From the Preface: "The present monograph deals with the mathematical theory of Huygens' principle in optics and its application to the theory of diffraction. No attempt has been made to give a complete account of the various methods of solving special diffraction problems. [The authors] are concerned only with the general theory of the solution of the partial differential equations governing the propagation of light and [they] discuss some of the simpler diffraction problems merely as illustrative examples."

Table of Contents

• The Analytical Representation of Huygens' Principle: 1 The principle of Huygens; 2 Huygens' construction as a contact-transformation; 3 The propagation of sound waves in air; 4 Huygens' principle for monochromatic phenomena; 5; Wave-motions in three dimensions; 6 Wave-motions in two dimensions; 7 Marcel Riesz's solution of the equation of cylindrical waves
• Huygens' Principle and the Theory of Diffraction: 1 Kirchhoff's theory of diffraction; 2 Maggi's transformation; 3 Diffraction by a black half-plane; 4 Kottler's theory of diffraction by a black screen
• Huygens' Principle for Electromagnetic Waves: 1 Huygens' principle and Maxwell's equations; 2 The failure of the Kirchhoff and the Larmor-Tedone formulæ; 3 Kottler's formulation of Huygens' principle for electromagnetic waves; 4 The diffraction of electromagnetic waves by a black screen
• Sommerfeld's Theory of Diffraction: 1 Sommerfeld's many-valued wave-functions; 2 The diffraction of plane-polarized light by a reflecting half-plane; 3 Diffraction of plane-polarized light by a black half-plane
• Diffraction by a Plane Screen: 1 Introduction; 2 Diffraction of sound by a plane screen; 3 Diffraction of electromagnetic waves; 4 Sommerfeld's diffraction problem; 5 Schwarzschild's diffraction problem; 6 Approximate solutions
• Index