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Principles of Optics, Seventh Edition

Book Description

Principles of Optics is one of the classic science books of the twentieth century, and probably the most influential book in optics published in the past 40 years. The new edition is the first ever thoroughly revised and expanded edition of this standard text. Among the new material, much of which is not available in any other optics text, is a section on the CAT scan (computerized axial tomography), which has revolutionized medical diagnostics. The book also includes a new chapter on scattering from inhomogeneous media which provides a comprehensive treatment of the theory of scattering of scalar as well as of electromagnetic waves, including the Born series and the Rytov series. The chapter also presents an account of the principles of diffraction tomography - a refinement of the CAT scan - to which Emil Wolf, one of the authors, has made a basic contribution by formulating in 1969 what is generally regarded to be the basic theorem in this field. The chapter also includes an account of scattering from periodic potentials and its connection to the classic subject of determining the structure of crystals from X-ray diffraction experiments, including accounts of von Laue equations, Bragg's law, the Ewald sphere of reflection and the Ewald limiting sphere, both generalized to continuous media. These topics, although originally introduced in connection with the theory of X-ray diffraction by crystals, have since become of considerable relevance to optics, for example in connection with deep holograms. Other new topics covered in this new edition include interference with broad-band light, which introduces the reader to an important phenomenon discovered relatively recently by Emil Wolf, namely the generation of shifts of spectral lines and other modifications of spectra of radiated fields due to the state of coherence of a source. There is also a section on the so-called Rayleigh-Sommerfield diffraction theory which, in recent times, has been finding increasing popularity among optical scientists. There are also several new appendices, including one on energy conservation in scalar wavefields, which is seldom discussed in books on optics. The new edition of this standard reference will continue to be invaluable to advanced undergraduates, graduate students and researchers working in most areas of optics.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Preface
  6. Contents
  7. Historical introduction
  8. I Basic properties of the electromagnetic field
    1. 1.1 The electromagnetic field
      1. 1.1.1 Maxwell’s equations
      2. 1.1.2 Material equations
      3. 1.1.3 Boundary conditions at a surface of discontinuity
      4. 1.1.4 The energy law of the electromagnetic field
    2. 1.2 The wave equation and the velocity of light
    3. 1.3 Scalar waves
      1. 1.3.1 Plane waves
      2. 1.3.2 Spherical waves
      3. 1.3.3 Harmonic waves. The phase velocity
      4. 1.3.4 Wave packets. The group velocity
    4. 1.4 Vector waves
      1. 1.4.1 The general electromagnetic plane wave
      2. 1.4.2 The harmonic electromagnetic plane wave
        1. (a) Elliptic polarization
        2. (b) Linear and circular polarization
        3. (c) Characterization of the state of polarization by Stokes parameters
      3. 1.4.3 Harmonic vector waves of arbitrary form
    5. 1.5 Reflection and refraction of a plane wave
      1. 1.5.1 Thelawsof reflection and refraction
      2. 1.5.2 Fresnel formulae
      3. 1.5.3 The reflectivity and transmissivity; polarization on reflection and refraction
      4. 1.5.4 Total reflection
    6. 1.6 Wave propagation in a stratified medium. Theory of dielectric films
      1. 1.6.1 The basic differential equations
      2. 1.6.2 The characteristic matrix of a stratified medium
        1. (a) A homogeneous dielectric film
        2. (b) A stratified medium as a pile of thin homogeneous films
      3. 1.6.3 The reflection and transmission coefficients
      4. 1.6.4 A homogeneous dielectric film
