Born Max, Wolf Emil. Principles of Optics. 60th Anniversary Edition

7th edition. — Cambridge University Press, 2019. — 992 p. — ISBN: 978-1-108-47743-7.Principles of Optics is one of the most highly cited and most influential physics books ever published, and one of the classic science books of the twentieth century. To celebrate the 60th anniversary of this remarkable book's first publication, the seventh expanded edition has been reprinted with a special foreword by Sir Peter Knight. The seventh edition was the first thorough revision and expansion of this definitive text. Amongst the material introduced in the seventh edition is a section on CAT scans, a chapter on scattering from inhomogeneous media, including an account of the principles of diffraction tomography, an account of scattering from periodic potentials, and a section on the so-called Rayleigh–Sommerfield diffraction theory. This expansive and timeless book continues to be invaluable to advanced undergraduates, graduate students and researchers working in all areas of optics.2019 marks sixty years since the first edition of this book was published
This reissue of the seventh expanded edition, which was the first ever radical revision of the book, includes a new foreword by Sir Peter KnightCo-authored by Max Born, recipient of the Nobel Prize in Physics (1954)Foreword by Sir Peter Knight
Historical introduction
Basic properties of the electromagnetic field
The electromagnetic field
Maxwell's equations
Material equations
Boundary conditions at a surface of discontinuity
The energy law of the electromagnetic field
The wave equation and the velocity of light
Scalar waves
Plane waves
Spherical waves
Harmonic wavesThe phase velocity
Wave packetsThe group velocity
Vector waves
The general electromagnetic plane wave
The harmonic electromagnetic plane wave
Elliptic polarization
Linear and circular polarization
Characterization of the state of polarization by Stokes parameters
Harmonic vector waves of arbitrary form
Reflection and refraction of a plane wave
The laws of reflection and refraction
Fresnel formulae
The reflectivity and transmissivity; polarization on reflection and refraction
Total reflection
Wave propagation in a stratified mediumTheory of dielectric films
The basic differential equations
The characteristic matrix of a stratified medium
A homogeneous dielectric film
A stratified medium as a pile of thin homogeneous films
The reflection and transmission coefficients
A homogeneous dielectric film
Periodically stratified media
Electromagnetic potentials and polarization
The electrodynamic potentials in the vacuum
The vector and scalar potentials
Retarded potentials
Polarization and magnetization
The potentials in terms of polarization and magnetization
Hertz vectors
The field of a linear electric dipole
The Lorentz-Lorenz formula and elementary dispersion theory
The dielectric and magnetic susceptibilities
The effective field
The mean polarizability: the Lorentz-Lorenz formula
Elementary theory of dispersion
Propagation of electromagnetic waves treated by integral equations
The basic integral equation
The Ewald-Oseen extinction theorem and a rigorous derivation of the Lorentz-Lorenz formula
Refraction and reflection of a plane wave, treated with the help of the Ewald-Oseen extinction theorem
Foundations of geometrical optics
Approximation for very short wavelengths
Derivation of the eikonal equation
The light rays and the intensity law of geometrical optics
Propagation of the amplitude vectors
Generalizations and the limits of validity of geometrical optics
General properties of rays
The differential equation of light rays
The laws of refraction and reflection
Ray congruences and their focal properties
Other basic theorems of geometrical optics
Lagrange's integral invariant
The principle of Fermat
The theorem of Malus and Dupin and some related theorems
Geometrical theory of optical imaging
The characteristic functions of Hamilton
The point characteristic
The mixed characteristic
The angle characteristic
Approximate form of the angle characteristic of a refracting surface of revolution
Approximate form of the angle characteristic of a reflecting surface of revolution
Perfect imaging
General theorems
Maxwell's 'fish-eye'
Stigmatic imaging of surfaces
Projective transformation (collineation) with axial symmetry
General formulae
The telescopic case
Classification of projective transformations
