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

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Abstract

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.

© 2019 Optical Society of America

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Supplementary Material (3)

NameDescription
Code 1       Mathematica code to plot freeform surfaces free of spherical aberration
Visualization 1       Back view of singlet lens with sinusoidal input surfaces
Visualization 2       Subplot (a) singlet lenses with input surfaces mixing concave/convex with oscillating behavior.

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Equations (16)

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