This book presents an in-depth look at lenses free of spherical aberrations and is provided
using illustrative examples. Mathematical principles behind lenses free of spherical …

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 …

We generalize the shape of the traditional axicon by analytically finding the function of the
output surface when the input surface is not flat but an arbitrary continuous function that …

Cartesian ovals, also known as rigorously stigmatic surfaces, are the simplest optical
systems capable of producing a perfect point image. Exist both implicit and explicit …

It is known that, besides being stigmatic, spherical refracting surfaces are aplanatic at their
Young points since they satisfy the Abbe sine condition rigorously. The Abbe sine condition …

This paper describes a method to design families of singlet lenses free of all orders of
spherical aberration. These lenses can be mass produced according to Schwarzschild's …

We study the formation of caustic surfaces produced by conic lenses, considering a plane
wavefront propagating parallel to the optical axis. The shape of the caustic can be modified …

Given an arbitrary input wavefront, we derive the analytical refractive surface that refracts the
wavefront into a single image point. The derivation of the surface is fully analytical without …

In this paper we propose a mathematical model as a theoretical and practical contribution to
the theory of aspheric surfaces, that allows the geometrical calculation of an aspherical …

Monochromatic and chromatic aberrations are imaging defects mainly studied from a
geometrical optics point of view. These defects are treated through optimization and …