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An analytical closed-form formula for the design of freeform lenses free ofspherical aberration is presented. Given the equation of the freeform inputsurface, the formula gives the equation of the second surface in order tocorrect the spherical aberration. The derivation is based on the formalapplication of the variational Fermat principle under the standard geometricaloptics approximation.

Rigorous analytical formula for freeform singlet lens design free of spherical aberration