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Photon-Counting Statistics of Optical Scintillation

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Inverse Scattering Problems in Optics

Part of the book series: Topics in Current Physics ((TCPHY,volume 20))

Abstract

In contrast to the weak statistical scatterers and their first-order correlation and average scattered intensity studied in Sect.2.5, this chapter aims at strong scatterers and the fluctuations and higher-order correlations of the scattered radiation as explored by photon-counting techniques. The pertinent inverse detection and scattering problems are discussed with emphasis on a new class of distributions — the K distributions — which were recently found to characterize the fluctuations in scattered intensity for a wide class of experimental situations.

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References

  1. H.Z. Cummins, E.R. Pike (eds.): Photon Correlation and Light Beating Spectro-scopy ( Plenum Press, New York 1974 )

    Google Scholar 

  2. E.R. Pike, E. Jakeman: Adv. Quantum Electro. 2, 1 (1974)

    Google Scholar 

  3. B. Saleh: Photoelectron Statistics, Springer Series in Optical Sciences, Vol. 6 ( Springer, Berlin, Heidelberg, New York 1978 )

    Google Scholar 

  4. E. Jakeman, E.R. Pike, P.N. Pusey: Nature 263, 215 (1976)

    Article  ADS  Google Scholar 

  5. G. Parry, P.N. Pusey, E. Jakeman, J.G. McWhirter: Opt. Commun. 22, 195 (1977)

    Article  ADS  Google Scholar 

  6. E. Jakeman, G. Parry, E.R. Pike, P.N. Pusey: Contemp. Phys. 19, 127 (1978)

    Article  ADS  Google Scholar 

  7. C.J. Oliver: “Correlation Techniques”, in Ref.[3.1], pp.151–236

    Google Scholar 

  8. E. Jakeman, C.J. Oliver, E.R. Pike: Adv. Phys. 24, 349 (1975)

    Article  ADS  Google Scholar 

  9. C.J. Oliver: Infrared Phys. 18, 303 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  10. E. Jakeman, P.N. Pusey: Phys. Rev. Lett. 40, 546 (1978)

    Article  ADS  Google Scholar 

  11. E. Jakeman: J. Phys.A 13, 31–48 (1980)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. A. Zardecki: “Statistical Features of Phase Screens from Scattering Data”, in Inverse Source Problems in Optics, ed. by H.P. Baltes, Topics in Current Physics, Vol. 9 ( Springer, Berlin, Heidelberg, New York 1978 ) pp. 155–189

    Google Scholar 

  13. H.G. Booker, J.A. Ratcliffe, D.H. Shinn: Phil. Trans. Roy. Soc. (London) 242, 579 (1950)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. R.P. Mercier: Proc. Camb. Phil. Soc. 58, 382 (1962)

    Article  MATH  ADS  Google Scholar 

  15. E.E. Salpeter: Astrophys. J. 147, 433 (1967)

    Article  ADS  Google Scholar 

  16. R. Buckley: Austral. J. Phys. 24, 351, 373 (1971)

    ADS  Google Scholar 

  17. V.I. Shishov: Izv. Vuz. Radiofuz. 14, 85 (1971)

    Google Scholar 

  18. L.S. Taylor, C.J. Infosino: J. Opt. Soc. Am. 65, 78 (1975)

    Article  ADS  Google Scholar 

  19. E. Jakeman, J.G. McWhirter: J. Phys. A 9, 1599 (1977)

    Article  ADS  Google Scholar 

  20. J.W. Strohbehn: Proc. IEEE 56, 1301 (1968)

    Article  Google Scholar 

  21. R.S. Lawrence, J.W. Strohbehn: Proc. IEEE 58, 1523 (1970)

    Article  Google Scholar 

  22. R.L. Fante: Proc. IEEE 63, 1669 (1975)

    Article  ADS  Google Scholar 

  23. A.M. Prokhorov, F.V. Bunkin, K.S. Gochelashvily, V.I. Shishov: Proc. IEEE 63, 790 (1975)

    Article  ADS  Google Scholar 

  24. G. Parry, P.N. Pusey, E. Jakeman, J.G. McWhirter: The Statistical and Corr-lation Properties of Light Scattered by a Random Phase Screen“, in Coherenc and Quantum optics IV, ed. by L. Mandel, E. Wolf ( Plenum Press, New York 1978 ) pp. 351–361

