Abstract

A laser beam was passed through a turbulent mixture of hot and cold water. The optical path contained no solid scattering particles. It was, therefore, similar to an atmospheric path containing only clear-air turbulence. The field irradiance was accurately described by a truncated three-parameter log-normal probability density. The statistics of the integral of the field irradiance over an area comparable in size to one coherence area was also always characterized by a three-parameterlog-normal density. This probability density, when used in the Mandel formula for the single-photon-counting probability, correctly predicted the observed results. The parameters of the irradiance density could be varied by changing the temperature of the hot- and cold-water mixture, or the position of the optical path. The observed photon-counting probabilities could not be obtained by use of a two-parameter log-normal irradiance density (more commonly called the log-normal density) in the Mandel formula.

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  36. B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).
  37. Reference 34, Ch. 9.
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  41. E. Jakeman, E. R. Pike, and S. Swain, J. Phys. A (Lond.) 4, 517 (1971).
  42. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972).

Aitchison, J.

J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge U. P., Cambridge, 1957).

Alley, C. O.

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

Armstrong, J. A.

J. A. Armstrong and A. W. Smith, in Progress in Optics, VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213.

Bergman, R. R.

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Brown, J. A. C.

J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge U. P., Cambridge, 1957).

Carnahan, B.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

Chang, R. F.

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

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Randon Medium (translated from Russian) (McGraw-Hill, New York, 1960).

de Wolf, D. A.

D. A. de Wolf, J. Opt. Soc. Am. 59, 1455 (1969).

D. A. de Wolf, J. Opt. Soc. Am. 64, 360 (1974).

D. A. de Wolf, J. Opt. Soc. Am. 58, 461 (1968).

D. A. de Wolf, J. Opt. Soc. Am. 63, 171 (1973).

D. A. de Wolf, J. Opt. Soc. Am. 63, 1249 (1973).

Deitz, P. H.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).

Detenbeck, R. W.

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

Diament, P.

P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 1489 (1970).

Dunphy, J. R.

J. R. Kerr and J. R. Dunphy, J. Opt. Soc. Am. 63, 1 (1973).

J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 63, 981 (1973).

Fried, D. L.

D. L. Fried, G. E. Mevers, and M. P. Keister, J. Opt. Soc. Am. 57, 787 (1967).

Furutsu, K.

K. Furutsu, J. Opt. Soc. Am. 62, 240 (1972).

Glauber, R. J.

R. J. Glauber, in Physics of Quantum Electronics, Conference Proceedings, edited by P. L. Kelley, B. Lax, and P. E. Tannenwald (McGraw-Hill, New York, 1966), p. -788.

Gracheva, M. E.

M. E. Gracheva, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 10, 775 (1967).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Intensity Fluctuations of Laser Radiation [Akademiia Nauk. SSSR, Moscow (1973)] (translated from Russian), (The Aerospace Corp. Library Services, Literature Research Group, Los Angeles, Calif., Translation No. LRG-73-T-28).

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 13, 55 (1970).

M. E. Gracheva and A. S. Gurvich, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 8, 717 (1965).

Gurvich, A. S.

M. E. Gracheva and A. S. Gurvich, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 8, 717 (1965).

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 13, 55 (1970).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Intensity Fluctuations of Laser Radiation [Akademiia Nauk. SSSR, Moscow (1973)] (translated from Russian), (The Aerospace Corp. Library Services, Literature Research Group, Los Angeles, Calif., Translation No. LRG-73-T-28).

Jakeman, E.

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

Kallistratova, M. A.

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 13, 55 (1970).

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Intensity Fluctuations of Laser Radiation [Akademiia Nauk. SSSR, Moscow (1973)] (translated from Russian), (The Aerospace Corp. Library Services, Literature Research Group, Los Angeles, Calif., Translation No. LRG-73-T-28).

Keister, M. P.

D. L. Fried, G. E. Mevers, and M. P. Keister, J. Opt. Soc. Am. 57, 787 (1967).

Kerr, J. R.

J. R. Kerr, J. Opt. Soc. Am. 62, 1040 (1972).

J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 63, 981 (1973).

J. R. Kerr and J. R. Dunphy, J. Opt. Soc. Am. 63, 1 (1973).

Klauder, J. R.

J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New Yo;.k, 1968).

Klyatskin, V. I.

V. I. Klyatskin, Zh. Eksp. Teor. Fiz. 57, 952 (1969) [Sov. Phys.-JETP 30, 520 (1970)].

V. I. Klyatskin and V. I. Tatarskii, Zh. Eksp. Teor. Fiz. 58, 624 (1970) [Sov. Phys.-JETP31, 335 (1970)].

V. I. Klyatskin, Zh. Eksp. Teor. Fiz. 60, 1300 (1971) [Sov. Phys.-JETP 33, 703 (1971) ].

Korenman, V.

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

Lawrence, R. S.

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970). Review paper, containing extensive references to works published until 1970.

G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).

Lumley, J. L.

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972).

Luther, H. A.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

Mandel, L.

L. Mandel, Proc. Phys. Soc. (Lond.) 72, 1037 (1958).

L. Mandel, in Progress in Optics, II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 181.

Mevers, G. E.

D. L. Fried, G. E. Mevers, and M. P. Keister, J. Opt. Soc. Am. 57, 787 (1967).

Ochs, G. R.

G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Pike, E. R.