Combination of projective transformations
Gaussian optics
Refracting surface of revolution
Reflecting surface of revolution
The thick lens
The thin lens
The general centred system
Stigmatic imaging with wide-angle pencils
The sine condition
The Herschel condition
Astigmatic pencils of rays
Focal properties of a thin pencil
Refraction of a thin pencil
Chromatic aberrationDispersion by a prism
Chromatic aberration
Dispersion by a prism
Radiometry and apertures
Basic concepts of radiometry
Stops and pupils
Brightness and illumination of images
Ray tracing
Oblique meridional rays
Paraxial rays
Skew rays
Design of aspheric surfaces
Attainment of axial stigmatism
Attainment of aplanatism
Image-reconstruction from projections (computerized tomography)Beam propagation in an absorbing medium
Ray integrals and projections
The N-dimensional Radon transform
Reconstruction of cross-sections and the projection-slice theorem of computerized tomography
Geometrical theory of aberrations
Wave and ray aberrations; the aberration function
The perturbation eikonal of Schwarzschild
The primary (Seidel) aberrations
Spherical aberration (B ≠ 0)
Coma (F ≠ 0)
Astigmatism (C ≠ 0) and curvature of field (D ≠ 0)
Distortion (E ≠ 0)
Addition theorem for the primary aberrations
The primary aberration coefficients of a general centred lens system
The Seidel formulae in terms of two paraxial rays
The Seidel formulae in terms of one paraxial ray
Petzval's theorem
Example: The primary aberrations of a thin lens
The chromatic aberration of a general centred lens system
Image-forming instruments
The eye
The camera
The refracting telescope
The reflecting telescope
Instruments of illumination
The microscope
Elements of the theory of interference and interferometersInterference of two monochromatic waves
Two-beam interference: division of wave-front
Young's experiment
Fresnel's mirrors and similar arrangements
Fringes with quasi-monochromatic and white light
Use of slit sources; visibility of fringes
Application to the measurement of optical path difference: the Rayleigh interferometer
Application to the measurement of angular dimensions of sources: the Michelson stellar interferometer
Standing waves
Two-beam interference: division of amplitude
Fringes with a plane-parallel plate
Fringes with thin films; the Fizeau interferometer
Localization of fringes
The Michelson interferometer
The Twyman-Green and related interferometers
Fringes with two identical plates: the Jamin interferometer and interference microscopes
The Mach-Zehnder interferometer; the Bates wave-front shearing interferometer
The coherence length; the application of two-beam interference to the study of the fine structure of spectral lines
Multiple-beam interference
Multiple-beam fringes with a plane-parallel plate
The Fabry-Perot interferometer
The application of the Fabry-Perot interferometer to the study of the fine structure of spectral lines
The application of the Fabry-Perot interferometer to the comparison of wavelengths
The Lummer-Gehrcke interferometer
Interference filters
Multiple-beam fringes with thin films
Multiple-beam fringes with two plane-parallel plates
Fringes with monochromatic and quasi-monochromatic light
Fringes of superposition
The comparison of wavelengths with the standard metre
Elements of the theory of diffractionThe Huygens-Fresnel principle
Kirchhoff's diffraction theory
The integral theorem of Kirchhoff
Kirchhoff's diffraction theory
Fraunhofer and Fresnel diffraction
Transition to a scalar theory
The image field due to a monochromatic oscillator
The total image field
Fraunhofer diffraction at apertures of various forms
The rectangular aperture and the slit
The circular aperture
Other forms of aperture
Fraunhofer diffraction in optical instruments
Diffraction gratings
The principle of the diffraction grating
Types of grating
Grating spectrographs
Resolving power of image-forming systems
Image formation in the microscope
Incoherent illumination
Coherent illumination - Abbe's theory
Coherent illumination - Zernike's phase contrast method of observation
Fresnel diffraction at a straight edge
The diffraction integral
Fresnel's integrals
Fresnel diffraction at a straight edge
The three-dimensional light distribution near focus
Evaluation of the diffraction integral in terms of Lommel functions
The distribution of intensity
Intensity in the geometrical focal plane
Intensity along the axis
