• Giovanni GiusfrediEmail author
Part of the UNITEXT for Physics book series (UNITEXTPH)


Diffraction, whose name was introduced by Grimaldi in 1665, when he first discovered it and described its effects, has been conveniently defined by Sommerfeld (1949), paraphrasing the Grimaldi’s expression, as «any deviation of the light rays from rectilinear paths which cannot be interpreted as reflection or refraction». For example, if an opaque object is placed between a point source and a screen, the shadow thrown by the object does not have an edge as sharp as the one predicted by Geometrical Optics. In fact, careful observation of the shadow edge reveals that a bit of light goes into the shaded area, while darkened fringes appear in the illuminated area.


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Bibliographical References

  1. Arnaud J.A., Nonorthogonal optical waveguides and resonators, The Bell Systems Technical Journal 49, 2311-2348 (November 1970).MathSciNetCrossRefGoogle Scholar
  2. Abramowitz M. and Stegun I.A., Handbook of Mathematical Functions, Dover Publications Inc., New York (1972).Google Scholar
  3. Born M. and Wolf E., Principles of Optics, Pergamon Press, Paris (1980).Google Scholar
  4. Collins S.A. Jr., Lens-system diffraction integral written in terms of Matrix optics, J. Opt. Soc. Am. 60, 1168-1177 (September 1970).ADSCrossRefGoogle Scholar
  5. Ditchburn R.W., Light, Vol. I and II, Academic Press Inc., London (1976).Google Scholar
  6. Ehrlich M.J., Silver S. and Held G., Studies of the Diffraction of Electromagnetic Waves by Circular Apertures and Complementary Obstacles: The Near-Zone Field, J. Appl. Phys. 26, 336-345 (1955).ADSCrossRefGoogle Scholar
  7. Erdélyi A., Asymptotic expansion, Dover Publications, inc., New York (1956).Google Scholar
  8. Fowles G.R., Introduction to Modern Optics, Holt, Rinehart, and Winston, New York (1968).Google Scholar
  9. Guenther R., Modern Optics, John Wiley & Sons, New York (1990).Google Scholar
  10. Goodman J.W., Introduction to Fourier Optics, II ed., McGraw-Hill, San Francisco (1996).Google Scholar
  11. Hecht E., Optics, 2nd ed., Addison-Wesley, Madrid (1987).Google Scholar
  12. Jenkins F.A. and White H.E., Fundamental of Optics, McGraw-Hill, New York (1957).Google Scholar
  13. Keller J.B., Diffraction by an Aperture, J. Appl. Phys. 28, 426-444 (1957). Geometrical Theory of Diffraction, J. Opt. Soc. Am. 52, 116-130 (1962).Google Scholar
  14. Kottler F., Zur Theorie der Beugung an schwarzen Schirmen, Ann. Physik 375, 405-456 (1923). Elektromagnetische Theorie der Beugung an schwarzen Schirmen, Ann. Physik 376, 457-508 (1923). Diffraction at a black screen, part I: Kirchhoff theory, Progress in Optics IV, 281-314 (1966), reprinted in Scalar Wave Diffraction, K. E. Oughstun ed., SPIE Milestone Series Vol. MS51, p. 108 (1992). Diffraction at a black screen, part II: electromagnetic theory, Progress in Optics VI, 331-377, Elsevier Science Publ. (1967).Google Scholar
  15. Landau L. and Lifchitz E., (II), Théorie du Champ, MIR, Mosca (1966).Google Scholar
  16. Landsberg G.S., Ottica, MIR, Mosca (1979).Google Scholar
  17. Lipson S.G., Lipson H. and Tannhauser D.S., Optical Physics, III ed., Cambridge University Press, Cambridge (1995).Google Scholar
  18. Maggi G.A., Sulla propagazione libera e perturbata delle onde luminose in un mezzo isotropo, Annali di Matematica 16, 21-48 (1888).CrossRefGoogle Scholar
  19. Mansuripur M., Classical Optics and its Applications, Cambridge Univ. Press, Cambridge (2002).Google Scholar
  20. Marchand E.W and Wolf E., Consistent Formulation of Kirchhoff’s Diffraction Theory, J. Opt. Soc. Am. 56, 1712-1722 (1966). Diffraction at Small Apertures in Black Screens, J. Opt. Soc. Am. 59, 79-90 (1969).Google Scholar
  21. Miyamoto K. and Wolf E., Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave, J. Opt. Soc. Am. 52, Part I: 615-625, Part II: 626-637 (1962).Google Scholar
  22. Möller K.D., Optics, University Science Book, Mill Valley (1988).Google Scholar
  23. Osterberg H. and Smith L.W., Closed solutions of Rayleigh’s diffraction integral for axial points, J. Opt. Soc. Am. 51, 1050-1054 (1961).ADSCrossRefGoogle Scholar
  24. Rubinowicz A., Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen, Ann. Physik 358, 257-278 (1917). Zur Kirchhoffschen Beugungstheorie, Ann. Physik 378, 339-364 (1924). - Thomas Young and the theory of diffraction, Nature 180, 160-162 (1957).Google Scholar
  25. Sheppard C.J.R. and Hrynevych M., Diffraction by a circular aperture: a generalization of Fresnel diffraction theory, J. Opt. Soc. Am. A 9, 274-281 (1992).ADSCrossRefGoogle Scholar
  26. Siegman A. E., Lasers, University Science Books, Mill Valley, California (1986).Google Scholar
  27. Sivoukhine D., Optique, MIR, Mosca (1984).Google Scholar
  28. Solimeno S., Crosignani B., Di Porto P., Guiding, Diffraction, and Confinement of Optical Radiation, Academic Press, inc., Orlando (1986).Google Scholar
  29. Sommerfeld A., Lectures on Theoretical Physics: Optics, Academic Press, New York (1949).Google Scholar
  30. Stamnes J.J., Waves in Focal Regions, A. Hilger, Bristol (1986).Google Scholar
  31. Stamnes J.J., Spjekavik B. and Pedersen H.M., Evaluation of diffraction integrals using local phase and amplitude approximations, Opt. Acta 30, 227-222 (1983).MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.European Laboratory for Non-Linear Spectroscopy (LENS)Istituto Nazionale di Ottica—Consiglio Nazionale delle Ricerche (INO-CNR)Sesto FiorentinoItaly

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