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

Pokasov, V. V.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Intensity Fluctuations of Laser Radiation [Akademiia Nauk. SSSR, Moscow (1973)] (translated from Russian), (The Aerospace Corp. Library Services, Literature Research Group, Los Angeles, Calif., Translation No. LRG-73-T-28).

Smith, A. W.

J. A. Armstrong and A. W. Smith, in Progress in Optics, VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213.

Snyder, J. R.

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Strohbehn, J. W.

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968) (review paper).

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970). Review paper, containing extensive references to works published until 1970.

T-i, Wang and J. W. Strohbehn, J. Opt. Soc. Am. 64, 583 (1974).

T-i. Wang and J. W. Strohbehn, J. Opt. Soc. Am. 64, 994 (1974).

J. W. Strohbehn, in Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971), p. 75 (review paper).

J. W. Strohbehn and T-i. Wang, J. Opt. Soc. Am. 62, 1061 (1972).

Sudarshan, E. C. G.

J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New Yo;.k, 1968).

Swain, S.

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

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 5319 (translated from Russian) (National Technical Information Service, U. S. Dept. of Commerce, Springfield, Va., 1971).

V. I. Klyatskin and V. I. Tatarskii, Zh. Eksp. Teor. Fiz. 58, 624 (1970) [Sov. Phys.-JETP31, 335 (1970)].

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (translated from Russian) (McGraw-Hill, New York, 1961).

Teich, M. C.

P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 1489 (1970).

Tennekes, H.

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972).

Wang, T-i

T-i. Wang and J. W. Strohbehn, J. Opt. Soc. Am. 64, 994 (1974).

T-i, Wang and J. W. Strohbehn, J. Opt. Soc. Am. 64, 583 (1974).

Wang, T-i.

J. W. Strohbehn and T-i. Wang, J. Opt. Soc. Am. 62, 1061 (1972).

Wilkes, J. O.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

Wright, N. J.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).

Other (42)

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970). Review paper, containing extensive references to works published until 1970.

J. W. Strohbehn, in Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971), p. 75 (review paper).

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968) (review paper).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (translated from Russian) (McGraw-Hill, New York, 1961).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 5319 (translated from Russian) (National Technical Information Service, U. S. Dept. of Commerce, Springfield, Va., 1971).

L. A. Chernov, Wave Propagation in a Randon Medium (translated from Russian) (McGraw-Hill, New York, 1960).

D. A. de Wolf, J. Opt. Soc. Am. 58, 461 (1968).

D. A. de Wolf, J. Opt. Soc. Am. 59, 1455 (1969).

D. A. de Wolf, J. Opt. Soc. Am. 63, 171 (1973).

D. A. de Wolf, J. Opt. Soc. Am. 63, 1249 (1973).

D. A. de Wolf, J. Opt. Soc. Am. 64, 360 (1974).

K. Furutsu, J. Opt. Soc. Am. 62, 240 (1972).

V. I. Klyatskin and V. I. Tatarskii, Zh. Eksp. Teor. Fiz. 58, 624 (1970) [Sov. Phys.-JETP31, 335 (1970)].

V. I. Klyatskin, Zh. Eksp. Teor. Fiz. 57, 952 (1969) [Sov. Phys.-JETP 30, 520 (1970)].

V. I. Klyatskin, Zh. Eksp. Teor. Fiz. 60, 1300 (1971) [Sov. Phys.-JETP 33, 703 (1971) ].

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).

J. R. Kerr, J. Opt. Soc. Am. 62, 1040 (1972).

J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 63, 981 (1973).

M. E. Gracheva and A. S. Gurvich, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 8, 717 (1965).

M. E. Gracheva, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 10, 775 (1967).

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vyssh. Ucheb. Zaved. Radiofiz. 13, 55 (1970).

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Intensity Fluctuations of Laser Radiation [Akademiia Nauk. SSSR, Moscow (1973)] (translated from Russian), (The Aerospace Corp. Library Services, Literature Research Group, Los Angeles, Calif., Translation No. LRG-73-T-28).

J. W. Strohbehn and T-i. Wang, J. Opt. Soc. Am. 62, 1061 (1972).

T-i, Wang and J. W. Strohbehn, J. Opt. Soc. Am. 64, 583 (1974).

T-i. Wang and J. W. Strohbehn, J. Opt. Soc. Am. 64, 994 (1974).

D. L. Fried, G. E. Mevers, and M. P. Keister, J. Opt. Soc. Am. 57, 787 (1967).

J. R. Kerr and J. R. Dunphy, J. Opt. Soc. Am. 63, 1 (1973).

J. A. Armstrong and A. W. Smith, in Progress in Optics, VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213.

Handbook of Chemistry and Physics, 48th Edition, edited by R. C. Weast (The Chemical Rubber Co., Cleveland, Ohio, 1967), p. E-159.

L. Mandel, Proc. Phys. Soc. (Lond.) 72, 1037 (1958).

L. Mandel, in Progress in Optics, II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 181.

J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge U. P., Cambridge, 1957).

P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 1489 (1970).

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

Reference 34, Ch. 9.

R. J. Glauber, in Physics of Quantum Electronics, Conference Proceedings, edited by P. L. Kelley, B. Lax, and P. E. Tannenwald (McGraw-Hill, New York, 1966), p. -788.

J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New Yo;.k, 1968).

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

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

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972).

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