Abstract

Partial polarization may be the result of a scattering process from a fully polarized incident beam. It is shown how the “loss of polarization” is connected with the nature of scatterers (surface roughness, bulk heterogeneity) and on the receiver solid angle. These effects are theoretically predicted and confirmed via multiscale polarization measurements in the speckle pattern of rough surfaces. “Full” polarization can be recovered when reducing the receiver aperture.

© 2008 Optical Society of America

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References

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    [CrossRef]
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2007

2006

2005

2003

2002

J. Li, G. Yao, and L. V. Wang, "Degree of polarization in laser speckles from turbid media: implications in tissue optics," J. Biomed. Opt. 7, 307 (2002).
[CrossRef] [PubMed]

1993

1992

1983

Amra, C.

Arnaud, L.

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: Theoretical analysis," Opt. Commun. 281, 1739-1744 (2008).
[CrossRef]

Bennett, J. M.

Boccara, A. -C.

Bruel, L.

Bulkin, P.

Bussemer, P.

Chumakov, A.

De Martino, A.

Deumié, C.

Drévillon, B.

Duparre, A.

Elson, J. M.

Geddes, C. D.

Georges, G.

G. Georges, C. Deumié, and C. Amra, "Selective probing and imaging in random media based on the elimination of polarized scattering," Opt. Express 15, 9804-9816 (2007).
[CrossRef] [PubMed]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: Theoretical analysis," Opt. Commun. 281, 1739-1744 (2008).
[CrossRef]

Gilbert, O.

Graham, D. J. L.

Grezes-Besset, C.

Hehl, K.

Kassam, S.

Li, J.

J. Li, G. Yao, and L. V. Wang, "Degree of polarization in laser speckles from turbid media: implications in tissue optics," J. Biomed. Opt. 7, 307 (2002).
[CrossRef] [PubMed]

Loriette, V.

Moreau, J.

Neubert, J.

Nguyen, Q.

Novikova, T.

Parkins, A. S.

Popov, V.

Previte, M. J. R.

Rahn, J. P.

Wang, L. V.

J. Li, G. Yao, and L. V. Wang, "Degree of polarization in laser speckles from turbid media: implications in tissue optics," J. Biomed. Opt. 7, 307 (2002).
[CrossRef] [PubMed]

Watkins, L. R.

Yao, G.

J. Li, G. Yao, and L. V. Wang, "Degree of polarization in laser speckles from turbid media: implications in tissue optics," J. Biomed. Opt. 7, 307 (2002).
[CrossRef] [PubMed]

Appl. Opt.

J. Biomed.Opt.

J. Li, G. Yao, and L. V. Wang, "Degree of polarization in laser speckles from turbid media: implications in tissue optics," J. Biomed. Opt. 7, 307 (2002).
[CrossRef] [PubMed]

Opt. Express

Other

L. Arnaud, G. Georges, C. Deumié, and C. Amra, "Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: Theoretical analysis," Opt. Commun. 281, 1739-1744 (2008).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Propagation angles (θ,ϕ) of a retrograde plane wave in the far field, with the associated wave vector k and spatial pulsation σ

Fig. 2.
Fig. 2.

Transverse electric (S) and magnetic (P) polarization modes with respect to the wave vector k and normal z. The tangential P mode is also drawn.

Fig. 3.
Fig. 3.

Resulting intensity versus rotation angle of the analyzer (see text)

Fig. 4.
Fig. 4.

Retrograde wave packet and sensor

Fig. 5.
Fig. 5.

Maximum (left) and minimum (right) average signals measured for the speckle of a polished black glass (see text). The field view is 2080×2600µm2

Fig. 6.
Fig. 6.

Speckle pattern of a metallic lambertian sample (see text) measured for an arbitrary position of analyzer and quarterwave plates. The field view is 2500×2020 µm. The circled zone is studied in figure 7.

Fig. 7.
Fig. 7.

Multiscale measurements of the speckle pattern of figure 6 (see text). 3 zones are investigated and are fitted into each other

Fig. 8.
Fig. 8.

Variations for each zone (1–3) of the average polarimetric signal versus rotation angles of quarterwave (horizontal unit) and analyzer (vertical units) plates. Left figure is for zone 1, middle figure is for zone 2 and right figure is for zone 3 (see text).

Fig. 9.
Fig. 9.

Pictures recorded for each zone at minima and maxima values of the average signal (see text).

