General formula to design a freeform singlet free of spherical aberration and astigmatism

In this paper, an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface to correct the spherical aberration. The derivation is...

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Bibliographic Details
Published in:Applied optics (2004) 2019-02, Vol.58 (4), p.1010
Main Authors: González-Acuña, Rafael G, Chaparro-Romo, Héctor A, Gutiérrez-Vega, Julio C
Format: Article
Language:English
Subjects:
Aberration
Astigmatism
Astigmatism - pathology
Fermat principle
Formulas (mathematics)
Geometrical optics
Humans
Lens, Crystalline - pathology
Mathematical analysis
Optics and Photonics
Refractive Errors - pathology
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Summary:In this paper, an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface to correct the spherical aberration. The derivation is based on the formal application of the variational Fermat principle under the standard geometrical optics approximation.
ISSN:1559-128X
2155-3165
DOI:10.1364/AO.58.001010