This book presents the solution for designing an on-axis stigmatic lens, a lens free of spherical aberration. The history behind the problem, which has persisted for millennia, is reviewed and an in-depth look at lenses free of spherical aberrations is provided using illustrative examples and historical contexts. Mathematical principles behind lenses free of spherical aberration are included with an introduction to set theory, the conics, continuity, real analysis and topology. Physical principles are covered as well as a step by step guide to mathematical model for deducing the general formula of the stigmatic lens, in order to design a singlet free of spherical aberration. Subsequently, the characteristics of these lenses and the equations that describes them are studied. Finally, several implications of these lenses are studied, such as freeform lenses, optical systems, axicons, telescopes and more. Scenarios with on-axis objects and off-axis objects are considered. Cases where the object is real or virtual, and the image is real or virtual are also presented. The book is a valuable resource for industrial specialists and academics in lens design and optics, and an insightful guide for optical physics students.

Rafael G González-Acuña studied industrial physics engineering at the Tecnológico de Monterrey, Mexico, and earned a master's degree in optomechatronics at Centro de Investigaciones en Óptica. He is currently studying for a PhD at the Tecnológico de Monterrey.

Héctor A Chaparro-Romo is an electronic engineer specialising in scienti¿c computation. He has years of experience in optics research and applications.

Julio C Gutiérrez-Vega is a full professor within the Physics Department at the Tecnológico de Monterrey, México, where he also heads the Photonics and Mathematical Optics Group.