Abstract

As an emerging technology, division-of-focal-plane (DoFP) polarization cameras have raised attention due to their integrated structure. In this paper, we address the fundamental precision limits of full Stokes polarimeters based on a linear DoFP polarization camera and a controllable retarder in the presence of additive and Poisson shot noise. We demonstrate that if the number of image acquisitions is greater than or equal to three, there exists retarder configurations that reach the theoretical lower bound on estimation variance. Examples of such configurations are one rotatable retarder with fixed retardance of 125.26° or two rotatable quarter-waveplates (QWPs) in pair. In contrast, the lower bound cannot be reached with a single QWP or a single variable retarder with fixed orientation. These results are important to get the most out of DoFP polarization imagers in real applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Precision analysis of arbitrary full-Stokes polarimeters in the presence of additive and Poisson noise

Jun Dai and François Goudail
J. Opt. Soc. Am. A 36(7) 1229-1240 (2019)

Precision of retardance autocalibration in full-Stokes division-of-focal-plane imaging polarimeters

François Goudail, Xiaobo Li, Matthieu Boffety, Stéphane Roussel, Tiegen Liu, and Haofeng Hu
Opt. Lett. 44(22) 5410-5413 (2019)

Error analysis of single-snapshot full-Stokes division-of-aperture imaging polarimeters

Tingkui Mu, Chunmin Zhang, Qiwei Li, and Rongguang Liang
Opt. Express 23(8) 10822-10835 (2015)

References

  • View by:
  • |
  • |
  • |

  1. D. Goldstein, Polarized Light (Dekker, 2003).
  2. X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
    [Crossref]
  3. R. M. A. Azzam, “Stokes-vector and Mueller-matrix polarimetry,” J. Opt. Soc. Am. A 33(7), 1396–1408 (2016).
    [Crossref]
  4. X. Li, F. Goudail, H. Hu, Q. Han, Z. Cheng, and T. Liu, “Optimal ellipsometric parameter measurement strategies based on four intensity measurements in presence of additive Gaussian and Poisson noise,” Opt. Express 26(26), 34529–34546 (2018).
    [Crossref]
  5. E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.
  6. J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
    [Crossref]
  7. N. Li, Y. Zhao, Q. Pan, and S. G. Kong, “Demosaicking dofp images using Newton’s polynomial interpolation and polarization difference model,” Opt. Express 27(2), 1376–1391 (2019).
    [Crossref]
  8. S. Roussel, M. Boffety, and F. Goudail, “Polarimetric precision of micropolarizer grid-based camera in the presence of additive and Poisson shot noise,” Opt. Express 26(23), 29968–29982 (2018).
    [Crossref]
  9. S. Shibata, N. Hagen, and Y. Otani, “Robust full Stokes imaging polarimeter with dynamic calibration,” Opt. Lett. 44(4), 891–894 (2019).
    [Crossref]
  10. J. Qi, C. He, and D. S. Elson, “Real time complete Stokes polarimetric imager based on a linear polarizer array camera for tissue polarimetric imaging,” Biomed. Opt. Express 8(11), 4933–4946 (2017).
    [Crossref]
  11. S. Roussel, M. Boffety, and F. Goudail, “On the optimal ways to perform full Stokes measurements with a linear division-of-focal-plane polarimetric imager and a retarder,” Opt. Lett. 44(11), 2927–2930 (2019).
    [Crossref]
  12. X. Li, T. Liu, B. Huang, Z. Song, and H. Hu, “Optimal distribution of integration time for intensity measurements in Stokes polarimetry,” Opt. Express 23(21), 27690–27699 (2015).
    [Crossref]
  13. F. Goudail, “Equalized estimation of Stokes parameters in the presence of Poisson noise for any number of polarization analysis states,” Opt. Lett. 41(24), 5772–5775 (2016).
    [Crossref]
  14. 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(11), 802–804 (2000).
    [Crossref]
  15. M. R. Foreman, A. Favaro, and A. Aiello, “Optimal frames for polarization state reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
    [Crossref]
  16. S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
    [Crossref]
  17. K. M. Twietmeyer and R. A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16(15), 11589–11603 (2008).
    [Crossref]
  18. J. S. Tyo, “Noise equalization in stokes parameter images obtained by use of variable-retardance polarimeters,” Opt. Lett. 25(16), 1198–1200 (2000).
    [Crossref]
  19. F. Goudail, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34(5), 647–649 (2009).
    [Crossref]
  20. G. Anna and F. Goudail, “Optimal Mueller matrix estimation in the presence of Poisson shot noise,” Opt. Express 20(19), 21331–21340 (2012).
    [Crossref]
  21. J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41(4), 619–630 (2002).
    [Crossref]
  22. F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49(4), 683–693 (2010).
    [Crossref]
  23. J. S. Tyo, “Optimum linear combination strategy for an N-channel polarization sensitive imaging or vision system,” J. Opt. Soc. Am. A 15(2), 359–366 (1998).
    [Crossref]
  24. X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
    [Crossref]
  25. Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “Shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76(3), 501–521 (1993).
    [Crossref]
  26. M. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
    [Crossref]
  27. A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, “Optimized Stokes polarimeters based on a single twisted nematic liquid-crystal device for the minimization of noise propagation,” Appl. Opt. 50(28), 5437–5445 (2011).
    [Crossref]
  28. L. Pouget, J. Fade, C. Hamel, and M. Alouini, “Polarimetric imaging beyond the speckle grain scale,” Appl. Opt. 51(30), 7345–7356 (2012).
    [Crossref]
  29. A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
    [Crossref]
  30. N. Hagen and Y. Otani, “Stokes polarimeter performance: general noise model and analysis,” Appl. Opt. 57(15), 4283–4296 (2018).
    [Crossref]
  31. M. Kupinski, R. Chipman, and E. Clarkson, “Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector,” Opt. Eng. 53(11), 113108 (2014).
    [Crossref]
  32. F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49(4), 683–693 (2010).
    [Crossref]
  33. R. Ossikovski and O. Arteaga, “Complete Mueller matrix from a partial polarimetry experiment: the nine-element case,” J. Opt. Soc. Am. A 36(3), 403–415 (2019).
    [Crossref]
  34. J. J. G. Perez and R. Ossikovski, Polarized light and the Mueller matrix approach (CRC, 2017).

