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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 5 — May. 1, 1978
  • pp: 614–622

Second-order statistics of speckle patterns observed through finite-size scanning apertures

Richard Barakat and Julian Blake  »View Author Affiliations


JOSA, Vol. 68, Issue 5, pp. 614-622 (1978)
http://dx.doi.org/10.1364/JOSA.68.000614


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Abstract

The second-order statistics for speckle patterns are derived through the use of an integral equation which determines the moment generating function. A specific geometry of apertures is treated as an example of the techniques developed. The inversion problem of determining the field correlation function from measurements of the integrated intensities is examined in the context of singular-value decomposition. The joint probability density function for the integrated intensities is evaluated.

© 1978 Optical Society of America

Citation
Richard Barakat and Julian Blake, "Second-order statistics of speckle patterns observed through finite-size scanning apertures," J. Opt. Soc. Am. 68, 614-622 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-5-614


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References

  1. Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer, Berlin, 1975).
  2. J. C. Dainty, "The Statistics of Speckle Patterns," in Progress in Optics, Vol. 14, edited by E. Wolf (North-Holland, Amsterdam, 1977).
  3. Special issue on "Speckle Phenomena," J. Opt. Soc. Am. 66, Nov. 1976.
  4. M. A. Condie, "An Experimental Investigation of the Statistics of Diffusely Reflected Coherent Light," thesis (Standford University, 1966).
  5. J. C. Dainty, "Detection of Images Immersed in Speckle Noise," Opt. Acta 18, 327 (1971).
  6. R. Barakat, "First-Order Probability Densities of Laser Speckle Patterns Observed Through Finite Size Scanning Apertures," Opt. Acta 20, 729 (1973).
  7. G. Parry, "The Scattering of Polychromatic Light from Rough Surfaces: First Order Statistics," Opt. Quant. Elec. 7, 311 (1975).
  8. T. S. McKechnie, "Reduction of Speckle by a Moving Aperture— First Order Statistics," Opt. Comm. 13, 35 (1975).
  9. A. Scribot, "First Order Probability Density Functions of Speckle Measured with a Finite Aperture," Opt. Comm. 11, 238 (1974).
  10. F. Gori and C. Palma, "On the Eigenvalues of the Sinc2 Kernel," J. Phys. A 8, 1709 (1975).
  11. R. Barakat and P. Fortini, "Extreme Value Statistics of Speckle Patterns Observed Through Finite Size Scanning Apertures," J. Opt. Soc. Am. (to be published),
  12. R. Barakat and R. Glauber, Quantum Theory of Photoelectron Counting Statistics (Unpublished report, Physics Dept., Harvard University, 1966).
  13. E. Jakeman and E. R. Pike, "The Intensity Distribution of Gaussian Light," J. Phys. A. 1, 128 (1968).
  14. E. Jakeman, "Theory of Optical Spectroscopy by Digital Autocorrelation of Photon-Counting Fluctuations," J. Phys. A 3, 201 (1970).
  15. J. Blake and R. Barakat, Twofold Photoelectron Counting Statistics: the Clipped Correlation Function, J. Phys. A 6, 1196 (1973).
  16. R. Barakat, "First Order Statistics of Random Sinusoidal Waves with Applications to Laser Speckle Patterns," Opt. Acta 21, 903 (1974).
  17. R. Barakat and J. Blake, "Onefold Photoelectron Counting Statistics for Non-Gaussian Light: Scattering from Polydispersive Suspensions," Phys. Rev. A 13, 1122 (1976). See Appendix B.
  18. M. Kac and A. Siegert, "On the Theory of Noise in Radio Receivers with Square Law Detectors," J. Appl. Phys. 18, 383 (1947).
  19. J. B. Thomas, Statistical Communication Theory (Wiley, New York, 1969).
  20. R. Glauber, "Photon Statistics," in Fundamental Problems in Statistical Mechanics, edited by E. D. G. Cohen (North-Holland, Amsterdam, 1969).
  21. W. Martienssen and E. Spiller, "Coherence and Fluctuations in Light Beams," Am. J. Phys. 32, 919 (1964).
  22. J. Blake and R. Barakat, "Threefold Photoelectron Counting Statistics for Gaussian Light," Opt. Commun. 16, 303 (1976).
  23. J. Blake and R. Barakat, "The Inversion Problem for Twofold Photoelectron Counting Statistics," Can. J. Phys. 53, 1215 (1975).
  24. C/ L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, NJ, 1974), Chaps. 4 and 5.
  25. G. H. Golub and C. Reinsch, "Singular Value Decomposition and Least Squares Solutions," Nuiner. Math. 14, 403 (1970).
  26. I. N. Sneddon, Special Functions of Mathematical Physics and Chemistry (Oliver and Boyd, Edinburgh, 1956).
  27. G. Szegö, Orthogonal Polynomials, 3rd ed. (American Mathematical Society, Providence, 1967).

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