Tables (1)

Tables Icon

Table 1: Angular aperture and dynamic for each zone (see text)

Equations (42)

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E ( ρ ) = A ( σ ) exp [ j k ( σ ) . ρ ]
k = [ σ , α ( σ ) ] σ = ( σ x , σ y )
α ( σ ) = ( k 2 σ 2 ) 0.5 k = 2 π n λ
σ = σ ( cos ϕ , sin ϕ ) σ = k sin θ α = k cos θ
A = A S + A P
A S = A S v ( σ )
A P , tg = A P , tg u ( σ )
with : u ( σ ) = σ σ and v ( σ ) = ( 1 σ ) d σ d ϕ
and : A S = A S exp ( j δ S ) and A P = A P exp ( j δ P )
E ( ρ , t ) = Re [ E ( ρ ) exp ( j ω t ) ] =
[ A S cos ( ω t k . ρ δ S ) , A P cos ( ω t k . ρ δ P ) ]
A = A S cos ψ + A P sin ψ
I ( ψ ) = A S 2 cos 2 ψ + A P 2 sin 2 ψ + 2 sin ψ cos ψ A S A P cos δ
A = A S exp ( j η S ) cos ψ + A P exp ( j η P ) sin ψ
I ( ψ ) = A S 2 cos 2 ψ + A P 2 sin 2 ψ + 2 sin ψ cos ψ A S A P cos ( δ + η )
E ( ρ ) = σ A ( σ ) exp [ j k ( σ ) . ρ ] d σ = σ E ̂ ( σ , z ) exp [ j σ . r ] d σ
E * ( ρ ) = σ A * ( σ ) exp [ j k ( σ ) . ρ ] d σ
A * ( σ ) = A S ( σ ) cos ψ + A P ( σ ) sin ψ
F = ( 4 π 2 2 ω μ ) Δ σ α ( σ ) A * ( σ ) 2 d σ
α ( σ ) = Real [ α ( σ ) ]
F = ( 4 π 2 2 ω μ ) [ cos 2 ψ Δ σ α ( σ ) A S ( σ ) 2 d σ
+ sin 2 ψ Δ σ α ( σ ) A P ( σ ) 2 d σ + X ]
X = 2 sin ψ cos ψ Δ σ α ( σ ) A S ( σ ) A P ( σ ) cos [ δ ( σ ) ] d σ
F ( ψ ) = cos 2 ψ F S + sin 2 ψ F P + 2 β sin ψ cos ψ ( F S F P ) 0.5
F S = ( 4 π 2 2 ω μ ) Δ σ α ( σ ) A S ( σ ) 2 d σ
F P = ( 4 π 2 2 ω μ ) Δ σ α ( σ ) A P ( σ ) 2 d σ
β = ( 4 π 2 2 ω μ ) [ 1 ( F S F P ) 0.5 ] Δ σ α ( σ ) A S ( σ ) A P ( σ ) cos [ δ ( σ ) ] d σ
β 1 = > β = cos δ *
β = ( 4 π 2 2 ω μ ) [ 1 ( F S F P ) 0.5 ] Δ σ α ( σ ) A S ( σ ) A P ( σ ) cos [ δ ( σ ) + η ] d σ
E d S ( σ ) = C S ( σ ) g ̂ ( σ ) , E d P ( σ ) = C P ( σ ) g ̂ ( σ )
= > δ ( σ ) = Arg ( E d S E d P ) = Arg [ C S ( σ ) C P ( σ ) ]
F S = ( 4 π 2 2 ω μ ) α C S 2 Δ σ g ̂ ( σ ) 2 d σ
F P = ( 4 π 2 2 ω μ ) α C P 2 Δ σ g ̂ ( σ ) 2 d σ
β = ( 4 π 2 2 ω μ ) [ 1 ( F S F P ) 0.5 ] α C S C P cos δ Δ σ g ̂ ( σ ) 2 d σ
{ ( 4 π 2 2 ω μ ) α [ Δ σ g ̂ ( σ ) 2 d σ ] } 1 F =
cos 2 ψ C S 2 + sin 2 ψ C P 2 + 2 sin ψ cos ψ cos ( δ + η ) C S C P
S 0 = < A S 2 + A P 2 > , S 1 = < A S 2 A P 2 >
S 2 = 2 < A S A P cos δ > , S 3 = 2 j < A S A P sin δ >
2 < I ( ψ ) > = S 0 + S 1 cos 2 ψ + S 2 sin 2 ψ
ρ L = ( 1 S 0 ) [ S 1 2 + S 2 2 ] 0.5 1
d = ( 1 + ρ L ) ( 1 ρ L )
β = S 2 [ S 0 2 S 1 2 ] 0.5 1

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