Abstract

An experimental method for accurate polarimetric characterization of speckle field below its transverse correlation width is proposed. Using a polarimetric analyzer, the speckle field under investigation is probed by a set of polarimetric projections describing the full Poincaré sphere surface. Spatial polarimetric variations of the speckle field are thus observed with an accuracy of 1% for each Stokes parameter. Moreover, all the experimental data can be guaranteed by a validity criterion. Using white paper sheet and rough metal samples, the method exhibits strong potential to analyze and differentiate speckle fields generated by bulk and surface scattering.

© 2014 Optical Society of America

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References

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  1. J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company Pub., 2007) 48–50.
  2. I. Bergoënd, X. Orlik, and E. Lacot, “Study of a circular Gaussian transition in an optical speckle field,” J. Europ. Opt. Soc. 3, 1990–2573 (2008).
    [Crossref]
  3. O. Vasseur, I. Bergoënd, and X. Orlik, “A Gaussian transition of an optical speckle field studied by the minimal spanning tree method,” J. Europ. Opt. Soc. 5, 10052 (2010).
    [Crossref]
  4. P. Bergström, D. Khodadad, E. Hällstig, and M. Sjödahl, “Dual-wavelength digital holography: single-shot shape evaluation using speckle displacements and regularization,” Appl. Opt. 53, 123–131 (2014).
    [Crossref] [PubMed]
  5. J. Petit, G. Montayb, and M. François, “Strain rate measurements by speckle interferometry for necking investigation in stainless steel,” Int. J. Solids Struc. 51, 540–550 (2014).
    [Crossref]
  6. L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).
  7. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Multiscale spatial depolarization of light,” Proc. SPIE 8171, Physical Optics, 81710C (2011)
  8. L. Pouget, J. Fade, C. Hamel, and M. Alouini, “Polarimetric imaging beyond the speckle grain size,” Appl. Opt. 51, 7345–7356 (2012).
    [Crossref] [PubMed]
  9. 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] [PubMed]
  10. G. G. Stokes, Trans. Camb. Phil. Soc., 9, 399 (1852).
  11. D. H. Goldstein, Polarized Light (CRC Press, 2003) 34.
  12. H. Poincaré, Théorie mathématique de la lumière (GABAY, 1892).
  13. 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]
  14. G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22, 12603–12613 (2014).
    [Crossref] [PubMed]

2014 (4)

2013 (1)

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

2012 (1)

2010 (1)

O. Vasseur, I. Bergoënd, and X. Orlik, “A Gaussian transition of an optical speckle field studied by the minimal spanning tree method,” J. Europ. Opt. Soc. 5, 10052 (2010).
[Crossref]

2009 (1)

2008 (1)

I. Bergoënd, X. Orlik, and E. Lacot, “Study of a circular Gaussian transition in an optical speckle field,” J. Europ. Opt. Soc. 3, 1990–2573 (2008).
[Crossref]

Alouini, M.

Amra, C.

Bergoënd, I.

O. Vasseur, I. Bergoënd, and X. Orlik, “A Gaussian transition of an optical speckle field studied by the minimal spanning tree method,” J. Europ. Opt. Soc. 5, 10052 (2010).
[Crossref]

I. Bergoënd, X. Orlik, and E. Lacot, “Study of a circular Gaussian transition in an optical speckle field,” J. Europ. Opt. Soc. 3, 1990–2573 (2008).
[Crossref]

Bergström, P.

Dhadwal, G.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

Fade, J.

François, M.

J. Petit, G. Montayb, and M. François, “Strain rate measurements by speckle interferometry for necking investigation in stainless steel,” Int. J. Solids Struc. 51, 540–550 (2014).
[Crossref]

Ghabbach, A.

Goldstein, D. H.

D. H. Goldstein, Polarized Light (CRC Press, 2003) 34.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company Pub., 2007) 48–50.

Hällstig, E.

Hamel, C.

Kalia, S.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

Khodadad, D.

Lacot, E.

I. Bergoënd, X. Orlik, and E. Lacot, “Study of a circular Gaussian transition in an optical speckle field,” J. Europ. Opt. Soc. 3, 1990–2573 (2008).
[Crossref]

Lee, TL.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

Lui, H.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

McLean, DI.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

Montayb, G.

J. Petit, G. Montayb, and M. François, “Strain rate measurements by speckle interferometry for necking investigation in stainless steel,” Int. J. Solids Struc. 51, 540–550 (2014).
[Crossref]

Orlik, X.

O. Vasseur, I. Bergoënd, and X. Orlik, “A Gaussian transition of an optical speckle field studied by the minimal spanning tree method,” J. Europ. Opt. Soc. 5, 10052 (2010).
[Crossref]

I. Bergoënd, X. Orlik, and E. Lacot, “Study of a circular Gaussian transition in an optical speckle field,” J. Europ. Opt. Soc. 3, 1990–2573 (2008).
[Crossref]

Petit, J.

