Abstract

In active polarization imaging, one frequently needs to be insensitive to noninformative spatial intensity fluctuations. We investigate a way of solving this issue with general state contrast (GSC) imaging. It consists in acquiring two scalar polarimetric images with optimized illumination and analysis polarization states, then forming a ratio. We propose a method for maximizing the discrimination ability between a target and a background in GSC images by determining the optimal illumination and analysis states. A further advantage of this approach is to provide an objective way of quantifying the performance improvement obtained by increasing the number of degrees of freedom of a GSC imager. The efficiency of this approach is demonstrated on simulated and real-world images.

© 2012 Optical Society of America

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  1. J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
    [CrossRef]
  2. R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).
  3. J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, “Target detection in optical scattering media by polarization-difference imaging,” Appl. Opt. 35, 1855–1870 (1996).
    [CrossRef]
  4. L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15, 81–93 (1997).
    [CrossRef]
  5. P. J. Wu, J. Joseph, and T. Walsh, “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt. 11, 014031 (2006).
    [CrossRef]
  6. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [CrossRef]
  7. M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
    [CrossRef]
  8. J. M. Bueno, J. Hunter, C. Cookson, M. Kisilak, and M. Campbell, “Improved scanning laser fundus imaging using polarimetry,” J. Opt. Soc. Am. A 24, 1337–1348 (2007).
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  9. P. Terrier, V. Devlaminck, and J. M. Charbois, “Segmentation of rough surfaces using a polarization imaging system,” J. Opt. Soc. Am. A 25, 423–430 (2008).
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  10. A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–991 (1987).
    [CrossRef]
  11. A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
    [CrossRef]
  12. B. G. Hoover and J. S. Tyo, “Polarization components analysis for invariant discrimination,” Appl. Opt. 46, 8364–8373 (2007).
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    [CrossRef]
  15. J. S. Tyo, Z. Wang, S. J. Johnson, and B. Hoover, “Design and optimization of partial Mueller matrix polarizers,” Appl. Opt. 49, 2326–2333 (2010).
    [CrossRef]
  16. D. Upadhyay, M. Richert, E. Lacot, A. D. Martino, and X. Orlik, “Effect of speckle on APSCI method and Mueller imaging,” Opt. Express 19, 4553–4559 (2011).
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  18. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
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  19. R. Ossikovski, “Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition,” J. Opt. Soc. Am. A 25, 473–482 (2008).
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  20. F. Goudail and P. Réfrégier, “Statistical techniques for target detection in polarisation diversity images,” Opt. Lett. 26, 644–646 (2001).
    [CrossRef]
  21. S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806  nm,” Opt. Eng. 39, 2681–2688 (2000).
    [CrossRef]
  22. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
    [CrossRef]
  23. A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
    [CrossRef]
  24. A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Precision of degree of polarization estimation in the presence of additive Gaussian detector noise,” Opt. Commun. 278, 264–269(2007).
    [CrossRef]
  25. F. Goudail and A. Bénière, “Optimization of the contrast in polarimetric scalar images,” Opt. Lett. 34, 1471–1473 (2009).
    [CrossRef]
  26. F. Goudail and J. S. Tyo, “When is polarimetric imaging preferable to intensity imaging for target detection?” J. Opt. Soc. Am. A 28, 46–53 (2011).
    [CrossRef]
  27. F. Goudail, “Comparison of the maximal achievable contrast in scalar, Stokes and Mueller images,” Opt. Lett. 35, 2600–2602 (2010).
    [CrossRef]
  28. H. D. Noble and R. A. Chipman, “Mueller matrix roots algorithm and computational considerations,” Opt. Express 20, 17–31 (2012).
    [CrossRef]
  29. A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Estimation precision of degree of polarization in the presence of signal-dependent and additive Poisson noises,” J. Eur. Opt. Soc. Rapid Publ. 3, 08002 (2008).
    [CrossRef]
  30. F. Goudail, P. Réfrégier, and G. Delyon, “Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images,” J. Opt. Soc. Am. A 21, 1231–1240(2004).
    [CrossRef]
  31. Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
    [CrossRef]
  32. G. Anna, F. Goudail, and D. Dolfi, “Optimal discrimination of multiple regions with an active polarimetric imager,” Opt. Express 19, 25367–25378 (2011).
    [CrossRef]

2012 (1)

2011 (4)

2010 (2)

2009 (4)

2008 (3)

2007 (3)

2006 (3)

P. J. Wu, J. Joseph, and T. Walsh, “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt. 11, 014031 (2006).
[CrossRef]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[CrossRef]

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

2004 (1)

2002 (1)

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef]

2001 (1)

2000 (1)

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806  nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

1997 (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15, 81–93 (1997).
[CrossRef]

1996 (2)

1993 (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

1988 (1)

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

1987 (1)

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–991 (1987).
[CrossRef]

1981 (2)

J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
[CrossRef]

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

Alouini, M.

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Estimation precision of degree of polarization in the presence of signal-dependent and additive Poisson noises,” J. Eur. Opt. Soc. Rapid Publ. 3, 08002 (2008).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Precision of degree of polarization estimation in the presence of additive Gaussian detector noise,” Opt. Commun. 278, 264–269(2007).
[CrossRef]

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Anna, G.

