Table of Contents

About the Editors ...... vii

Preface ...... ix

Acknowledgments ...... xi

Chapter 1: Overview ...... 1 The Fresnel diffraction phenomena ...... 3 W. Arkadiew The geometrical theory of diffraction ...... 13 J. B. Keller Diffraction theory ...... 17 C. J. Bouwkamp

Developments in our concepts of diffraction phenomena (on the 130th anniversary of the death of Thomas Young) ...... 57 G. D. Malyuzhinets Rays, waves and asymptotics ...... 67 J. B. Keller Rubinowicz and the modern theory of diffracted rays ...... 81 P. Ya. Ufimtsev

Chapter 2: Early Developments in Diffraction Theory ...... 89 Translation editor’s introduction ...... 107 K. Helbig A physico-mathematical treatise on light, colors and the rainbow, Proposition 1 ...... 108 F. M. Grimaldi Treatise on light, Chapter 1: On the rectilinear propagation of rays ...... 117 C. Huygens The Bakerian lecture: Experiments and calculations relative to physical optics ...... 123 T. Young

Chapter 3: The Classical Mathematical Theory of Diffraction ...... 129 Memoir on the diffraction of light ...... 147 A. Fresnel

An essay on the application of mathematical analysis to the theories of electricity and magnetism ...... 177 G. Green Theory of air vibration in pipes with open ends ...... 187 H. Helmholtz vi Classical and Modern Diffraction Theory

On the ray theory of light ...... 191 G. Kirchhoff On the passage of waves through apertures in plane screens, and allied problems ...... 205 Lord Rayleigh (J. W. Strutt)

Chapter 4: Foundations of Modern Diffraction Theory ...... 213 Reciprocal diffraction relations between circular and elliptical plates ...... 217 J. Coulson and G. G. Becknell An extension of the principle of the diffraction evolute, and some of its structural detail ...... 223 G. G. Becknell and J. Coulson An asymptotic treatment of diffraction problems ...... 227 N. G. Van Kampen Boundary layer problems in diffraction theory ...... 235 R. N. Buchal and J. B. Keller Geometrical theory of diffraction ...... 251 J. B. Keller A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface ...... 267 R. G. Kouyoumjian and P. H. Pathak The ray method and the theory of edge waves ...... 283 K. D. Klem-Musatov and A. M. Aizenberg Resolution and super-resolution in inverse diffraction ...... 293 M. Bertero, P. Boccacci, and M. Piana

Appendix A: The Cornu Spiral ...... 303 New method for the discussion of diffraction problems in the case of a cylindrical wave ...... 305 M. A. Cornu

Appendix B: Babinet’s Principle ...... 315 Memoirs on meteorological optics ...... 317 M. Babinet The London and Edinburgh Philosophical Magazine and Journal of Science ...... 319 A. Necker

References: Reprinted Technical Papers ...... 323

References: General ...... 325