    Google Scholar 

  25. R.J. Glauber: “Optical Coherence and Photon Statistics”, in Quantum Optics nd Electronics, ed. by C. DeWitt, A. Blandin, C. Cohen-Tannoudji ( Gordon and Breach, New York 1965 ) pp. 65–185

    Google Scholar 

  26. N. Tornau, A. Bach: Opt. Commun. 11, 46 (1974)

    Article  ADS  Google Scholar 

  27. D. Stoler: Phys. Rev. Lett. 33, 1397 (1974)

    Article  ADS  Google Scholar 

  28. H.D. Simaan, R. Loudon: J. Phys.A 8, 539 (1975)

    Article  ADS  Google Scholar 

  29. H.J. Carmichael, D.F. Walls: J. Phys.B 9, L43 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  30. H.J. Kimble, M. Dagenais, L. Mandel: Phys. Rev. Lett. 39, 691 (1977)

    Article  ADS  Google Scholar 

  31. L. Mandel: Proc. Phys. Soc. 74, 233 (1959)

    Article  ADS  Google Scholar 

  32. E. Wolf, C.L. Mehta: Phys. Rev. Lett. 13, 705 (1964)

    Article  ADS  Google Scholar 

  33. S.O. Rice: Bell Syst. Tech. J. 23, 282 (1944)

    MATH  MathSciNet  Google Scholar 

  34. L. Mandel, E. Wolf: Rev. Mod. Phys. 37, 231 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  35. ] R. Loudon: The Quantum Theory of Light (Clarendon Press, Oxford 1973) Chap.10

    Google Scholar 

  36. A. Schell, R. Barakat: J. Phys.A 6, 826 (1973)

    Article  ADS  Google Scholar 

  37. A.J.F. Siegert: MIT Rad. Lab. Rpt. No. 465 (1943)

    Google Scholar 

  38. D. Middleton: Quart. Appl. Math. 5, 455 (1948)

    MathSciNet  Google Scholar 

  39. I.S. Reed: IRE Trans. Inf. Theory IT-8, 194 (1962)

    Google Scholar 

  40. E. Jakeman, C.J. Oliver, E.R. Pike: J. Phys.A 1, 406 (1968)

    Article  ADS  Google Scholar 

  41. E.E. Serrallach, M. Zulauf: J. Appl. Math. Phys. 26, 669 (1975)

    Article  Google Scholar 

  42. G. Bedard, J.C. Chang, L. Mandel: Phys. Rev. 160, 1496 (1967)

    Article  ADS  Google Scholar 

  43. G. Lachs: J. Appl. Phys. 42, 602 (1971)

    Article  ADS  Google Scholar 

  44. S.K. Srinivasan, S. Sukavanam: J. Phys. A 5, 682 (1972)

    Article  ADS  Google Scholar 

  45. B.E.A. Saleh: J. Appl. Phys. 46, 943 (1975)

    Article  ADS  Google Scholar 

  46. S.K. Srinivasan, S. Sukavanam: Phys. Lett. 60A, 287 (1977)

    Google Scholar 

  47. E. Jakeman: J. Phys. A 3, 201 (1970)

    Article  ADS  Google Scholar 

  48. V. Degiorgio, J.B. Lastovka: Phys. Rev.A 4, 2033 (1971)

    Article  ADS  Google Scholar 

  49. R.G.W. Brown, R.D. Callan, W. Jenkins, I. Miller, C.J. Oliver, E.R. Pike, D.J. Watson, M. Wood: In “Photon Correlation Techniques in Fluid Mechanics”, Proc. 2nd Intern. Conf., Stockholm, Sweden, June 14–16, 1978, Phys. Scr. 19, 365 (1979)

