Abstract

Experimental results are presented for the angular correlation function of far-field speckle patterns scattered in the double passage of waves through a one-dimensional random-phase screen. The theoretical analysis of the symmetry of speckle patterns around the backscattering direction and the motion of the speckle as the source is moved, made by Escamilla et al. [Appl. Opt. 32, 2734 (1993)], are verified in this paper.

© 2000 Optical Society of America

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References

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  1. S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
    [CrossRef] [PubMed]
  2. I. Freund, M. Rosenbluh, S. Feng, “Memory effect in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
    [CrossRef] [PubMed]
  3. V. Albada, M. P. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
    [CrossRef] [PubMed]
  4. A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (Singapore, World Scientific, 1990).
    [CrossRef]
  5. A. R. McGurn, A. A. Maradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13168 (1989).
    [CrossRef]
  6. T. R. Michel, K. A. O’Donnell, “Angular correlation functions of amplitudes scattered from a one-dimensional, perfectly conducting rough surface,” J. Opt. Soc. Am. A 9, 1374–1384 (1992).
    [CrossRef]
  7. J. Q. Lu, Z.-H. Gu, “Angular correlation function of speckle patterns scattered from a one-dimensional rough dielectric film on a glass substrate,” Appl. Opt. 36, 4562–4570 (1997).
    [CrossRef] [PubMed]
  8. Z. Q. Lin, Z.-H. Gu, “Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen,” Waves Random Media 7, 435–456 (1997).
    [CrossRef]
  9. V. Malyshkin, A. R. Mcgurn, T. A. Leskova, A. A. Maradudin, M. Nieto-Vesperinas, “Speckle correlation in the light scattered from a weakly rough one-dimensional random metal surface,” Opt. Lett. 22, 946–948 (1997).
    [CrossRef] [PubMed]
  10. I. Simonsen, A. A. Maradudin, T. A. Leskova, “The angular intensity correlation functions C(1) and C(10) for the scattering of S-polarized light from a one-dimensional randomly rough dielectric surface,” in Rough Surface Scattering and Contamination, P. Chen, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 218–231 (1999).
    [CrossRef]
  11. H. M. Escamilla, E. Mendez, D. F. Hotz, “Angular intensity correlation in the double passage of waves through a random phase screen,” Appl. Opt. 32, 2734–2743 (1993).
    [CrossRef] [PubMed]
  12. T. Chan, Y. Kuga, A. Ishimaru, “Detection of a target in a homogeneous medium using angular correlation function,” in International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2140–2142.
  13. E. R. Mendez, M. A. Ruiz-Cortes, Z.-H. Gu, “Photofabrication of one-dimensional rough surfaces for light-scattering experiments,” Appl. Opt. 30, 4103–4112 (1993).
    [CrossRef]

1997 (3)

1993 (2)

1992 (1)

1990 (1)

V. Albada, M. P. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

1989 (1)

A. R. McGurn, A. A. Maradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13168 (1989).
[CrossRef]

1988 (2)

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, “Memory effect in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Albada, V.

V. Albada, M. P. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

Chan, T.

T. Chan, Y. Kuga, A. Ishimaru, “Detection of a target in a homogeneous medium using angular correlation function,” in International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2140–2142.

de Boer, M. P.

V. Albada, M. P. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

Escamilla, H. M.

Feng, S.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, “Memory effect in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Freund, I.

I. Freund, M. Rosenbluh, S. Feng, “Memory effect in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Genack, A. Z.

A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (Singapore, World Scientific, 1990).
[CrossRef]

Gu, Z.-H.

Hotz, D. F.

Ishimaru, A.

T. Chan, Y. Kuga, A. Ishimaru, “Detection of a target in a homogeneous medium using angular correlation function,” in International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2140–2142.

Kane, C.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Kuga, Y.

T. Chan, Y. Kuga, A. Ishimaru, “Detection of a target in a homogeneous medium using angular correlation function,” in International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2140–2142.

Lagendijk, A.

V. Albada, M. P. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Leskova, T. A.

V. Malyshkin, A. R. Mcgurn, T. A. Leskova, A. A. Maradudin, M. Nieto-Vesperinas, “Speckle correlation in the light scattered from a weakly rough one-dimensional random metal surface,” Opt. Lett. 22, 946–948 (1997).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, T. A. Leskova, “The angular intensity correlation functions C(1) and C(10) for the scattering of S-polarized light from a one-dimensional randomly rough dielectric surface,” in Rough Surface Scattering and Contamination, P. Chen, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 218–231 (1999).
[CrossRef]

Lin, Z. Q.

Z. Q. Lin, Z.-H. Gu, “Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen,” Waves Random Media 7, 435–456 (1997).
[CrossRef]

Lu, J. Q.

Malyshkin, V.

Maradudin, A. A.

