Sensitivity control to surface irregularity

Yabe, Akira

doi:10.1117/12.692246

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Modified Orthogonal Functions1

Introduction1

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2016

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Cited by 4 publications

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“…Yabe used these polynomials to control the sensitivity to the surface irregularity [6]. The polynomials P 4 10 ρ, P 4 12 ρ, and P 4 14 ρ are given in the paper of Forbes [7].…”

Section: Modified Orthogonal Functionsmentioning

confidence: 99%

Representation of freeform surfaces suitable for optimization

Yabe

2012

Appl. Opt.

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“…Yabe used these polynomials to control the sensitivity to the surface irregularity [6]. The polynomials P 4 10 ρ, P 4 12 ρ, and P 4 14 ρ are given in the paper of Forbes [7].…”

Section: Modified Orthogonal Functionsmentioning

confidence: 99%

Representation of freeform surfaces suitable for optimization

Yabe

2012

Appl. Opt.

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“…[1][2][3][4][5] In particular, the effectiveness of odd-order surfaces, which are expressed with terms including an odd-integer power of the radius, has begun to be recognized via the designs of viewfinders, 6 microscopes, 7 camera lenses, 8 projection display optics, 9 EUV optical systems, [10][11][12] and so on. Since aberration characteristics of odd-order surfaces differ largely from those of conventional aspheric surfaces, it is meaningful and important to analyze the features of odd-order surfaces mathematically.…”

Section: Introductionmentioning

confidence: 99%

Convergence and differentiation of Zernike expansion: application for an analysis of odd-order surfaces

2016

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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. © The Authors.Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Lens design with Forbes aspheres

Youngworth¹,

Betensky²

2008

SPIE Proceedings

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Sensitivity control to surface irregularity

Cited by 4 publications

References 3 publications

Representation of freeform surfaces suitable for optimization

Representation of freeform surfaces suitable for optimization

Convergence and differentiation of Zernike expansion: application for an analysis of odd-order surfaces

Lens design with Forbes aspheres

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