Abstract

Spectralons are reference radiometric samples which exhibit a calibrated reflectance. However, in case of low reflectance samples, the degree of polarization (DOP) of scattered light is hard to characterize. Here, an accurate determination of spectralon spatial depolarization is proposed. Based on a spatially resolved polarimetric imaging system, the polarization state of the scattered light is characterized for every pixel. A statistic distribution analysis is carried out over the entire image. The relative phase shift distribution between two orthogonal components of the scattered electric field clearly exhibits a high sensitivity to the reflectance, the phase statistics following a circular Voigt profile. The intrinsic part of the spatial depolarization is demonstrated to be linked to the circular Cauchy contribution of that phase dispersion. An analytic equation is proposed to estimate the monochromatic spatially integrated DOP, as a function of the reflectance.

© 2017 Optical Society of America

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References

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  1. A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
    [Crossref] [PubMed]
  2. M. J. Kavaya, R. T. Menzies, D. A. Haner, U. P. Oppenheim, and P. H. Flamant, “Target reflectance measurements for calibration of lidar atmospheric backscatter data,” Appl. Opt. 22, 2619–2628 (1983).
    [Crossref] [PubMed]
  3. M. J. Kavaya, “Polarization effects on hard target calibration of lidar systems,” Appl. Opt. 26, 796–804 (1987).
    [Crossref] [PubMed]
  4. C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
    [Crossref]
  5. R. Ceolato, M. Golzio, C. Riou, X. Orlik, and N. Riviere, “Spectral degree of linear polarization of light from healthy skin and melanoma,” Opt. Express 23, 13605–13612 (2015).
    [Crossref] [PubMed]
  6. S. Seager, B. A. Whitney, and D. D. Sasselov, “Photometric light curves and polarization of close-in extrasolar giant planets,” Astrophys. J. 540, 504–520 (2000).
    [Crossref]
  7. P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
    [Crossref]
  8. J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34, 2429–2431 (2009).
    [Crossref] [PubMed]
  9. Ø. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and Ø. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards,” Opt. Express 20, 15045–15053 (2012).
    [Crossref] [PubMed]
  10. J. M. Sanz, C. Extremiana, and J. M. Saiz, “Comprehensive polarimetric analysis of Spectralon white reflectance standard in a wide visible range,” Appl. Opt. 52, 6051–6062 (2013).
    [Crossref] [PubMed]
  11. M. Kildemo, J. Maria, P. G. Ellingsen, and L. M. S. Aas, “Parametric model of the Mueller matrix of a Spectralon white reflectance standard deduced by polar decomposition techniques,” Opt. Express 21, 18509–18524 (2013).
    [Crossref] [PubMed]
  12. J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
    [Crossref] [PubMed]
  13. A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
    [Crossref] [PubMed]
  14. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
    [Crossref] [PubMed]
  15. M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
    [Crossref] [PubMed]
  16. R. Ossikovski and K. Hingerl, “General formalism for partial spatial coherence in reflection Mueller matrix polarimetry,” Opt. Lett. 41, 4044–4047 (2016).
    [Crossref] [PubMed]
  17. J. Dupont, X. Orlik, A. Gabbach, M. Zerrad, G. Soriano, and C. Amra, “Polarization analysis of speckle field below its transverse correlation width: application to surface and bulk scattering,” Opt. Express 22, 24133–24141 (2014).
    [Crossref] [PubMed]
  18. J. Dupont and X. Orlik, “Polarized vortices in optical speckle field: observation of rare polarization singularities,” Opt. Express 23, 6041–6049 (2015).
    [Crossref] [PubMed]
  19. R. Gatto and S. R. Jammalamadaka, “The generalized Von Mises distribution,” Stat. Methodol. 4, 341–353 (2007).
    [Crossref]
  20. P. McCullagh, “Möbius transformation and Cauchy parameter estimation,” Ann. Statist. 24, 787–808 (1996).
    [Crossref]
  21. W. D. Elderton and N. L. Johnson, Systems of Frequency Curves (Cambridge University, 1969, pp. 77–78).
  22. M. M. Hall, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10, 66–68 (1977).
    [Crossref]
  23. D. Goldstein, Polarized Light (CRC Press, 2003, pp. 32–42).
  24. J. Dupont and X. Orlik, “Speckle fields polarimetry: statistical analysis and polarization singularities measurements,” Proc. SPIE 9660, 96601B (2015).
  25. J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Roberts & Company Pub., 2006, pp. 25–40).
  26. J. Dupont and X. Orlik, “Simulation of polarized optical speckle fields: effects of the observation scale on polarimetry,” Opt. Express 24, 11151–11163 (2016).
    [Crossref] [PubMed]

