Abstract

Light of arbitrary incident polarization that diffuses through a sufficiently thick multiply scattering medium emerges totally depolarized with a Stokes vector that is that of natural light. It is shown how to reconstruct the Stokes vector of the incident beam by making four speckle correlation measurements on the totally depolarized, diffusely scattered light. The theory is confirmed by experiment.

© 1990 Optical Society of America

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References

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  1. W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), Chap. 2.
  2. R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
    [Crossref]
  3. Since each photon carries all the available information, in the classical limit of large photon numbers considered here, photon loss by absorption is unimportant, but photon degradation due to inelastic (dephasing) collisions is important.
  4. I. Freund, M. Rosenbluh, S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
    [Crossref] [PubMed]
  5. I. Freund, M. Rosenbluh, R. Berkovits, Phys. Rev. B 39, 12403 (1989).
    [Crossref]
  6. S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
    [Crossref] [PubMed]
  7. I. Freund, Phys. Lett. A 147, 502 (1990).
    [Crossref]
  8. B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
    [Crossref] [PubMed]
  9. Many currently popular schemes assume a pure phase aberrator, which is inappropriate for the multiple-scattering regime. Among the best introductions to this area are J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968); Statistical Optics (Wiley, New York, 1985). Methods suitable for the multiple-scattering regime are related to those employed in stellar speckle interferometry. See also, for example, J. C. Dainty, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 7.
  10. I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
    [Crossref]
  11. These filters, which in the notation used here may be labeled Fx, Fy, Fxy, and F+, pass only the corresponding polarization components of the incident light, i.e., Fx passes only the x-polarized component, F+ only the right circularly polarized component, etc.
  12. Kodak white reflectance coating 6080, Eastman Kodak Company, Rochester, N.Y. 14650.
  13. These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
    [Crossref] [PubMed]
  14. R. Lap-Tung Cheung, A. Ishimaru, Appl. Opt. 20, 3792 (1982).
    [Crossref]
  15. M. J. Stephen, G. Cwillich, Phys. Rev. B 34, 7565 (1986).
    [Crossref]
  16. F. C. MacKintosh, S. John, Phys. Rev. B 37, 1884 (1988).
    [Crossref]
  17. E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
    [Crossref]
  18. M. P. van Albada, A. Lagendijk, Phys. Rev. B 36, 2353 (1987).
    [Crossref]
  19. B. Shapiro, Phys. Rev. Lett. 56, 1809 (1986).
    [Crossref]
  20. Since definite polarization states are assumed, the sum rule S12 − S22 − S32 − S42 = 0 is used to reduce the results to compact form.

1990 (2)

I. Freund, Phys. Lett. A 147, 502 (1990).
[Crossref]

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
[Crossref]

1989 (2)

B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, R. Berkovits, Phys. Rev. B 39, 12403 (1989).
[Crossref]

1988 (4)

S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref] [PubMed]

F. C. MacKintosh, S. John, Phys. Rev. B 37, 1884 (1988).
[Crossref]

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
[Crossref]

1987 (1)

M. P. van Albada, A. Lagendijk, Phys. Rev. B 36, 2353 (1987).
[Crossref]

1986 (3)

B. Shapiro, Phys. Rev. Lett. 56, 1809 (1986).
[Crossref]

These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[Crossref] [PubMed]

M. J. Stephen, G. Cwillich, Phys. Rev. B 34, 7565 (1986).
[Crossref]

1982 (1)

1961 (1)

R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
[Crossref]

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
[Crossref]

Berkovits, R.

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
[Crossref]

I. Freund, M. Rosenbluh, R. Berkovits, Phys. Rev. B 39, 12403 (1989).
[Crossref]

Cwillich, G.

M. J. Stephen, G. Cwillich, Phys. Rev. B 34, 7565 (1986).
[Crossref]

Edrei, I.

These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[Crossref] [PubMed]

Feng, S.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref] [PubMed]

Freund, I.

I. Freund, Phys. Lett. A 147, 502 (1990).
[Crossref]

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
[Crossref]

I. Freund, M. Rosenbluh, R. Berkovits, Phys. Rev. B 39, 12403 (1989).
[Crossref]

I. Freund, M. Rosenbluh, S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref] [PubMed]

These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[Crossref] [PubMed]

Goodman, J. W.

Many currently popular schemes assume a pure phase aberrator, which is inappropriate for the multiple-scattering regime. Among the best introductions to this area are J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968); Statistical Optics (Wiley, New York, 1985). Methods suitable for the multiple-scattering regime are related to those employed in stellar speckle interferometry. See also, for example, J. C. Dainty, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 7.

Ishimaru, A.

John, S.

F. C. MacKintosh, S. John, Phys. Rev. B 37, 1884 (1988).
[Crossref]

Kane, C.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
[Crossref] [PubMed]

Kaveh, M.

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
[Crossref]

These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[Crossref] [PubMed]

Lagendijk, A.

M. P. van Albada, A. Lagendijk, Phys. Rev. B 36, 2353 (1987).
[Crossref]

Landauer, R.

R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
[Crossref]

Lap-Tung Cheung, R.

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
[Crossref] [PubMed]

MacKintosh, F. C.

F. C. MacKintosh, S. John, Phys. Rev. B 37, 1884 (1988).
[Crossref]

Maret, G.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
[Crossref]

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
[Crossref]

Papanicolaou, G.

B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
[Crossref] [PubMed]

Postel, M.

B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
[Crossref] [PubMed]

Rosenbluh, M.

