Optical Path Theory

This treatise is mostly based in an equation that was recently published, the equation is the general formula for adaptive optics mirrors, which was published in January 2021, General mirror formula for adaptive optics, Applied Optics 60(2). The treatise address the introductory topics, the solution (general formula for adaptive optics mirrors), the implications, and the potential applications.
Optical Path Theory: Fundamentals to freeform adaptive optics focuses on the potential to find analytical close form solutions using optical path theory to solve and design adaptive optics systems, with a thorough introduction to the subject.
After the main axioms are presented, the book moves into exploring optical systems in the plane. The refractive mirror, refractive surface, lens, and the transfer function lens are discussed. Equations are provided with each of these various systems to plot their waves, putting emphasis on the mathematical derivations and showing a variety of examples.
As the various systems continue to be explored, they are generalized to three dimensions. Presented mathematically, the generalization to three dimensions focuses on the key steps on each derivation. These generalisations are richer and lead to freeform shapes which are explored in detail.
Mathematica codes for all the examples in the book are provided. With a step-by-step mathematical presentation of concepts, this book is complete with details, problems, solutions, and a multitude of useful examples. Ideal for graduates in optics.

Rafael G González-Acuña studied industrial physics engineering at the Tecnológico de Monterrey gaining a master's degree in optomechatronics at the Optics Research Center, A.C., and studied his PhD at the Tecnológico de Monterrey. His doctoral thesis focuses on the design of free spherical aberration lenses. Rafael has been awarded the 2019 Optical Design and Engineering Scholarship by SPIE and he is the co-author of three IOP books.
Héctor A Chaparro-Romo, Electronic Engineer with Master's studies in Computer Science specialised in scientific computation and years of experience in optics research and applications, he is co-author of the solution to the problem of designing bi-aspheric singlet lenses free of spherical aberration. Héctor is the co-author of the IOP book, Analytical lens design.