      5. 1.6.5 Periodically stratified media
  9. II Electromagnetic potentials and polarization
    1. 2.1 The electrodynamic potentials in the vacuum
      1. 2.1.1 The vector and scalar potentials
      2. 2.1.2 Retarded potentials
    2. 2.2 Polarization and magnetization
      1. 2.2.1 The potentials in terms of polarization and magnetization
      2. 2.2.2 Hertz vectors
      3. 2.2.3 The field of a linear electric dipole
    3. 2.3 The Lorentz-Lorenz formula and elementary dispersion theory
      1. 2.3.1 The dielectric and magnetic susceptibilities
      2. 2.3.2 The effective field
      3. 2.3.3 The mean polarizability: the Lorentz-Lorenz formula
      4. 2.3.4 Elementary theory of dispersion
    4. 2.4 Propagation of electromagnetic waves treated by integral equations
      1. 2.4.1 The basic integral equation
      2. 2.4.2 The Ewald-Oseen extinction theorem and a rigorous derivation of the Lorentz-Lorenz formula
      3. 2.4.3 Refraction and reflection of a plane wave, treated with the help of the Ewald-Oseen extinction theorem
  10. III Foundations of geometrical optics
    1. 3.1 Approximation for very short wavelengths
      1. 3.1.1 Derivation of the eikonal equation
      2. 3.1.2 The light rays and the intensity law of geometrical optics
      3. 3.1.3 Propagation of the amplitude vectors
      4. 3.1.4 Generalizations and the limits of validity of geometrical optics
    2. 3.2 General properties of rays
      1. 3.2.1 The differential equation of light rays
      2. 3.2.2 The laws of refraction and reflection
      3. 3.2.3 Ray congruences and their focal properties
    3. 3.3 Other basic theorems of geometrical optics
      1. 3.3.1 Lagrange’s integral invariant
      2. 3.3.2 The principle of Fermat
      3. 3.3.3 The theorem of Malus and Dupin and some related theorems
  11. IV Geometrical theory of optical imaging
    1. 4.1 The characteristic functions of Hamilton
      1. 4.1.1 The point characteristic
      2. 4.1.2 The mixed characteristic
      3. 4.1.3 The angle characteristic
      4. 4.1.4 Approximate form of the angle characteristic of a refracting surface of revolution
      5. 4.1.5 Approximate form of the angle characteristic of a reflecting surface of revolution
    2. 4.2 Perfect imaging
      1. 4.2.1 General theorems
      2. 4.2.2 Maxwell’s ‘fish-eye’
      3. 4.2.3 Stigmatic imaging of surfaces
    3. 4.3 Projective transformation (collineation) with axial symmetry
      1. 4.3.1 General formulae
      2. 4.3.2 The telescopic case
      3. 4.3.3 Classification of projective transformations
      4. 4.3.4 Combination of projective transformations
    4. 4.4 Gaussian optics
      1. 4.4.1 Refracting surface of revolution
      2. 4.4.2 Reflecting surface of revolution
      3. 4.4.3 The thick lens
      4. 4.4.4 The thin lens
      5. 4.4.5 The general centred system
    5. 4.5 Stigmatic imaging with wide-angle pencils
      1. 4.5.1 The sine condition
      2. 4.5.2 The Herschel condition
    6. 4.6 Astigmatic pencils of rays
      1. 4.6.1 Focal properties of a thin pencil
      2. 4.6.2 Refraction of a thin pencil
    7. 4.7 Chromatic aberration. Dispersion by a prism
      1. 4.7.1 Chromatic aberration
      2. 4.7.2 Dispersion by a prism
    8. 4.8 Radiometry and apertures
      1. 4.8.1 Basic concepts of radiometry
      2. 4.8.2 Stops and pupils
      3. 4.8.3 Brightness and illumination of images
    9. 4.9 Ray tracing
      1. 4.9.1 Oblique meridional rays
      2. 4.9.2 Paraxial rays
      3. 4.9.3 Skew rays
    10. 4.10 Design of aspheric surfaces
      1. 4.10.1 Attainment of axial stigmatism
      2. 4.10.2 Attainment of aplanatism
    11. 4.11 Image-reconstruction from projections (computerized tomography)
      1. 4.11.1 Introduction
      2. 4.11.2 Beam propagation in an absorbing medium
      3. 4.11.3 Ray integrals and projections
      4. 4.11.4 The V-dimensional Radon transform
      5. 4.11.5 Reconstruction of cross-sections and the projection-slice theorem of computerized tomography
  12. V Geometrical theory of aberrations