2016 (2)

2015 (6)

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

J. Dupont and X. Orlik, “Speckle fields polarimetry: statistical analysis and polarization singularities measurements,” Proc. SPIE 9660, 96601B (2015).

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

R. Ceolato, M. Golzio, C. Riou, X. Orlik, and N. Riviere, “Spectral degree of linear polarization of light from healthy skin and melanoma,” Opt. Express 23, 13605–13612 (2015).
[Crossref] [PubMed]

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

J. Dupont and X. Orlik, “Polarized vortices in optical speckle field: observation of rare polarization singularities,” Opt. Express 23, 6041–6049 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (2)

2012 (1)

2010 (1)

2009 (1)

2007 (1)

R. Gatto and S. R. Jammalamadaka, “The generalized Von Mises distribution,” Stat. Methodol. 4, 341–353 (2007).
[Crossref]

2002 (1)

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

2000 (1)

S. Seager, B. A. Whitney, and D. D. Sasselov, “Photometric light curves and polarization of close-in extrasolar giant planets,” Astrophys. J. 540, 504–520 (2000).
[Crossref]

1996 (1)

P. McCullagh, “Möbius transformation and Cauchy parameter estimation,” Ann. Statist. 24, 787–808 (1996).
[Crossref]

1995 (1)

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref] [PubMed]

1987 (1)

1983 (1)

1977 (1)

M. M. Hall, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10, 66–68 (1977).
[Crossref]

Aas, L. M. S.

Abboud, M.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Abou Nader, C.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Amra, C.

Ceolato, R.

Derode, A.

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref] [PubMed]

Dupont, J.

Elderton, W. D.

W. D. Elderton and N. L. Johnson, Systems of Frequency Curves (Cambridge University, 1969, pp. 77–78).

Ellingsen, P. G.

Extremiana, C.

Fink, M.

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref] [PubMed]

Flamant, P. H.

Frette, Ø.

Gabbach, A.

Gallenne, A.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Gatto, R.

R. Gatto and S. R. Jammalamadaka, “The generalized Von Mises distribution,” Stat. Methodol. 4, 341–353 (2007).
[Crossref]

Ghabbach, A.

Girard, J. H.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Goldstein, D.

D. Goldstein, Polarized Light (CRC Press, 2003, pp. 32–42).

Golzio, M.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Roberts & Company Pub., 2006, pp. 25–40).

Hall, M. M.

M. M. Hall, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10, 66–68 (1977).
[Crossref]

Haner, D. A.

Haubois, X.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Hingerl, K.

Jammalamadaka, S. R.

R. Gatto and S. R. Jammalamadaka, “The generalized Von Mises distribution,” Stat. Methodol. 4, 341–353 (2007).
[Crossref]

Johnson, N. L.

W. D. Elderton and N. L. Johnson, Systems of Frequency Curves (Cambridge University, 1969, pp. 77–78).

Kavaya, M. J.

Kervella, P.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Kildemo, M.

Lagadec, E.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Le Brun, G.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Le Jeune, B.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Li, J.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Liukaityte, S.

Loutfi, H.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Mansour, R.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Maria, J.

McCullagh, P.

P. McCullagh, “Möbius transformation and Cauchy parameter estimation,” Ann. Statist. 24, 787–808 (1996).
[Crossref]

Menzies, R. T.

Montargès, M.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Ohnaka, K.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Oppenheim, U. P.

Orlik, X.

Ossikovski, R.

Pellen, F.

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Perrin, G.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Ridgway, S. T.

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Riou, C.

Riviere, N.

Roux, P.

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref] [PubMed]

Saiz, J. M.

Sanz, J. M.

Sasselov, D. D.

