Principles of Optics

Principles of Optics

Electromagnetic Theory of Propagation, Interference and Diffraction of Light

6th Edition - January 1, 1980

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  • Authors: Max Born, Emil Wolf
  • eBook ISBN: 9781483103204

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Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Sixth Edition covers optical phenomenon that can be treated with Maxwell’s phenomenological theory. The book is comprised of 14 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves. The selection will be most useful to researchers whose work involves understanding the behavior of light.

Table of Contents

  • Historical Introduction

    I. Basic Properties of the Electromagnetic Field

    1.1. The Electromagnetic Field

    1.1.1. Maxwell's Equations

    1.1.2. Material Equations

    1.1.3. Boundary Conditions at a Surface of Discontinuity

    1.1.4. The Energy Law of the Electromagnetic Field

    1.2. The Wave Equation and the Velocity of Light

    1.3. Scalar Waves

    1.3.1. Plane Waves

    1.3.2. Spherical Waves

    1.3.3. Harmonic Waves. The Phase Velocity

    1.3.4. Wave Packets. The Group Velocity

    1.4. Vector Waves

    1.4.1. The General Electromagnetic Plane Wave

    1.4.2. The Harmonic Electromagnetic Plane Wave

    1.4.3. Harmonic Vector Waves of Arbitrary Form

    1.5. Reflection and Refraction of a Plane Wave

    1.5.1. The Laws of Reflection and Refraction

    1.5.2. Fresnel Formula

    1.5.3. The Reflectivity and Transmissivity; Polarization on Reflection and Refraction

    1.5.4. Total Reflection

    1.6. Wave Propagation in a Stratified Medium. Theory of Dielectric Films

    1.6.1. The Basic Differential Equations

    1.6.2. The Characteristic Matrix of a Stratified Medium

    1.6.3. The Reflection and Transmission Coefficients

    1.6.4. A Homogeneous Dielectric Film

    1.6.5. Periodically Stratified Media

    II. Electromagnetic Potentials and Polarization

    2.1. The Electrodynamic Potentials in the Vacuum

    2.1.1. The Vector and Scalar Potentials

    2.1.2. Retarded Potentials

    2.2. Polarization and Magnetization

    2.2.1. The Potentials in Terms of Polarization and Magnetization

    2.2.2. Hertz Vectors

    2.2.3. The Field of a Linear Electric Dipole

    2.3. The Lorentz-Lorenz Formula and Elementary Dispersion Theory

    2.3.1. The Dielectric and Magnetic Susceptibilities

    2.3.2. The Effective Field

    2.3.3. The Mean Polarizability: the Lorentz-Lorenz Formula

    2.3.4. Elementary Theory of Dispersion

    2.4. Propagation of Electromagnetic Waves Treated by Integral Equations

    2.4.1. The Basic integral Equation

    2.4.2. The Ewald-Oseen Extinction Theorem and a Rigorous Derivation of the Lorentz-Lorenz Formula

    2.4.3. Refraction and Reflection of a Plane Wave, Treated with the Help of the Ewald-Oseen Extinction Theorem

    III. Foundations of Geometrical Optics

    3.1. Approximation for Very Short Wavelengths

    3.1.1. Derivation of the Eikonal Equation

    3.1.2. The Light Rays and the Intensity Law of Geometrical Optics

    3.1.3. Propagation of the Amplitude Vectors

    3.1.4. Generalizations and the Limits of Validity of Geometrical Optics

    3.2. General Properties of Rays

    3.2.1. The Differential Equation of Light Rays

    3.2.2. The Laws of Refraction and Reflection

    3.2.3. Ray Congruences and Their Focal Properties

    3.3. Other Basic Theorems of Geometrical Optics

    3.3.1. Lagrange's Integral Invariant

    3.3.2. The Principle of Fermat

    3.3.3. The Theorem of Malus and Dupin and Some Related Theorems

    IV. Geometrical Theory of Optical Imaging

