Abstract

We consider active polarimetric imaging systems that illuminate a scene with an incident polarization state and project the backscattered light on another polarization state in order to produce a scalar intensity image. We present and analyze a method for determining the configuration of illumination and analysis polarization states 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. A. B. Kostinski and W. M. Boerner, IEEE Trans. Antennas Propag. 35, 988 (1987).
    [CrossRef]
  2. A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
    [CrossRef]
  3. M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
    [CrossRef]
  4. D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).
    [CrossRef]
  5. F. Goudail, P. Réfrégier, and G. Delyon, J. Opt. Soc. Am. A 21, 1231 (2004).
    [CrossRef]
  6. G. Golub and W. Kahan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 2, 205 (1965).
    [CrossRef]
  7. R. S. Cloude and E. Pottier, Opt. Eng. 34, 1599 (1995).
    [CrossRef]
  8. V. L. Gamiz and J. F. Belsher, Opt. Eng. 41, 973 (2002).
    [CrossRef]

2004

2002

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

1998

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

1995

R. S. Cloude and E. Pottier, Opt. Eng. 34, 1599 (1995).
[CrossRef]

1988

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

1987

A. B. Kostinski and W. M. Boerner, IEEE Trans. Antennas Propag. 35, 988 (1987).
[CrossRef]

1965

G. Golub and W. Kahan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 2, 205 (1965).
[CrossRef]

Belsher, J. F.

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

Boerner, W. M.

A. B. Kostinski and W. M. Boerner, IEEE Trans. Antennas Propag. 35, 988 (1987).
[CrossRef]

Cariou, J.

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

Cloude, R. S.

R. S. Cloude and E. Pottier, Opt. Eng. 34, 1599 (1995).
[CrossRef]

Delyon, G.

Floc'h, M.

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

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]

Golub, G.

G. Golub and W. Kahan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 2, 205 (1965).
[CrossRef]

Goudail, F.

Kahan, W.

G. Golub and W. Kahan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 2, 205 (1965).
[CrossRef]

Kieleck, C.

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

Kong, J. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

Kostinski, A. B.

A. B. Kostinski and W. M. Boerner, IEEE Trans. Antennas Propag. 35, 988 (1987).
[CrossRef]

Le Brun, G.

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

Lotrian, J.

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

Novak, L. M.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

Pottier, E.

R. S. Cloude and E. Pottier, Opt. Eng. 34, 1599 (1995).
[CrossRef]

Réfrégier, P.

Shin, R. T.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

Swartz, A. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

Yueh, H. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

IEEE Trans. Antennas Propag.

A. B. Kostinski and W. M. Boerner, IEEE Trans. Antennas Propag. 35, 988 (1987).
[CrossRef]

J. Geophys. Res.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

R. S. Cloude and E. Pottier, Opt. Eng. 34, 1599 (1995).
[CrossRef]

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

Pure Appl. Opt.

M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.

G. Golub and W. Kahan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 2, 205 (1965).
[CrossRef]

Other

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

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Figures (4)

Fig. 1
Fig. 1

Principle of active scalar polarimetric imaging. PSG, polarization state generator; PSA, polarization state analyzer; IO, illumination optics; CO, collection optics.

Fig. 2
Fig. 2

Reduced contrast function G ( α s , ε s ) for γ = 0.096 .

Fig. 3
Fig. 3

Representation of s opt (●) and t opt (○) for different values of γ from 0 to 0.1 on the Poincaré sphere. Arrows indicate increasing values of γ.

Fig. 4
Fig. 4

Simulated images of a square piece of material ( M a with γ = 0.096 ) on a background ( M b ) with I 0 = 30 , σ = 10 . Each configuration is detailed in Table 1.

Tables (1)

Tables Icon

Table 1 Configurations of s = ( cos 2 α s cos 2 ε s , sin 2 α s cos 2 ε s , sin 2 ε s ) T and t = ( cos 2 α t cos 2 ε t , sin 2 α t cos 2 ε t , sin 2 ε t ) T considered in Fig. 4

Equations (15)

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I u = 1 2 ( T T M u S ) ,
C ( S , T ) = 1 σ 2 ( I a I b ) 2 = 1 4 σ 2 ( T T D S ) 2 ,
F ( S , T ) = T T D S .
S = ( 1 s ) , T = ( 1 t ) , D = [ D 00 m T n D ̃ ] ,
F ( s , t ) = D 00 + s T m + t T n + t T D ̃ s .
D ̃ = Y Λ X T ,
u = X T s , v = Y T t , p = X T m , q = Y T n .
F ( u , v ) = D 00 + p T u + v T ( q + Λ u ) .
v + = q + Λ u q + Λ u , v = v + .
F ( u , v + ) = A ( u ) + B ( u ) ,
F ( u , v ) = A ( u ) B ( u ) ,
A ( u ) = D 00 + p T u , B ( u ) = q + Λ u .
G ( u ) = max v { [ F ( u , v ) ] 2 } = [ A ( u ) + B ( u ) ] 2 .
v opt = sign [ A ( u opt ) ] q + Λ u opt q + Λ u opt ,
M a = [ 1 0 0 γ 0 0.5 0 0 4 γ 0 0.3 0 γ 0 0 0.4 ] ,

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