    1. 5.1 Wave and ray aberrations; the aberration function
    2. 5.2 The perturbation eikonal of Schwarzschild
    3. 5.3 The primary (Seidel) aberrations
      1. (a) Spherical aberration (B ≠ 0)
      2. (b) Coma (F ≠ 0)
      3. (c) Astigmatism (C ≠ 0) and curvature of field (D ≠ 0)
      4. (d) Distortion (E ≠ 0)
    4. 5.4 Addition theorem for the primary aberrations
    5. 5.5 The primary aberration coefficients of a general centred lens system
      1. 5.5.1 The Seidel formulae in terms of two paraxial rays
      2. 5.5.2 The Seidel formulae in terms of one paraxial ray
      3. 5.5.3 Petzval’s theorem
    6. 5.6 Example: The primary aberrations of a thin lens
    7. 5.7 The chromatic aberration of a general centred lens system
  13. VI Image-forming instruments
    1. 6.1 The eye
    2. 6.2 The camera
    3. 6.3 The refracting telescope
    4. 6.4 The reflecting telescope
    5. 6.5 Instruments of illumination
    6. 6.6 The microscope
  14. VII Elements of the theory of interference and interferometers
    1. 7.1 Introduction
    2. 7.2 Interference of two monochromatic waves
    3. 7.3 Two-beam interference: division of wave-front
      1. 7.3.1 Young’s experiment
      2. 7.3.2 Fresnel’s mirrors and similar arrangements
      3. 7.3.3 Fringes with quasi-monochromatic and white light
      4. 7.3.4 Use of slit sources; visibility of fringes
      5. 7.3.5 Application to the measurement of optical path difference: the Rayleigh interferometer
      6. 7.3.6 Application to the measurement of angular dimensions of sources: the Michelson stellar interferometer
    4. 7.4 Standing waves
    5. 7.5 Two-beam interference: division of amplitude
      1. 7.5.1 Fringes with a plane-parallel plate
      2. 7.5.2 Fringes with thin films; the Fizeau interferometer
      3. 7.5.3 Localization of fringes
      4. 7.5.4 The Michelson interferometer
      5. 7.5.5 The Twyman–Green and related interferometers
      6. 7.5.6 Fringes with two identical plates: the Jamin interferometer and interference microscopes
      7. 7.5.7 The Mach–Zehnder interferometer; the Bates wave-front shearing interferometer
      8. 7.5.8 The coherence length; the application of two-beam interference to the study of the fine structure of spectral lines
    6. 7.6 Multiple-beam interference
      1. 7.6.1 Multiple-beam fringes with a plane-parallel plate
      2. 7.6.2 The Fabry–Perot interferometer
      3. 7.6.3 The application of the Fabry–Perot interferometer to the study of the fine structure of spectral lines
      4. 7.6.4 The application of the Fabry–Perot interferometer to the comparison of wavelengths
      5. 7.6.5 The Lummer–Gehrcke interferometer
      6. 7.6.6 Interference filters
      7. 7.6.7 Multiple-beam fringes with thin films
      8. 7.6.8 Multiple-beam fringes with two plane-parallel plates
        1. (a) Fringes with monochromatic and quasi-monochromatic light
        2. (b) Fringes of superposition
    7. 7.7 The comparison of wavelengths with the standard metre
  15. VIII Elements of the theory of diffraction
    1. 8.1 Introduction
    2. 8.2 The Huygens–Fresnel principle
    3. 8.3 Kirchhoff’s diffraction theory
      1. 8.3.1 The integral theorem of Kirchhoff
      2. 8.3.2 Kirchhoff’s diffraction theory
      3. 8.3.3 Fraunhofer and Fresnel diffraction
    4. 8.4 Transition to a scalar theory
      1. 8.4.1 The image field due to a monochromatic oscillator
      2. 8.4.2 The total image field
    5. 8.5 Fraunhofer diffraction at apertures of various forms
      1. 8.5.1 The rectangular aperture and the slit
      2. 8.5.2 The circular aperture
      3. 8.5.3 Other forms of aperture
    6. 8.6 Fraunhofer diffraction in optical instruments
      1. 8.6.1 Diffraction gratings
        1. (a) The principle of the diffraction grating
        2. (b) Types of grating
        3. (c) Grating spectrographs
      2. 8.6.2 Resolving power of image-forming systems
      3. 8.6.3 Image formation in the microscope
        1. (a) Incoherent illumination
        2. (b) Coherent illumination – Abbe’s theory
        3. (c) Coherent illumination – Zernike’s phase contrast method of observation