2019 (5)

2018 (4)

2017 (2)

2016 (3)

R. M. A. Azzam, “Stokes-vector and Mueller-matrix polarimetry,” J. Opt. Soc. Am. A 33(7), 1396–1408 (2016).
[Crossref]

F. Goudail, “Equalized estimation of Stokes parameters in the presence of Poisson noise for any number of polarization analysis states,” Opt. Lett. 41(24), 5772–5775 (2016).
[Crossref]

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

2015 (2)

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal frames for polarization state reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

X. Li, T. Liu, B. Huang, Z. Song, and H. Hu, “Optimal distribution of integration time for intensity measurements in Stokes polarimetry,” Opt. Express 23(21), 27690–27699 (2015).
[Crossref]

2014 (2)

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
[Crossref]

M. Kupinski, R. Chipman, and E. Clarkson, “Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector,” Opt. Eng. 53(11), 113108 (2014).
[Crossref]

2012 (2)

2011 (1)

2010 (2)

2009 (1)

2008 (1)

2002 (2)

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41(4), 619–630 (2002).
[Crossref]

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
[Crossref]

2000 (2)

1998 (1)

1993 (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “Shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76(3), 501–521 (1993).
[Crossref]

Aiello, A.

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal frames for polarization state reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Alouini, M.

Amra, C.

Anna, G.

Arteaga, O.

Azzam, R. M. A.

Bénière, A.

Boffety, M.

Campos, J.

Chang, J.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Cheng, Z.

Chipman, R.

M. Kupinski, R. Chipman, and E. Clarkson, “Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector,” Opt. Eng. 53(11), 113108 (2014).
[Crossref]

Chipman, R. A.

Clarkson, E.

M. Kupinski, R. Chipman, and E. Clarkson, “Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector,” Opt. Eng. 53(11), 113108 (2014).
[Crossref]

Dereniak, E. L.

Descour, M. R.

Drévillon, B.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

Duan, Q. Y.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “Shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76(3), 501–521 (1993).
[Crossref]

Elson, D. S.

Fade, J.

Favaro, A.

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal frames for polarization state reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Foldyna, M.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

Foreman, M.

M. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
[Crossref]

Foreman, M. R.

