Principles of Optics

Citation

Born, M., & Wolf, E. (2019). Principles of Optics (7th expanded ed., 60th anniversary printing). Cambridge University Press.

Chapter Summary

The book has fifteen chapters, a historical introduction and twelve appendices, with the text running to page 921 and the author and subject indexes following. It treats optics as a branch of electromagnetic theory, working from Maxwell's equations through geometrical optics and imaging to interference, diffraction, partial coherence, scattering, and the optics of metals and crystals. The seventh edition added a section on computerized tomography, a chapter on scattering from inhomogeneous media, an account of scattering from periodic potentials, and a section on Rayleigh–Sommerfeld diffraction theory.

Chapter 1: Basic Properties of the Electromagnetic Field

Maxwell's equations, material equations, boundary conditions and the energy law; the wave equation and the velocity of light; scalar and vector waves with polarization and Stokes parameters; reflection and refraction of a plane wave with the Fresnel formulae; and wave propagation in a stratified medium, the theory of dielectric films.

Chapter 2: Electromagnetic Potentials and Polarization

Electrodynamic potentials in a vacuum, polarization and magnetization with the Hertz vectors, the Lorentz–Lorenz formula and elementary dispersion theory, and the propagation of waves treated by integral equations, including the Ewald–Oseen extinction theorem.

Chapters 3–4: Foundations of Geometrical Optics; Geometrical Theory of Optical Imaging

Chapter 3 derives geometrical optics as the limit of very short wavelengths (the eikonal equation and the intensity law), then treats general properties of rays, Fermat's principle and related theorems. Chapter 4 builds the theory of imaging: Hamilton's characteristic functions, perfect imaging, projective transformations, Gaussian optics, stigmatic imaging with wide-angle pencils, astigmatic pencils, chromatic aberration, radiometry and apertures, ray tracing, aspheric surfaces and, in the seventh edition, image reconstruction from projections.

Chapters 5–6: Geometrical Theory of Aberrations; Image-Forming Instruments

Chapter 5 develops the aberration function and the primary (Seidel) aberrations: spherical aberration, coma, astigmatism and curvature of field, and distortion, together with chromatic aberration. Chapter 6 applies the theory to the eye, the camera, the refracting and reflecting telescope, instruments of illumination and the microscope.

Chapters 7–8: Elements of the Theory of Interference and Interferometers; Elements of the Theory of Diffraction

Chapter 7 covers two-beam interference by division of wave-front and of amplitude (Young, Michelson, Mach–Zehnder and others), the coherence length and multiple-beam interference with the Fabry–Perot interferometer. Chapter 8 develops the Huygens–Fresnel principle and Kirchhoff's diffraction theory, Fraunhofer diffraction at various apertures and in gratings and instruments, Fresnel diffraction at a straight edge, the three-dimensional light distribution near focus, holography and the Rayleigh–Sommerfeld integrals.

Chapter 9: The Diffraction Theory of Aberrations

The diffraction integral in the presence of aberrations, the Zernike circle polynomials, tolerance conditions, the diffraction patterns of the primary aberrations, and imaging of extended objects under coherent and incoherent illumination.

Chapter 10: Interference and Diffraction with Partially Coherent Light

Complex representation of polychromatic fields, correlation functions and the mutual coherence function, interference with quasi-monochromatic light, correlation-induced spectral changes, applications to microscope illumination and imaging, the rigorous theory of partial coherence, and the coherency matrix, degree of polarization and Stokes parameters.

Chapters 11–12: Rigorous Diffraction Theory; Diffraction of Light by Ultrasonic Waves

Chapter 11 treats exact solutions: boundary conditions, diffraction by a plane screen and half-plane in two and three dimensions, and uniqueness of solution. Chapter 12 describes diffraction of light by ultrasonic waves with an integral-equation method and the Raman–Nath approximation.

Chapter 13: Scattering from Inhomogeneous Media

The scalar theory of scattering (the first-order Born approximation, scattering from periodic potentials, multiple scattering), principles of diffraction tomography, the optical cross-section theorem, a reciprocity relation, the Rytov series, and scattering of electromagnetic waves.

Chapters 14–15: Optics of Metals; Optics of Crystals

Chapter 14 covers wave propagation in a conductor, reflection and refraction at a metal surface, the electron theory of optical constants, thin metallic films and Mie's theory of diffraction by a conducting sphere. Chapter 15 covers the dielectric tensor of anisotropic media, wave propagation in crystals, uniaxial and biaxial crystals, measurements in crystal optics (compensators, interference figures), stress and form birefringence, and absorbing crystals.

Appendices

Twelve appendices cover the calculus of variations, light optics, electron optics and wave mechanics, asymptotic approximations to integrals, the Dirac delta function, several mathematical lemmas and proofs, and Zernike polynomials.

