Abstract

AbstractThis chapter addresses fundamental concepts of X-ray optics and X-ray coherence, in view of the increasing number of X-ray applications requiring nano-focused X-ray beams. The chapter is meant as a tutorial to facilitate the understanding of later chapters of this book. After the introduction and an overview over focusing optics and recent benchmarks in X-ray focusing, we present refractive, reflective and diffractive X-ray optics in more detail. Particular emphasis is given to two kinds of X-ray optics which are particularly relevant for later chapters in this book, namely X-ray waveguides (XWG) and multilayer zone plates (MZP). Both are geared towards ultimate confinement and focusing, respectively, i.e. applications at the forefront of what is currently possible for multi-keV radiation. Since optics must be designed in view of coherence properties, we include a basic treatment of coherence theory and simulation for X-ray optics. Finally, the chapter closes with a brief outlook on compound (combined) optical schemes for hard X-ray microscopy.

Highlights

  • X-ray optics can be considered as optics in the “vacuum limit”

  • The primary challenge for X-ray microscopy is to narrow down the gap between the theoretical resolution limit associated with the wavelength λ and the actual resolution limited by the optical systems

  • Refractive optics as used for visible and UV light seem at the first glance, unsuitable due to the small X-ray refractive index, with δ ranging in the order of 10−5 for hard X-rays

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Summary

General Aspects of X-ray Optics and Focusing

X-ray optics can be considered as optics in the “vacuum limit”. the index of refraction n = 1 − δ + iβ asymptotically approaches one for high photon energy E, as δ and β decrease algebraically for E ≥ Er , where Er stands for an atomic resonance, i.e. an absorption edge given by the corresponding electronic binding energy. X-ray micro- and nanofocussing can be implemented today by either diffractive (example: Fresnel zone plates), reflective (examples: Kirckpatrick-Baez mirror, waveguides) and refractive optical elements (example: compound refractive lenses), and/or combinations thereof. X-ray optics and in particular nanofocusing has been an enabling tool to extend X-ray microscopy over the recent years, in spectral range, in resolution and in contrast mechanism This is true for the classical full-field scheme of transmission X-ray microscopy (TXM) which is based on objective zone plates, or scanning X-ray transmission microscopy (STXM), and for coherent diffraction imaging (CDI) and holography, which take advantage of X-ray focusing, even if the resolution limits are no longer limited by the focal size. We close by briefly addressing compound optics and different variants of X-ray microscopes (Sect. 3.7)

X-ray Reflectivity and Reflective X-ray Optics
X-ray Reflectivity of an Ideal Single Interface
Multiple Interfaces and Multilayers
Interfacial Roughness
X-ray Mirrors
Kirkpatrick-Baez Geometry
Multilayer Mirrors
Waveguide Modes
Coupling and Propagation
Fabrication and Characterisation of X-ray Waveguides
Advanced Waveguide Configurations
C Mo d n3
Diffractive Optics and Zone Plates
Basic Theory of Fresnel Zone Plates
Fabrication Techniques
Diffractive Optics Beyond the Projection Approximation
Basic Coherence Theory and Simulations for X-ray Optics
Basic Definitions
Stochastic Model
Coherence Propagation and Filtering
Findings
Putting It All Together
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