The Optics of Rays, Wavefronts, and Caustics

The Optics of Rays, Wavefronts, and Caustics

1st Edition - October 28, 1972

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  • Author: O Stavroudis
  • eBook ISBN: 9780323155557

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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.

Table of Contents

  • Preface


    I Introduction

    The Seventeenth Century


    Newton and Fermat


    The Nineteenth Century

    The Brachistochrone


    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


    III Space Curves

    The Frenet Equations

    The Cylindrical Helix

    The Osculating Sphere

    Optical Applications

    The Directional Derivative


    IV Applications

    Maxwell's Fish Eye

    The Heated Window

    The Brachistochrone


    V The Hubert Integral

    The Hubert Integral Defined

    A Lemma

    The Main Theorem

    An Illustration

    The Parametric Case

    Snell's Law

    Wavefronts and Caustics


    VI Ray Tracing




    The Sphere

    Conic Surfaces

    Transfer for Conic Surfaces

    The Cylindrical Lens

    Cartesian Ovals


    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


    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


    IX Surfaces

    The Theorems of Meusner and Gauss

    The Weingarten Equations

    Transformation of the Parameters

    Generalized Ray Tracing

    Caustic Surfaces


    X Generalized Ray Tracing

    Spherical Refracting Surfaces

    The General Rotationally Symmetric Surface

    Conic Surfaces

    The Plane Refracting Surface

    The in-the-Large Problem


    XI The Inhomogeneous Medium

    Geodesic Curves

    Some Vector Identities

    Geodesies on a Wavefront

    More on the Fish Eye

    The Pseudo-Maxwell Equations


    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


    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


    XIV The Lens Equation

    The Transfer Matrix

    The Refraction Matrix

    The Refraction Calculations

    The Perfect Lens


    XV The Lens Group

    The Full Linear Group

    The Lie Group


    The Optical Application

    Essential Parameters


    Further Optical Applications

    The Paraxial Case


    XVI Conclusion


Product details

  • No. of pages: 332
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: October 28, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9780323155557

About the Author

O Stavroudis

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