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
[Crossref]

I. Freund, M. Rosenbluh, R. Berkovits, Phys. Rev. B 39, 12403 (1989).
[Crossref]

I. Freund, M. Rosenbluh, S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref] [PubMed]

These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[Crossref] [PubMed]

Shapiro, B.

B. Shapiro, Phys. Rev. Lett. 56, 1809 (1986).
[Crossref]

Sheng, P.

B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
[Crossref] [PubMed]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), Chap. 2.

Stephen, M. J.

M. J. Stephen, G. Cwillich, Phys. Rev. B 34, 7565 (1986).
[Crossref]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
[Crossref] [PubMed]

van Albada, M. P.

M. P. van Albada, A. Lagendijk, Phys. Rev. B 36, 2353 (1987).
[Crossref]

White, B.

B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
[Crossref] [PubMed]

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
[Crossref]

Appl. Opt. (1)

IBM J. Res. Dev. (1)

R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
[Crossref]

J. Phys. (Paris) (1)

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
[Crossref]

Phys. Lett. A (1)

I. Freund, Phys. Lett. A 147, 502 (1990).
[Crossref]

Phys. Rev. B (5)

I. Freund, M. Rosenbluh, R. Berkovits, Phys. Rev. B 39, 12403 (1989).
[Crossref]

M. P. van Albada, A. Lagendijk, Phys. Rev. B 36, 2353 (1987).
[Crossref]

M. J. Stephen, G. Cwillich, Phys. Rev. B 34, 7565 (1986).
[Crossref]

F. C. MacKintosh, S. John, Phys. Rev. B 37, 1884 (1988).
[Crossref]

I. Freund, M. Kaveh, R. Berkovits, M. Rosenbluh, Phys. Rev. B 42, 2613 (1990).
[Crossref]

Phys. Rev. Lett. (5)

B. Shapiro, Phys. Rev. Lett. 56, 1809 (1986).
[Crossref]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, Phys. Rev. Lett. 61, 834 (1988); R. Berkovits, M. Kaveh, R. Berkovits, S. Feng, Phys. Rev. B 40, 737 (1989).
[Crossref] [PubMed]

B. White, P. Sheng, M. Postel, G. Papanicolaou, Phys. Rev. Lett. 63, 2228 (1989).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref] [PubMed]

These coatings have been used in the study of other multiple-scattering phenomena such as enhanced coherent backscattering. See, for example, M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[Crossref] [PubMed]

Other (6)

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), Chap. 2.

Since each photon carries all the available information, in the classical limit of large photon numbers considered here, photon loss by absorption is unimportant, but photon degradation due to inelastic (dephasing) collisions is important.

Many currently popular schemes assume a pure phase aberrator, which is inappropriate for the multiple-scattering regime. Among the best introductions to this area are J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968); Statistical Optics (Wiley, New York, 1985). Methods suitable for the multiple-scattering regime are related to those employed in stellar speckle interferometry. See also, for example, J. C. Dainty, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 7.

Since definite polarization states are assumed, the sum rule S12 − S22 − S32 − S42 = 0 is used to reduce the results to compact form.

These filters, which in the notation used here may be labeled Fx, Fy, Fxy, and F+, pass only the corresponding polarization components of the incident light, i.e., Fx passes only the x-polarized component, F+ only the right circularly polarized component, etc.

Kodak white reflectance coating 6080, Eastman Kodak Company, Rochester, N.Y. 14650.

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Tables (1)

Tables Icon

Table 1 Reconstruction of Stokes Vectorsa

Equations (19)

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S 1 = C x + C y ,
S 2 = C x C y ,
S 3 = 2 C xy ( C x + C y ) ,
S 4 = 2 C + ( C x + C y ) .
C = [ 1 Γ 0 0 Γ 1 0 0 0 0 ρ δ 0 0 δ ρ ] ,
I i I j I i I j = | E i | E j | 2 ,
C ( I , I ) = N ( I , I ) / [ D ( I ) D ( I ) ] 1 / 2 ,
N ( I , I ) = | E x | E x | 2 + | E y | E y | 2 + | E x | E y | 2 + | E y | E x | 2 ,
D ( I ) = | | E x | 2 | 2 + | | E y | 2 | 2 + 2 | E x | E y | 2 ,
E in = [ a u x + b exp ( ) u y ] / ( a 2 + b 2 ) 1 / 2 ,
E x = [ a E xx + b exp ( ) E yx ] / ( a 2 + b 2 ) 1 / 2 ,
E y = [ a E xy + b exp ( ) E yy ] / ( a 2 + b 2 ) 1 / 2 ,
E x | E y = ab [ Γ exp ( ) + δ exp ( ) ] / ( a 2 + b 2 ) = 0 ,
C x = a 2 / ( a 2 + b 2 ) ,
C y = b 2 / ( a 2 + b 2 ) ,
C xy = 1 / 2 + [ ab / ( a 2 + b 2 ) ] cos φ ,
C + = 1 / 2 + [ ab / ( a 2 + b 2 ) ] sin φ .
N ( S , S ) = ( 1 / 2 ) ( 1 + ρ 2 + Γ 2 + δ 2 ) S 1 S 1 + ( 1 / 2 ) ( 1 + ρ 2 Γ 2 δ 2 ) S 2 S 2 + ( ρ + Γ δ ) S 3 S 3 + ( ρ Γ δ ) S 4 S 4 ,
D ( S ) = ( 1 / 2 ) [ ( 1 + ρ ) 2 S 1 2 + ( 1 ρ ) 2 S 2 2 + ( Γ + δ ) 2 S 3 2 + ( Γ δ ) 2 S 4 2 ] ,

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