The Optics of Rays, Wavefronts, and Caustics presents the fundamental principles of geometrical optics and its unique role in modern technology. It also discusses the procedures used in optical design, which are based on geometrical optics.

Organized into 16 chapters, this volume begins with an overview of the underlying general mathematical facts, which constitute the substance of geometrical optics. It then presents the various techniques used to solve the ray and wavefront problems in general inhomogeneous medium. Other chapters consider the concept of ray tracing as a tool for calculating the principal curvatures of a wavefront as it propagates through a lens. In addition, the book tackles several topics, including the aspects of lens design, as well as a system of equations that are similar to the Maxwell equations. The last chapter deals with orthotomic systems of rays.
Optical designers, optical physicists, theoretical physicists, and mathematicians will find the information and methods in this book extremely useful.

Contenu

Preface
Acknowledgments
I Introduction
The Seventeenth Century
Descartes
Newton and Fermat
Huygens
The Nineteenth Century
The Brachistochrone
References
II The Calculus of Variations
The Statement of the Problem
The Problem in Three Dimensions
The Shortest Distance between Two Points
The Problem in Parametric Form
The Application to Geometrical Optics
References
III Space Curves
The Frenet Equations
The Cylindrical Helix
The Osculating Sphere
Optical Applications
The Directional Derivative
References
IV Applications
Maxwell's Fish Eye
The Heated Window
The Brachistochrone
References
V The Hubert Integral
The Hubert Integral Defined
A Lemma
The Main Theorem
An Illustration
The Parametric Case
Snell's Law
Wavefronts and Caustics
References
VI Ray Tracing
Refraction
Reflection
Transfer
The Sphere
Conic Surfaces
Transfer for Conic Surfaces
The Cylindrical Lens
Cartesian Ovals
References
VII Orthotomic Systems of Ray
The Total Differential Equation
Exactness and Integrability
Orthotomic Systems
Some Properties
The Orthogonal Surface
Canonical Variables and the Hamilton-Jacobi Equations
The Application to Geometrical Optics
The Theorem of Malus
References
VIII Wavefronts
The Nonlinear, First-Order Equation
The Bracket
The Complete Integral
The Eikonal Equation
The Singular and General Integrals
The General Integral for Homogeneous Media
References
IX Surfaces
The Theorems of Meusner and Gauss
The Weingarten Equations
Transformation of the Parameters
Generalized Ray Tracing
Caustic Surfaces
References
X Generalized Ray Tracing
Spherical Refracting Surfaces
The General Rotationally Symmetric Surface
Conic Surfaces
The Plane Refracting Surface
The in-the-Large Problem
References
XI The Inhomogeneous Medium
Geodesic Curves
Some Vector Identities
Geodesies on a Wavefront
More on the Fish Eye
The Pseudo-Maxwell Equations
References
XII Classical Aberration Theory
The Point Eikonal
The Angle Eikonal
The Rotationally Symmetric System
The First Order: Gaussian Optics
Some Practical Formulas
Pupil Planes
The Third Order
The Seidel Aberrations
Herzberger's Diapoint Theory
The Convergence Problem
References
XIII The Fundamental Optical Invariant
The Inhomogeneous Medium
The Lens Equation
The Rotationally Symmetric System
A General Solution
The Residual Equations
A Change of Variables
The Final Factorization
References
XIV The Lens Equation
The Transfer Matrix
The Refraction Matrix
The Refraction Calculations
The Perfect Lens
References
XV The Lens Group
The Full Linear Group
The Lie Group
Subgroups
The Optical Application
Essential Parameters
Generators
Further Optical Applications
The Paraxial Case
References
XVI Conclusion
Index