Baarstad, I.

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Bénière, A.

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
[CrossRef]

F. Goudail and A. Bénière, “Optimization of the contrast in polarimetric scalar images,” Opt. Lett. 34, 1471–1473 (2009).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Estimation precision of degree of polarization in the presence of signal-dependent and additive Poisson noises,” J. Eur. Opt. Soc. Rapid Publ. 3, 08002 (2008).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Precision of degree of polarization estimation in the presence of additive Gaussian detector noise,” Opt. Commun. 278, 264–269(2007).
[CrossRef]

Boerner, W. M.

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–991 (1987).
[CrossRef]

Bourderionnet, J.

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Breugnot, S.

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806  nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

Bueno, J. M.

Campbell, M.

Charbois, J. M.

Chenault, D. B.

Chipman, R. A.

Clémenceau, P.

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806  nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

Cookson, C.

De Martino, A.

Delyon, G.

Devlaminck, V.

Dolfi, D.

G. Anna, F. Goudail, and D. Dolfi, “Polarimetric target detection in the presence of spatially fluctuating Mueller matrices,” Opt. Lett. 36, 4590–4592 (2011).
[CrossRef]

G. Anna, F. Goudail, and D. Dolfi, “Optimal discrimination of multiple regions with an active polarimetric imager,” Opt. Express 19, 25367–25378 (2011).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Estimation precision of degree of polarization in the presence of signal-dependent and additive Poisson noises,” J. Eur. Opt. Soc. Rapid Publ. 3, 08002 (2008).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Precision of degree of polarization estimation in the presence of additive Gaussian detector noise,” Opt. Commun. 278, 264–269(2007).
[CrossRef]

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Duan, Q. Y.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Engheta, N.

Goldstein, D. L.

Goudail, F.

G. Anna, F. Goudail, and D. Dolfi, “Polarimetric target detection in the presence of spatially fluctuating Mueller matrices,” Opt. Lett. 36, 4590–4592 (2011).
[CrossRef]

G. Anna, F. Goudail, and D. Dolfi, “Optimal discrimination of multiple regions with an active polarimetric imager,” Opt. Express 19, 25367–25378 (2011).
[CrossRef]

F. Goudail and J. S. Tyo, “When is polarimetric imaging preferable to intensity imaging for target detection?” J. Opt. Soc. Am. A 28, 46–53 (2011).
[CrossRef]

F. Goudail, “Comparison of the maximal achievable contrast in scalar, Stokes and Mueller images,” Opt. Lett. 35, 2600–2602 (2010).
[CrossRef]

F. Goudail and A. Bénière, “Optimization of the contrast in polarimetric scalar images,” Opt. Lett. 34, 1471–1473 (2009).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
[CrossRef]

F. Goudail, “Optimization of the contrast in active Stokes images,” Opt. Lett. 34, 121–123 (2009).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Estimation precision of degree of polarization in the presence of signal-dependent and additive Poisson noises,” J. Eur. Opt. Soc. Rapid Publ. 3, 08002 (2008).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Precision of degree of polarization estimation in the presence of additive Gaussian detector noise,” Opt. Commun. 278, 264–269(2007).
[CrossRef]

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

F. Goudail, P. Réfrégier, and G. Delyon, “Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images,” J. Opt. Soc. Am. A 21, 1231–1240(2004).
[CrossRef]

F. Goudail and P. Réfrégier, “Statistical techniques for target detection in polarisation diversity images,” Opt. Lett. 26, 644–646 (2001).
[CrossRef]

Grisard, A.

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Gupta, V. K.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Hoover, B.

Hoover, B. G.

Hunter, J.

Jacques, S. L.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef]

Johnson, S. J.

Joseph, J.

P. J. Wu, J. Joseph, and T. Walsh, “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt. 11, 014031 (2006).
[CrossRef]

Kaspersen, P.

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Kisilak, M.

Kong, J. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Kostinski, A. B.

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–991 (1987).
[CrossRef]

Lacot, E.

Lee, K.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef]

Løke, T.

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Lu, S. Y.

Martino, A. D.

Noble, H. D.

Normandin, X.

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

Novak, L. M.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Orlik, X.

Ossikovski, R.

Pugh, E. N.

Ramella-Roman, J. C.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef]

Réfrégier, P.

Richert, M.

Rowe, M. P.

Shaw, J. A.

Shin, R. T.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Solomon, J. E.

Sorooshian, S.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Swartz, A. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Terrier, P.

Tyo, J. S.

Upadhyay, D.

Walraven, R.

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

Walsh, T.

P. J. Wu, J. Joseph, and T. Walsh, “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt. 11, 014031 (2006).
[CrossRef]

Wang, Z.

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15, 81–93 (1997).
[CrossRef]

Wu, P. J.

