Abstract

We quantitatively determine the target detection performance of different passive polarization imaging architectures perturbed by signal-independent detection noise or signal-dependent Poisson shot noise. We compare the fully adaptive polarimetric imager and the best channel of a static polarimetric imager, and in each case, we compare the use of a polarizer and a polarizing beam splitter as the polarization analyzing device. For all these configurations, we derive a closed-form expression of the target/background separability and quantify the performance gain brought by polarization imaging compared to standard intensity imaging. We show in particular that all the considered polarimetric imaging configurations but one require a minimum value of the polarimetric contrast in order to outperform intensity imaging. The only configuration that always performs better than intensity imaging uses a polarizing beam splitter in the presence of background shot noise. These results are useful in evaluating the fundamental limits of the gain brought by polarization imaging and determining, in practice, which type of imaging architecture is preferable for a given application.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. 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]
  3. S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806  nm,” Opt. Eng. 39, 2681–2688 (2000).
    [Crossref]
  4. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
    [Crossref]
  5. A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.
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    [Crossref]
  7. 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).
    [Crossref]
  8. C. U. Keller and F. Snik, “Polarimetry from the ground up,” in Solar Polarization 5, S. V. Berdyugina, K. Nagendra, and R. Ramelli, eds., Vol. 405 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, 2009), pp. 371–382.
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    [Crossref]
  10. N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  18. P. Réfrégier and F. Goudail, “Invariant polarimetric contrast parameters for coherent light,” J. Opt. Soc. Am. A 19, 1223–1233 (2002).
    [Crossref]
  19. D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).
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    [Crossref]
  21. F. Goudail and M. Boffety, “Optimal configuration of static polarization imagers for target detection,” J. Opt. Soc. Am. A 33, 9–16 (2016).
    [Crossref]
  22. G. Anna, H. Sauer, F. Goudail, and D. Dolfi, “Fully tunable active polarization imager for contrast enhancement and partial polarimetry,” Appl. Opt. 51, 5302–5309 (2012).
    [Crossref]
  23. N. Vannier, F. Goudail, C. Plassart, M. Boffety, P. Feneyrou, L. Leviandier, F. Galland, and N. Bertaux, “Active polarimetric imager with near infrared laser illumination for adaptive contrast optimization,” Appl. Opt. 54, 7622–7631 (2015).
    [Crossref]
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    [Crossref]
  25. J. S. Tyo, “Design of optimal polarimeters: maximization of the signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
    [Crossref]
  26. F. Goudail, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34, 647–649 (2009).
    [Crossref]
  27. K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, 1990).
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  29. 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]
  30. J. S. Tyo and H. Wei, “Optimizing imaging polarimeters constructed with imperfect optics,” Appl. Opt. 45, 5497–5503 (2006).
    [Crossref]
  31. A. Peinado, A. Lizana, and J. Campos, “Optimization and tolerance analysis of a polarimeter with ferroelectric liquid crystals,” Appl. Opt. 52, 5748–5757 (2013).
    [Crossref]

2016 (4)

2015 (1)

2014 (1)

2013 (1)

2012 (1)

2011 (2)

2009 (3)

2008 (2)

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).
[Crossref]

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

2006 (2)

2004 (2)

2002 (3)

2000 (2)

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
[Crossref]

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

1996 (1)

1981 (1)

Alenin, A. S.

Alouini, M.

Amoss, M. S.

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.

Anastasiadou, M.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Anna, G.

Antonelli, M.-R.

Baba, J. S.

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.

Baldwin, A. M.

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.

Benali, A.

Bénière, A.

Bertaux, N.

Bigué, L.

Boffety, M.

Bretenaker, F.

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]

Campos, J.

Carré, A.

Charbois, J. M.

Chenault, D. B.

Chung, J. R.

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.

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]

Clement, D.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Cohen, H.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Cote, G. L.

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.

De Martino, A.

A. Pierangelo, A. Benali, M.-R. Antonelli, T. Novikova, P. Validire, P. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19, 1582–1593 (2011).
[Crossref]

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Delyon, G.

Dereniak, E. L.

Descour, M. R.

Devlaminck, V.

Dolfi, D.

Dreyfuss, J.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Engheta, N.

Fade, J.

Feneyrou, P.

Frein, L.

Fukunaga, K.

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

Galland, F.

Gayet, P.

Ghosh, N.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Goldstein, D.

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

Goldstein, D. L.

Goudail, F.

