Abstract

We present laboratory results for measurements of the four-point coherence function of a spherical wave in the region of coherence enhancement after backscattering through turbulence. Experimental results are compared with the theoretical predictions. We conclude that the shape of the four-point coherence function in our experiment depends on the value of the inner scale of turbulence.

© 1996 Optical Society of America

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  1. A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).
  2. A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarisation in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1993).
  3. W. T. Rhodes, G. Welch, “Determination of a coherent wave field after double passage through a diffuser,” J. Opt. Soc. Am. A 9, 341–343 (1992).
  4. A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).
  5. A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).
  6. A. S. Gurvich, V. Kan, B. Potapov, “Measurements of the four-point coherence function of a laser radiation field in a turbulent medium,” Radiophys. Quantum Electron. 19, 276–281 (1976).
  7. A. S. Gurvich, V. Kan, “Measurements of the four-point coherence function of a laser radiation field in a turbulent atmosphere,” Radiophys. Quantum Electron. 22, 131–135 (1979).
  8. A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–712 (1977).
  9. R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–556 (1978).
  10. R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).
  11. A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence function spectra,” Radiophys. Quantum Electron. 14, 580–584 (1971).
  12. R. J. Hill, G. R. Ochs, J. J. Wilson, “Measuring surface fluxes of heat and momentum using optical scintillation,” Boundary-Layer Meteorol. 58, 391–408 (1992).
  13. Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress In Optics, E. Wolf, ed. (Elsevier, New York, 1991), Vol. 29, pp. 65–195.

1994 (1)

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

1993 (1)

1992 (3)

W. T. Rhodes, G. Welch, “Determination of a coherent wave field after double passage through a diffuser,” J. Opt. Soc. Am. A 9, 341–343 (1992).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

R. J. Hill, G. R. Ochs, J. J. Wilson, “Measuring surface fluxes of heat and momentum using optical scintillation,” Boundary-Layer Meteorol. 58, 391–408 (1992).

1979 (2)

A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).

A. S. Gurvich, V. Kan, “Measurements of the four-point coherence function of a laser radiation field in a turbulent atmosphere,” Radiophys. Quantum Electron. 22, 131–135 (1979).

1978 (2)

1977 (1)

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–712 (1977).

1976 (1)

A. S. Gurvich, V. Kan, B. Potapov, “Measurements of the four-point coherence function of a laser radiation field in a turbulent medium,” Radiophys. Quantum Electron. 19, 276–281 (1976).

1971 (1)

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence function spectra,” Radiophys. Quantum Electron. 14, 580–584 (1971).

Artem’ev, A. V.

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence function spectra,” Radiophys. Quantum Electron. 14, 580–584 (1971).

Barabanenkov, Yu. N.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress In Optics, E. Wolf, ed. (Elsevier, New York, 1991), Vol. 29, pp. 65–195.

Bogaturov, A. N.

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarisation in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1993).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Bogaturov, A.N.

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

Canas, A. A. D.

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Clifford, S. F.

Dainty, J. C.

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarisation in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1993).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Gurvich, A. S.

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarisation in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1993).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).

A. S. Gurvich, V. Kan, “Measurements of the four-point coherence function of a laser radiation field in a turbulent atmosphere,” Radiophys. Quantum Electron. 22, 131–135 (1979).

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–712 (1977).

A. S. Gurvich, V. Kan, B. Potapov, “Measurements of the four-point coherence function of a laser radiation field in a turbulent medium,” Radiophys. Quantum Electron. 19, 276–281 (1976).

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence function spectra,” Radiophys. Quantum Electron. 14, 580–584 (1971).

Hill, R. J.

R. J. Hill, G. R. Ochs, J. J. Wilson, “Measuring surface fluxes of heat and momentum using optical scintillation,” Boundary-Layer Meteorol. 58, 391–408 (1992).

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–556 (1978).

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–712 (1977).

Kan, V.

A. S. Gurvich, V. Kan, “Measurements of the four-point coherence function of a laser radiation field in a turbulent atmosphere,” Radiophys. Quantum Electron. 22, 131–135 (1979).

A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).

A. S. Gurvich, V. Kan, B. Potapov, “Measurements of the four-point coherence function of a laser radiation field in a turbulent medium,” Radiophys. Quantum Electron. 19, 276–281 (1976).

Kravtsov, Yu. A.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress In Optics, E. Wolf, ed. (Elsevier, New York, 1991), Vol. 29, pp. 65–195.

Martvel, F. E.

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–712 (1977).

Myakinin, V. A.

Myakinin, V.A.

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Ochs, G. R.

R. J. Hill, G. R. Ochs, J. J. Wilson, “Measuring surface fluxes of heat and momentum using optical scintillation,” Boundary-Layer Meteorol. 58, 391–408 (1992).

Ozrin, V. D.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress In Optics, E. Wolf, ed. (Elsevier, New York, 1991), Vol. 29, pp. 65–195.

Potapov, B.

A. S. Gurvich, V. Kan, B. Potapov, “Measurements of the four-point coherence function of a laser radiation field in a turbulent medium,” Radiophys. Quantum Electron. 19, 276–281 (1976).

Rhodes, W. T.

