Overview
- Explores the connection between optimal transport and geometric optics, focusing on the design of free-form lenses
- Offers self-contained presentation, with detailed explanations and full proofs of the theorems and results
- Leverages optimal transport principles for the design of non-rotationally symmetric lenses
Part of the book series: SpringerBriefs on PDEs and Data Science (SBPDEDS)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
- Monge-Kantorovich problem
- Wasserstein distance
- Kantorovich-Rubinstein duality
- Monge-Ampère equation
- Optimal maps
- Transhipment problem
- Disintegration of measures
- Sinkhorn algorithm
- Brenier polar factorization
- Benamou and Brenier formula
- Snell’s law of refraction
- Refractor problem
- Near field refraction
- Far field refraction
- Legendre transform
- cyclical monotonicity
- network flow problem
About this book
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area.
Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.
Authors and Affiliations
About the author
Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.
Bibliographic Information
Book Title: Optimal Transport and Applications to Geometric Optics
Authors: Cristian E. Gutiérrez
Series Title: SpringerBriefs on PDEs and Data Science
DOI: https://doi.org/10.1007/978-981-99-4867-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
Softcover ISBN: 978-981-99-4866-6Published: 10 December 2023
eBook ISBN: 978-981-99-4867-3Published: 09 December 2023
Series ISSN: 2731-7595
Series E-ISSN: 2731-7609
Edition Number: 1
Number of Pages: X, 135
Number of Illustrations: 1 b/w illustrations
Topics: Optimization, Operations Research, Management Science, Atomic, Molecular, Optical and Plasma Physics, Analysis