Abstract

We address an experimental Stokes imaging setup allowing one to explore the polarimetric properties of a speckle light field with spatial resolution well beyond the speckle grain scale. We detail how the various experimental difficulties inherent to such measurements can be overcome with a dedicated measurement protocol involving a careful speckle registration step. The setup and protocol are then validated on a metallic reference sample, and used to measure the state of polarization (SOP) of light in each pixel of highly resolved speckle patterns (>2000 pixels per speckle grain) resulting from the scattering of an incident coherent beam on samples exhibiting different polarimetric properties. Evolution of the SOP with spatial averaging and across adjacent speckle grains is eventually addressed.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  35. M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
    [CrossRef]
  36. M. S. Soskin, V. Denisenko, and I. Freund, “Optical polarization singularities and elliptic stationary points,” Opt. Lett. 28, 1475–1477 (2003).
    [CrossRef]

2012 (1)

2011 (3)

2010 (4)

J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18, 20105–20113 (2010).
[CrossRef]

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]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of two-photon speckle patterns,” Phys. Rev. Lett. 104, 173601 (2010).
[CrossRef]

2009 (4)

2008 (3)

M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
[CrossRef]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[CrossRef]

2007 (2)

2005 (1)

2004 (1)

2003 (1)

2002 (2)

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

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

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]

1999 (2)

1995 (1)

M. Lehman, J. A. Pomarico, and R. D. Torroba, “Digital speckle pattern interferometry applied to a surface roughness study,” Opt. Eng. 34, 1148–1152 (1995).
[CrossRef]

1992 (1)

1990 (1)

1989 (1)

N. Garcia and A. Z. Genack, “Crossover to strong intensity correlation for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678–1681 (1989).
[CrossRef]

1984 (1)

J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the K-distribution,” IEEE Trans. Antennas Propag. AP-32, 1049–1062 (1984).
[CrossRef]

1975 (1)

1972 (1)

Alouini, M.

Amra, C.

Andrés, N.

Angelsky, O. V.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Arroyo, M. P.

Baarstad, I.

Béniére, A.

Berginc, G.

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Bondareff, P.

Bourderionnet, J.

Breugnot, S.

M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
[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]

Broky, J.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

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]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, 1993).

Compain, E.

Curry, N.

Denisenko, V.

Deumié, C.

Dogariu, A.

Dolfi, D.

Drevillon, B.

Ellis, J.

Fade, J.

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Freund, I.

Friberg, A. T.

J. Tervo, T. Setälä, A. Roueff, P. Réfrégier, and A. T. Friberg, “Two-point stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[CrossRef]

Garcia, N.

N. Garcia and A. Z. Genack, “Crossover to strong intensity correlation for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678–1681 (1989).
[CrossRef]

Genack, A. Z.

S. Zhang, Y. D. Lockerman, J. Park, and A. Z. Genack, “Interplay between generic and mesoscopic speckle statistics in transmission through random media,” J. Opt. A 11, 094018 (2009).
[CrossRef]

N. Garcia and A. Z. Genack, “Crossover to strong intensity correlation for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678–1681 (1989).
[CrossRef]

Georges, G.

Gigan, S.

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena: Theory and Applications (Roberts & Company, 2007).

Goudail, F.

Grésillon, S.

Grisard, A.

Hartemann, P.

M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
[CrossRef]

Hinrichs, H.

Jao, J. K.

J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the K-distribution,” IEEE Trans. Antennas Propag. AP-32, 1049–1062 (1984).
[CrossRef]

Kaivola, M.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[CrossRef]

Kaspersen, P.

Korotkova, O.

Le Hors, L.

M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
[CrossRef]

Leclercq, M.

Léger, D.

Lehman, M.

M. Lehman, J. A. Pomarico, and R. D. Torroba, “Digital speckle pattern interferometry applied to a surface roughness study,” Opt. Eng. 34, 1148–1152 (1995).
[CrossRef]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Li, J.

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

Lockerman, Y. D.