    4.1. The Characteristic Functions of Hamilton

    4.1.1. The Point Characteristic

    4.1.2. The Mixed Characteristic

    4.1.3. The Angle Characteristic

    4.1.4. Approximate Form of the Angle Characteristic of a Refracting Surface of Revolution

    4.1.5. Approximate Form of the Angle Characteristic of a Reflecting Surface of Revolution

    4.2. Perfect Imaging

    4.2.1. General Theorems

    4.2.2. Maxwell's "Fish-Eye"

    4.2.3. Stigmatic Imaging of Surfaces

    4.3. Projective Transformation (Collineation) with Axial Symmetry

    4.3.1. General Formula

    4.3.2. The Telescopic Case

    4.3.3. Classification of Projective Transformations

    4.3.4. Combination of Projective Transformations

    4.4. Gaussian Optics

    4.4.1. Refracting Surface of Revolution

    4.4.2. Reflecting Surface of Revolution

    4.4.3. The Thick Lens

    4.4.4. The Thin Lens

    4.4.5. The General Centered System

    4.5. Stigmatic Imaging with Wide-angle Pencils

    4.5.1. The Sine Condition

    4.5.2. The Herschel Condition

    4.6. Astigmatic Pencils of Rays

    4.6.1. Focal Properties of a Thin Pencil

    4.6.2. Refraction of a Thin Pencil

    4.7. Chromatic Aberration. Dispersion by a Prism

    4.7.1. Chromatic Aberration

    4.7.2. Dispersion by a Prism

    4.8. Photometry and Apertures

    4.8.1. Basic Concepts of Photometry

    4.8.2. Stops and Pupils

    4.8.3. Brightness and Illumination of Images

    4.9. Ray Tracing

    4.9.1. Oblique Meridional Rays

    4.9.2. Paraxial Rays

    4.9.3. Skew Rays

    4.10. Design of Aspheric Surfaces

    4.10.1. Attainment of Axial Stigmatism

    4.10.2. Attainment of Aplanatism

    V. Geometrical Theory of Aberrations

    5.1. Wave and Ray Aberrations; the Aberration Function

    5.2. The Perturbation Eikonal of Schwarzschild

    5.3. The Primary (Seidel) Aberrations

    5.4. Addition Theorem for the Primary Aberrations

    5.5. The Primary Aberration Coefficients of a General Centered Lens System

    5.5.1. The Seidel Formula in Terms of Two Paraxial Rays

    5.5.2. The Seidel Formula in Terms of one Paraxial Ray

    5.5.3. Petzval's Theorem

    5.6. Example: The Primary Aberrations of a Thin Lens

    5.7. The Chromatic Aberration of a General Centered Lens System

    VI. Image-Forming Instruments

    6.1. The Eye

    6.2. The Camera

    6.3. The Refracting Telescope

    6.4. The Reflecting Telescope

    6.5. Instruments of Illumination

    6.6. The Microscope

    VII. Elements of the Theory of Interference and Interferometers

    7.1. Introduction

    7.2. Interference of Two Monochromatic Waves

    7.3. Two-Beam Interference: Division of Wave-Front

    7.3.1. Young's Experiment

    7.3.2. Fresnel's Mirrors and Similar Arrangements

    7.3.3. Fringes with Quasi-Monochromatic and White Light

    7.3.4. Use of Slit Sources; Visibility of Fringes

    7.3.5. Application to the Measurement of optical Path Difference: the Rayleigh Interferometer

    7.3.6. Application to the Measurement of Angular Dimensions of Sources: the Michelson Stellar Interferometer

    7.4. Standing Waves

    7.5. Two-Beam Interference: Division of Amplitude

    7.5.1. Fringes with a Plane Parallel Plate

    7.5.2. Fringes with Thin Films; the Fizeau Interferometer

    7.5.3. Localization of Fringes

    7.5.4. The Michelson Interferometer

    7.5.5. The Twyman-Green and Related Interferometers

    7.5.6. Fringes with Two Identical Plates: the Jamin Interferometer and Interference Microscopes

    7.5.7. The Mach-Zehnder Interferometer; the Bates Wave-Front Shearing Interferometer

    7.5.8. The Coherence Length; the Application of Two-Beam Interference to the Study of the Fine Structure of Spectral Lines

