Curriculum Vitae ............................................. 149 Erklärung .................................................... 151