S. Zhang, Y. D. Lockerman, J. Park, and A. Z. Genack, “Interplay between generic and mesoscopic speckle statistics in transmission through random media,” J. Opt. A 11, 094018 (2009).
[CrossRef]

Løke, T.

Mathieu, E.

Moerman, J. J. D.

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of two-photon speckle patterns,” Phys. Rev. Lett. 104, 173601 (2010).
[CrossRef]

Mokhun, A. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Mokhun, I. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Normandin, X.

Park, J.

S. Zhang, Y. D. Lockerman, J. Park, and A. Z. Genack, “Interplay between generic and mesoscopic speckle statistics in transmission through random media,” J. Opt. A 11, 094018 (2009).
[CrossRef]

Peeters, W. H.

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of two-photon speckle patterns,” Phys. Rev. Lett. 104, 173601 (2010).
[CrossRef]

Perrin, J. C.

Poirier, S.

Pomarico, J. A.

M. Lehman, J. A. Pomarico, and R. D. Torroba, “Digital speckle pattern interferometry applied to a surface roughness study,” Opt. Eng. 34, 1148–1152 (1995).
[CrossRef]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Quintanilla, M.

Réfrégier, P.

Roche, M.

Roueff, A.

Roux, N.

M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
[CrossRef]

Sapienza, R.

Setälä, T.

J. Tervo, T. Setälä, A. Roueff, P. Réfrégier, and A. T. Friberg, “Two-point stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[CrossRef]

Sheng, P.

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd ed. (Springer, 2006).

Shevchenko, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[CrossRef]

Siozade, L.

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems, 3rd ed. (McGraw-Hill, 2001).

Soriano, G.

Sorrentini, J.

Soskin, M. S.

M. S. Soskin, V. Denisenko, and I. Freund, “Optical polarization singularities and elliptic stationary points,” Opt. Lett. 28, 1475–1477 (2003).
[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Sprague, R. A.

Tervo, J.

Torroba, R. D.

M. Lehman, J. A. Pomarico, and R. D. Torroba, “Digital speckle pattern interferometry applied to a surface roughness study,” Opt. Eng. 34, 1148–1152 (1995).
[CrossRef]

van Exter, M. P.

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of two-photon speckle patterns,” Phys. Rev. Lett. 104, 173601 (2010).
[CrossRef]

van Hulst, N. F.

Wang, L. V.

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

Wolf, E.

Yao, G.

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

Zerrad, M.

Zhang, S.

S. Zhang, Y. D. Lockerman, J. Park, and A. Z. Genack, “Interplay between generic and mesoscopic speckle statistics in transmission through random media,” J. Opt. A 11, 094018 (2009).
[CrossRef]

Appl. Opt. (5)

Eur. Phys. J. Appl. Phys. (1)

M. Alouini, F. Goudail, N. Roux, L. Le Hors, P. Hartemann, S. Breugnot, and D. Dolfi, “Active spectro-polarimetric imaging: signature modeling, imaging demonstrator and target detection,” Eur. Phys. J. Appl. Phys. 42, 129–139 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the K-distribution,” IEEE Trans. Antennas Propag. AP-32, 1049–1062 (1984).
[CrossRef]

J. Biomed. Opt. (1)

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

J. Opt. A (1)

S. Zhang, Y. D. Lockerman, J. Park, and A. Z. Genack, “Interplay between generic and mesoscopic speckle statistics in transmission through random media,” J. Opt. A 11, 094018 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

M. Lehman, J. A. Pomarico, and R. D. Torroba, “Digital speckle pattern interferometry applied to a surface roughness study,” Opt. Eng. 34, 1148–1152 (1995).
[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]

Opt. Express (5)

Opt. Lett. (9)

Phys. Rev. A (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[CrossRef]

Phys. Rev. E (1)

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of two-photon speckle patterns,” Phys. Rev. Lett. 104, 173601 (2010).
[CrossRef]

N. Garcia and A. Z. Genack, “Crossover to strong intensity correlation for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678–1681 (1989).
[CrossRef]

Other (4)

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd ed. (Springer, 2006).

