Theoretical investigation of the meaning of odd-order aspherical surface and numerical confirmation of effectiveness in rotational-symmetric but off-axis optics

Masato Shibuya, Kazuhisa Maehara, Yoshihito Ishikawa, Akira Takada, Kei Kobayashi, Mitsunori Toyoda, Masanori Tanikawa, Suezou Nakadate

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Even though odd-order aspherical surfaces have sometimes been used in optics, their meaning and effectiveness have not been discussed enough to be fully understood. However, we have already discussed and derived mathematically that odd-order aspherical surfaces cannot be represented in the form of a power series of even-order even when rotationally symmetric. We have also explained that this result does not contradict the fact that the set of Zernike's circle polynominals forms a complete system and that their rotational symmetric terms consist only of even-order terms of radial coordinates. First, we reconsider these mathematical discussions. Second, we reveal that the first- and third-order aspherical surfaces are valuable in practical lens designing for catoptoric projection optics of extreme ultraviolet lithography.

Original languageEnglish
Article number073003
JournalOptical Engineering
Volume49
Issue number7
DOIs
Publication statusPublished - 2010 Jul 1

Keywords

  • Zernike's circle polynominals
  • aspherical surface
  • extreme ultraviolet lithography
  • odd-order aspherical surface
  • optical design

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering(all)

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