    7. 8.7 Fresnel diffraction at a straight edge
      1. 8.7.1 The diffraction integral
      2. 8.7.2 Fresnel’s integrals
      3. 8.7.3 Fresnel diffraction at a straight edge
    8. 8.8 The three-dimensional light distribution near focus
      1. 8.8.1 Evaluation of the diffraction integral in terms of Lommel functions
      2. 8.8.2 The distribution of intensity
        1. (a) Intensity in the geometrical focal plane
        2. (b) Intensity along the axis
        3. (c) Intensity along the boundary of the geometrical shadow
      3. 8.8.3 The integrated intensity
      4. 8.8.4 The phase behaviour
    9. 8.9 The boundary diffraction wave
    10. 8.10 Gabor’s method of imaging by reconstructed wave-fronts (holography)
      1. 8.10.1 Producing the positive hologram
      2. 8.10.2 The reconstruction
    11. 8.11 The Rayleigh–Sommerfeld diffraction integrals
      1. 8.11.1 The Rayleigh diffraction integrals
      2. 8.11.2 The Rayleigh–Sommerfeld diffraction integrals
  16. IX The diffraction theory of aberrations
    1. 9.1 The diffraction integral in the presence of aberrations
      1. 9.1.1 The diffraction integral
      2. 9.1.2. The displacement theorem. Change of reference sphere
      3. 9.1.3. A relation between the intensity and the average deformation of wave-fronts
    2. 9.2 Expansion of the aberration function
      1. 9.2.1 The circle polynomials of Zernike
      2. 9.2.2 Expansion of the aberration function
    3. 9.3 Tolerance conditions for primary aberrations
    4. 9.4 The diffraction pattern associated with a single aberration
      1. 9.4.1 Primary spherical aberration
      2. 9.4.2 Primary coma
      3. 9.4.3 Primary astigmatism
    5. 9.5 Imaging of extended objects
      1. 9.5.1 Coherent illumination
      2. 9.5.2 Incoherent illumination
  17. X Interference and diffraction with partially coherent light
    1. 10.1 Introduction
    2. 10.2 A complex representation of real polychromatic fields
    3. 10.3 The correlation functions of light beams
      1. 10.3.1 Interference of two partially coherent beams. The mutual coherence function and the complex degree of coherence
      2. 10.3.2 Spectral representation of mutual coherence
    4. 10.4 Interference and diffraction with quasi-monochromatic light
      1. 10.4.1 Interference with quasi-monochromatic light. The mutual intensity
      2. 10.4.2 Calculation of mutual intensity and degree of coherence for light from an extended incoherent quasi-monochromatic source
        1. (a) The van Cittert–Zernike theorem
        2. (b) Hopkins’ formula
      3. 10.4.3 An example
      4. 10.4.4 Propagation of mutual intensity
    5. 10.5 Interference with broad-band light and the spectral degree of coherence. Correlation-induced spectral changes
    6. 10.6 Some applications
      1. 10.6.1 The degree of coherence in the image of an extended incoherent quasi-monochromatic source
      2. 10.6.2 The influence of the condenser on resolution in a microscope
        1. (a) Critical illumination
        2. (b) Köhler’s illumination
      3. 10.6.3 Imaging with partially coherent quasi-monochromatic illumination
        1. (a) Transmission of mutual intensity through an optical system
        2. (b) Images of transilluminated objects
    7. 10.7 Some theorems relating to mutual coherence
      1. 10.7.1 Calculation of mutual coherence for light from an incoherent source
      2. 10.7.2 Propagation of mutual coherence
    8. 10.8 Rigorous theory of partial coherence
      1. 10.8.1 Wave equations for mutual coherence
      2. 10.8.2 Rigorous formulation of the propagation law for mutual coherence
      3. 10.8.3 The coherence time and the effective spectral width
    9. 10.9 Polarization properties of quasi-monochromatic light
      1. 10.9.1 The coherency matrix of a quasi-monochromatic plane wave
        1. (a) Completely unpolarized light (natural light)
        2. (b) Complete polarized light
      2. 10.9.2 Some equivalent representations. The degree of polarization of a light wave