J. Petit, G. Montayb, and M. François, “Strain rate measurements by speckle interferometry for necking investigation in stainless steel,” Int. J. Solids Struc. 51, 540–550 (2014).
[Crossref]

Poincaré, H.

H. Poincaré, Théorie mathématique de la lumière (GABAY, 1892).

Pouget, L.

Sjödahl, M.

Soriano, G.

Sorrentini, J.

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]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Multiscale spatial depolarization of light,” Proc. SPIE 8171, Physical Optics, 81710C (2011)

Stokes, G. G.

G. G. Stokes, Trans. Camb. Phil. Soc., 9, 399 (1852).

Tchvialeva, L.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

Vasseur, O.

O. Vasseur, I. Bergoënd, and X. Orlik, “A Gaussian transition of an optical speckle field studied by the minimal spanning tree method,” J. Europ. Opt. Soc. 5, 10052 (2010).
[Crossref]

Zeng, H.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

Zerrad, M.

Appl. Opt. (2)

Int. J. Solids Struc. (1)

J. Petit, G. Montayb, and M. François, “Strain rate measurements by speckle interferometry for necking investigation in stainless steel,” Int. J. Solids Struc. 51, 540–550 (2014).
[Crossref]

J. Biomed. Opt. (1)

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, DI. McLean, and TL. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 6, 061211 (2013).

J. Europ. Opt. Soc. (2)

I. Bergoënd, X. Orlik, and E. Lacot, “Study of a circular Gaussian transition in an optical speckle field,” J. Europ. Opt. Soc. 3, 1990–2573 (2008).
[Crossref]

O. Vasseur, I. Bergoënd, and X. Orlik, “A Gaussian transition of an optical speckle field studied by the minimal spanning tree method,” J. Europ. Opt. Soc. 5, 10052 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (5)

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company Pub., 2007) 48–50.

G. G. Stokes, Trans. Camb. Phil. Soc., 9, 399 (1852).

D. H. Goldstein, Polarized Light (CRC Press, 2003) 34.

H. Poincaré, Théorie mathématique de la lumière (GABAY, 1892).

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Multiscale spatial depolarization of light,” Proc. SPIE 8171, Physical Optics, 81710C (2011)

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Figures (5)

Fig. 1
Fig. 1 (a) First polarimetric states of projection homogeneously distributed at the surface of the Poincaré sphere. During the acquisition procedure used for polarimetric analysis, the incident field is projected sequentially on every projection state by the use of the PSA. The green disc corresponds to the SOP of the field that is being analyzed. (b) Simulated variation of intensity at the output of the PSA and corresponding to the projections of the incident field shown in (a). Each curve of intensity variation during such a scan signs a unique incident SOP.
Fig. 2
Fig. 2 Scheme of the experimental setup. A laser diode emits a beam at 532 nm through the Polarization State Generator (PSG) composed of a linear vertical polarizer Plin and a quarter waveplate λ/4 oriented at 45 ° from each other, followed by 2 nematic liquid crystals LC1 and LC2 with their eigen axis oriented at 45 ° from each other. The quarter waveplate of the PSG ensures the ability to generate any Stokes vector on the Poincaré sphere surface, whatever the orientation of the entrance linear polarizer is. After scattering on the sample, the field goes through a pinhole P before entering the PSA that is composed of the same optical elements than the PSG but in reverse order. Its quarter waveplate is not essential but makes our calibration procedure easier by keeping the symmetry between the PSG and the PSA.
Fig. 3
Fig. 3 Representation of the spatial variations of the SOP of a speckle field generated by a rough metallic surface and analyzed in terms of Stokes parameters using (a) subtraction of intensity images and (b) the SOPAFP method. In this RGB color representation, R =|S1|, G =|S2|, B =|S3| where the values of R, G and B vary from 0 to 1. (c) DOP histograms : the red curve corresponds to the classical method and the blue one to the SOPAFP method.
Fig. 4
Fig. 4 For respectively the scattering from a rough metal (upper line) and from a white paper sheet (lower line) : (a) and (e) show the sum of intensity images obtained by the whole set of polarimetric projections, (b) and (f) the degree of polarization with filtered physical results that are encircled by dotted lines, (c) and (g) the RGB representation of polarimetric states, (d) and (h) the Poincaré sphere representation of the full vertical cross section of the middle of respectively figure (c) and (g) as indicated by white dotted lines. The red dots represent the initial states of illumination. An additional cross section analysis named A in (g) is plotted on (h). Polarimetric states remain localized with high DOP values in the case of surface scattering while they spread all over and inside the Poincaré sphere with lower DOP values in the case of bulk scattering.
Fig. 5
Fig. 5 (a) (c) (e) show the DOP histograms of the fields scattered from respectively a mirror, a rough metal sample and a white paper sheet. (b) (d) (f) show the corresponding Poincaré sphere representation of the SOP. The green dots represent the illumination polarimetric states.

Equations (1)

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DOP = S 1 2 + S 2 2 + S 3 2 S 0

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