Abstract

Underwater target detection is investigated by combining active polarization imaging and optical correlation-based approaches. Experiments were conducted in a glass tank filled with tap water with diluted milk or seawater and containing targets of arbitrary polarimetric responses. We found that target estimation obtained by imaging with two orthogonal polarization states always improves detection performances when correlation is used as detection criterion. This experimental study illustrates the potential of polarization imaging for underwater target detection and opens interesting perspectives for the development of underwater imaging systems.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” Mar. Technol. Soc. J. 42, 52–67 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt. 6, 741–746 (1967).
    [CrossRef]
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    [CrossRef]
  16. J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, “Visibility depth improvement in active polarization imaging in scattering media,” Appl. Opt. 39, 4933–4941 (2000).
    [CrossRef]
  17. D. A. Miller and E. L. Dereniak, “Selective polarization imager for contrast enhancements in remote scattering media,” Appl. Opt. 51, 4092–4102 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  30. Y. Ouerhani, M. Jridi, and A. Alfalou, “Implementation techniques of high-order FFT into low-cost FPGA,” 54th IEEE International Midwest Symposium on Circuits and Systems, Yonsei University, Seoul, Korea, August 7–10, 2011.
  31. Y. Ouerhani, M. Jridi, and A. Alfalou, “Fast face recognition approach using a graphical processing unit,” in Proceedings of IST: International Conference on Imaging Systems and Techniques (IEEE, 2010), pp. 80–84.
  32. P. C. Miller and R. S. Caprari, “Demonstration of improved automatic target-recognition performance by moment analysis of correlation peaks,” Appl. Opt. 38, 1325–1331 (1999).
    [CrossRef]
  33. F. T. S. Yu and D. A. Gregory, “Optical pattern recognition: architectures and techniques,” Proc. IEEE 84, 733–752 (1996).
    [CrossRef]
  34. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
    [CrossRef]
  35. C. S. Weaver and J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef]
  36. Y. Piederrière, F. Boulvert, J. Cariou, B. Le Jeune, Y. Guern, and G. Le Brun, “Backscattered speckle size as a function of polarization: influence of particle-size and -concentration,” Opt. Express 13, 5030–5039 (2005).
    [CrossRef]
  37. P. Clemenceau, A. Dogariu, and J. Stryewski, “Polarization active imaging,” in Laser Radar Technology and Applications V, Proc. SPIE 4035, 401–409 (2000).
  38. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [CrossRef]
  39. T. Kohlgraf-Owens and A. Dogariu, “Spatially resolved scattering polarimeter,” Opt. Lett. 34, 1321 (2009).
    [CrossRef]

2012

2011

2010

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Signal Process. 2010, 746052 (2010).
[CrossRef]

2009

2008

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” Mar. Technol. Soc. J. 42, 52–67 (2008).
[CrossRef]

2007

2006

2005

2003

2002

2000

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, “Visibility depth improvement in active polarization imaging in scattering media,” Appl. Opt. 39, 4933–4941 (2000).
[CrossRef]

P. Clemenceau, A. Dogariu, and J. Stryewski, “Polarization active imaging,” in Laser Radar Technology and Applications V, Proc. SPIE 4035, 401–409 (2000).

1999

1998

1996

F. T. S. Yu and D. A. Gregory, “Optical pattern recognition: architectures and techniques,” Proc. IEEE 84, 733–752 (1996).
[CrossRef]

1992

1990

J. Cariou, B. Le Jeune, J. Lotrian, and Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt. 29, 1689–1695 (1990).
[CrossRef]

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE Ocean. Eng. 15, 101–110 (1990).
[CrossRef]

1984

1967

1966

1964

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

Ahmed, S. A.

Alam, M. S.

I. Leonard, A. Alfalou, M. S. Alam, and A. Arnold-Bos, “Adaptive nonlinear fringe-adjusted joint transform correlator,” Opt. Eng. 51, 098201 (2012).
[CrossRef]

A. Alfalou, C. Brosseau, P. Katz, and M. S. Alam, “Decision optimization for face recognition based on an alternate correlation plane quantification metric,” Opt. Lett. 37, 1562–1564 (2012).
[CrossRef]

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012) Chap. 11, pp. 201–229.

Alfalou, A.