      3. 10.9.3 The Stokes parameters of a quasi-monochromatic plane wave
  18. XI Rigorous diffraction theory
    1. 11.1 Introduction
    2. 11.2 Boundary conditions and surface currents
    3. 11.3 Diffraction by a plane screen: electromagnetic form of Babinet’s principle
    4. 11.4 Two-dimensional diffraction by a plane screen
      1. 11.4.1 The scalar nature of two-dimensional electromagnetic fields
      2. 11.4.2 An angular spectrum of plane waves
      3. 11.4.3 Formulation in terms of dual integral equations
    5. 11.5 Two-dimensional diffraction of a plane wave by a half-plane
      1. 11.5.1 Solution of the dual integral equations for E-polarization
      2. 11.5.2 Expression of the solution in terms of Fresnel integrals
      3. 11.5.3 The nature of the solution
      4. 11.5.4 The solution for H-polarization
      5. 11.5.5 Some numerical calculations
      6. 11.5.6 Comparison with approximate theory and with experimental results
    6. 11.6 Three-dimensional diffraction of a plane wave by a half-plane
    7. 11.7 Diffraction of a field due to a localized source by a half-plane
      1. 11.7.1 A line-current parallel to the diffracting edge
      2. 11.7.2 A dipole
    8. 11.8 Other problems
      1. 11.8.1 Two parallel half-planes
      2. 11.8.2 An infinite stack of parallel, staggered half-planes
      3. 11.8.3 A strip
      4. 11.8.4 Further problems
    9. 11.9 Uniqueness of solution
  19. XII Diffraction of light by ultrasonic waves
    1. 12.1 Qualitative description of the phenomenon and summary of theories based on Maxwell’s differential equations
      1. 12.1.1 Qualitative description of the phenomenon
      2. 12.1.2 Summary of theories based on Maxwell’s equations
    2. 12.2 Diffraction of light by ultrasonic waves as treated by the integral equation method
      1. 12.2.1 Integral equation for E-polarization
      2. 12.2.2 The trial solution of the integral equation
      3. 12.2.3 Expressions for the amplitudes of the light waves in the diffracted and reflected spectra
      4. 12.2.4 Solution of the equations by a method of successive approximations
      5. 12.2.5 Expressions for the intensities of the first and second order lines for some special cases
      6. 12.2.6 Some qualitative results
      7. 12.2.7 The Raman–Nath approximation
  20. XIII Scattering from inhomogeneous media
    1. 13.1 Elements of the scalar theory of scattering
      1. 13.1.1 Derivation of the basic integral equation
      2. 13.1.2 The first-order Born approximation
      3. 13.1.3 Scattering from periodic potentials
      4. 13.1.4 Multiple scattering
    2. 13.2 Principles of diffraction tomography for reconstruction of the scattering potential
      1. 13.2.1 Angular spectrum representation of the scattered field
      2. 13.2.2 The basic theorem of diffraction tomography
    3. 13.3 The optical cross-section theorem
    4. 13.4 A reciprocity relation
    5. 13.5 The Rytov series
    6. 13.6 Scattering of electromagnetic waves
      1. 13.6.1 The integro-differential equations of electromagnetic scattering theory
      2. 13.6.2 The far field
      3. 13.6.3 The optical cross-section theorem for scattering of electromagnetic waves
  21. XIV Optics of metals
    1. 14.1 Wave propagation in a conductor
    2. 14.2 Refraction and reflection at a metal surface
    3. 14.3 Elementary electron theory of the optical constants of metals
    4. 14.4 Wave propagation in a stratified conducting medium. Theory of metallic films
      1. 14.4.1 An absorbing film on a transparent substrate
      2. 14.4.2 A transparent film on an absorbing substrate
    5. 14.5 Diffraction by a conducting sphere; theory of Mie
      1. 14.5.1 Mathematical solution of the problem
        1. (a) Representation of the field in terms of Debye’s potentials
        2. (b) Series expansions for the field components
        3. (c) Summary of formulae relating to the associated Legendre functions and to the cylindrical functions
      2. 14.5.2 Some consequences of Mie’s formulae
        1. (a) The partial waves
        2. (b) Limiting cases
