Abstract

The recording and reconstruction of the Stokes parameter is of paramount importance for the description of the vectorial interference of light. Polarization holography provides a complete vectorial wavefront, however, direct recording and reconstruction of the hologram is not possible in a situation where the object is located behind the random scattering layer. The Stokes holography plays an important role in such situations and makes use of the Fourier transform relation between the Stokes parameters (SPs) at the scattering plane and the generalized Stokes parameters (GSPs) of the random field. In this paper, we propose and experimentally demonstrate the Stokes holography with the Hanbury Brown-Twiss (HBT) interferometer. We also propose and implement a lensless Fourier configuration for the Stokes holography. This permits us to reconstruct the wavefront from the GSPs at any arbitrary distance from the scattering plane. The application of the proposed technique is experimentally demonstrated for the 3D imaging of two different objects lying behind the random scattering medium. Depth information of the 3D objects is obtained by digitally propagating the generalized Stokes parameters to a different longitudinal distance. The quality of the reconstruction is assessed by measuring the overall visibility, efficiency, and PSNR of the reconstruction parameters.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2017 (3)

R. K. Singh, S. Vyas, and Y. Miyamoto, “Lensless Fourier transform holography for coherence waves,” J. Opt. 19(11), 115705 (2017).
[Crossref]

A. S. Somkuwar, B. Das, R. V. Vinu, Y. Park, and R. K. Singh, “Holographic imaging through a scattering layer using speckle interferometry,” J. Opt. Soc. Am. A 34(8), 1392–1399 (2017).
[Crossref] [PubMed]

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

2016 (2)

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

N. K. Soni, R. V. Vinu, and R. K. Singh, “Polarization modulation for imaging behind the scattering medium,” Opt. Lett. 41(5), 906–909 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (4)

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

M. Takeda, W. Wang, D. N. Naik, and R. K. Singh, “Spatial statistical optics and spatial correlation holography: A review,” Opt. Rev. 21(6), 849–861 (2014).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

R. K. Singh, A. M. Sharma, and B. Das, “Quantitative phase-contrast imaging through a scattering media,” Opt. Lett. 39(17), 5054–5057 (2014).
[Crossref] [PubMed]

2013 (2)

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

2012 (3)

2011 (2)

2010 (4)

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

S. Sahin, “Generalized Stokes parameters in phase space,” Opt. Lett. 35(10), 1704–1706 (2010).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

M. Takeda, W. Wang, and S. G. Hanson, “Polarization speckles and generalized Stokes vector wave: a review,” Proc. SPIE 7387, 73870V (2010).
[Crossref]

2008 (1)

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78(3), 033817 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2002 (1)

2001 (1)

1965 (2)

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6(10), 201–203 (1965).
[Crossref]

A. W. Lohmann, “Reconstruction of vectorial wavefronts,” Appl. Opt. 4(12), 1667–1668 (1965).
[Crossref]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, “Correlations between photons in 2 coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Banerji, J.

A. Kumar, J. Banerji, and R. P. Singh, “Hanbury Brown–Twiss-type experiments with optical vortices and observation of modulated intensity correlation on scattering from rotating ground glass,” Phys. Rev. A 86(1), 013815 (2012).
[Crossref]

Beghuin, D.

Bifano, T.

Bokor, J.

Boutu, W.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Brasselet, S.

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Carré, B.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Cho, C. H.

Choi, W.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Colomb, T.

Cuche, E.

Dahlgren, P.

Das, B.

Dasari, R. R.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

de Aguiar, H. B.

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Depeursinge, C.

Ezawa, T.

Feld, M. S.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Fienup, J. R.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Friberg, A. T.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78(3), 033817 (2008).
[Crossref]

T. Setälä, J. Tervo, and A. T. Friberg, “Contrasts of Stokes parameters in Young’s interference experiment and electromagnetic degree of coherence,” Opt. Lett. 31(18), 2669–2671 (2006).
[Crossref] [PubMed]

Gauthier, D.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Ge, X.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Gigan, S.

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Goldberg, K. A.

