Abstract

We present a theoretical analysis on use of polarized light in the detection of a model target in a scattering and absorbing medium similar to seawater. Monte Carlo numerical simulations are used in the calculation of the effective Mueller matrix which describes the scattering process. A target in the shape of a disk is divided into three regions, each of which has the same albedo but different reduced Mueller matrices. Contrast between various parts of the target and background is analyzed in the images created by ordinary radiance, by various elements of the Mueller matrix, and by certain suitable combinations of these elements. It is shown that the application of polarized light has distinct advantages in target detection and characterization when compared with use of unpolarized light.

© 1999 Optical Society of America

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References

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  2. A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
    [CrossRef]
  3. M. J. Raković, G. W. Kattawar, “Theoretical analysis of polarization patterns from incoherent backscattering of light,” Appl. Opt. 37, 3333–3338 (1998).
    [CrossRef]
  4. B. D. Cameron, M. J. Raković, M. Mehrubeoglu, G. Kattawar, S. Rastegar, L. V. Wang, G. L. Coté, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998).
    [CrossRef]
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    [CrossRef]
  6. J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. S. Chandrasekhar, Radiative Transfer (Oxford U. Press, London, 1950).
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    [CrossRef]

1999 (2)

1998 (2)

1997 (1)

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

1995 (1)

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

1991 (1)

1990 (1)

1984 (1)

Bigio, I. J.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Cameron, B. D.

Cariou, J.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, London, 1950).

Chipman, R. A.

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Coté, G. L.

Eick, A. A.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Freyer, J. P.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Fry, E. S.

Guern, Y.

Hielscher, A. H.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Jordan, D. L.

Kattawar, G.

Kattawar, G. W.

Le Jeune, B.

Lewis, G. D.

Lotrian, J.

McLean, J. W.

Mehrubeoglu, M.

Mourant, J. R.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Pezzaniti, J. L.

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Rakovic, M. J.

Rastegar, S.

Roberts, P. J.

Shen, D.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Voss, K. J.

Wang, L. V.

Appl. Opt. (6)

Opt. Eng. (1)

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Opt. Exp. (1)

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp. 1, 441–454 (1997).
[CrossRef]

Opt. Lett. (1)

Other (2)

T. Gehrels, ed., Planets, Stars and Nebulae (University of Arizona, Tucson, Ariz., 1974).

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, London, 1950).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the scattering system.

Fig. 2
Fig. 2

(a) Several scattering trajectories reaching the detector from various directions. (b) Several scattering trajectories that all reach the detector from the same direction defined by spherical angles θ, ϕ.

Fig. 3
Fig. 3

(a) Example of the representative trajectory, thick solid line, and the corresponding class of trajectories used in the estimation procedure. Two of these trajectories, thin solid lines, miss the target, whereas the dashed-line trajectories hit the target before reaching the detector. (b) Possible paths (with no additional scatterings from the medium) connecting the scattering point r i j and the detector: direct path (thin solid line) and paths by way of target reflection (dashed lines).

Fig. 4
Fig. 4

Three regions of the disk-shaped target with three different single-scattering Mueller matrices.

Fig. 5
Fig. 5

Detected signal as a function of the radial distance from the target center. Target distance is 2 mfp’s and the sequence of the target regions is 1, depolarizing; 2, polarization preserving; and 3, painted surface. Dashed vertical lines correspond to polarization boundaries (PB) inside the target, and the solid vertical lines correspond to the target–medium boundary (TB). (a) Scalar radiance for the case of unpolarized incoming light beam of unit irradiance or, equivalently, the matrix element M 11(ρ, ϕ) = 11(ρ). (b) Normalized diagonal matrix elements: 22(ρ)/ 11(ρ) (dotted curve), 33(ρ)/ 11(ρ) (dashed curve), and 44(ρ)/ 11(ρ) (solid curve). (c) Normalized sum of the squares of the radial Mueller matrix elements ∑ ij 2(ρ)/ 11 2(ρ).

Fig. 6
Fig. 6

Same as Fig. 5, but for the target distance of 4 mfp’s. Note that in (b) the dotted curve shows the negative normalized matrix element: - 22(ρ)/ 11(ρ).

Fig. 7
Fig. 7

Same as Fig. 5, but for the sequence of target regions 1, 3, 2.

Fig. 8
Fig. 8

Same as Fig. 6, but for the sequence of the target regions 1, 3, 2.

Fig. 9
Fig. 9

Same as Fig. 5, but for the sequence of the target regions 3, 2, 1.

Fig. 10
Fig. 10

Same as Fig. 6, but for the sequence of the target regions 3, 2, 1.

Equations (15)

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Iθ, ϕ=Mθ, ϕF0,
Mθ, ϕ = C j wjMj,
mij=ϖ0 exp-c|rij|wijpθsRmMscθsRsMij.
tij=ϖ0 exp-c|rij-rk|pθs×ϖtexp-c|rk||rij-rk|2ptθk cosθcosθk×wijRmMtRtMscθsRsMij
Mθ, ϕ=Cm  mij+Ct  tij,
It1θ, ϕ=Ctj t1j,
Im1θ, ϕ=Cmj m1j,
It1θ, ϕ=Im1θ, ϕ=I0 exp-cL/cos θ, I0=πϖ0ϖt exp-cLpt00π/2 pα×sin2α1-cosα1-exp-rcα×1-cosαdα,
rcα=R/sin α, tan α>R/LL/cos α, tan α<R/L.
pθ=p0θ0θ02+θ23/2,
2π 02π pθsinθdθ=1.
Mscθ=1bθ00bθ10000dθ0000dθ, bθ=-1+cos2 θ1+cos2 θ, dθ=2 cos θ1+cos2 θ.
Mtdθ=diag1, 0, 0, 0, Mt1θ=diag1, 1, 1, 1, Mtpθ=diag1, 0.61, -0.58, -0.51.
Mρ, ϕ=M˜ρR-ϕ,
Rϕ=10000cos 2ϕsin 2ϕ00-sin 2ϕcos 2ϕ00001,

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