J. W. Goodman, Speckle Phenomena: Theory and Applications (Roberts & Company, 2007).

M. I. Skolnik, Introduction to Radar Systems, 3rd ed. (McGraw-Hill, 2001).

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, 1993).

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Figures (12)

Fig. 1.
Fig. 1.

Experimental setup (see text for details).

Fig. 2.
Fig. 2.

Schematic description of the PA in a linear analyzer configuration. The PA mechanical mount provides two angular degrees of freedom (rotation θ about axis e⃗x and rotation ψ about axis e⃗y) used during the speckle registration procedure.

Fig. 3.
Fig. 3.

Reference speckle intensity pattern (a) acquired on a metallic slab, (b) wavefront distortions caused by rotation of the PA modify the speckle intensity pattern, and (c) the reference speckle pattern can be fairly recovered after speckle registration.

Fig. 4.
Fig. 4.

Contour plots: speckle intensity patterns observed after speckle registration with four orientations of the PA on a metallic reference slab. Grayscale background image: total intensity image S0.

Fig. 5.
Fig. 5.

Time evolution of the intensity of 10 pixels in a speckle intensity pattern with perturbations when the sample is a metallic slab. (1) Cover is opened and air is blown inside, (2) 360° rotation about e⃗z of the PA, and (3) 360° rotation about e⃗y of the PA.

Fig. 6.
Fig. 6.

Time evolution (30 min) of the intensity of 10 pixels when the sample is a cardboard sheet sample.

Fig. 7.
Fig. 7.

Time evolution (20 min) of the intensity of 10 pixels when the sample is a red paint deposited on a heavy marble block.

Fig. 8.
Fig. 8.

Schematic illustration of (a) surface and (b) volume scattering regimes obtained by scattering of a green illumination on red and green samples, respectively. The white arrows symbolize the electric field polarization direction.

Fig. 9.
Fig. 9.

Stokes imaging of a speckle intensity pattern obtained on the metallic reference slab. (a) Example of raw image acquisition (Ix) and selection of the ROI. From the six acquisitions, the four Stokes images are determined. (b) First Stokes image S0 (total intensity). Two sub-ROIs are defined to compare the SOP in distinct speckle grains. (c) Second normalized Stokes image S1. (d) Third normalized Stokes image S2. (e) Fourth normalized Stokes image S3. (f) DOP. Total intensity repartition is indicated in contour plots in (c), (d), (e), and (f) thumbnails.

Fig. 10.
Fig. 10.

Stokes imaging beyond the speckle grain scale of a speckle intensity pattern obtained on a red paint sample [(a), (c), and (e)] and a green paint sample [(b), (d), and (f)]. (a), (b) First Stokes image S0 (total intensity). Two sub-ROIs are defined to compare the SOP in distinct speckle grains. (c), (d) Map of the computed DOP. (e), (f) Map of the computed OSC. Total intensity repartition is indicated in contour plots in (c), (d), (e), and (f) thumbnails.

Fig. 11.
Fig. 11.

Repartition of the pixels SOP on Poincaré’s sphere for a metallic sample (first line), a red paint sample (second line), and a green paint sample (third line). First column, SOP in the whole ROI; second column, SOP in sub-ROI 1; third column, SOP in sub-ROI 2. Sub-ROIs are respectively defined in Figs. 9(b), 10(a), and 10(b).

Fig. 12.
Fig. 12.

Observation of the adiabatic polarization state transition along the geometrical path defined in Fig. 10(b) between two adjacent speckle grains on the green paint sample exhibiting bulk scattering regime. (a) Evolution of the SOP on Poincaré’s sphere. (b) Evolution of the OSC (dotted curve) and DOP (plain curve).

Tables (2)

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Table 1. Large Scale Polarimetric Characterization of Light Backscattered by the Three Samples Considereda

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Table 2. Average Value of the DOP and of the OSC for Different Binning Pitchesa

Equations (5)

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S=(S0=Ix+IyS1=IxIyS2=I+45°I45°S3=IRIL).
DOP=S12+S22+S32S0=S12+S22+S32,
OSC=S1S0=S1,
δ=1.22λ2Dϕ0.4mm,
c=IσI,

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