Guizar-Sicairos, M.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, “Correlations between photons in 2 coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Hanson, S. G.

M. Takeda, W. Wang, and S. G. Hanson, “Polarization speckles and generalized Stokes vector wave: a review,” Proc. SPIE 7387, 73870V (2010).
[Crossref]

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Hillman, T. R.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Itou, H.

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Stokes holography,” Opt. Lett. 37(5), 966–968 (2012).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vectorial coherence holography,” Opt. Express 19(12), 11558–11567 (2011).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

Javidi, B.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32(5), 481–483 (2007).
[Crossref] [PubMed]

Jeong, S.

Kaivola, M.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78(3), 033817 (2008).
[Crossref]

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Korotkova, O.

Kumar, A.

A. Kumar, J. Banerji, and R. P. Singh, “Hanbury Brown–Twiss-type experiments with optical vortices and observation of modulated intensity correlation on scattering from rotating ground glass,” Phys. Rev. A 86(1), 013815 (2012).
[Crossref]

Lee, S. H.

Lohmann, A. W.

Marquet, P.

Merdji, H.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Miyamoto, Y.

R. K. Singh, S. Vyas, and Y. Miyamoto, “Lensless Fourier transform holography for coherence waves,” J. Opt. 19(11), 115705 (2017).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Stokes holography,” Opt. Lett. 37(5), 966–968 (2012).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vectorial coherence holography,” Opt. Express 19(12), 11558–11567 (2011).
[Crossref] [PubMed]

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19(2), 1408–1421 (2011).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

Murata, S.

Naik, D. N.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

M. Takeda, W. Wang, D. N. Naik, and R. K. Singh, “Spatial statistical optics and spatial correlation holography: A review,” Opt. Rev. 21(6), 849–861 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Stokes holography,” Opt. Lett. 37(5), 966–968 (2012).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vectorial coherence holography,” Opt. Express 19(12), 11558–11567 (2011).
[Crossref] [PubMed]

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19(2), 1408–1421 (2011).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

Naulleau, P.

Nitanai, E.

Nomura, T.

Numata, T.

Osten, O.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

Osten, W.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Park, Y.

A. S. Somkuwar, B. Das, R. V. Vinu, Y. Park, and R. K. Singh, “Holographic imaging through a scattering layer using speckle interferometry,” J. Opt. Soc. Am. A 34(8), 1392–1399 (2017).
[Crossref] [PubMed]

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Paxman, R.

Pedrini, G.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Sahin, S.

Setälä, T.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78(3), 033817 (2008).
[Crossref]

T. Setälä, J. Tervo, and A. T. Friberg, “Contrasts of Stokes parameters in Young’s interference experiment and electromagnetic degree of coherence,” Opt. Lett. 31(18), 2669–2671 (2006).
[Crossref] [PubMed]

Sharma, A. M.

Shevchenko, A.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78(3), 033817 (2008).
[Crossref]

Singh, A. K.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

Singh, R. K.

R. K. Singh, S. Vyas, and Y. Miyamoto, “Lensless Fourier transform holography for coherence waves,” J. Opt. 19(11), 115705 (2017).
[Crossref]

A. S. Somkuwar, B. Das, R. V. Vinu, Y. Park, and R. K. Singh, “Holographic imaging through a scattering layer using speckle interferometry,” J. Opt. Soc. Am. A 34(8), 1392–1399 (2017).
[Crossref] [PubMed]

N. K. Soni, R. V. Vinu, and R. K. Singh, “Polarization modulation for imaging behind the scattering medium,” Opt. Lett. 41(5), 906–909 (2016).
[Crossref] [PubMed]

R. V. Vinu and R. K. Singh, “Experimental determination of generalized Stokes parameters,” Opt. Lett. 40(7), 1227–1230 (2015).
[Crossref] [PubMed]

R. K. Singh, A. M. Sharma, and B. Das, “Quantitative phase-contrast imaging through a scattering media,” Opt. Lett. 39(17), 5054–5057 (2014).
[Crossref] [PubMed]

M. Takeda, W. Wang, D. N. Naik, and R. K. Singh, “Spatial statistical optics and spatial correlation holography: A review,” Opt. Rev. 21(6), 849–861 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Stokes holography,” Opt. Lett. 37(5), 966–968 (2012).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vectorial coherence holography,” Opt. Express 19(12), 11558–11567 (2011).
[Crossref] [PubMed]

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19(2), 1408–1421 (2011).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

Singh, R. P.

