Abstract

We compare the performances of three different polarimetric imaging modalities, scalar, Stokes, and Mueller, in terms of achievable contrast for target detection applications. These modalities require, respectively, 1, 4, and 16 intensity measurements to form the polarimetric image. We show that the technique that leads to the best contrast is the scalar one, which requires only one optimized measurement.

© 2010 Optical Society of America

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References

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  1. A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, J. Geophys. Res. 93, 15252 (1988).
    [CrossRef]
  2. M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, Pure Appl. Opt. 7, 1327 (1998).
    [CrossRef]
  3. F. Goudail, Opt. Lett. 34, 121 (2009).
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  4. F. Goudail and A. Bénière, Opt. Lett. 34, 1471 (2009).
    [CrossRef] [PubMed]
  5. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, Opt. Lett. 25, 802 (2000).
    [CrossRef]
  6. J. S. Tyo, Z. Wang, S. J. Johnson, and B. Hoover, Appl. Opt. 49, 2326 (2010).
    [CrossRef] [PubMed]

2010 (1)

2009 (2)

2000 (1)

1998 (1)

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

1988 (1)

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

Bénière, A.

Brun, G. Le

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

Cariou, J.

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

Dereniak, E. L.

Descour, M. R.

Floc’h, M.

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

Goudail, F.

Hoover, B.

Johnson, S. J.

Kemme, S. A.

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]

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]

Phipps, G. S.

Sabatke, D. S.

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]

Sweatt, W. C.

Tyo, J. S.

Wang, Z.

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]

Appl. Opt. (1)

J. Geophys. Res. (1)

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

Opt. Lett. (3)

Pure Appl. Opt. (1)

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

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Figures (2)

Fig. 1
Fig. 1

Normalized values of the square root of the contrast for scalar, Stokes, and Mueller images as a function of α; see Eq. (9). ◊, [ C Scal i ( α ) / C Scal i ( 0 ) ] 1 / 2 ; *, [ C Stokes i ( α ) / C Scal i ( 0 ) ] 1 / 2 ; □ , [ C Mueller i ( α ) / C Scal i ( 0 ) ] 1 / 2 . In each case: solid line, i = 1 (Type I noise); dotted line, i = 2 (Type II noise).

Fig. 2
Fig. 2

Gain of scalar imaging with respect to Stokes and Mueller imaging as a function of α; see Eq. (9). *, ρ Stokes i ( α ) ; □ , ρ Mueller i ( α ) . In each case: solid line, i = 1 (Type I noise); dotted line, i = 2 (Type II noise).

Equations (9)

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i u = f 0 t o × 1 2 t T M u s + n u ,
C ( s , t ) = ( f 0 t o σ ) 2 × 1 4 ( t T Δ M s ) 2 ,
i u = f 0 t o 4 × 1 2 W M u s + n u ,
C ( s ) = ( f 0 t o σ ) 2 ( 1 4 ) 2 × 1 4 ( W Δ M ) s 2 ,
I u = f 0 t o 16 × 1 2 W M u X + N u ,
C = ( f 0 t o σ ) 2 ( 1 16 ) 2 × 1 4 W Δ M X f 2 ,
C Scalar 1 = f 0 2 t o 2 4 σ 2 × max s , t [ ( t T Δ M s ) 2 ] , C Stokes 1 = 1 4 [ f 0 2 t o 2 4 σ 2 ] × max s [ 1 4 k = 0 3 ( t k T Δ M s ) 2 ] , C Mueller 1 = 1 16 [ f 0 2 t o 2 4 σ 2 ] × [ 1 16 k = 0 3 l = 0 3 ( t k T Δ M s l ) 2 ] .
C Scalar 2 = f 0 2 t o 4 α × max s , t [ ( t T Δ M s ) 2 , C Stokes 2 = f 0 2 t o 4 α × max s [ 1 4 k = 0 3 ( t k T Δ M s ) 2 ] , C Mueller 2 = f 0 2 t o 4 α × [ 1 16 k = 0 3 l = 0 3 ( t k T Δ M s l ) 2 ] .
M a ( α ) = [ 0.8 α 0 0 α 0.5 0 0 0 0 0.5 0 0 0 0 0.4 ] ,

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