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal frames for polarization state reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Garcia-Caurel, E.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

Ghabbach, A.

Goldstein, D.

D. Goldstein, Polarized Light (Dekker, 2003).

Goudail, F.

M. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
[Crossref]

S. Roussel, M. Boffety, and F. Goudail, “On the optimal ways to perform full Stokes measurements with a linear division-of-focal-plane polarimetric imager and a retarder,” Opt. Lett. 44(11), 2927–2930 (2019).
[Crossref]

S. Roussel, M. Boffety, and F. Goudail, “Polarimetric precision of micropolarizer grid-based camera in the presence of additive and Poisson shot noise,” Opt. Express 26(23), 29968–29982 (2018).
[Crossref]

X. Li, F. Goudail, H. Hu, Q. Han, Z. Cheng, and T. Liu, “Optimal ellipsometric parameter measurement strategies based on four intensity measurements in presence of additive Gaussian and Poisson noise,” Opt. Express 26(26), 34529–34546 (2018).
[Crossref]

F. Goudail, “Equalized estimation of Stokes parameters in the presence of Poisson noise for any number of polarization analysis states,” Opt. Lett. 41(24), 5772–5775 (2016).
[Crossref]

G. Anna and F. Goudail, “Optimal Mueller matrix estimation in the presence of Poisson shot noise,” Opt. Express 20(19), 21331–21340 (2012).
[Crossref]

F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49(4), 683–693 (2010).
[Crossref]

F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49(4), 683–693 (2010).
[Crossref]

F. Goudail, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34(5), 647–649 (2009).
[Crossref]

Gupta, V. K.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “Shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76(3), 501–521 (1993).
[Crossref]

Hagen, N.

Hamel, C.

Han, Q.

He, C.

J. Qi, C. He, and D. S. Elson, “Real time complete Stokes polarimetric imager based on a linear polarizer array camera for tissue polarimetric imaging,” Biomed. Opt. Express 8(11), 4933–4946 (2017).
[Crossref]

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

He, H.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Hu, H.

Huang, B.

Huang, Y.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Iemmi, C.

Kemme, S. A.

Kong, S. G.

Kupinski, M.

M. Kupinski, R. Chipman, and E. Clarkson, “Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector,” Opt. Eng. 53(11), 113108 (2014).
[Crossref]

Li, N.

Li, X.

X. Li, F. Goudail, H. Hu, Q. Han, Z. Cheng, and T. Liu, “Optimal ellipsometric parameter measurement strategies based on four intensity measurements in presence of additive Gaussian and Poisson noise,” Opt. Express 26(26), 34529–34546 (2018).
[Crossref]

X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
[Crossref]

X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
[Crossref]

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

X. Li, T. Liu, B. Huang, Z. Song, and H. Hu, “Optimal distribution of integration time for intensity measurements in Stokes polarimetry,” Opt. Express 23(21), 27690–27699 (2015).
[Crossref]

Liao, R.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Liu, S.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Liu, T.

Lizana, A.

Ma, H.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Martino, A. D.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

Ossikovski, R.

R. Ossikovski and O. Arteaga, “Complete Mueller matrix from a partial polarimetry experiment: the nine-element case,” J. Opt. Soc. Am. A 36(3), 403–415 (2019).
[Crossref]

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

J. J. G. Perez and R. Ossikovski, Polarized light and the Mueller matrix approach (CRC, 2017).

Otani, Y.

Pan, Q.

Peinado, A.

Perez, J. J. G.

J. J. G. Perez and R. Ossikovski, Polarized light and the Mueller matrix approach (CRC, 2017).

Phipps, G. S.

Pierangelo, A.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

Pouget, L.

Qi, J.

Roussel, S.

Sabatke, D. S.

Savenkov, S. N.

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
[Crossref]

Shibata, S.

Song, Z.

Soriano, G.

Sorooshian, S.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “Shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76(3), 501–521 (1993).
[Crossref]

Sweatt, W. C.

Twietmeyer, K. M.

Tyo, J. S.

Vidal, J.

Wang, H.

X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
[Crossref]

Wang, Y.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Wu, L.

X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
[Crossref]

X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
[Crossref]

Yu, Y.

X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
[Crossref]

Zeng, N.

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

Zerrad, M.

Zhao, L.

X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
[Crossref]

Zhao, Y.