A. Kumar, J. Banerji, and R. P. Singh, “Hanbury Brown–Twiss-type experiments with optical vortices and observation of modulated intensity correlation on scattering from rotating ground glass,” Phys. Rev. A 86(1), 013815 (2012).
[Crossref]

Situ, G.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Somkuwar, A. S.

Soni, N. K.

Stroke, G. W.

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6(10), 201–203 (1965).
[Crossref]

Takeda, M.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

M. Takeda, W. Wang, D. N. Naik, and R. K. Singh, “Spatial statistical optics and spatial correlation holography: A review,” Opt. Rev. 21(6), 849–861 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Stokes holography,” Opt. Lett. 37(5), 966–968 (2012).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vectorial coherence holography,” Opt. Express 19(12), 11558–11567 (2011).
[Crossref] [PubMed]

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19(2), 1408–1421 (2011).
[Crossref] [PubMed]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

M. Takeda, W. Wang, and S. G. Hanson, “Polarization speckles and generalized Stokes vector wave: a review,” Proc. SPIE 7387, 73870V (2010).
[Crossref]

Tervo, J.

Toussaint, K. C.

Tripathi, S.

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, “Correlations between photons in 2 coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Vinu, R. V.

Vyas, S.

R. K. Singh, S. Vyas, and Y. Miyamoto, “Lensless Fourier transform holography for coherence waves,” J. Opt. 19(11), 115705 (2017).
[Crossref]

Wang, D.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Wang, W.

M. Takeda, W. Wang, D. N. Naik, and R. K. Singh, “Spatial statistical optics and spatial correlation holography: A review,” Opt. Rev. 21(6), 849–861 (2014).
[Crossref]

M. Takeda, W. Wang, and S. G. Hanson, “Polarization speckles and generalized Stokes vector wave: a review,” Proc. SPIE 7387, 73870V (2010).
[Crossref]

Wolf, E.

Yamauchi, T.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Yaqoob, Z.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6(10), 201–203 (1965).
[Crossref]

J. Opt. (2)

R. K. Singh, S. Vyas, and Y. Miyamoto, “Lensless Fourier transform holography for coherence waves,” J. Opt. 19(11), 115705 (2017).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Characterization of spatial polarization fluctuations in scattered field,” J. Opt. 16(10), 105010 (2014).
[Crossref]

J. Opt. Soc. Am. A (1)

Light Sci. Appl. (1)

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and O. Osten, “Exploiting scattering media for exploring 3D objects,” Light Sci. Appl. 6(2), e16219 (2016).
[Crossref]

Nat. Photonics (1)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Nature (1)

R. Hanbury Brown and R. Q. Twiss, “Correlations between photons in 2 coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Opt. Commun. (1)

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier-transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (8)

Opt. Rev. (1)

M. Takeda, W. Wang, D. N. Naik, and R. K. Singh, “Spatial statistical optics and spatial correlation holography: A review,” Opt. Rev. 21(6), 849–861 (2014).
[Crossref]

Phys. Rev. A (2)

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78(3), 033817 (2008).
[Crossref]

A. Kumar, J. Banerji, and R. P. Singh, “Hanbury Brown–Twiss-type experiments with optical vortices and observation of modulated intensity correlation on scattering from rotating ground glass,” Phys. Rev. A 86(1), 013815 (2012).
[Crossref]

Phys. Rev. Lett. (1)

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105(9), 093901 (2010).
[Crossref] [PubMed]

Proc. SPIE (2)

M. Takeda, W. Wang, and S. G. Hanson, “Polarization speckles and generalized Stokes vector wave: a review,” Proc. SPIE 7387, 73870V (2010).
[Crossref]

R. K. Singh, D. N. Naik, H. Itou, Y. Miyamoto, and M. Takeda, “Vortices in generalized Stokes parameters,” Proc. SPIE 7782, 778209 (2010).
[Crossref]

Sci. Adv. (1)

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Sci. Rep. (1)

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
[Crossref] [PubMed]

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J. W. Goodman, Statistical Optics, 1st Ed (Wiley, 1985).