S. Seager, B. A. Whitney, and D. D. Sasselov, “Photometric light curves and polarization of close-in extrasolar giant planets,” Astrophys. J. 540, 504–520 (2000).
[Crossref]

Seager, S.

S. Seager, B. A. Whitney, and D. D. Sasselov, “Photometric light curves and polarization of close-in extrasolar giant planets,” Astrophys. J. 540, 504–520 (2000).
[Crossref]

Soriano, G.

Sorrentini, J.

Stamnes, J. J.

Svensen, Ø.

Tortel, H.

Wang, L. V.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Whitney, B. A.

S. Seager, B. A. Whitney, and D. D. Sasselov, “Photometric light curves and polarization of close-in extrasolar giant planets,” Astrophys. J. 540, 504–520 (2000).
[Crossref]

Yao, G.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Zerrad, M.

Ann. Statist. (1)

P. McCullagh, “Möbius transformation and Cauchy parameter estimation,” Ann. Statist. 24, 787–808 (1996).
[Crossref]

Appl. Opt. (3)

Astron. Astrophys. (1)

P. Kervella, M. Montargès, E. Lagadec, S. T. Ridgway, X. Haubois, J. H. Girard, K. Ohnaka, G. Perrin, and A. Gallenne, “The dust disk and companion of the nearby AGB star L2 Puppis SPHERE/ZIMPOL polarimetric imaging at visible wavelengths,” Astron. Astrophys. 578, A77 (2015).
[Crossref]

Astrophys. J. (1)

S. Seager, B. A. Whitney, and D. D. Sasselov, “Photometric light curves and polarization of close-in extrasolar giant planets,” Astrophys. J. 540, 504–520 (2000).
[Crossref]

J. Appl. Cryst. (1)

M. M. Hall, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10, 66–68 (1977).
[Crossref]

J. Biomed. Opt. (2)

C. Abou Nader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Opt. Express (9)

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[Crossref] [PubMed]

Ø. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and Ø. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards,” Opt. Express 20, 15045–15053 (2012).
[Crossref] [PubMed]

M. Kildemo, J. Maria, P. G. Ellingsen, and L. M. S. Aas, “Parametric model of the Mueller matrix of a Spectralon white reflectance standard deduced by polar decomposition techniques,” Opt. Express 21, 18509–18524 (2013).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

J. Dupont, X. Orlik, A. Gabbach, M. Zerrad, G. Soriano, and C. Amra, “Polarization analysis of speckle field below its transverse correlation width: application to surface and bulk scattering,” Opt. Express 22, 24133–24141 (2014).
[Crossref] [PubMed]

J. Dupont and X. Orlik, “Polarized vortices in optical speckle field: observation of rare polarization singularities,” Opt. Express 23, 6041–6049 (2015).
[Crossref] [PubMed]

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

R. Ceolato, M. Golzio, C. Riou, X. Orlik, and N. Riviere, “Spectral degree of linear polarization of light from healthy skin and melanoma,” Opt. Express 23, 13605–13612 (2015).
[Crossref] [PubMed]

J. Dupont and X. Orlik, “Simulation of polarized optical speckle fields: effects of the observation scale on polarimetry,” Opt. Express 24, 11151–11163 (2016).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref] [PubMed]

Proc. SPIE (1)

J. Dupont and X. Orlik, “Speckle fields polarimetry: statistical analysis and polarization singularities measurements,” Proc. SPIE 9660, 96601B (2015).

Stat. Methodol. (1)

R. Gatto and S. R. Jammalamadaka, “The generalized Von Mises distribution,” Stat. Methodol. 4, 341–353 (2007).
[Crossref]

Other (3)

D. Goldstein, Polarized Light (CRC Press, 2003, pp. 32–42).

W. D. Elderton and N. L. Johnson, Systems of Frequency Curves (Cambridge University, 1969, pp. 77–78).

J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Roberts & Company Pub., 2006, pp. 25–40).

