Abstract

In this paper, we introduce the Mueller matrix imaging concepts for 3D Integral Imaging Polarimetry. The Mueller matrix of a complex scene is measured and estimated with 3D integral imaging. This information can be used to analyze the complex polarimetric behavior of any 3D scene. In particular, we show that the degree of polarization can be estimated at any selected plane for any arbitrary synthetic illumination source which may be difficult to produce in practice. This tool might open new perspectives for polarimetric analysis in the 3D domain. Also, we illustrate that 2D polarimetric images are noisier than 3D reconstructed polarimetric integral imaging. To the best of our knowledge, this is the first report on Mueller matrix polarimetry in 3D Integral Imaging.

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

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2018 (1)

M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512–566 (2018).
[Crossref]

2017 (1)

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

2016 (1)

2015 (2)

W. Freda, J. Piskozub, and H. Toczek, “Polarization imaging over sea surface- a method for measurements of Stokes components angular distribution,” J Eur Opt Soc-Rapid. 10, 15060 (2015).

E. Y. Lam, “Computational photography with plenoptic camera and light field capture: tutorial,” J. Opt. Soc. Am. A 32(11), 2021–2032 (2015).
[Crossref] [PubMed]

2014 (1)

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10(4), 255–262 (2014).
[Crossref]

2013 (1)

2012 (3)

2009 (1)

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (2)

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14(25), 12096–12108 (2006).
[Crossref] [PubMed]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

2004 (5)

2003 (1)

2001 (1)

2000 (1)

1999 (2)

1997 (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
[Crossref]

1995 (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995).
[Crossref]

1993 (1)

C. R. Givens and A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40(3), 471–481 (1993).
[Crossref]

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7(1), 821–825 (1908).
[Crossref]

Arimoto, H.

Azzam, R. M. A.

Bovik, A. C.

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[Crossref] [PubMed]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Burckhardt, C. B.

Chipman, R. A.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995).
[Crossref]

Collet, C.

Dereniak, E. L.

Descour, M. R.

Eismann, M.

Freda, W.

W. Freda, J. Piskozub, and H. Toczek, “Polarization imaging over sea surface- a method for measurements of Stokes components angular distribution,” J Eur Opt Soc-Rapid. 10, 15060 (2015).

Germer, T. A.

Givens, C. R.

C. R. Givens and A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40(3), 471–481 (1993).
[Crossref]

He, X.-F.

X.-F. He, “Polarization-based imaging: Basics and benefits,” Photon. Spectra (2016).

Hong, S. H.

Huang, Y.-P.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Ives, H. E.

Jang, J. S.

Javidi, B.

M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512–566 (2018).
[Crossref]

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10(4), 255–262 (2014).
[Crossref]

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. 52(4), 546–560 (2013).
[Crossref] [PubMed]

X. Xiao, B. Javidi, G. Saavedra, M. Eismann, and M. Martinez-Corral, “Three-dimensional polarimetric computational integral imaging,” Opt. Express 20(14), 15481–15488 (2012).
[Crossref] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational Integral Imaging,” Opt. Express 16(7), 4426–4436 (2008).
[Crossref] [PubMed]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14(25), 12096–12108 (2006).
[Crossref] [PubMed]

J. S. Jang and B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29(11), 1230–1232 (2004).
[Crossref] [PubMed]

S. H. Hong, J. S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12(3), 483–491 (2004).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Three-dimensional polarimetric integral imaging,” Opt. Lett. 29(20), 2375–2377 (2004).
[Crossref] [PubMed]

A. Stern and B. Javidi, “3D image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42(35), 7036–7042 (2003).
[Crossref] [PubMed]

H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26(3), 157–159 (2001).
[Crossref] [PubMed]

Jordan, D. L.

Kattawar, G. W.

Kemme, S. A.

Kostinski, A. B.

C. R. Givens and A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40(3), 471–481 (1993).
[Crossref]

Lam, E. Y.

Latorre-Carmona, P.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Lewis, G. D.

Lippmann, G.

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7(1), 821–825 (1908).
[Crossref]

MacKenty, J. W.

Markman, A. S.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Martínez Sotoca, J.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Martinez-Corral, M.

Martínez-Corral, M.

M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512–566 (2018).
[Crossref]

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10(4), 255–262 (2014).
[Crossref]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Martínez-Uso, A.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Matoba, O.

Mittal, A.

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[Crossref] [PubMed]

Moon, I.

Moorthy, A. K.

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[Crossref] [PubMed]

Navarro, H.

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10(4), 255–262 (2014).
[Crossref]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995).
[Crossref]

Phipps, G. S.

Piskozub, J.

W. Freda, J. Piskozub, and H. Toczek, “Polarization imaging over sea surface- a method for measurements of Stokes components angular distribution,” J Eur Opt Soc-Rapid. 10, 15060 (2015).

Pla, F.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Pons, A.

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10(4), 255–262 (2014).
[Crossref]

Rakovic, M. J.

Roberts, P. J.

Saavedra, G.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10(4), 255–262 (2014).
[Crossref]

X. Xiao, B. Javidi, G. Saavedra, M. Eismann, and M. Martinez-Corral, “Three-dimensional polarimetric computational integral imaging,” Opt. Express 20(14), 15481–15488 (2012).
[Crossref] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Sabatke, D. S.