        3. (c) Intensity and polarization of the scattered light
      3. 14.5.3 Total scattering and extinction
        1. (a) Some general considerations
        2. (b) Computational results
  22. XV Optics of crystals
    1. 15.1 The dielectric tensor of an anisotropic medium
    2. 15.2 The structure of a monochromatic plane wave in an anisotropic medium
      1. 15.2.1 The phase velocity and the ray velocity
      2. 15.2.2 Fresnel’s formulae for the propagation of light in crystals
      3. 15.2.3 Geometrical constructions for determining the velocities of propagation and the directions of vibration
        1. (a) The ellipsoid of wave normals
        2. (b) The ray ellipsoid
        3. (c) The normal surface and the ray surface
    3. 15.3 Optical properties of uniaxial and biaxial crystals
      1. 15.3.1 The optical classification of crystals
      2. 15.3.2 Light propagation in uniaxial crystals
      3. 15.3.3 Light propagation in biaxial crystals
      4. 15.3.4 Refraction in crystals
        1. (a) Double refraction
        2. (b) Conical refraction
    4. 15.4 Measurements in crystal optics
      1. 15.4.1 The Nicol prism
      2. 15.4.2 Compensators
        1. (a) The quarter-wave plate
        2. (b) Babinet’s compensator
        3. (c) Soleil’s compensator
        4. (d) Berek’s compensator
      3. 15.4.3 Interference with crystal plates
      4. 15.4.4 Interference figures from uniaxial crystal plates
      5. 15.4.5 Interference figures from biaxial crystal plates
      6. 15.4.6 Location of optic axes and determination of the principal refractive indices of a crystalline medium
    5. 15.5 Stress birefringence and form birefringence
      1. 15.5.1 Stress birefringence
      2. 15.5.2 Form birefringence
    6. 15.6 Absorbing crystals
      1. 15.6.1 Light propagation in an absorbing anisotropic medium
      2. 15.6.2 Interference figures from absorbing crystal plates
        1. (a) Uniaxial crystals
        2. (b) Biaxial crystals
      3. 15.6.3 Dichroic polarizers
  23. Appendices
    1. I The Calculus of variations
      1. 1 Euler’s equations as necessary conditions for an extremum
      2. 2 Hilbert’s independence integral and the Hamilton–Jacobi equation
      3. 3 The field of extremals
      4. 4 Determination of all extremals from the solution of the Hamilton–Jacobi equation
      5. 5 Hamilton’s canonical equations
      6. 6 The special case when the independent variable does not appear explicitly in the integrand
      7. 7 Discontinuities
      8. 8 Weierstrass’ and Legendre’s conditions (sufficiency conditions for an extremum)
      9. 9 Minimum of the variational integral when one end point is constrained to a surface
      10. 10 Jacobi’s criterion for a minimum
      11. 11 Example I: Optics
      12. 12 Example II: Mechanics of material points
    2. II Light optics, electron optics and wave mechanics
      1. 1 The Hamiltonian analogy in elementary form
      2. 2 The Hamiltonian analogy in variational form
      3. 3 Wave mechanics of free electrons
      4. 4 The application of optical principles to electron optics
    3. III Asymptotic approximations to integrals
      1. 1 The method of steepest descent
      2. 2 The method of stationary phase
      3. 3 Double integrals
    4. IV The Dirac delta function
    5. V A mathematical lemma used in the rigorous derivation of the Lorentz–Lorenz formula (§2.4.2)
    6. VI Propagation of discontinuities in an electromagnetic field (§3.1.1)
      1. 1 Relations connecting discontinuous changes in field vectors
      2. 2 The field on a moving discontinuity surface
    7. VII The circle polynomials of Zernike (§9.2.1)
      1. 1 Some general considerations
      2. 2 Explicit expressions for the radial polynomials Rmm(ρ)
    8. VIII Proof of the inequality |μ12(v)| < 1 for the spectral degree of coherence (§10.5)
    9. IX Proof of a reciprocity inequality (§10.8.3)
    10. X Evaluation of two integrals (§12.2.2)
    11. XI Energy conservation in scalar wavefields (§13.3)
    12. XII Proof of Jones’ lemma (§13.3)
  24. Author index
  25. Subject index