A. Alfalou, C. Brosseau, P. Katz, and M. S. Alam, “Decision optimization for face recognition based on an alternate correlation plane quantification metric,” Opt. Lett. 37, 1562–1564 (2012).
[CrossRef]

I. Leonard, A. Alfalou, and C. Brosseau, “Spectral optimized asymmetric segmented phase-only correlation filter,” Appl. Opt. 51, 2638–2650 (2012).
[CrossRef]

I. Leonard, A. Alfalou, M. S. Alam, and A. Arnold-Bos, “Adaptive nonlinear fringe-adjusted joint transform correlator,” Opt. Eng. 51, 098201 (2012).
[CrossRef]

Y. Ouerhani, M. Jridi, and A. Alfalou, “Implementation techniques of high-order FFT into low-cost FPGA,” 54th IEEE International Midwest Symposium on Circuits and Systems, Yonsei University, Seoul, Korea, August 7–10, 2011.

I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012), Chap. 3, pp. 57–80.

Y. Ouerhani, M. Jridi, and A. Alfalou, “Fast face recognition approach using a graphical processing unit,” in Proceedings of IST: International Conference on Imaging Systems and Techniques (IEEE, 2010), pp. 80–84.

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012) Chap. 11, pp. 201–229.

A. Alfalou and C. Brosseau, “Understanding correlation techniques for face recognition: from basics to applications,” in Face Recognition, Milos Oravec, ed. (In-Tech, 2010), Available from: http://www.intechopen.com/articles/show/title/understanding-correlation-techniques-for-face-recognition-from-basics-to-applications .

Allais, A. G.

Arnold-Bos, A.

I. Leonard, A. Alfalou, M. S. Alam, and A. Arnold-Bos, “Adaptive nonlinear fringe-adjusted joint transform correlator,” Opt. Eng. 51, 098201 (2012).
[CrossRef]

Bartolini, L.

Bazeille, S.

S. Bazeille, I. Quidu, and L. Jaulin, “Color-based underwater object recognition using water light attenuation,” Intel. Serv. Robotics 5, 109–118 (2012).
[CrossRef]

Boffety, M.

Bonin, F.

F. Bonin, A. Burguera, and G. Olivier, “Imaging systems for advanced underwater vehicles,” J. Mar. Res. 13, 65–86 (2011).

Boulvert, F.

Brady, P.

Brennan, M. J.

Brosseau, C.

I. Leonard, A. Alfalou, and C. Brosseau, “Spectral optimized asymmetric segmented phase-only correlation filter,” Appl. Opt. 51, 2638–2650 (2012).
[CrossRef]

A. Alfalou, C. Brosseau, P. Katz, and M. S. Alam, “Decision optimization for face recognition based on an alternate correlation plane quantification metric,” Opt. Lett. 37, 1562–1564 (2012).
[CrossRef]

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012) Chap. 11, pp. 201–229.

A. Alfalou and C. Brosseau, “Understanding correlation techniques for face recognition: from basics to applications,” in Face Recognition, Milos Oravec, ed. (In-Tech, 2010), Available from: http://www.intechopen.com/articles/show/title/understanding-correlation-techniques-for-face-recognition-from-basics-to-applications .

I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012), Chap. 3, pp. 57–80.

Burguera, A.

F. Bonin, A. Burguera, and G. Olivier, “Imaging systems for advanced underwater vehicles,” J. Mar. Res. 13, 65–86 (2011).

Caimi, F. M.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” Mar. Technol. Soc. J. 42, 52–67 (2008).
[CrossRef]

Caprari, R. S.

Cariou, J.

Chang, P. C. Y.

Chenault, D. B.

Clemenceau, P.

P. Clemenceau, A. Dogariu, and J. Stryewski, “Polarization active imaging,” in Laser Radar Technology and Applications V, Proc. SPIE 4035, 401–409 (2000).

Cochenour, B.

Corchs, S.

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Signal Process. 2010, 746052 (2010).
[CrossRef]

Cummings, M. E.

Dalgleish, F. R.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” Mar. Technol. Soc. J. 42, 52–67 (2008).
[CrossRef]

De Dominicis, L.

Dereniak, E. L.

Dierssen, H. M.

Dogariu, A.

T. Kohlgraf-Owens and A. Dogariu, “Spatially resolved scattering polarimeter,” Opt. Lett. 34, 1321 (2009).
[CrossRef]

P. Clemenceau, A. Dogariu, and J. Stryewski, “Polarization active imaging,” in Laser Radar Technology and Applications V, Proc. SPIE 4035, 401–409 (2000).

Flitton, J. C.

Fornetti, G.

Francucci, M.

Fry, E. S.

Galland, F.

Gilbert, G. D.

Gilerson, A. A.

Goldstein, D. L.

Goodman, J. W.

Gorman, G. A.

G. A. Gorman, “Field deployable dynamic lightning system for turbid water imaging,” M. S. Thesis, Massachusetts Institute of Technology, Cambridge, USA (2011).

Gregory, D. A.

