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Synchrotron Light Sources and Free-Electron Lasers pp 1–28Cite as

Sub-micrometer Focusing and High-Resolution Imaging with Refractive Lenses and Multilayer Laue Optics

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Abstract

In this chapter we describe the fundamentals of X-ray optics with a particular emphasis on refractive and diffractive optics for high-resolution X-ray microscopy. To understand the physical limitations of X-ray microscopy and X-ray optics, a wave-optical treatment of the interaction of X-rays with the optical elements is needed. As all optics exploit elastic X-ray scattering in the form of refraction, reflection, or diffraction, these phenomena are reviewed, modeling matter by its complex index of refraction. The smallest probe sizes are reached at the diffraction limit. In that case, the focal spot size depends only on the numerical aperture of the optical element at a given wavelength. We discuss refractive and diffractive optics in view of optimal numerical aperture and give a few application examples in full-field and scanning microscopy.

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Notes

  1. 1.

    This holds for all refractive, reflective, and diffractive optics with the exception of crystal optics, for which the deflection angles can violate the paraxial approximation.

  2. 2.

    Due to the dispersion ∝ ω −2 in the hard X-ray range (cf. Eq. (4)), the group velocity is smaller than the speed of light.

  3. 3.

    Depending on the context, the definition of the lateral coherence length varies slightly. The various definitions typically differ by a factor close to unity (e.g., Als-Nielsen 2002).

  4. 4.

    Equation (19) holds in the thin lens approximation for the whole stack. For thick lens stacks, the focal length is slightly longer as given by Eq. (22) due to propagation effects inside the stack (Schroer et al. 2013).

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Authors and Affiliations

  1. DESY, Notkestraße 85, Hamburg, Germany

    Saša Bajt

  2. DESY, Notkestraße 85, Hamburg, Germany

    Christian G. Schroer

  3. Department Physik, Universität Hamburg, Hamburg, Germany

    Christian G. Schroer

Authors
  1. Saša Bajt
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  2. Christian G. Schroer
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Correspondence to Christian G. Schroer .

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Editors and Affiliations

  1. Helmholtz-Zentrum Berlin, Berlin, Germany

    Eberhard Jaeschke

  2. Zentrum für Synchrotronstrahlung, TU Dortmund, Dortmund, Germany

    Shaukat Khan

  3. FS-CFEL-1, DESY, Hamburg, Germany

    Jochen R. Schneider

  4. SLAC National Accelerator Laboratory Linac Coherent Light Source, Stanford University, Menlo Park, CA, USA

    Jerome B. Hastings

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Bajt, S., Schroer, C.G. (2019). Sub-micrometer Focusing and High-Resolution Imaging with Refractive Lenses and Multilayer Laue Optics. In: Jaeschke, E., Khan, S., Schneider, J., Hastings, J. (eds) Synchrotron Light Sources and Free-Electron Lasers. Springer, Cham. https://doi.org/10.1007/978-3-319-04507-8_62-1

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  • DOI: https://doi.org/10.1007/978-3-319-04507-8_62-1

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  • Print ISBN: 978-3-319-04507-8

  • Online ISBN: 978-3-319-04507-8

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