Q. Huynh-Thu, M. Ghanbari, “Scope of validity of PSNR in image/video quality assessment,” Elec. Lett. 44, 800 (2008).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (Mc-Graw Hill, 1996).

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

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Figures (6)

Fig. 1
Fig. 1 Conceptual diagram shows the propagation of light from the scatter plane 1 to an observation plane 2. Here p stands for orthogonal polarization vector in x and y direction.
Fig. 2
Fig. 2 Experimental set-up for the lensless Stokes holography. MO: microscope objective; S: pinhole; (L): lens; BS: beam splitter; SLM: spatial light modulator; GG: ground glass; (M): mirror; QWP: quarter wave plate; LP: linear polarizer; CCD: charge coupled device.
Fig. 3
Fig. 3 (a) Formation of Fourier hologram. (b). Set of two objects with longitudinal distance of 50mm, and its Fourier transform hologram.
Fig. 4
Fig. 4 Raw intensity speckle images recorded in CCD.
Fig. 5
Fig. 5 Imaging of a 3D object through a scattering media. Figures 5(a)-5(h) are the elements of GSPs and their amplitude distribution (a) S 0 (Δr), (b) S 1 (Δr), (c) S 2 (Δr), and (d) S 3 (Δr)at z = 280mm plane and (e) S 0 (Δr), (f) S 1 (Δr), (g) S 2 (Δr), and (h) S 3 (Δr)at z = 330mm plane. (i) Shows the reconstructed phase of the two objects. (j) 3D representative diagram showing focusing of the two objects with depth separation of ∆�� = 50mm.
Fig. 6
Fig. 6 Imaging of an object through a scattering media. Figures 6(a)-6(h) are the elements of GSPs and their amplitude distribution (a) S 0 (Δr), (b) S 1 (Δr), (c) S 2 (Δr), and (d) S 3 (Δr)at z = 280mm plane and (e) S 0 (Δr), (f) S 1 (Δr), (g) S 2 (Δr), and (h) S 3 (Δr) at z = 310mm plane (i) Shows the reconstructed phase of the object. (j) 3D representative diagram showing focusing of the object with different depth separations.

Equations (19)