    7.6. Multiple-Beam Interference

    7.6.1. Multiple-Beam Fringes with a Plane Parallel Plate

    7.6.2. The Fabry-Perot Interferometer

    7.6.3. The Application of the Fabry-Perot Interferometer to the Study of the Fine Structure of Spectral Lines

    7.6.4. The Application of the Fabry-Perot Interferometer to the Comparison of Wavelengths

    7.6.5. The Lummer-Gehrcke Interferometer

    7.6.6. Interference Filters

    7.6.7. Multiple-Beam Fringes with Thin Films

    7.6.8. Multiple-Beam Fringes with Two Plane Parallel Plates

    7.7. The Comparison of Wavelengths with the Standard Meter

    VIII. Elements of the Theory of Diffraction

    8.1. Introduction

    8.2. The Huygens-Fresnel Principle

    8.3. Kirchhoff's Diffraction Theory

    8.3.1. The Integral Theorem of Kirchhoff

    8.3.2. Kirchhoff's Diffraction Theory

    8.3.3. Fraunhofer and Fresnel Diffraction

    8.4. Transition to a Scalar Theory

    8.4.1. The Image Field Due to a Monochromatic oscillator

    8.4.2. The Total Image Field

    8.5. Fraunhofer Diffraction at Apertures of Various Forms

    8.5.1. The Rectangular Aperture and the Slit

    8.5.2. The Circular Aperture

    8.5.3. Other Forms of Aperture

    8.6. Fraunhofer Diffraction in Optical Instruments

    8.6.1. Diffraction Gratings

    8.6.2. Resolving Power of Image-forming Systems

    8.6.3. Image Formation in the Microscope

    8.7. Fresnel Diffraction at a Straight Edge

    8.7.1. The Diffraction Integral

    8.7.2. Fresnel's Integrals

    8.7.3. Fresnel Diffraction at a Straight Edge

    8.8. The Three-Dimensional Light Distribution near Focus

    8.8.1. Evaluation of the Diffraction Integral in Terms of Lommel Functions

    8.8.2. The Distribution of Intensity

    8.8.3. The Integrated Intensity

    8.8.4. The Phase Behavior

    8.9. The Boundary Diffraction Wave

    8.10. Gabor's Method of Imaging by Reconstructed Wave-Fronts (Holography)

    8.10.1. Producing the Positive Hologram

    8.10.2. The Reconstruction

    IX. The Diffraction Theory of Aberrations

    9.1. The Diffraction Integral in the Presence of Aberrations

    9.1.1. The Diffraction Integral

    9.1.2. The Displacement Theorem. Change of Reference Sphere

    9.1.3. A Relation between the Intensity and the Average Deformation of Wave-Fronts

    9.2. Expansion of the Aberration Function

    9.2.1. The Circle Polynomials of Zernike

    9.2.2. Expansion of the Aberration Function

    9.3. Tolerance Conditions for Primary Aberrations

    9.4 The Diffraction Pattern Associated with a Single Aberration

    9.4.1. Primary Spherical Aberration

    9.4.2. Primary Coma

    9.4.3. Primary Astigmatism

    9.5. Imaging of Extended Objects

    9.5.1. Coherent Illumination

    9.5.2. Incoherent Illumination

    X. Interference and Diffraction with Partially Coherent Light

    10.1. Introduction

    10.2. A Complex Representation of Real Polychromatic Fields

    10.3. The Correlation Functions of Light Beams

    10.3.1. Interference of Two Partially Coherent Beams. The Mutual Coherence Function and the Complex Degree of Coherence

    10.3.2. Spectral Representation of Mutual Coherence

    10.4. Interference and Diffraction with Quasi-monochromatic Light

    10.4.1. Interference with Quasi-monochromatic Light. The Mutual Intensity

    10.4.2. Calculation of Mutual Intensity and Degree of Coherence for Light from an Extended Incoherent Quasi-Monochromatic Source

