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

doi:10.1117/1.3461991

1 July 2010 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

Author Affiliations +

Optical Engineering, Vol. 49, Issue 7, 073003 (July 2010). https://doi.org/10.1117/1.3461991

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.

©(2010) Society of Photo-Optical Instrumentation Engineers (SPIE)

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Masato Shibuya, Kazuhisa Maehara, Yoshihito Ishikawa, Akira Takada, Kei Kobayashi, Mitsunori Toyoda, Masanori Tanikawa, and Suezou Nakadate "Theoretical investigation of the meaning of odd-order aspherical surface and numerical confirmation of effectiveness in rotational-symmetric but off-axis optics," Optical Engineering 49(7), 073003 (1 July 2010). https://doi.org/10.1117/1.3461991

Published: 1 July 2010

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