Abstract

Active Stokes imaging consists in illuminating a scene with polarized light and in measuring the Stokes vector of the scattered light. We present a method for determining the polarization state of illumination that maximizes the observed contrast between a target and the background when the scene is partially depolarizing and in the presence of additive Gaussian detection noise.

© 2009 Optical Society of America

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References

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  1. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, Appl. Opt. 45, 5453 (2006).
    [CrossRef] [PubMed]
  2. F. Goudail, P. Réfrégier, and G. Delyon, J. Opt. Soc. Am. A 21, 1231 (2004).
    [CrossRef]
  3. D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).
    [CrossRef]
  4. K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, 1990).
  5. J. S. Tyo, Opt. Lett. 25, 1198 (2000).
    [CrossRef]
  6. A. B. Kostinski, B. D. James, and W. M. Boerner, J. Opt. Soc. Am. A 5, 58 (1988).
    [CrossRef]
  7. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 2002).
  8. V. L. Gamiz and J. F. Belsher, Opt. Eng. 41, 973 (2002).
    [CrossRef]

2006

2004

2002

V. L. Gamiz and J. F. Belsher, Opt. Eng. 41, 973 (2002).
[CrossRef]

2000

1988

Belsher, J. F.

V. L. Gamiz and J. F. Belsher, Opt. Eng. 41, 973 (2002).
[CrossRef]

Boerner, W. M.

Chenault, D. B.

Delyon, G.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 2002).

Fukunaga, K.

K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, 1990).

Gamiz, V. L.

V. L. Gamiz and J. F. Belsher, Opt. Eng. 41, 973 (2002).
[CrossRef]

Goldstein, D.

D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).
[CrossRef]

Goldstein, D. L.

Goudail, F.

James, B. D.

Kostinski, A. B.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 2002).

Réfrégier, P.

Shaw, J. A.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 2002).

Tyo, J. S.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 2002).

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

V. L. Gamiz and J. F. Belsher, Opt. Eng. 41, 973 (2002).
[CrossRef]

Opt. Lett.

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 2002).

D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).
[CrossRef]

K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, 1990).

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Figures (3)

Fig. 1
Fig. 1

Principle of active Stokes imaging.

Fig. 2
Fig. 2

Solid curve, optimal polarization state on the Poincaré sphere as a varies (solid curve). The matrix M a is diagonal with elements D a = ( 1 , 0.5 , 0.4 , 0.1 ) , and the matrix M b is in Eq. (9). Diamond, reduced Stokes vector s m collinear to m .

Fig. 3
Fig. 3

Variation of the contrast C ( s ) for different states of illumination s , and σ 2 = 1 3 . Solid curve, optimal value s max . Dashed curve, left circular; dotted curve, linear with azimuth 95.1°.

Equations (11)

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I = W S + b ,
S ̂ = W I = S + n ,
Γ n = n n T = σ 2 ( W T W ) 1 .
C ( S ) = ( S a S b ) T Γ n 1 ( S a S b ) = S T G S σ 2 ,
G = ( M a M b ) T W T W ( M a M b ) .
G = [ G 00 m T m G ̃ ] ,
C ( s ) = I 0 2 σ 2 ( G 00 + 2 s T m + s T G ̃ s ) .
F μ ( u ) = 2 i = 1 3 p i u i + i = 1 3 λ i u i 2 μ i = 1 3 u i 2 ,
p 1 t 2 t 3 + p 2 t 1 t 3 + p 3 t 1 t 2 = t 1 t 2 t 3 ,
u i k = p i ( μ k λ i ) .
M b = [ 1 0 0 0 a × 0.866 0.3 0 0 a × 0.5 0 0.3 0 0 0 0 0.4 ] ,

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