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| X-ray wave-fields in free space | |
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| Vacuum wave equations for electromagnetic fields | |
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| Spectral decomposition and the analytic signal | |
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| Angular spectrum of plane waves | |
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| Fresnel diffraction | |
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| Operator formulation | |
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| Convolution formulation | |
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| Fraunhofer diffraction | |
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| Kirchhoff and Rayleigh-Sommerfeld diffraction theory | |
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| Kirchhoff diffraction integral | |
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| Rayleigh-Sommerfeld diffraction integrals | |
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| Partially coherent fields | |
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| Random variables and random processes | |
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| Intermediate states of coherence | |
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| Spatial coherence | |
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| Temporal coherence | |
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| The mutual coherence function | |
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| Propagation of two-point correlation functions | |
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| Vacuum wave equations | |
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| Operator formulation | |
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| Green function formulation | |
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| Van Cittert-Zernike theorem | |
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| Higher-order correlation functions | |
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| Summary | |
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| X-ray interactions with matter | |
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| Wave equations in the presence of scatterers | |
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| The projection approximation | |
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| Point scatterers and the outgoing Green function | |
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| First method for obtaining Green function | |
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| Second method for obtaining Green function | |
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| Integral-equation formulation of scattering | |
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| First Born approximation for kinematical scattering | |
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| Fraunhofer and first Born approximation | |
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| Angular spectrum and first Born approximation | |
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| The Ewald sphere | |
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| Born series and dynamical scattering | |
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| Multislice approximation | |
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| Eikonal approximation and geometrical optics | |
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| Scattering, refractive index, and electron density | |
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| Inelastic scattering and absorption | |
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| Compton scattering | |
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| Photoelectric absorption and fluorescence | |
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| Information content of scattered fields | |
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| Scattered monochromatic fields | |
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| Scattered polychromatic fields | |
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| Summary | |
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| X-ray sources, optical elements, and detectors | |
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| Sources | |
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| Brightness and emittance | |
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| Fixed-anode and rotating-anode sources | |
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| Synchrotron sources | |
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| Free-electron lasers | |
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| Energy-recovering linear accelerators | |
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| Soft X-ray lasers | |
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| Diffractive optical elements | |
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| Diffraction gratings | |
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| Fresnel zone plates | |
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| Analyser crystals | |
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| Crystal monochromators | |
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| Crystal beam-splitters and interferometers | |
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| Bragg-Eresnel crystal optics | |
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| Free space | |
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| Reflective optical elements | |
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| X-ray reflection from surfaces | |
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| Capillary optics | |
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| Square-channel arrays | |
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| X-ray mirrors | |
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| Refractive optical elements | |
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| Prisms | |
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| Compound refractive lenses | |
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| Virtual optical elements | |
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| X-ray detectors | |
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| Critical detector parameters | |
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| Types of X-ray detector | |
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| Detectors and coherence | |
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| Summary | |
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| Coherent X-ray imaging | |
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| Operator theory of imaging | |
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| Imaging using coherent fields | |
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| Imaging using partially coherent fields | |
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| Cascaded systems | |
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| Self imaging | |
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| Talbot effect for monochromatic fields | |
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| Talbot effect for polychromatic fields | |
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| Montgomery effect for monochromatic fields | |
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| Montgomery effect for polychromatic fields | |
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| Holography | |
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| In-line holography | |
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| Off-axis holography | |
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| Fourier holography | |
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| Phase contrast | |
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| Zernike phase contrast | |
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| Differential interference contrast | |
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| Analyser-based phase contrast | |
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| Propagation-based phase contrast | |
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| Hybrid phase contrast | |
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| Phase retrieval | |
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| Gerchberg-Saxton algorithm and extensions | |
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| The transport-of-intensity equation | |
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| One-dimensional phase retrieval | |
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| Interferometry | |
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| Bonse-Hart interferometer | |
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| Young interferometer | |
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| Intensity interferometer | |
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| Other means for coherence measurement | |
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| Virtual optics for coherent X-ray imaging | |
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| General remarks on virtual optics | |
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| Example of virtual optics | |
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| Summary | |
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| Singular X-ray optics | |
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| Vortices in complex scalar fields | |
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| Nodal lines | |
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| Nodal lines are vortex cores | |
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| Polynomial vortex solutions to d'Alembert equation | |
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| Vortex dynamics | |
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| Vortex nucleation and annihilation | |
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| Stability with respect to perturbations | |
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| Vortex interaction with a background field | |
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| Means of generating wave-field vortices | |
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| Interference of three coherent plane waves | |
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| Synthetic holograms | |
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| Spiral phase masks | |
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| Spontaneous vortex formation | |
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| Domain walls and other topological phase defects | |
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| Caustics and the singularity hierarchy | |
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| Summary | |
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| A Review of Fourier analysis | |
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| Fourier transforms in one and two dimensions | |
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| Convolution theorem | |
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| Fourier shift theorem | |
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| Fourier derivative theorem | |
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| Sifting property of Dirac delta | |
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| Fresnel scaling theorem | |
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| Reciprocity theorem for monochromatic scalar fields | |
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| Index | |