    Google Scholar 

  50. J.H. Van Vleck: Harvard Univ. Rad. Res. Lab. Rpt. No. 51 (1943)

    Google Scholar 

  51. J.H. Van Vleck, D. Middleton: Proc. IEEE 54, 2 (1966)

    Article  Google Scholar 

  52. E. Jakeman, E.R. Pike: J. Phys.A 2, 411 (1969)

    Article  ADS  Google Scholar 

  53. E. Jakeman, E.R. Pike, S. Swain: J. Phys.A 3, L55 (1970)

    Article  ADS  Google Scholar 

  54. E. Jakeman, E.R. Pike, S. Swain: J. Phys. A 4, 517 (1971)

    Article  ADS  Google Scholar 

  55. A.J. Hughes, E. Jakeman, C.J. Oliver, E.R. Pike: J. Phys. A6, 1327 (1973)

    Google Scholar 

  56. P.N. Pusey, W.I. Goldburg: Phys. Rev. A 3, 766 (1971)

    Article  ADS  Google Scholar 

  57. D.W. Schaefer, B.J. Berne: Phys. Rev. Lett. 28, 475 (1972)

    Article  ADS  Google Scholar 

  58. E. Jakeman, C.J. Oliver, E.R. Pike, P.N. Pusey: J. Phys.A 5, L93 (1972)

    Article  ADS  Google Scholar 

  59. E. Jakeman, C.J. Oliver, E.R. Pike: J. Phys.A 3, L45 (1970)

    Article  ADS  Google Scholar 

  60. M. Born, E. Wolf: Principles of Optics (Pergamon, London, New York 1959 ) p. 397

    Google Scholar 

  61. ] E. Jakeman: In Ref.[3.1], pp.75–149

    Google Scholar 

  62. D.E. Koppel: J. Appl. Phys. 42, 3216 (1971)

    Article  ADS  Google Scholar 

  63. S.H. Chen, P. Tartaglia: Opt. Commun. 6, 119 (1972)

    Article  ADS  Google Scholar 

  64. G. Lachs: Phys. Rev. 138, B1012 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  65. J. Peina: Phys. Lett. 24A, 333 (1967)

    Google Scholar 

  66. E. Jakeman, J.G. McWhirter, P.N. Pusey: J. Opt. Soc. Am. 66, 1175 (1976)

    Article  ADS  Google Scholar 

  67. A.S. Clarke: RARDE Tech. Rpt. 7 /77 (1977)

    Google Scholar 

  68. F.A. Johnson, R. Jones, T.P. McLean, E.R. Pike: Phys. Rev. Lett. 16, 589 (1966)

    Article  ADS  Google Scholar 

  69. G. Bedard: Proc. Phys. Soc. 90, 131 (1967)

    Article  ADS  Google Scholar 

  70. I. Delotto, P.F. Manfredi, P. Principio: Energia Nucl. (Milan) 11, 557 (1964)

    Google Scholar 

  71. R.F. Chang, V. Korenman, C.O. Alley, R.W. Detenbeck: Phys. Rev. 178, 612 (1969)

    Article  ADS  Google Scholar 

  72. E. Jakeman, E.R. Pike: J. Phys.A 1, 690 (1968)

    Article  ADS  Google Scholar 

  73. Y.N. Barabanenkov, Y.A. Kraystov, S.M. Rytov, V.I. Tatarskii: Usp. Fiz. Nauk. 102, 1 (1970)

    Google Scholar 

  74. B.J. Uscinski: The Elements of Wave Propagation in Random Media ( McGraw-Hill, New York 1977 )

    Google Scholar 

  75. B.J. Uscinski: J. Atmos. Terrest. Phys. 40, 1257 (1978)

    Article  ADS  Google Scholar 

  76. R. Dashen: Stanford Res. Inst. Tech. Rpt. JSR-76–1 (1977)

    Google Scholar 

  77. E. Jakeman, P.N. Pusey: J. Phys.A 6, L88 (1973)

    Article  ADS  Google Scholar 

  78. E. Jakeman, P.N. Pusey: IEEE Trans. AP-24, 806 (1976)

    Google Scholar 

  79. P.N. Pusey: “Statistical Properties of Scattered Radiation”, in Photon Correlation Spectroscopy and Velocimetry, ed. by H.Z. Cummins, E.R. Pike ( Plenum Press, New York 1977 ) pp. 45–141

    Google Scholar 

  80. J.C. Kluyver: Proc. Roy. Acad. Sci. Amsterdam 8, 341 (1905)

    Google Scholar 

  81. K. Pearson: “A Mathematical Theory of Random Migration”, in Draper’s Company Research Memoirs Biometric Series III, No. 15 (1906)