Intensity along the boundary of the geometrical shadow
The integrated intensity
The phase behaviour
The boundary diffraction wave
Gabor's method of imaging by reconstructed wave-fronts (holography)
Producing the positive hologram
The reconstruction
The Rayleigh-Sommerfeld diffraction integrals
The Rayleigh diffraction integrals
The Rayleigh-Sommerfeld diffraction integrals
The diffraction theory of aberrations
The diffraction integral in the presence of aberrations
The diffraction integral
The displacement theoremChange of reference sphere
A relation between the intensity and the average deformation of wave-fronts
Expansion of the aberration function
The circle polynomials of Zernike
Expansion of the aberration function
Tolerance conditions for primary aberrations
The diffraction pattern associated with a single aberration
Primary spherical aberration
Primary coma
Primary astigmatism
Imaging of extended objects
Coherent illumination
Incoherent illumination
Interference and diffraction with partially coherent lightA complex representation of real polychromatic fields
The correlation functions of light beams
Interference of two partially coherent beamsThe mutual coherence function and the complex degree of coherence
Spectral representation of mutual coherence
Interference and diffraction with quasi-monochromatic light
Interference with quasi-monochromatic lightThe mutual intensity
Calculation of mutual intensity and degree of coherence for light from an extended incoherent quasi-monochromatic source
The van Cittert-Zernike theorem
Hopkins' formula
An example
Propagation of mutual intensity
Interference with broad-band light and the spectral degree of coherenceCorrelation-induced spectral changes
Some applications
The degree of coherence in the image of an extended incoherent quasi-monochromatic source
The influence of the condenser on resolution in a microscope
Critical illumination
Kohler's illumination
Imaging with partially coherent quasi-monochromatic illumination
Transmission of mutual intensity through an optical system
Images of transilluminated objects
Some theorems relating to mutual coherence
Calculation of mutual coherence for light from an incoherent source
Propagation of mutual coherence
Rigorous theory of partial coherence
Wave equations for mutual coherence
Rigorous formulation of the propagation law for mutual coherence
The coherence time and the effective spectral width
Polarization properties of quasi-monochromatic light
The coherency matrix of a quasi-monochromatic plane wave
Completely unpolarized light (natural light)
Complete polarized light
Some equivalent representationsThe degree of polarization of a light wave
The Stokes parameters of a quasi-monochromatic plane wave
Rigorous diffraction theoryBoundary conditions and surface currents
Diffraction by a plane screen: electromagnetic form of Babinet's principle
Two-dimensional diffraction by a plane screen
The scalar nature of two-dimensional electromagnetic fields
An angular spectrum of plane waves
Formulation in terms of dual integral equations
Two-dimensional diffraction of a plane wave by a half-plane
Solution of the dual integral equations for E-polarization
Expression of the solution in terms of Fresnel integrals
The nature of the solution
The solution for H-polarization
Some numerical calculations
Comparison with approximate theory and with experimental results
Three-dimensional diffraction of a plane wave by a half-plane
Diffraction of a field due to a localized source by a half-plane
A line-current parallel to the diffracting edge
A dipole
Other problems
Two parallel half-planes
An infinite stack of parallel, staggered half-planes
A strip
Further problems
Uniqueness of solution
Diffraction of light by ultrasonic waves
Qualitative description of the phenomenon and summary of theories based on Maxwell's differential equations
Qualitative description of the phenomenon
Summary of theories based on Maxwell's equations
Diffraction of light by ultrasonic waves as treated by the integral equation method
Integral equation for E-polarization
The trial solution of the integral equation
Expressions for the amplitudes of the light waves in the diffracted and reflected spectra
Solution of the equations by a method of successive approximations
Expressions for the intensities of the first and second order lines for some special cases
Some qualitative results
The Raman-Nath approximation