Appl. Opt. (6)

Biomed. Opt. Express (1)

J. Biomed. Opt. (1)

J. Chang, H. He, Y. Wang, Y. Huang, X. Li, C. He, R. Liao, N. Zeng, S. Liu, and H. Ma, “Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: a potential tool for quick diagnosis of human carcinoma tissues,” J. Biomed. Opt. 21(5), 056002 (2016).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Optim. Theory Appl. (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “Shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76(3), 501–521 (1993).
[Crossref]

Opt. Eng. (3)

M. Foreman and F. Goudail, “On the equivalence of optimization metrics in Stokes polarimetry,” Opt. Eng. 58(08), 1 (2019).
[Crossref]

M. Kupinski, R. Chipman, and E. Clarkson, “Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector,” Opt. Eng. 53(11), 113108 (2014).
[Crossref]

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
[Crossref]

Opt. Express (8)

K. M. Twietmeyer and R. A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16(15), 11589–11603 (2008).
[Crossref]

X. Li, T. Liu, B. Huang, Z. Song, and H. Hu, “Optimal distribution of integration time for intensity measurements in Stokes polarimetry,” Opt. Express 23(21), 27690–27699 (2015).
[Crossref]

X. Li, F. Goudail, H. Hu, Q. Han, Z. Cheng, and T. Liu, “Optimal ellipsometric parameter measurement strategies based on four intensity measurements in presence of additive Gaussian and Poisson noise,” Opt. Express 26(26), 34529–34546 (2018).
[Crossref]

N. Li, Y. Zhao, Q. Pan, and S. G. Kong, “Demosaicking dofp images using Newton’s polynomial interpolation and polarization difference model,” Opt. Express 27(2), 1376–1391 (2019).
[Crossref]

S. Roussel, M. Boffety, and F. Goudail, “Polarimetric precision of micropolarizer grid-based camera in the presence of additive and Poisson shot noise,” Opt. Express 26(23), 29968–29982 (2018).
[Crossref]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
[Crossref]

G. Anna and F. Goudail, “Optimal Mueller matrix estimation in the presence of Poisson shot noise,” Opt. Express 20(19), 21331–21340 (2012).
[Crossref]

X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
[Crossref]

Opt. Lett. (6)

Phys. Rev. Lett. (1)

M. R. Foreman, A. Favaro, and A. Aiello, “Optimal frames for polarization state reconstruction,” Phys. Rev. Lett. 115(26), 263901 (2015).
[Crossref]

Sci. Rep. (1)

X. Li, H. Hu, L. Zhao, H. Wang, Y. Yu, L. Wu, and T. Liu, “Polarimetric image recovery method combining histogram stretching for underwater imaging,” Sci. Rep. 8(1), 12430 (2018).
[Crossref]

Other (3)

D. Goldstein, Polarized Light (Dekker, 2003).

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drévillon, and A. D. Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013), Chap. 2.

J. J. G. Perez and R. Ossikovski, Polarized light and the Mueller matrix approach (CRC, 2017).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. (a) Structure of the linear DOFP polarization camera. (b) Setup of the full Stokes polarimeter based on a linear DoFP camera and a controllable retarder.
Fig. 2.
Fig. 2. For the setup based on a QWP, the value of 1/EWVAWN as a function of the ${\theta _2}$ and ${\theta _3}$ under the assumptions of ${\theta _1} = {0^ \circ }$ and ${\theta _2} \le {\theta _3}$ . The black crosses mark the minima of EWVAWN.
Fig. 3.
Fig. 3. The value of EWVAWN as a function of the retardance of the rotatable retarder.
Fig. 4.
Fig. 4. For the setup based on a retarder with retardance of 125.26° or 54.74°, the value of 1/EWVAWN as a function of ${\theta _2}$ and ${\theta _3}$ under the assumptions of ${\theta _1} = {0^ \circ }$ and ${\theta _2} \le {\theta _3}$. The black cross marks the minima of EWVAWN.
Fig. 5.
Fig. 5. Individual estimation variances of four Stokes parameters as a function of the orientation angle of the variable retarder in the presence of AWN and PSN with number of N acquisitions.

Tables (2)

Tables Icon

Table 1. Individual estimation variances and the corresponding EWV in the presence of AWN and PSN.