    Google Scholar 

  82. Lord Rayleigh: Philos. Mag. 6, 321 (1919)

    Google Scholar 

  83. D.W. Schaefer, P.N. Pusey: Phys. Rev. Lett. 29, 843 (1972)

    Article  ADS  Google Scholar 

  84. P.N. Pusey, D.W. Schaefer, D.E. Koppel: J. Phys.A 7, 530 (1974)

    Article  ADS  Google Scholar 

  85. S.H. Chen, P. Tartaglia, P.N. Pusey: J. Phys. A6, 490 (1973)

    Google Scholar 

  86. E. Jakeman, P.N. Pusey: Radar 77 ( IEE, London 1977 ) p. 105

    Google Scholar 

  87. B.J. Hoenders, E. Jakeman, H.P. Baltes, B. Steinle: Opt. Acta 26, 1307–1319 (1979)

    Article  Google Scholar 

  88. W. Feller: An Introduction to Probability Theory and its Applications, Vol.1 (Wiley, New York 1968 ) p. 285

    MATH  Google Scholar 

  89. ] M.S. Bartlett: An Introduction to Stochastic Processes (Cambridge University Press, Cambridge 1966) Chap.3

    Google Scholar 

  90. E. Jakeman, P.N. Pusey: Phys. Lett. 44A, 456 (1973)

    Google Scholar 

  91. E. Jakeman, P.N. Pusey: J. Phys.A 8, 369 (1975)

    Article  ADS  Google Scholar 

  92. P.N. Pusey, E. Jakeman: J. Phys. A 8, 392 (1975)

    Article  ADS  Google Scholar 

  93. C. Deutsch, P.N. Keating: J. Appl. Phys. 40, 4049 (1969)

    Article  ADS  Google Scholar 

  94. G. Parry, P.N. Pusey: J. Opt. Soc. Am. 69, 796 (1979)

    Article  ADS  Google Scholar 

  95. V.I. Tatarskii: Wave Propagation in a Turbulent Medium ( Dover, New York 1967 )

    Google Scholar 

  96. E. Jakeman, C.J. Oliver, E.R. Pike: J. Phys. A1, 497 (1968)

    Google Scholar 

  97. Pike, E.R.: The Malvern correlator. Case study in development. Phys. Technol. 10, 104–109 (1979)

    Article  ADS  Google Scholar 

  98. Parry, G., Walker, J.G., Scaddan, R.J.: On the statistics of stellar speckle patterns and pupil plane scintillation. Opt. Acta 26, 563–574 (1979)

    Article  ADS  Google Scholar 

  99. Oliver, C.J.: Spectral analysis with short data batches. J. Phys. A12, 591–617 (1979)

    Article  ADS  Google Scholar 

  100. Fujii, H.: Contrast variation of non-gaussian speckle. Opt. Acta 27, 409–418 (1980)

    Article  ADS  Google Scholar 

  101. Jakeman, E.: Statistics of integrated gamma-lorentzian intensity fluctuations. Opt. Acta 27, 735–741 (1980)

    Article  ADS  Google Scholar 

  102. Chapter 4

    Google Scholar 

  103. Davies, E.B.: Quantum Theory of Open Systems (Academic Press, London 1976) Chap. 5, pp. 69–84

    Google Scholar 

  104. Srinivas, M.D., Davies, E.B.: Photon counting probabilities in quantum optics. To be published

    Google Scholar 

  105. Aoki, T., Sakurai, K.: Photon statistics of partially polarized Gaussian light. Phys. Rev. A20, 1593–1598 (1979)

    Article  ADS  Google Scholar 

  106. Barakat, R.: Intensity correlations in the presence of additive background noise. Opt. Commun. 28, 4–6 (1979)

    Article  ADS  Google Scholar 

  107. Mandel, L.: Inversion problem in photon counting with dead time. J. Opt. Soc. Am. 70, 873–874 (1980)

    Article  ADS  Google Scholar 

  108. McGuire, D.: Coherent detection of partially coherent sources. Opt. Letts. 5, 73–75 (1980)

    Article  ADS  Google Scholar 

  109. Selloni, A., Quattropani, A., Schwendimann, P., Baltes, H.P.: Temperature effects in photodetection: additional results. Phys. Rev. A22, 315–317 (1980)

    Google Scholar 

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Jakeman, E., Pusey, P.N. (1980). Photon-Counting Statistics of Optical Scintillation. In: Baltes, H.P. (eds) Inverse Scattering Problems in Optics. Topics in Current Physics, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81472-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-81472-3_3

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