    10.4.3. An Example

    10.4.4. Propagation of Mutual Intensity

    10.5. Some Applications

    10.5.1. The Degree of Coherence in the Image of an Extended Incoherent Quasi-Monochromatic Source

    10.5.2. The Influence of the Condenser on Resolution in a Microscope

    10.5.3. Imaging with Partially Coherent Quasi-monochromatic Illumination

    10.6. Some Theorems Relating to Mutual Coherence

    10.6.1. Calculation of Mutual Coherence for Light from an Incoherent Source

    10.6.2. Propagation of Mutual Coherence

    10.7. Rigorous Theory of Partial Coherence

    10.7.1. Wave Equations for Mutual Coherence

    10.7.2. Rigorous Formulation of the Propagation Law for Mutual Coherence

    10.7.3. The Coherence Time and the Effective Spectral Width

    10.8. Polarization Properties of Quasi-Monochromatic Light

    10.8.1. The Coherency Matrix of a Quasi-Monochromatic Plane Wave

    10.8.2. Some Equivalent Representations. The Degree of Polarization of a Light Wave

    10.8.3. The Stokes Parameters of a Quasi-Monochromatic Plane Wave

    XI. Rigorous Diffraction Theory

    11.1. Introduction

    11.2. Boundary Conditions and Surface Currents

    11.3. Diffraction by a Plane Screen: Electromagnetic Form of Babinet's Principle

    11.4. Two-Dimensional Diffraction by a Plane Screen

    11.4.1. The Scalar nature of Two-dimensional Electromagnetic Fields

    11.4.2. An Angular Spectrum of Plane Waves

    11.4.3. Formulation in Terms of Dual Integral Equations

    11.5. Two-Dimensional Diffraction of a Plane Wave by a Half-Plane

    11.5.1. Solution of the Dual Integral Equations for E-Polarization

    11.5.2. Expression of the Solution in Terms of Fresnel Integrals

    11.5.3. The nature of the Solution

    11.5.4. The Solution for H-Polarization

    11.5.5. Some numerical Calculations

    11.5.6. Comparison with Approximate Theory and with Experimental Results

    11.6. Three-Dimensional Diffraction of a Plane Wave by a Half-Plane

    11.7. Diffraction of a Localized Source by a Half-Plane

    11.7.1. A Line-Current Parallel to the Diffracting Edge

    11.7.2. A Dipole

    11.8. Other Problems

    11.8.1. Two Parallel Half-Planes

    11.8.2. An Infinite Stack of Parallel, Staggered Half-Planes

    11.8.3. A Strip

    11.8.4. Further Problems

    11.9. Uniqueness of Solution

    XII. Diffraction of Light by Ultrasonic Waves

    12.1. Qualitative Description of the Phenomenon and Summary of Theories Based on Maxwell's Differential Equations

    12.1.1. Qualitative Description of the Phenomenon

    12.1.2. Summary of Theories Based on Maxwell's Equations

    12.2. Diffraction of Light by Ultrasonic Waves as Treated by the Integral Equation Method

    12.2.1. Integral Equation for E-Polarization

    12.2.2. The Trial Solution of the Integral Equation

    12.2.3. Expressions for the Amplitudes of the Light Waves in the Diffracted and Reflected Spectra

    12.2.4. Solution of the Equations by a Method of Successive Approximations

    12.2.5. Expressions for the Intensities of the First and Second Order Lines for some Special Cases

    12.2.6. Some Qualitative Results

    12.2.7. The Raman-Nath Approximation

    XIII. Optics of Metals

    13.1. Wave Propagation in a Conductor

    13.2. Refraction and Reflection at a Metal Surface

    13.3. Elementary Electron Theory of the Optical Constants of Metals

    13.4. Wave Propagation in a Stratified Conducting Medium. Theory of Metallic Films

    13.4.1. An Absorbing Film on a Transparent Substrate

    13.4.2. A Transparent Film on an Absorbing Substrate

    13.5. Diffraction by a Conducting Sphere; Theory of Mie

    13.5.1. Mathematical Solution of the Problem

