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Optical Engineering • Open Access

Convergence and differentiation of Zernike expansion: application for an analysis of odd-order surfaces
Author(s): Takao Tanabe; Masato Shibuya; Kazuhisa Maehara

Paper Abstract

Odd-order surfaces have begun to be used in optics. In order to investigate the aberration characteristics of such surfaces, Zernike expansion is widely used since it directly and explicitly corresponds to wavefront aberrations. Since the Zernike expansion of an odd-order surface contains an infinite number of terms, the convergence of the expanded sum and the possibility of termwise derivatives are not explicitly guaranteed mathematically. We give a complete proof for these problems. For an application of this result, we analyze the aberration characteristics of odd-order surfaces and present their effectiveness in optical design.

Paper Details

Date Published: 1 March 2016
PDF: 9 pages
Opt. Eng. 55(3) 035101 doi: 10.1117/1.OE.55.3.035101
Published in: Optical Engineering Volume 55, Issue 3
Show Author Affiliations
Takao Tanabe, Topcon Corp. (Japan)
Tokyo Polytechnic Univ. (Japan)
Masato Shibuya, Tokyo Polytechnic Univ. (Japan)
Kazuhisa Maehara, Tokyo Polytechnic Univ. (Japan)

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