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Optical Path Theory

Fundamentals to freeform adaptive optics
Rafael G González-Acuña, Hector A Chaparro-Romo


This book 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 book addresses 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. The book moves into exploring optical systems in the plane. Step-by-step equations provide each of these systems to plot their waves, emphasising the mathematical derivations.

With a mathematical presentation of concepts, this book is complete with details, problems, solutions, and a multitude of useful examples. Ideal for graduates in optics.

Key Features

• Provides an introduction of the three main axioms implemented in optical path theory

• Includes worked examples and problems in each chapter

• Presents codes and algorithms

• Details the physical concepts and mathematical tools needed to understand eikonal and the closed form solution of stigmatic optical systems

• Contains Mathematica throughout.

About Editors

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.

Table of Contents

About the Authors 3
Acknowledgements 5
Preface 9
Dedication 11

1 The path of the light 19

2 General catoptric stigmatic surfaces 53

3 General dioptric stigmatic surfaces 101

4 The aspheric transfer function lens 143

5 General equation of the aspheric wavefront generator lens 167

6 General mirror for adaptive optical systems 205

7 General freeform dioptric stigmatic surfaces 247

8 The freeform transfer function lens 287

9 General equation of the freeform wavefront generator lens 319


Hardback ISBN: 9780750347037

Ebook ISBN: 9780750347051

DOI: 10.1088/978-0-7503-4705-1

Publisher: Institute of Physics Publishing

Series: IOP Series in Emerging Technologies in Optics and Photonics


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