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Figures (7)

Fig. 1
Fig. 1 Schema of the experimental setup. The source is a SLM laser @532nm. The illumination SOP is set to the vertical by Plin. The samples are Lambertian Spectralons, the polarimetric projections of the scattered fields are performed by two Nematic Liquid Crystals (NLC) and a vertical polarizer. The resulting intensity is imaged by a lens, in which the imaging pupil is reduced using a diaphragm P, and a CCD camera.
Fig. 2
Fig. 2 First row: R = 1%, second row: R = 7%, third row: R = 99%. (a, e, i) Intensity I scattered by the samples, expressed in numerical counts. (b, f, j) Totally depolarized intensity and experimental noises C2, expressed in numerical counts. (c, g, k) Relative phase shifts ϕ between the orthogonal plane waves polarized along the x and y directions. (d, h, l) Probability density functions of the measured SOPs represented in the Poincaré sphere.
Fig. 3
Fig. 3 Evolution of the measured spatially integrated D O P ¯ in function of the size of the window of spatial summation, for the 6 different samples with various reflectances. The asymptotic values only depend on the sample reflectance, and correspond to the values that one would measure with a large pupil aperture relatively to the wavelength.
Fig. 4
Fig. 4 Representation of the measured relative phase shifts probability density functions, weighted by the intensity value, for the samples with various reflectances and a mirror as a reference. The PDFs integral are normalized to 1. One can see that when the reflectance increases, the phase distribution tends to be uniform.
Fig. 5
Fig. 5 Evolution of the measured standard deviation σ of the relative phase shifts ϕ in function of the reflectance R of the samples (black crosses). Regression of Eq. (9) on experimental measurements (red). Standard deviation of an uniform distribution on [0; 2π] (black dashed line).
Fig. 6
Fig. 6 Measured ρ parameters (cross, black) of respectively the best circular Voigt (R < 7%) and circular Cauchy (R ≥ 7%) distributions describing the p(ϕ) distributions, for each sample. (red) Regression of the ρ fluctuations with Eq. (11). Dots: mean error between the p(ϕ) distribution and respectively the best circular Voigt (R < 7%) and circular Cauchy (R ≥ 7%) distributions.
Fig. 7
Fig. 7 Measured ρ values for each sample, using a circular Voigt profile for R < 7% and a circular Cauchy profile for R ≥ 7% (red crosses). For the sample R = 1%, we display the ρ measurement using also a circular Cauchy distribution (blue cross). Measured spatially integrated D O P ¯ (black crosses). D O P ¯ and ρ best adjusted Eq. (11) (dashed lines, resp. black and red). Mean level of local depolarization and experimental noises Rc (green dots). One can see a good agreement between ρ and D O P ¯ .

Tables (1)

Tables Icon

Table 1 Diffuse reflectance R of each sample measured using a PerkinElmer Spectrophotometer @ 532 nm.

Equations (14)

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

S = { I = E x 2 + E y 2 + C 2 Q = 2 E x E y cos ( ϕ ) U = E x 2 E y 2 V = 2 E x E y sin ( ϕ )
D O P = Q 2 + U 2 + V 2 I = 1 C 2 I
R x = < I x > < I > R y = < I y > < I > R c = < C 2 > < I >
D O P ¯ = < Q > 2 + < U > 2 + < V > 2 < I >
r x y = m n ( x m n x ¯ ) ( y m n y ¯ ) ( m n ( x m n x ¯ ) 2 ) ( m n ( y m n y ¯ ) 2 )
V M ( ϕ ) = 1 2 π exp ( κ . c o s ( ϕ ϕ 0 ) ) I 0 ( κ ) , 0 ϕ < 2 π
C C ( ϕ ) = 1 2 π 1 ρ 2 1 + ρ 2 2 ρ c o s ( ϕ ϕ 0 ) , 0 ϕ < 2 π
C V = V M C C
σ ( R ) = σ M I N + τ σ τ σ + 1 / R *
e r r = ϕ | y ( ϕ ) p ( ϕ ) | ϕ p ( ϕ )
ρ ( R ) = ρ M I N + τ ρ τ ρ + R *
Q = 0 2 π c o s ( ϕ ) p ( ϕ ) d ϕ V = 0 2 π s i n ( ϕ ) p ( ϕ ) d ϕ
D O P ¯ = ρ
ρ ( R ) = D O P ¯ ( R ) = D O P ¯ M I N + τ d o p τ d o p + R *

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