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E p ( r ^ )=| E p ( r ^ ) |exp[ i( ϕ p ( r ^ )+φ( r ^ ) ) ]
E p (r,z)= E p ( r ^ )exp( i k z ( r ^ )z )exp( i 2π λf r r ^ )
W pp' ( r 1 , z 1 ; r 1 +Δr, z 2 )= E p * ( r 1 , z 1 ) E p' ( r 1 +Δr, z 2 ) s = E p * ( r ^ 1 ) E p' ( r ^ 2 ) exp( i k z ( r ^ 1 ) z 1 )exp( i k z ( r ^ 2 ) z 2 ) ×exp( i 2π λf ( ( r ^ 2 r ^ 1 ) r 1 + r ^ 2 Δr ) )d r ^ 1 d r ^ 2 d r 1 = E p * ( r ^ ) E p' ( r ^ )exp[ i k z ( r ^ )Δz ]exp( i 2π λf Δr r ^ )d r ^
S 0 ( r 1 , r 2 )= E x * ( r 1 ) E x ( r 2 ) + E y * ( r 1 ) E y ( r 2 ) S 1 ( r 1 , r 2 )= E x * ( r 1 ) E x ( r 2 ) E y * ( r 1 ) E y ( r 2 ) S 2 ( r 1 , r 2 )= E x * ( r 1 ) E y ( r 2 ) + E y * ( r 1 ) E x ( r 2 ) S 3 ( r 1 , r 2 )=i[ E y * ( r 1 ) E x ( r 2 ) E x * ( r 1 ) E y ( r 2 ) ]
S n (Δr,Δz)= s n ( r ^ )exp[ i k z ( r ^ )Δz ]exp[ i 2π λf r ^ Δr ] d r ^
E p (r)= E p 1 ( r ^ ) G(r, r ^ )d r ^ + E p 2 ( r ^ )G(r, r ^ )d r ^
G(r, r ^ ) exp(ikz) iλz exp( ik | r | 2 2r r ^ + | r ^ | 2 2z )
E p (r)=exp( ik | r | 2 2z ) E p 1 ( r ^ )exp( i k 2z | r ^ | 2 )exp( i k z r r ^ )d r ^ +exp( ik | r | 2 2z ) E p 2 ( r ^ )exp( i k 2z | r ^ | 2 )exp( i k z r r ^ )d r ^
S 0 ( r 1 , r 2 )= [ ( E x 1 ( r ^ 1 )+ E x 2 ( r ^ 1 ) )( E x 1 ( r ^ 2 )+ E x 2 ( r ^ 2 ) )× exp( i k 2z ( | r ^ 2 | 2 | r ^ 1 | 2 ) )exp( i k z ( r 2 r ^ 2 r 1 r ^ 1 ) ) ]d r ^ 1 d r ^ 2 d r 1 + [ ( E y 1 ( r ^ 1 )+ E y 2 ( r ^ 1 ) )( E y 1 ( r ^ 2 )+ E y 2 ( r ^ 2 ) )× exp( i k 2z ( | r ^ 2 | 2 | r ^ 1 | 2 ) )exp( i k z ( r 2 r ^ 2 r 1 r ^ 1 ) ) ]d r ^ 1 d r ^ 2 d r 1
S 0 ( r 1 , r 2 )= [ E x 1* ( r ^ ) E x 1 ( r ^ )+ E y 1* ( r ^ ) E y 1 ( r ^ ) ]exp( i k z ( r 2 r 1 ) r ^ ) d r ^ + [ E x 2* ( r ^ ) E x 2 ( r ^ )+ E y 2* ( r ^ ) E y 2 ( r ^ ) ]exp( i k z ( r 2 r 1 ) r ^ ) d r ^
S n ( r 1 , r 2 )= s n 1 ( r ^ )exp( i k z ( r 2 r 1 ) r ^ )d r ^ + s n 2 ( r ^ )exp( i k z ( r 2 r 1 ) r ^ )d r ^
S n ( r 1 , r 2 )= S n 1 ( r 1 , r 2 )+ S n 2 ( r 1 , r 2 ).
Γ( r 1 , r 2 )= ΔI( r 1 )ΔI( r 2 ) = 1 2 n=0 3 | S n ( r 1 , r 2 ) | 2
E θ (r,z)=[ cos 2 θ+isinθ ] E x (r,z)+[ (1i)cosθsinθ ] E y (r,z)
Γ( r 1 , r 2 ,θ)= | S 0 ( r 1 , r 2 )+ S 1 ( r 1 , r 2 ) cos 2 2θ+ S 2 ( r 1 , r 2 ) sin 2 4θ 2 + S 2 ( r 1 , r 2 )sin2θ | 2
Γ( r 1 , r 2 , θ 1 )= | S 0 ( r 1 , r 2 )+ S 1 ( r 1 , r 2 ) | 2 Γ( r 1 , r 2 , θ 2 )= | S 0 ( r 1 , r 2 )+ S 1 ( r 1 , r 2 ) 2 + S 2 ( r 1 , r 2 ) 2 + S 3 ( r 1 , r 2 ) 2 | 2 Γ( r 1 , r 2 , θ 3 )= | S 0 ( r 1 , r 2 )+ S 3 ( r 1 , r 2 ) | 2 Γ( r 1 , r 2 , θ 4 )= | S 0 ( r 1 , r 2 ) S 3 ( r 1 , r 2 ) | 2
V obj = I O avg I B avg
η= I O avg I O avg + I B avg
PSNR=10 log 10 MA X o 2 MSE

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