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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 61, Iss. 10 — Oct. 1, 1971
  • pp: 1307–1316

Statistical Properties of Optical Fields Scattered by Random Media. Application to Rotating Ground Glass

MARTINE ROUSSEAU  »View Author Affiliations

JOSA, Vol. 61, Issue 10, pp. 1307-1316 (1971)

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We give a sufficient condition for the field scattered from a surface (S) illuminated by a laser beam to be a stationary gaussian field. This condition is fulfilled for the optical shot noise. As an example we calculate the spectrum of the field scattered from a granular surface. We show that it does not depend on the statistical properties of (S) when the number of grains tends to infinity.

MARTINE ROUSSEAU, "Statistical Properties of Optical Fields Scattered by Random Media. Application to Rotating Ground Glass," J. Opt. Soc. Am. 61, 1307-1316 (1971)

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  1. Y. R. Shen, Phys. Rev. 155, 921 (1967).
  2. P. di Porto, B. Crosignani, and M. Bertolotti, J. Appl. Phys. 40, 5083 (1969).
  3. W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964); F. T. Arecchi, E. Gatti, and A. Sona, Phys. Letters 20, 27 (1966); F. T. Arecchi, A. Berné, and A. Sona, Phys. Rev. Letters 17, 260 (1966); Ch. Bendjaballah, Phys. Letters 31A, 471 (1970).
  4. E. Jakeman, C. J. Oliver, and R. E. Pike, J. Phys. A 1, 406 (1968); E. R. Pike, D. A. Jackson, P. J. Bourke, and D. I. Page, J. Phys. E 1, 727 (1968).
  5. R. A. Tuft, L. E. Estes, and L. M. Narducci, J. Opt. Soc. Am. 61, 691A (1971).
  6. H. Z. Cummins, in International School of Physics "Enrico Fermi" XLII course, Quantum Optics -Varenna (1967) (Academic, N. Y., London, 1968) and many others.
  7. B. Picinbono and M. Rousseau, Phys. Rev. A 1, 635 (1970).
  8. R. J. Glauber, in Quantumo Optics and Electronics, Les Houches 1964, edited by C. De Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 65.
  9. F. T. Arecchi, Phys. Rev. Letters 15, 912 (1965).
  10. B. Picinbono, thèse (Edition de la revue d'optique théorique et instrumentale, Paris, 1960).
  11. B. Picinbono, C. Bendjaballah, and J. Pouget, J. Math. Phys. 11, 2166 (1970).
  12. B. Crosignani, B. Daino, and P. di Porto, J. Appl. Phys. 42, 399 (1971). These authors have recently calculated the spectrum of the light scattered by a medium with a dielectric constant ∊(r,t) = ∊0+∊1(r,t). They did not attempt to find the conditions under which the scattered field is gaussian. They think that the field scattered by a ground-glass rotating disk may be expressed in the Born approximation, but other authors consider the ground disk as a pure phase object; see, for example, M. Rousseau, Compt. Rend. B, 269, 514 (1969).
  13. The temporal stationarity of the complex field Ek(t) does not necessitate such a strong condition as the spatial stationarity of the random transparency X(r) as we can easily see. The stationarity in the Ox direction is a necessary and sufficient condition; we shall here suppose that it is so.
  14. B. Picinbono and E. Boileau, J. Opt. Soc. Am. 58, 784 (1968).
  15. C. W. Helstrom, J. Opt. Soc. Am. 57, 353 (1967).
  16. A. Blanc-Lapierre and R. Fortet, Th. des Fonctions Aléatoires (Masson, Paris, 1953), p. 161.
  17. B. Picinbono, Phys. Letters 29, 614 (1969).

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