Imaging properties of an extreme ultraviolet microscope objective with reduced Fresnel number

Mitsunori Toyoda, Kota Kuramitsu, Mihiro Yanagihara

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


On imaging for full-field extreme ultraviolet microscopy, the Fresnel number on the image plane falls below unity since a high magnification objective remarkably reduces the numerical aperture on the image plane, while the Fresnel number on the object plane is relatively large in most cases. To understand imaging with the high-magnification objective with far different Fresnel numbers on these two planes, in this study, we experimentally confirmed the imaging properties by observing through-focus images of a point object on both the object and image sides. The experiments showed that, the defocus characteristics on the image side were found to be asymmetric with respect to the detector location, while those on the object side were found to be symmetric with respect to the object distance. To explain these unconventional imaging properties, we proposed a simple analytical model considering the two different Fresnel numbers on the high-magnification objective. The model showed that the magnification would vary even if the image plane was within the focal depth, and this yields the asymmetric defocus characteristics. At the same time, when we moved an object along an optical axis, the defocus aberrations were represented by the conventional equation for a large-Fresnel-number system, which can well explain the symmetric defocus characteristics on the object side. We also discuss the effect of an additional phase factor that modifies the amplitude on the image plane.

Original languageEnglish
Pages (from-to)312-317
Number of pages6
JournalOptics Communications
Publication statusPublished - 2017 Dec 15


  • Imaging theory
  • Multilayer mirror
  • Schwarzschild objective
  • Soft-X-ray

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering


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