Scattering from inhomogeneous media
Elements of the scalar theory of scattering
Derivation of the basic integral equation
The first-order Born approximation
Scattering from periodic potentials
Multiple scattering
Principles of diffraction tomography for reconstruction of the scattering potential
Angular spectrum representation of the scattered field
The basic theorem of diffraction tomography
The optical cross-section theorem
A reciprocity relation
The Rytov series
Scattering of electromagnetic waves
The integro-differential equations of electromagnetic scattering theory
The far field
The optical cross-section theorem for scattering of electromagnetic waves
Optics of metals
Wave propagation in a conductor
Refraction and reflection at a metal surface
Elementary electron theory of the optical constants of metals
Wave propagation in a stratified conducting mediumTheory of metallic films
An absorbing film on a transparent substrate
A transparent film on an absorbing substrate
Diffraction by a conducting sphere; theory of Mie
Mathematical solution of the problem
Representation of the field in terms of Debye's potentials
Series expansions for the field components
Summary of formulae relating to the associated Legendre functions and to the cylindrical functions
Some consequences of Mie's formulae
The partial waves
bimiting cases
Intensity and polarization of the scattered light
Total scattering and extinction
Some general considerations
Computational results
Optics of crystals
The dielectric tensor of an anisotropic medium
The structure of a monochromatic plane wave in an anisotropic medium
The phase velocity and the ray velocity
Fresnel's formulae for the propagation of light in crystals
Geometrical constructions for determining the velocities of propagation and the directions of vibration
The ellipsoid of wave normals
The ray ellipsoid
The normal surface and the ray surface
Optical properties of uniaxial and biaxial crystals
The optical classification of crystals
Light propagation in uniaxial crystals
Light propagation in biaxial crystals
Refraction in crystals
Double refraction
Conical refraction
Measurements in crystal optics
The Nicol prism
Compensators
The quarter-wave plate
Babinet's compensator
Soleil's compensator
Berek's compensator
Interference with crystal plates
Interference figures from uniaxial crystal plates
Interference figures from biaxial crystal plates
Location of optic axes and determination of the principal refractive indices of a crystalline medium
Stress birefringence and form birefringence
Stress birefringence
Form birefringence
Absorbing crystals
Light propagation in an absorbing anisotropic medium
Interference figures from absorbing crystal plates
Uniaxial crystals
Biaxial crystals
Dichroic polarizers
Appendices
The Calculus of variations
Euler's equations as necessary conditions for an extremum
Hilbert's independence integral and the Hamilton-Jacobi equation
The field of extremals
Determination of all extremals from the solution of the Hamilton-Jacobi equation
Hamilton's canonical equations
The special case when the independent variable does not appear explicitly in the integrand
Discontinuities
Weierstrass' and Legendre's conditions (sufficiency conditions for an extremum)
Minimum of the variational integral when one end point is constrained to a surface
Jacobi's criterion for a minimum
Example I: Optics
Example II: Mechanics of material points
Light optics, electron optics and wave mechanics
The Hamiltonian analogy in elementary form
The Hamiltonian analogy in variational form
Wave mechanics of free electrons
The application of optical principles to electron optics
Asymptotic approximations to integrals
The method of steepest descent
The method of stationary phase
Double integrals
The Dirac delta function
A mathematical lemma used in the rigorous derivation of the Lorentz-Lorenz formula (§2.4.2)
Propagation of discontinuities in an electromagnetic field (§3.1.1)
Relations connecting discontinuous changes in field vectors
The field on a moving discontinuity surface
The circle polynomials of Zernike (§9.2.1)
Some general considerations
Explicit expressions for the radial polynomials
Proof of the inequality for the spectral degree of coherence (§10.5)
Proof of a reciprocity inequality (§10.8.3)
Evaluation of two integrals (§12.2.2)
Energy conservation in scalar wavefields (§13.3)
Proof of Jones' lemma (§13.3)
Author index
Subject index