Stigmatic aspherical refracting surfaces from Cartesian ovoids

Abstract

A theory for Descartes ovoids has been developed in terms of four form parameters, (GOTS). This theory allows the design of optical imaging systems that, in addition to a rigorous stigmatism, exhibit the property of aplanatism, necessary for the proper imaging of extended objects. As a decisive step for the production of these systems, in this work, we propose a formulation of Descartes ovoids in the form of standard aspherical surfaces (ISO 10110-12: 2019), by means of explicit formulas for the corresponding aspheric coefficients. Thus, with these results, the designs developed with Descartes ovoids are finally translated into the language of aspherical surfaces for their production, inheriting the aspherical surfaces of all optical properties of Cartesian surfaces. Consequently, these results make this optical design methodology viable for the development of technological solutions using the current optical fabrication capabilities of the industry.