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

General formula for bi-aspheric singlet lens design free of spherical aberration

Rafael G. González-Acuña and Héctor A. Chaparro-Romo
Appl. Opt. 57(31) 9341-9345 (2018)

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

J. C. Valencia-Estrada and J. García-Márquez
Appl. Opt. 59(11) 3422-3424 (2020)

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

Rafael G. González-Acuña, Héctor A. Chaparro-Romo, and Julio C. Gutiérrez-Vega
Appl. Opt. 59(11) 3425-3426 (2020)

Singlet lens for generating aberration-free patterns on deformed surfaces

Rafael G. González-Acuña, Maximino Avendaño-Alejo, and Julio C. Gutiérrez-Vega
J. Opt. Soc. Am. A 36(5) 925-929 (2019)

Calculation of zonal power and astigmatism of a freeform gradient index lens with freeform surfaces

Nicholas S. Kochan and Greg R. Schmidt
Appl. Opt. 62(12) 2978-2987 (2023)