F. Goudail and M. Boffety, “Optimal configuration of static polarization imagers for target detection,” J. Opt. Soc. Am. A 33, 9–16 (2016).
[Crossref]

N. Vannier, F. Goudail, C. Plassart, M. Boffety, P. Feneyrou, L. Leviandier, F. Galland, and N. Bertaux, “Comparison of different active polarimetric imaging modes for target detection in outdoor environment,” Appl. Opt. 55, 2881–2891 (2016).
[Crossref]

F. Goudail and M. Boffety, “Performance comparison of fully adaptive and static passive polarimetric imagers in the presence of intensity and polarization contrast,” J. Opt. Soc. Am. A 33, 1880–1886 (2016).
[Crossref]

N. Vannier, F. Goudail, C. Plassart, M. Boffety, P. Feneyrou, L. Leviandier, F. Galland, and N. Bertaux, “Active polarimetric imager with near infrared laser illumination for adaptive contrast optimization,” Appl. Opt. 54, 7622–7631 (2015).
[Crossref]

G. Anna, H. Sauer, F. Goudail, and D. Dolfi, “Fully tunable active polarization imager for contrast enhancement and partial polarimetry,” Appl. Opt. 51, 5302–5309 (2012).
[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, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34, 647–649 (2009).
[Crossref]

F. Goudail and A. Bénière, “Optimization of the contrast in polarimetric scalar images,” Opt. Lett. 34, 1471–1473 (2009).
[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, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. Devlaminck, “Target detection with a liquid crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282 (2004).
[Crossref]

P. Réfrégier and F. Goudail, “Invariant polarimetric contrast parameters for coherent light,” J. Opt. Soc. Am. A 19, 1223–1233 (2002).
[Crossref]

F. Goudail, P. Réfrégier, and O. Ruch, “Definition of a signal-to-noise ratio for object segmentation using polygonal MDL-based statistical snakes,” in Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, 2003), pp. 373–388.

Hamel, C.

Huynh, B.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

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]

Keller, C. U.

C. U. Keller and F. Snik, “Polarimetry from the ground up,” in Solar Polarization 5, S. V. Berdyugina, K. Nagendra, and R. Ramelli, eds., Vol. 405 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, 2009), pp. 371–382.

Kemme, S. A.

Laude-Boulesteix, B.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

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]

Leviandier, L.

Li, R.-K.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Li, S.-H.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Liège, F.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Lizana, A.

Nazac, A.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Novikova, T.

Panigrahi, S.

Peinado, A.

Phipps, G. S.

Pierangelo, A.

Plassart, C.

Pugh, E. N.

Quang, N.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Ramachandran, H.

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]

Ratliff, B. M.

Réfrégier, P.

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]

P. Réfrégier and F. Goudail, “Invariant polarimetric contrast parameters for coherent light,” J. Opt. Soc. Am. A 19, 1223–1233 (2002).
[Crossref]

F. Goudail, P. Réfrégier, and O. Ruch, “Definition of a signal-to-noise ratio for object segmentation using polygonal MDL-based statistical snakes,” in Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, 2003), pp. 373–388.

Rowe, M. P.

Ruch, O.

F. Goudail, P. Réfrégier, and O. Ruch, “Definition of a signal-to-noise ratio for object segmentation using polygonal MDL-based statistical snakes,” in Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, 2003), pp. 373–388.

Sabatke, D. S.

Sauer, H.

Schwartz, L.

M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Shaw, J. A.

Snik, F.

C. U. Keller and F. Snik, “Polarimetry from the ground up,” in Solar Polarization 5, S. V. Berdyugina, K. Nagendra, and R. Ramelli, eds., Vol. 405 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, 2009), pp. 371–382.

Solomon, J. E.

Spiegelman, C. H.

A. M. Baldwin, J. R. Chung, J. S. Baba, C. H. Spiegelman, M. S. Amoss, and G. L. Cote, “Mueller matrix imaging for cancer detection,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2003), Vol. 2, pp. 1027–1030.

Sweatt, W. C.

Takakura, Y.

Terrier, P.

Tyo, J. S.

Validire, P.

Vannier, N.

Vitkin, I. A.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Wei, H.