V. Malyshkin, A. R. Mcgurn, T. A. Leskova, A. A. Maradudin, M. Nieto-Vesperinas, “Speckle correlation in the light scattered from a weakly rough one-dimensional random metal surface,” Opt. Lett. 22, 946–948 (1997).
[CrossRef] [PubMed]

A. R. McGurn, A. A. Maradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13168 (1989).
[CrossRef]

I. Simonsen, A. A. Maradudin, T. A. Leskova, “The angular intensity correlation functions C(1) and C(10) for the scattering of S-polarized light from a one-dimensional randomly rough dielectric surface,” in Rough Surface Scattering and Contamination, P. Chen, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 218–231 (1999).
[CrossRef]

Mcgurn, A. R.

V. Malyshkin, A. R. Mcgurn, T. A. Leskova, A. A. Maradudin, M. Nieto-Vesperinas, “Speckle correlation in the light scattered from a weakly rough one-dimensional random metal surface,” Opt. Lett. 22, 946–948 (1997).
[CrossRef] [PubMed]

A. R. McGurn, A. A. Maradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13168 (1989).
[CrossRef]

Mendez, E.

Mendez, E. R.

Michel, T. R.

Nieto-Vesperinas, M.

O’Donnell, K. A.

Rosenbluh, M.

I. Freund, M. Rosenbluh, S. Feng, “Memory effect in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Ruiz-Cortes, M. A.

Simonsen, I.

I. Simonsen, A. A. Maradudin, T. A. Leskova, “The angular intensity correlation functions C(1) and C(10) for the scattering of S-polarized light from a one-dimensional randomly rough dielectric surface,” in Rough Surface Scattering and Contamination, P. Chen, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 218–231 (1999).
[CrossRef]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Appl. Opt. (3)

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

Opt. Lett. (1)

Phys. Rev. B (1)

A. R. McGurn, A. A. Maradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13168 (1989).
[CrossRef]

Phys. Rev. Lett. (3)

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave propagation through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, “Memory effect in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

V. Albada, M. P. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

Waves Random Media (1)

Z. Q. Lin, Z.-H. Gu, “Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen,” Waves Random Media 7, 435–456 (1997).
[CrossRef]

Other (3)

A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (Singapore, World Scientific, 1990).
[CrossRef]

I. Simonsen, A. A. Maradudin, T. A. Leskova, “The angular intensity correlation functions C(1) and C(10) for the scattering of S-polarized light from a one-dimensional randomly rough dielectric surface,” in Rough Surface Scattering and Contamination, P. Chen, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 218–231 (1999).
[CrossRef]

T. Chan, Y. Kuga, A. Ishimaru, “Detection of a target in a homogeneous medium using angular correlation function,” in International Geoscience and Remote Sensing Symposium ’96 (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 2140–2142.

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Figures (7)

Fig. 1
Fig. 1

Scattering geometry of the double-passage configuration with a flat mirror. (a) Backscattering configuration. (b) Equivalent unfolded geometry with two identical screens.

Fig. 2
Fig. 2

Double-passage configuration with the phase screen at the center of curvature of a spherical mirror.

Fig. 3
Fig. 3

Relation between the change of the incident angle Δθ i and the corresponding change of the angle of the scattered speckle pattern Δθ s from (a) a double-passage configuration with the phase screen at the center of curvature of a spherical mirror and (b) the angular memory effect.

Fig. 4
Fig. 4

Optical path of the measurements. (a) Top view of the system. (b) Side view of the double-passage configuration with a flat mirror. (c) Side view of the system for the measurements of the conventional angular memory effect.

Fig. 5
Fig. 5

Experimental results of angular shift of the scattered pattern Δθ s versus the change of incident angle Δθ i for (a) pp and (b) ss polarization.

Fig. 6
Fig. 6

Sketch of the symmetry of speckle correlation around the backscattering direction.

Fig. 7
Fig. 7

Experimental results of the symmetry of the speckle correlation around the backscattering direction for a double passage of waves through a one-dimensional random-phase screen, where λ = 0.6328 µm, δ = 1.278 µm, a = 3.85 µm, d = 5 µm, D = 3 mm, and spherical mirror W m = 1.7 mm and d = 140 mm for (a) pp and (b) ss polarization.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

γAθi1, θs1; θi2, θs2=exp-18θi+-θs+2φm2+φe2-18θi--θs-2φm2×exp-18θi++θs+2φe2-14θi-+θs-2φs2+exp-18θi-+θs-2φe2-14θi++θs+2φs2,
θi+=sin θi1+sin θi2,
θi-=sin θi1-sin θi2,
θs+=sin θs1+sin θs2,
θs-=sin θs1-sin θs2,  φs=2kW,  φe=2σkξ,  φm=Wmd.
sin θi1-sin θi2=-sin θs1-sin θs2,
Δθs  -Δθi
Δθs=-Δθi.
sin θi1+sin θi2=-sin θs1+sin θs2,

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