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

Abstract

The comment made by Valencia-Estrada and García-Márquez [Appl. Opt. 59, 3422 (2020)APOPAI0003-693510.1364/AO.379238] to our paper [Appl. Opt. 58, 1010 (2019)APOPAI0003-693510.1364/AO.58.001010] consists of a trivial generalization of our formulation.

Analytic solution of the eikonal for a stigmatic singlet lens

“…In the first column of figure 4, we present other example of H(t, s) of equation (10), but now with a virtual image. At the left side: (top) we show the ray tracing; (centre) the wavefronts; (bottom) both rays and wavefronts [20][21][22]. To plot the eikonals when the object is virtual, we still apply equations (2)-( 5) but we slight modify H(t, s) as follows where = + R Ta nT and the conditions become…”