    13.5.2. Some Consequences of Mie's Formula

    13.5.3. Total Scattering and Extinction

    XIV. Optics of Crystals

    14.1. The Dielectric Tensor of an Anisotropic Medium

    14.2. The Structure of a Monochromatic Plane Wave in an Anisotropic Medium

    14.2.1. The Phase Velocity and the Ray Velocity

    14.2.2. Fresnel's Formula for the Propagation of Light in Crystals

    14.2.3. Geometrical Constructions for Determining the Velocities of Propagation and the Directions of Vibration

    14.3. Optical Properties of Uniaxial and Biaxial Crystals

    14.3.1. The Optical Classification of Crystals

    14.3.2. Light Propagation in Uniaxial Crystals

    14.3.3. Light Propagation in Biaxial Crystals

    14.3.4. Refraction in Crystals

    14.4. Measurements in Crystal Optics

    14.4.1. The Nicol Prism

    14.4.2. Compensators

    14.4.3. Interference with Crystal Plates

    14.4.4. Interference Figures from Uniaxial Crystal Plates

    14.4.5. Interference Figures from Biaxial Crystal Plates

    14.4.6. Location of Optic Axes and Determination of the Principal Refractive Indices of a Crystalline Medium

    14.5. Stress Birefringence and Form Birefringence

    14.5.1. Stress Birefringence

    14.5.2. Form Birefringence

    14.6. Absorbing Crystals

    14.6.1. Light Propagation in an Absorbing Anisotropic Medium

    14.6.2. Interference Figures from Absorbing Crystal Plates

    14.6.3. Dichroic Polarizers


    I. The Calculus of Variations

    1. Euler's Equations as necessary Conditions for an Extremum

    2. Hubert's Independence Integral and the Hamilton-Jacobi Equation

    3. The Field of Extremals

    4. Determination of All Extremals from the Solution of the Hamilton-Jacobi Equation

    5. Hamilton's Canonical Equations

    6. The Special Case When the Independent Variable Does not Appear Explicitly in the Integrand

    7. Discontinuities

    8. Weierstrass' and Legendre's Conditions (Sufficiency Conditions for an Extremum)

    9. Minimum of the Variational Integral When one End Point is Constrained to a Surface

    10. Jacobi's Criterion for a Minimum

    11. Example I: Optics

    12. Example II: Mechanics of Material Points

    II. Light Optics, Electron Optics and Wave Mechanics

    1. The Hamiltonian Analogy in Elementary Form

    2. The Hamiltonian Analogy in Variational Form

    3. Wave Mechanics of Free Electrons

    4. The Application of Optical Principles to Electron Optics

    III. Asymptotic Approximations to Integrals

    1. The Method of Steepest Descent

    2. The Method of Stationary Phase

    3. Double Integrals

    IV. The Dirac Delta Function

    V. A Mathematical Lemma Used in the Rigorous Derivation of the Lorentz-Lorenz Law (§2.4.2)

    VI. Propagation of Discontinuities in an Electromagnetic Field (§3.1.1)

    1. Relations Connecting Discontinuous Changes in Field Vectors

    2. The Field on a Moving Discontinuity Surface

    VII. The Circle Polynomials of Zernike (§9.2.1)

    1. Some General Considerations

    2. Explicit Expressions for the Radial Polynomials Rn±m(ρ)

    VIII. Proof of an Inequality (§10.7.3)

    IX. Evaluation of Two Integrals (§12.2.2)

    Author Index

    Subject Index

Product details

  • No. of pages: 836
  • Language: English
  • Copyright: © Pergamon 1980
  • Published: January 1, 1980
  • Imprint: Pergamon
  • eBook ISBN: 9781483103204

About the Authors

Max Born

Affiliations and Expertise

Formerly Professor at the Universities of Gottingen and Edinburgh

Emil Wolf

Professor Wolf works at the University of Rochester, NY, USA

Affiliations and Expertise

University of Rochester, NY, USA

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