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Optical Engineering

Theoretical investigation of the meaning of odd-order aspherical surface and numerical confirmation of effectiveness in rotational-symmetric but off-axis optics
Author(s): Masato Shibuya; Kazuhisa Maehara; Yoshihito Ishikawa; Akira Takada; Kei Kobayashi; Mitsunori Toyoda; Masanori Tanikawa; Suezou Nakadate
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Paper 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.

Paper Details

Date Published: 1 July 2010
PDF: 7 pages
Opt. Eng. 49(7) 073003 doi: 10.1117/1.3461991
Published in: Optical Engineering Volume 49, Issue 7
Show Author Affiliations
Masato Shibuya, Tokyo Polytechnic Univ. (Japan)
Kazuhisa Maehara, Tokyo Polytechnic Univ. (Japan)
Yoshihito Ishikawa, Tokyo Polytechnic Univ. (Japan)
Akira Takada, Topcon Corp. (Japan)
Kei Kobayashi, Tokyo Polytechnic Univ. (Japan)
Mitsunori Toyoda, Tohoku Univ. (Japan)
Masanori Tanikawa, Tokyo Polytechnic Univ. (Japan)
Suezou Nakadate, Tokyo Polytechnic Univ. (Japan)

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