Saichev, A. I.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress In Optics, E. Wolf, ed. (Elsevier, New York, 1991), Vol. 29, pp. 65–195.

Solomon, C. J.

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarisation in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1993).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Tatarskii, V. I.

A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).

Welch, G.

Wilson, J. J.

R. J. Hill, G. R. Ochs, J. J. Wilson, “Measuring surface fluxes of heat and momentum using optical scintillation,” Boundary-Layer Meteorol. 58, 391–408 (1992).

Wooder, N. J.

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarisation in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1993).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Zavorotnyi, V. U.

A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).

Boundary-Layer Meteorol. (1)

R. J. Hill, G. R. Ochs, J. J. Wilson, “Measuring surface fluxes of heat and momentum using optical scintillation,” Boundary-Layer Meteorol. 58, 391–408 (1992).

J. Fluid Mech. (1)

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–556 (1978).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

A. S. Gurvich, V. Kan, V. I. Tatarskii, V. U. Zavorotnyi, “Four-point field coherence function in a turbulent medium,” Opt. Acta 26, 543–553 (1979).

Opt. Commun. (2)

A. S. Gurvich, V.A. Myakinin, A.N. Bogaturov, C. J. Solomon, N. J. Wooder, J. C. Dainty, “The region of two point coherence enhancement after backscattering through turbulence,” Opt. Commun. 109, 387–392 (1994).

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V.A. Myakinin, C. J. Solomon, N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).

Opt. Lett. (1)

Radiophys. Quantum Electron. (4)

A. S. Gurvich, V. Kan, B. Potapov, “Measurements of the four-point coherence function of a laser radiation field in a turbulent medium,” Radiophys. Quantum Electron. 19, 276–281 (1976).

A. S. Gurvich, V. Kan, “Measurements of the four-point coherence function of a laser radiation field in a turbulent atmosphere,” Radiophys. Quantum Electron. 22, 131–135 (1979).

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–712 (1977).

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence function spectra,” Radiophys. Quantum Electron. 14, 580–584 (1971).

Other (1)

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress In Optics, E. Wolf, ed. (Elsevier, New York, 1991), Vol. 29, pp. 65–195.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental system.

Fig. 2
Fig. 2

Time-averaged one-dimensional intensity observed in the source plane. No turbulence is present. The target is in motion.

Fig. 3
Fig. 3

Time-averaged one-dimensional intensity observed in the source plane. The turbulence is switched on.

Fig. 4
Fig. 4

Comparison of the experimental data for Γ4 (curve 1) against the pure Kolmogorov model (l 0 = 0; curve 2) and the best least-squares fit (curve 3), corresponding to an estimated l 0 = 2.5 mm for the Tatarskii spectrum and l 0 = 1.6 mm for the Hill spectrum.

Equations (18)

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G ( 0 , r L , p ) = g ( 0 , r L , p ) V ( 0 , r L , p ) ,
g ( 0 , r L , p ) = k 2 π i L exp [ i k 2 L ( r p ) 2 ]
1 ( p ) = G ( 0 , r s L , p ) .
E e ¯ ( r ) = d 2 p O ( p ) G ( 0 , r s L , p ) G ( L , p 0 , r + d ) .
2 ( p ) = G ( 0 , r s + d L , p ) .
E o ¯ ( r ) = d 2 p O ( p ) G ( 0 , r s + d L , p ) G ( L , p 0 , r ) .
I ( r ) = | E o ¯ ( r ) + E e ¯ ( r ) | 2 .
I ( r ) = I 1 ( r + d ) { 1 + cos [ k L ( r r s ) d ] } ,
I 1 ( r ) = d 2 p + d 2 p O ( p + + p / 2 ) O * ( p + + p / 2 ) ¯ × exp [ i k L p ( 2 p + r s r ) ]
O ( p + + p / 2 ) O * ( p + + p / 2 ) ¯ | O ( p + ) | 2 δ ( p ) .
I ( r ) = const ( I bs ( r r s + d ) + I b s ( r r s d ) + 2 Re { Γ 4 ( r r s , d ) exp [ i k L ( r r s ) d ] } )
Γ 4 ( r , d ) = V ( 0 , ρ L , p + ) V * ( 0 , ρ + r L , p + )      × V ( 0 , ρ + d + d L , p + ) V *      × ( 0 , ρ + d L , p + ) ,
I ( r ) = const + Γ 4 ( r r s , d ) .
V ( 0 , ρ L , p ) = k 2 i π z ef d 2 q exp [ i k 2 z ef q 2      + i k 2 ε ( q + L z L ρ + z L p ) ] ,
Γ 4 ( r , p ) = ( k 2 π z ef ) 2 d 2 q 1 d 2 q 2 exp [ i k z ef q 1 q 2 Ψ ( q 1 + L z L r , q 2 + L z L p ) ] ,
Ψ ( p 1 , p 2 ) = 2 D ( p 1 ) + 2 D ( p 2 ) D ( p 1 + p 2 ) D ( p 1 p 2 ) ,
Φ ( κ ) = A κ 11 / 3 ϕ ( κ ) ,
ϕ ( κ ) = exp [ ( κ l 0 5.92 ) 2 ] .

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