Abstract

In dealing with random EM fields, ensemble averaging is an ubiquitous procedure. However, we demonstrate that spatial non-stationarities such as enhanced backscattering can be identified even from one single realization (snapshot) of the wave interaction with a random medium. Fourth-order correlations between field components at two different spatial points are shown to provide the necessary information.

© 2008 Optical Society of America

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References

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  4. Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
    [CrossRef]
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    [CrossRef]
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2006 (1)

C. Schwartz and A. Dogariu, "Enhanced backscattering of vortex waves from volume scattering media," Opt. Commun. 263, 135-140 (2006). Schwartz, Chaim Dogariu, Aristide.
[CrossRef]

2005 (1)

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

2004 (3)

1999 (1)

1992 (1)

M. Nieto-Vesperinas and J. A. Sanchez-Gil, "Enhanced long-range correlations of coherent waves reflected from disordered media," Phys. Rev. B 46, 3112-3115 (1992).
[CrossRef]

1991 (2)

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering - the universal wave phenomenon," Proc. IEEE 79, 1367-1370 (1991).
[CrossRef]

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
[CrossRef]

1990 (2)

1985 (1)

1976 (1)

Alfano, R. R.

Barabanenkov, Y. N.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering - the universal wave phenomenon," Proc. IEEE 79, 1367-1370 (1991).
[CrossRef]

Berezhnyy, I.

Bissonnette, D.

P. Rochon and D. Bissonnette, "Lensless imaging due to back-scattering," Nature 348, 708-710 (1990).
[CrossRef]

Derode, A.

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

Dogariu, A.

Ellis, J.

Goodman, J. W.

Ishimaru, A.

Jenson, F.

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

Kravtsov, Y. A.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering - the universal wave phenomenon," Proc. IEEE 79, 1367-1370 (1991).
[CrossRef]

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Laugier, P.

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

Mamou, V.

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

Nieto-Vesperinas, M.

M. Nieto-Vesperinas and J. A. Sanchez-Gil, "Enhanced long-range correlations of coherent waves reflected from disordered media," Phys. Rev. B 46, 3112-3115 (1992).
[CrossRef]

Ozrin, V. D.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering - the universal wave phenomenon," Proc. IEEE 79, 1367-1370 (1991).
[CrossRef]

Padilla, F.

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

Popescu, G.

Rochon, P.

P. Rochon and D. Bissonnette, "Lensless imaging due to back-scattering," Nature 348, 708-710 (1990).
[CrossRef]

Saichev, A. I.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering - the universal wave phenomenon," Proc. IEEE 79, 1367-1370 (1991).
[CrossRef]

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Sanchez-Gil, J. A.

M. Nieto-Vesperinas and J. A. Sanchez-Gil, "Enhanced long-range correlations of coherent waves reflected from disordered media," Phys. Rev. B 46, 3112-3115 (1992).
[CrossRef]

Schwartz, C.

C. Schwartz and A. Dogariu, "Enhanced backscattering of vortex waves from volume scattering media," Opt. Commun. 263, 135-140 (2006). Schwartz, Chaim Dogariu, Aristide.
[CrossRef]

Tang, G. C.

Tsang, L.

Yoo, K. M.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Derode, V. Mamou, F. Padilla, F. Jenson, and P. Laugier, "Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization," Appl. Phys. Lett. 87, 114101 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nature (1)

P. Rochon and D. Bissonnette, "Lensless imaging due to back-scattering," Nature 348, 708-710 (1990).
[CrossRef]

Opt. Commun. (1)

C. Schwartz and A. Dogariu, "Enhanced backscattering of vortex waves from volume scattering media," Opt. Commun. 263, 135-140 (2006). Schwartz, Chaim Dogariu, Aristide.
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

M. Nieto-Vesperinas and J. A. Sanchez-Gil, "Enhanced long-range correlations of coherent waves reflected from disordered media," Phys. Rev. B 46, 3112-3115 (1992).
[CrossRef]

Proc. IEEE (1)

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering - the universal wave phenomenon," Proc. IEEE 79, 1367-1370 (1991).
[CrossRef]

Prog. Opt. (1)

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, "Enhanced backscattering in optics," Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Other (5)

P. Sheng, Scattering and localization of classical waves in random media (World Scientific, Singapore, 1990).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Englewood, 2005), 3rd ed.

S. Huard, Polarization of Light (John Wiley & Sons, New York, 1997).

J. W. Goodman, Statistical Optics (John Wiley & Sons, Inc., New York, 1985).

G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

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Figures (1)

Fig. 1.
Fig. 1.

(color online) Images corresponding to samples A, B, C, and D as described in the text. (i) single realization speckle intensity image, (ii) ensemble average, (iii) image encoded in the calculated effective intensity, (iv) image encoded in the calculated effective degree of polarization, (v) image encoded in the calculated polarization decay.

Equations (8)

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

I ¯ A ( r ) = 1 A A I ( r + r 0 ) d r 0 ,
I ( r ) = E x * ( r ) E x ( r ) + E y * ( r ) E y ( r ) .
P ¯ A ( r ) = A S 1 2 d r + A S 2 2 d r + A S 3 2 d r A I d r .
S 1 ( r ) = E x * ( r ) E x ( r ) E y * ( r ) E y ( r )
S 2 ( r ) = E x * ( r ) E y ( r ) E y * ( r ) E x ( r )
S 3 ( r ) = i ( E x * ( r ) E y ( r ) E y * ( r ) E x ( r ) )
V 2 ( r 1 , r 2 ) = ( E x * ( r 1 ) E x ( r 2 ) + E y * ( r 1 ) E y ( r 2 ) ) 2 ( E x * ( r 1 ) E x ( r 1 ) + E y * ( r 1 ) E y ( r 1 ) ) ( E x * ( r 2 ) E x ( r 2 ) + E y * ( r 2 ) E y ( r 2 ) )
I ( k i , k f ) = I 0 + l , m A l m 2 cos ( k i + k f ) · ( r l r m ) + F ( k i , k f ) ,

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