Key Concepts

Chapters 1–2: Electromagnetic foundations

• Maxwell's equations and boundary conditions: the starting point for all later results.
• Stratified media: matrix treatment of dielectric films.
• Ewald–Oseen extinction theorem: refraction and reflection derived from integral equations.

Chapters 3–6: Geometrical optics and aberrations

• Eikonal equation and Fermat's principle: the short-wavelength limit.
• Hamilton's characteristic functions: the geometric theory of imaging.
• Seidel aberrations: spherical aberration, coma, astigmatism, field curvature and distortion.

Chapters 7–10: Interference, diffraction and coherence

• Kirchhoff diffraction theory: the standard scalar approach to diffraction.
• Fabry–Perot interferometer: multiple-beam interference.
• Mutual coherence function: the correlation description of partially coherent light.
• Zernike polynomials: expanding the aberration function.

Chapters 11–15: Exact solutions, scattering and materials

• Rigorous half-plane diffraction: an exact solution for a vector field.
• Born approximation and diffraction tomography: reconstructing a scatterer from its scattered field.
• Mie theory: scattering by a conducting sphere.
• Birefringence: the dielectric tensor and light in uniaxial and biaxial crystals.

Critical Analysis

Strengths

• A unified electromagnetic foundation. Choice's review (J. Lambropoulos) describes the book as starting from the electromagnetic field description of optics and ending with the optics of metals and crystals, a progression the contents confirm. The foreword by Sir Peter Knight quotes a description of the book as a systematic treatment based on electromagnetic theory of all optical phenomena describable by a continuous distribution of matter.
• Mathematical rigour. A review in Contemporary Physics (R. S. Shorter) credits the book's strength to its mathematical lucidity, and the foreword attributes to Born an approach that formulates a problem in general terms and then specializes to simpler cases.
• Coherence theory. The foreword points to the careful treatment of correlations of amplitudes and intensities, and the contents give partial coherence its own long chapter (Chapter 10).
• Reference apparatus. Twelve appendices, including the calculus of variations and asymptotic approximations, give proofs and techniques in one place; Choice's reviewer singles them out as adding great utility.
• Breadth of topics. The fifteen chapters range from aberration theory and instruments to rigorous diffraction, ultrasonic diffraction, scattering and crystal optics, so the book serves as a source for many specialties.

Limitations

• Classical optics only. The contents contain no chapter on lasers, nonlinear optics or quantum optics; the foreword notes that volumes on atomic and quantum optics were planned in the first edition's preface but are not part of this book.
• Very demanding mathematics. Sections such as Chapter 11 on rigorous diffraction, Chapter 14 on Mie theory and the appendices on asymptotic integrals expect fluency in vector calculus, Fourier analysis and complex functions. Choice's reviewer calls it a graduate-level textbook, though undergraduates may gain insight from parts such as the discussion of image-forming instruments.
• Reference format. At over 900 pages with a long appendix section, it is better consulted by topic than read straight through.
• Edition. This printing reproduces the 1999 seventh edition with a new foreword, so developments after that date in optics are not covered.

Where It Fits in the Course

Among the optics books in this list, Born and Wolf is the comprehensive graduate reference. Hecht's Optics and Pedrotti's Introduction to Optics are undergraduate textbooks that cover ray optics, interference, diffraction and polarization at a lower mathematical level and are the right first stops; French's Vibrations and Waves gives the wave background, and Walmsley's Light: A Very Short Introduction is a non-mathematical overview of what light is. Saleh and Teich's Fundamentals of Photonics is the neighbouring graduate text, moving from rays and waves to lasers, fibres and detectors, which Born and Wolf does not cover.

A typical path is Hecht or Pedrotti first, then Born and Wolf for a rigorous treatment of the same phenomena, and Saleh and Teich for modern photonics.

How to Use This Book

The book is for graduate students and researchers, and for advanced undergraduates who have studied optics and electromagnetism and are comfortable with vector calculus, Fourier analysis and complex functions.

A practical plan:

• Core: Chapter 1 for the electromagnetic foundations, Chapters 3 and 4 for geometrical optics and imaging, Chapter 7 for interference, and Chapter 8 for diffraction.
• For coherence and instrumentation: Chapter 10 on partial coherence, Chapter 6 on instruments, and Chapter 9 on diffraction and aberrations.
• Specialist chapters: Chapters 11 to 15 when a project needs rigorous diffraction, ultrasonic diffraction, scattering and tomography, metals, or crystals.
• Use the appendices: the calculus of variations and the asymptotic methods are worth reading before the chapters that depend on them.
• Read the foreword: it explains how the book was assembled and why topics such as coherence theory and diffraction tomography have their place.