X-ray focusing

X-rays interact weakly with matter and are thus difficult to focus. The x-ray refractive index of most materials is extremely close to 1.0, which means that refraction is extremely weak and the conventional kinds of optics used in visible-light optics (glass lenses, metal mirrors, polarizers, etc.) are not applicable. Nevertheless, a variety of tricks can be used to direct and focus x-rays.

For instance, since x-rays undergo total external reflection at very shallow angles (grazing-incidence), one can use extremely flat materials to slightly reflect x-rays. For instance, silicon wafers coated with metal stripes are typically used to achieved the required flatness, while having a sufficiently large electron density so that the critical angle is reasonably large. Because these mirrors are being used at grazing-angles, the beam projection is quite large: x-ray mirrors must typically be 100 mm to 2 m in length along the beam. An x-ray mirror can be very slightly bent, in which case the curvature effectively acts as a focusing optic. (Note that the radius of curvature is typically 6-30 km!)

Focusing Optics

• Mirrors: Grazing-incidence mirrors that are slightly curved in order to focus the x-ray beam.
  • Kirkpatrick-Baez Mirrors: Two mirrors oriented at right angles.
  • Wolter Mirrors: Can be used to form images of extended (non-point-source) objects. Cylindrically symmetric mirrors.
• Capillary optics: Bundles of light-guiding pipes/capillaries can be used to focus.
• Compound Refractive Lenses (CRL): Sequences of curved interfaces, to accumulate refractive effects and achieve focusing. (c.f. CRL)
• Fresnel Zone Plates (FZP): Use diffraction effects (from rings of progressively different spacing/size) to focus beam.
• Laue lens: Uses Bragg diffraction in order to focus beam (usually using a tilted crystal). Multilayer Laue lenses (MLL) can be used as effectively 1-D half-linear-zone-plates.
• Kinoform lenses: Combine refractive and diffractive designs. (c.f. Detlef Smilgies presentation)

See Also

• Xradia tutorial
• Wikipedia: Compound refractive lens
• Figure 2 in: Gene E. Ice, John D. Budai, Judy W. L. Pang The Race to X-ray Microbeam and Nanobeam Science Science 2011, 334 (6060), 1234-1239. doi: 10.1126/science.1202366
• Yoshinobu Nozue, Yuya Shinohara and Yoshiyuki Amemiya Application of Microbeam Small- and Wide-angle X-ray Scattering to Polymeric Material Characterization Polymer Journal 2007, 39, 1221–1237 doi:10.1295/polymj.PJ2007077
• Satoshi Matsuyama, Naotaka Kidani, Hidekazu Mimura, Yasuhisa Sano, Yoshiki Kohmura, Kenji Tamasaku, Makina Yabashi, Tetsuya Ishikawa, and Kazuto Yamauchi Hard-X-ray imaging optics based on four aspherical mirrors with 50 nm resolution Optics Express 2012, 20 (9), 10310-10319. doi: 10.1364/OE.20.010310
• Takashi Kimura, Satoshi Matsuyama, Kazuto Yamauchi, and Yoshinori Nishino Coherent x-ray zoom condenser lens for diffractive and scanning microscopy Optics Express 2013, 21 (8), 9267-9276. doi: 10.1364/OE.21.009267