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 journalArticlepeer-review

    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

    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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