Sadjadi, F. A.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Shen, X.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Snik, F.

Sparks, W.

Stern, A.

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martínez-Uso, J. Martínez Sotoca, F. Pla, M. Martínez-Corral, G. Saavedra, Y.-P. Huang, and A. Stern, “Multidimensional optical sensing and imaging systems (MOSIS): from macro to micro scales,” Proc. IEEE 105(5), 850–875 (2017).
[Crossref]

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. 52(4), 546–560 (2013).
[Crossref] [PubMed]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

A. Stern and B. Javidi, “3D image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42(35), 7036–7042 (2003).
[Crossref] [PubMed]

Sweatt, W. C.

Takakura, Y.

Tavakoli, B.

Toczek, H.

W. Freda, J. Piskozub, and H. Toczek, “Polarization imaging over sea surface- a method for measurements of Stokes components angular distribution,” J Eur Opt Soc-Rapid. 10, 15060 (2015).

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Watson, E.

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
[Crossref]

Xiao, X.

Yeom, S.

Zallat, J.

Adv. Opt. Photonics (1)

M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512–566 (2018).
[Crossref]

Appl. Opt. (6)

IEEE Trans. Image Process. (2)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[Crossref] [PubMed]

Image Vis. Comput. (1)

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Figures (9)

Fig. 1
Fig. 1 (a) Sketch of the capture system (QWP: quarter wave plate, LP: linear polarizer, LED: light emitting diode), and (b) the scene used in the experiments. The Lytro Illum camera captures the perspective images for 3D reconstruction.
Fig. 2
Fig. 2 Experimental evaluation of the 3D DoP out (i,j)at plane F. The six images of the DoP out (i,j)have been obtained when the scene is illuminated using input polarized light according to Table 1 or Eq. (7).
Fig. 3
Fig. 3 Experimental evaluation of the DoP out (i,j)at plane N.
Fig. 4
Fig. 4 Numerical estimation of the DoP est (i,j)at plane F.
Fig. 5
Fig. 5 Numerical estimation of the DoP est (i,j)at plane N.
Fig. 6
Fig. 6 Experimental evaluation of DoP out (i,j)using a single frame of the 3D camera.
Fig. 7
Fig. 7 Numerical estimation of DoP est (i,j) using a single frame of the 3D camera.
Fig. 8
Fig. 8 Experimental evaluation of DoP out (i,j)using a conventional 2D camera.
Fig. 9
Fig. 9 Numerical estimation of DoP est (i,j) at plane F using synthetic polarized light.

Tables (3)

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Table 1 Polarization States of the Input Illumination

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Table 2 SSIM and Normalized Correlation between DoP out (i,j) and DoP est (i,j)

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Table 3 BRISQUE Values for the DOP Imagesa

Equations (10)

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S out (i,j)=M(i,j) S inp
S 1 out ( L k ;i,j)= I 0 ( L k ;i,j) I 90 ( L k ;i,j), S 2 out ( L k ;i,j)= I 45 ( L k ;i,j) I 135 ( L k ;i,j).
S 3 out ( L k ;i,j)= I RC ( L k ;i,j) I LC ( L k ;i,j)
S 0 out ( L k ;i,j)= I 0 ( L k ;i,j)+ I 90 ( L k ;i,j), S 0 out ( L k ;i,j)= I 45 ( L k ;i,j)+ I 135 ( L k ;i,j), S 0 out ( L k ;i,j)= I RC ( L k ;i,j)+ I LC ( L k ;i,j).
S 0 out ( L k ;i,j)= 1 3 ( I 0 ( L k ;i,j)+ I 90 ( L k ;i,j)+ I 45 ( L k ;i,j)+ I 135 ( L k ;i,j)+ I RC ( L k ;i,j)+ I LC ( L k ;i,j)).
DoP( L k ;i,j )= S 1 out ( L k ;i,j ) 2 + S 2 out ( L k ;i,j ) 2 + S 3 out ( L k ;i,j ) 2 S 0 out ( L k ;i,j ) .
V inp =( 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 )
V out ( i,j )=( S 0 ( L 1 ;i,j) S 1 ( L 1 ;i,j) S 2 ( L 1 ;i,j) S 3 ( L 1 ;i,j) S 0 ( L 2 ;i,j) S 1 ( L 2 ;i,j) S 2 ( L 2 ;i,j) S 3 ( L 2 ;i,j) S 0 ( L 3 ;i,j) S 1 ( L 3 ;i,j) S 2 ( L 3 ;i,j) S 3 ( L 3 ;i,j) S 0 ( L 4 ;i,j) S 1 ( L 4 ;i,j) S 2 ( L 4 ;i,j) S 3 ( L 4 ;i,j) S 0 ( L 5 ;i,j) S 1 ( L 5 ;i,j) S 2 ( L 5 ;i,j) S 3 ( L 5 ;i,j) S 0 ( L 6 ;i,j) S 1 ( L 6 ;i,j) S 2 ( L 6 ;i,j) S 3 ( L 6 ;i,j) ).
V out (i,j)=M(i,j) V inp .
V est (i,j)= M est (i,j) V inp

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