P. J. Wu, J. Joseph, and T. Walsh, “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt. 11, 014031 (2006).
[CrossRef]

Yueh, H. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Appl. Opt. (6)

IEEE Trans. Antennas Propag. (1)

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propag. 35, 988–991 (1987).
[CrossRef]

Image Vis. Comput. (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15, 81–93 (1997).
[CrossRef]

J. Biomed. Opt. (2)

P. J. Wu, J. Joseph, and T. Walsh, “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt. 11, 014031 (2006).
[CrossRef]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ. (1)

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Estimation precision of degree of polarization in the presence of signal-dependent and additive Poisson noises,” J. Eur. Opt. Soc. Rapid Publ. 3, 08002 (2008).
[CrossRef]

J. Geophys. Res. (1)

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Optim. Theory Appl. (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Opt. Commun. (1)

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Precision of degree of polarization estimation in the presence of additive Gaussian detector noise,” Opt. Commun. 278, 264–269(2007).
[CrossRef]

Opt. Eng. (2)

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806  nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

Opt. Express (4)

Opt. Lett. (5)

Proc. SPIE (1)

M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, I. Baarstad, T. Løke, P. Kaspersen, and X. Normandin, “Active polarimetric and multispectral laboratory demonstrator: contrast enhancement for target detection,” Proc. SPIE 6396, 63960B (2006).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Polarimetric imaging setup.

Fig. 2.
Fig. 2.

(a) Scheme of the scene, (b) intensity image.

Fig. 3.
Fig. 3.

(a) GSC image of the scene in Fig. 2 after optimization of D ( θ ) , (b) PDF of the targets and of the background.

Fig. 4.
Fig. 4.

(a) GSC image of the scene in Fig. 2 after optimization of D ( θ ) , (b) PDFs of the targets and of the background.

Fig. 5.
Fig. 5.

(a) Schema of the scene, (b) intensity image.

Fig. 6.
Fig. 6.

GSC images of the scene in Fig. 5 after optimization of (a) D ( θ ) , (b) B ( θ ) .

Fig. 7.
Fig. 7.

Estimated PDFs of the target and the background in the images of Fig. 6, obtained after optimization of (a) D ( θ ) , (b) B ( θ ) .

Fig. 8.
Fig. 8.

(a) Intensity image of the scene, (b) scheme of the scene.

Fig. 9.
Fig. 9.

GSC images of the scene in Fig. 8 after optimization of (a) D ( θ ) , (b) B ( θ ) .

Fig. 10.
Fig. 10.

(a) Intensity image, (b) scheme of the scene.

Fig. 11.
Fig. 11.

Optimal GSC images in the different configurations presented in Section 4. B theo and B exp denote, respectively, the Bhattacharyya distance computed from the database and the real images.

Tables (5)

Tables Icon

Table 1. Average Mueller Matrices of the Target ( t ) and the Background ( b )

Tables Icon

Table 2. Optimal States Maximizing the Discrimination Criteria D ( θ ) [see Eq. (14)] and B ( θ ) [see Eq. (11)]a

Tables Icon

Table 3. Optimal States Maximizing the Discrimination Criteria D ( θ ) [see Eq. (14)] and B ( θ ) [see Eq. (11)]

Tables Icon

Table 4. GSC Imaging Configurations with Different Degrees of Freedoma

Tables Icon

Table 5. Optimal States for the GSC Images in the Different Configurations Presented in Table 4

Equations (16)

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i = η I 0 2 T T M S ,
i = η I 0 2 S T M S and i = η I 0 2 S T M S ,
OSC = i i i + i = S T M S S T M S S T M S + S T M S .
M = [ 1 0 0 0 0 a 0 0 0 0 a 0 0 0 0 b ] ,
i 1 = η I 0 2 T 1 T M S 1 and i 2 = η I 0 2 T 2 T M S 2 ,
γ ( θ ) = i 1 i 2 i 1 + i 2 = T 1 T M S 1 T 2 T M S 2 T 1 T M S 1 + T 2 T M S 2 ,
i 1 k = η I 0 2 T 1 T M k S 1 and i 2 k = η I 0 2 T 2 T M k S 2 ,
γ k ( θ ) = i 1 k i 2 k i 1 k + i 2 k = T 1 T M k S 1 T 2 T M k S 2 T 1 T M k S 1 + T 2 T M k S 2 .
γ k ( θ ) = n Ω k T 1 T M n S 1 n Ω k T 2 T M n S 2 n Ω k T 1 T M n S 1 + n Ω k T 2 T M n S 2 .
B = log [ D [ P t ( x ) P b ( x ) ] 1 / 2 d x ] ,
B ( θ ) = 1 4 [ γ ( θ ) t γ ( θ ) b ] 2 σ t 2 ( θ ) + σ b 2 ( θ ) + 1 2 log [ 1 2 ( σ t ( θ ) σ b ( θ ) + σ b ( θ ) σ t ( θ ) ) ] ,
σ 2 = ( 1 γ 2 ) N × i tot ,
i tot = i 1 + i 2 .
D ( θ ) = [ γ ( θ ) t γ ( θ ) b ] 2 .
σ u 2 ( θ ) = 1 N u k Ω u ( γ k ( θ ) γ u ¯ ( θ ) ) 2 ,
γ u ¯ ( θ ) = 1 N u k Ω u γ k ( θ ) .

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