Superconical aplanatic ovoid singlet lenses.

In this work, we return to Descartes's idea to develop a formalism to construct rigorously stigmatic singlet lenses comprising two Cartesian surfaces. Optical systems are built using a considerable number of spherical surfaces, presenting in most cases spherical aberration. Wasermann and Wolf proposed eliminating spherical aberration and minimizing third-order coma by using two adjacent aspherical surfaces. That is why, using a parametric formulation for Cartesian ovals, we propose the design of singlet lenses where the condition of rigorous stigmatism is guaranteed for each surface, and therefore, strictly speaking, in the pair of stigmatic points, the lens becomes an optical system free of spherical aberration. This formulation is unified to both refractive and reflective optical surfaces. Therefore, within the framework of the theory of rigorously stigmatic optical systems, making use of Cartesian surfaces for the construction of stigmatic ovoid singlet lenses, we achieve the same functionality of optical systems involving a set of spherical lenses. These lenses have the advantage of being formulated according to a generalized shape factor associated with the Coddington shape factor, allowing an easy classification of these stigmatic lenses. The ideal imaging is carried out by applying an exact ray-tracing method through these ovoid singlet lenses.