Weisel, R. D.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Wilson, B. C.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

Appl. Opt. (11)

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

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]

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]

J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53, 3854–3865 (2014).
[Crossref]

N. Vannier, F. Goudail, C. Plassart, M. Boffety, P. Feneyrou, L. Leviandier, F. Galland, and N. Bertaux, “Comparison of different active polarimetric imaging modes for target detection in outdoor environment,” Appl. Opt. 55, 2881–2891 (2016).
[Crossref]

F. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. Devlaminck, “Target detection with a liquid crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282 (2004).
[Crossref]

J. S. Tyo, “Design of optimal polarimeters: maximization of the signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
[Crossref]

G. Anna, H. Sauer, F. Goudail, and D. Dolfi, “Fully tunable active polarization imager for contrast enhancement and partial polarimetry,” Appl. Opt. 51, 5302–5309 (2012).
[Crossref]

N. Vannier, F. Goudail, C. Plassart, M. Boffety, P. Feneyrou, L. Leviandier, F. Galland, and N. Bertaux, “Active polarimetric imager with near infrared laser illumination for adaptive contrast optimization,” Appl. Opt. 54, 7622–7631 (2015).
[Crossref]

J. S. Tyo and H. Wei, “Optimizing imaging polarimeters constructed with imperfect optics,” Appl. Opt. 45, 5497–5503 (2006).
[Crossref]

A. Peinado, A. Lizana, and J. Campos, “Optimization and tolerance analysis of a polarimeter with ferroelectric liquid crystals,” Appl. Opt. 52, 5748–5757 (2013).
[Crossref]

J. Biomed. Opt. (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]

J. Biophoton. (1)

N. Ghosh, M. F. G. Wood, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).
[Crossref]

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

Opt. Eng. (1)

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Figures (2)

Fig. 1.
Fig. 1.

Representation of the different imaging modalities compared in this paper. (a) Intensity imaging. (b) Polarization imaging using a polarizer. (c) Polarization imaging using a polarizing beam splitter. D, detector; P, polarizer; R, variable retarder; PBS, polarizing beam splitter.

Fig. 2.
Fig. 2.

Square root of the contrasts Cint, Cpolada, Cpolbest1, Cpbsada, and Cpbsbest1 as a function of Δs in the presence of different sources of noise and in the presence of intensity contrast (ΔS0=1). (a) Type 1 noise, with ητ/σ=1. (b) Type 2 noise, with ητ/I0=1.

Tables (3)

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Table 1. Summary of the Contrast Values for Noise Sources of Type 1 and Type 2 and for Intensity and Different Polarimetric Imaging Configurations

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Table 2. Square Roots of the Contrast Values Obtained with the Different Polarimetric Imaging Modalities when |ΔS0| is Negligible Against Δs for Noise Sources of Type 1 and Type 2

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Table 3. Values of Δs for which the Contrast Obtained with the Different Polarimetric Imaging Modalities is Equal to that Obtained with the Intensity Imager for Noise Sources of Type 1 and Type 2

Equations (29)

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i=ητS0+ν,
ia=ητS0aandib=ητS0b
C=12σ2(iaib)2.
Cint=12(ητσ)2|ΔS0|2,
i=ητ2TTS+ν=ητ2(S0+tTs)+ν,
ia=ητ2TTSaandib=ητ2TTSb
Cpol=(ητ)28σ2(TTΔS)2=(ητ)28σ2(ΔS0+tTΔs)2,
Cpol=18(ητσ)2(ΔS0+Δs×tTu)2,
Cpolada=18(ητσ)2(|ΔS0|+Δs)2,
in=ητ2TnTS+νn,n[1,4].
Cpoln(u)=18(ητσ)2(ΔS0+Δs×tnTu)2.
t1=[111]T/3,t2=[111]T/3,t3=[111]T/3,t4=[111]T/3.
Cpolbest1=minu{maxn[Cpoln(u)]},
Cpolbest1=18(ητσ)2F(|ΔS0|,Δs),
F(|ΔS0|,Δs)={(|ΔS0|+Δs3)2if  Δs3|ΔS0|,(|ΔS0|+Δs232[ΔS0]2)2otherwise.
i=ητ2TTS+ν=ητ2(S0+tTs)+ν,i=ητ2TTS+ν=ητ2(S0tTs)+ν,
iwu=ητ2TvTSu,
Cw=12σ2(iwaiwb)2.
C=18(ητσ)2(ΔS0+tTΔs)2,C=18(ητσ)2(ΔS0tTΔs)2.
Cpbs=C+C,
Cpbs=18(ητσ)2[(ΔS0+tTΔs)2+(ΔS0tTΔs)2]=14(ητσ)2[|ΔS0|2+(tTΔs)2].
Cpbs=14(ητσ)2[|ΔS0|2+(Δs×tTu)2].
Cpbsada=14(ητσ)2[|ΔS0|2+Δs2].
[iw]n=ητ2[Tw]nTS+[νw]n.
Cpbsn(u)=14(ητσ)2[|ΔS0|2+(Δs×tnTu)2].
Cpbsbest1=minu{maxn[Cpbsn(u)]}
minu{maxn(|tnTu|)}=13.
Cpbsbest1=14(ητσ)2[|ΔS0|2+Δs23].
B=(iaib)2.

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