Optical Review

, Volume 23, Issue 2, pp 161–171 | Cite as

Design of axisymmetric multi-mirror grazing incidence system to increase the numerical aperture of neutron and X-ray microscopes

  • Sadao AokiEmail author
  • Norio Watanabe
  • Hiroshi Asami
  • Akihiro Shimada
Regular Paper


An axisymmetric multi-mirror system for neutron and X-ray microscopes is proposed to increase their numerical aperture and collection efficiency. A Wolter type-I mirror is used as the basis of the multi-mirror system at grazing incidence. The addition of an even number of hyperboloid mirrors to the Wolter type-I mirror can satisfy both an equal optical path length and Abbe’s sine condition. The numerical aperture increases in proportion to the number of mirrors. The optical parameters of the system with four tandem mirrors are calculated for neutrons and X-rays with a wavelength of 0.4 nm by assuming that the average grazing angle of incidence is 5.4 mrad and the magnification is 10. The inner diameters of the mirrors are limited to <10 mm considering the total length of the optical system. Tolerance of off-axis distance was calculated using a ray-tracing computer simulation. Ray tracing shows that a blur size <14 nm will be possible at an off-axis displacement of 10 μm.


Neutron X-ray Microscope Numerical aperture Grazing incidence Wolter mirror Ellipsoid Hyperboloid Resolution Total reflection Ray tracing 



This work was supported by Grant-in-Aid for Scientific Research (No. 25108003) from the Ministry of Education, Culture, Sports, Science and Technology and Grant-in-Aid for Scientific Research (No. 23656056) from the Japan Society for the Promotion of Science.


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Copyright information

© The Optical Society of Japan 2016

Authors and Affiliations

  • Sadao Aoki
    • 1
    Email author
  • Norio Watanabe
    • 1
  • Hiroshi Asami
    • 1
  • Akihiro Shimada
    • 1
  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

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