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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 62, Iss. 11 — Nov. 1, 1972
  • pp: 1309–1314

Photo-Count Distributions and Irradiance Fluctuations of a Log-Normally Distributed Light Field


JOSA, Vol. 62, Issue 11, pp. 1309-1314 (1972)

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We discuss some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with large surface inhomogeneities (average size 20 µm), when the illuminated area of the scattering surface contains only a few scattering centers. Photon-count distribution measurements indicate that, to a high degree of accuracy, the field amplitude of the scattered light fluctuates as a log-normal variate. The irradiance correlation function is a gaussian function of time with a half-width at half-height that varies inversely with the angular speed of the ground glass but is largely independent of the angle of scattering. Identical functional dependence was previously found, using a ground glass with much smaller surface inhomogeneities (average size 1 µm). Finally, we report some experimental tests of a recent calculation by Mitchell concerning what has been defined as the permanence of the log-normal distribution. We find that, even when the detecting surface of the photomultiplier is illuminated by several coherence areas of the scattered field during a single counting interval, the field-amplitude distribution remains log-normal to an excellent approximation.

VAN BLUEMEL, LORENZO M. NARDUCCI, and RICHARD A. TUFT, "Photo-Count Distributions and Irradiance Fluctuations of a Log-Normally Distributed Light Field," J. Opt. Soc. Am. 62, 1309-1314 (1972)

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  1. Ch. Bendjaballah, Phys. Letters 31A, 471 (1970).
  2. L. E. Estes, L. M. Narducci, and R. A. Tuft, J. Opt. Soc. Am. 61, 1301 (1971).
  3. M. Rousseau, J. Opt. Soc. Am. 61, 1307 (1971) and references therein, for previous work on rotating ground glass.
  4. An extensive discussion of gaussian optical fields can be found in B. Picinbono and M. Rousseau, Phys. Rev. A 1, 635 (1970). See also L. Mandel, Phys. Rev. 181, 75 (1969).
  5. R. L. Mitchell, J. Opt. Soc. Am. 58, 1267 (1968).
  6. Comprehensive discussions of the digital correlation technique as well as a comparison with other methods used in irradiance-fluctuation spectroscopy can be found in E. Jakeman, E. R. Pike, and S. Swain, J. Phys. A 4, 517 (1971); V. Degiorgio and J. B. Lastovka, Phys. Rev. A 4, 2033 (1971); and H. C. Kelly, IEEE J. QE-7, 541 (1971).
  7. From the acknowledgments of Ref. 5 we learn that the title "permanence of the log-normal distribution" was suggested to Mitchell by D. L. Fried.
  8. D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).
  9. Z. Kopal, Numerical Analysis (Chapman & Hall, London, 1955), Ch. 7.
  10. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, Natl. Bur. Std. (U. S.) Appl. Math. Ser. (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965), p. 923.

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