The Optics of Rays, Wavefronts, and Caustics - 1st Edition - ISBN: 9780126640502, 9780323155557

The Optics of Rays, Wavefronts, and Caustics

1st Edition

Authors: O Stavroudis
eBook ISBN: 9780323155557
Imprint: Academic Press
Published Date: 28th October 1972
Page Count: 332
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Description

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

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


Details

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

About the Author

O Stavroudis

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