Tables Icon

Table 2. Minimal EWVs and corresponding individual estimation variances of the investigated setups with number of N > 2 acquisition.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

I = W S ,
M R ( δ j , θ j ) = [ 1 0 0 0 0 cos 2 2 θ j + cos δ j sin 2 2 θ j ( 1 cos δ j ) sin 2 θ j cos 2 θ j sin δ j sin 2 θ j 0 ( 1 cos δ j ) sin 2 θ j cos 2 θ j sin 2 2 θ j + cos δ j cos 2 2 θ j sin δ j cos 2 θ j 0 sin δ j sin 2 θ j sin δ j cos 2 θ j cos δ j ] ,
M P ( φ i ) = 1 2 ( 1 cos 2 φ i sin 2 φ i 0 cos 2 φ i cos 2 2 φ i sin 2 φ i cos 2 φ i 0 sin 2 φ i sin 2 φ i cos 2 φ i sin 2 2 φ i 0 0 0 0 0 ) ,
W 4 ( j 1 ) + i = { 1 2 [ 1 , ( cos 2 2 θ j + cos δ j sin 2 2 θ j ) , ( 1 cos δ j ) sin 2 θ j cos 2 θ j , sin δ j sin 2 θ j ] ,  if  i = 1 1 2 [ 1 , ( cos 2 2 θ j + cos δ j sin 2 2 θ j ) , ( 1 cos δ j ) sin 2 θ j cos 2 θ j , sin δ j sin 2 θ j ] ,  if  i = 2 1 2 [ 1 , ( cos 2 2 θ j + cos δ j sin 2 2 θ j ) , ( 1 cos δ j ) sin 2 θ j cos 2 θ j , sin δ j sin 2 θ j ] ,  if  i = 3 1 2 [ 1 , ( cos 2 2 θ j + cos δ j sin 2 2 θ j ) , ( 1 cos δ j ) sin 2 θ j cos 2 θ j , sin δ j sin 2 θ j ] ,  if  i = 4 , with  j [ 1 , N ] .
S ^ = W + I ,
W + = [ W T W ] 1 W T
EW V AWN = σ 2 trace { [ W T W ] 1 } ,
θ i = θ 0 + ( i 1 ) 18 0 N , i [ 1 , N ]
[ W T W ] 1 = diag { 1 N , 4 N , 4 N , 2 N } ,
γ 0 = σ 2 N , γ 1 = γ 2 = 4 σ 2 N , γ 3 = 2 σ 2 N , EW V AWN = 11 σ 2 N .
i [ 0 , 3 ] , γ i = j = 0 3 s j n = 0 4 N 1 [ W i n ] 2 W n j = j = 0 3 Q i j s j ,
Q i j = n = 0 4 N 1 [ W i n + ] 2 W n j .
EW V PSN = s 0 ( 1 2 σ 2 EW V AWN + | | v | | ) ,
Q = 1 2 N [ 1 0 0 0 4 0 0 0 4 0 0 0 2 0 0 0 ] .
γ 0 = s o 2 N , γ 1 = γ 2 = 2 s o N , γ 3 = s o N ,  EW V PSN = 11 s o 2 N .
A i = θ 0 + ( ( i 1 ) 9 0 N , 90 + ( i 1 ) 9 0 N ) ,
( θ 2 , θ 3 ) = { ( 30 , 60 ) , ( 30 , 150 ) , ( 60 , 120 ) , ( 120 , 150 ) } .
diag { 1 N , 4 N ( 1 + cos 2 δ ) , 4 N ( 1 + cos 2 δ ) , 2 N sin 2 δ } .
EW V AWN = ( 11 6 cos 2 δ cos 4 δ ) N ( 1 cos 4 δ ) σ 2 .
diag { 1 N , 3 N , 3 N , 3 N } .
γ 0 = σ 2 N , γ 1 = γ 2 = γ 3 = 3 σ 2 N , EW V AWN = 10 σ 2 N .
j [ 1 , 3 ] , q j = i = 0 3 Q i j = 9 N 2 n = 0 4 N 1 W n j i = 0 3 [ W n i ] 2 = 0 .
γ 0 = s 0 2 N , γ 1 = γ 2 = γ 3 = 3 s 0 2 N , EW V PSN = 5 s 0 N .
δ i = δ 0  +  ( i 1 ) 18 0 N .

Metrics