F. T. S. Yu and D. A. Gregory, “Optical pattern recognition: architectures and techniques,” Proc. IEEE 84, 733–752 (1996).
[CrossRef]

Guarneri, M.

Guern, Y.

Hopcraft, K. I.

Horner, J. L.

Jaffe, J.

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE Ocean. Eng. 15, 101–110 (1990).
[CrossRef]

Jakeman, E.

Jaulin, L.

S. Bazeille, I. Quidu, and L. Jaulin, “Color-based underwater object recognition using water light attenuation,” Intel. Serv. Robotics 5, 109–118 (2012).
[CrossRef]

Jordan, D. L.

Jridi, M.

Y. Ouerhani, M. Jridi, and A. Alfalou, “Implementation techniques of high-order FFT into low-cost FPGA,” 54th IEEE International Midwest Symposium on Circuits and Systems, Yonsei University, Seoul, Korea, August 7–10, 2011.

Y. Ouerhani, M. Jridi, and A. Alfalou, “Fast face recognition approach using a graphical processing unit,” in Proceedings of IST: International Conference on Imaging Systems and Techniques (IEEE, 2010), pp. 80–84.

Karpel, N.

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[CrossRef]

Kattawar, G. W.

Katz, P.

A. Alfalou, C. Brosseau, P. Katz, and M. S. Alam, “Decision optimization for face recognition based on an alternate correlation plane quantification metric,” Opt. Lett. 37, 1562–1564 (2012).
[CrossRef]

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012) Chap. 11, pp. 201–229.

Kim, A. D.

Kocak, D. M.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” Mar. Technol. Soc. J. 42, 52–67 (2008).
[CrossRef]

Kohlgraf-Owens, T.

Kouzoubov, A.

Le Brun, G.

Le Jeune, B.

Leonard, I.

I. Leonard, A. Alfalou, M. S. Alam, and A. Arnold-Bos, “Adaptive nonlinear fringe-adjusted joint transform correlator,” Opt. Eng. 51, 098201 (2012).
[CrossRef]

I. Leonard, A. Alfalou, and C. Brosseau, “Spectral optimized asymmetric segmented phase-only correlation filter,” Appl. Opt. 51, 2638–2650 (2012).
[CrossRef]

I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (eds.). (Nova Science Publishers, 2012), Chap. 3, pp. 57–80.

Lewis, G. D.

Lotrian, J.

Mahon, R.

Miller, D. A.

Miller, P. C.

Moscoso, M.

Mullen, L.

Muth, J.

Olivier, G.

F. Bonin, A. Burguera, and G. Olivier, “Imaging systems for advanced underwater vehicles,” J. Mar. Res. 13, 65–86 (2011).

Ouerhani, Y.

Y. Ouerhani, M. Jridi, and A. Alfalou, “Fast face recognition approach using a graphical processing unit,” in Proceedings of IST: International Conference on Imaging Systems and Techniques (IEEE, 2010), pp. 80–84.

Y. Ouerhani, M. Jridi, and A. Alfalou, “Implementation techniques of high-order FFT into low-cost FPGA,” 54th IEEE International Midwest Symposium on Circuits and Systems, Yonsei University, Seoul, Korea, August 7–10, 2011.

Pernicka, J. C.

Piederrière, Y.

Poggi, C.

Quidu, I.

S. Bazeille, I. Quidu, and L. Jaulin, “Color-based underwater object recognition using water light attenuation,” Intel. Serv. Robotics 5, 109–118 (2012).
[CrossRef]

Rabinovich, W.

Rakovic, M. J.

Ricci, R.

Roberts, P. J.

Schechner, Y. Y.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. PAMI 31, 385–399 (2009).
[CrossRef]

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” Mar. Technol. Soc. J. 42, 52–67 (2008).
[CrossRef]

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[CrossRef]

Schettini, R.

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Signal Process. 2010, 746052 (2010).
[CrossRef]

Shaw, J. A.

Stryewski, J.

P. Clemenceau, A. Dogariu, and J. Stryewski, “Polarization active imaging,” in Laser Radar Technology and Applications V, Proc. SPIE 4035, 401–409 (2000).

Sullivan, J. M.

Thomas, J. C.

Tonizzo, A.

Treibitz, T.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. PAMI 31, 385–399 (2009).
[CrossRef]

Twardowski, M. S.

Tyo, J. S.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

Voss, K. J.

Walker, J. G.

Weaver, C. S.

You, Y.

Yu, F. T. S.

F. T. S. Yu and D. A. Gregory, “Optical pattern recognition: architectures and techniques,” Proc. IEEE 84, 733–752 (1996).
[CrossRef]

Appl. Opt.

G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt. 6, 741–746 (1967).
[CrossRef]

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23, 4427–4439 (1984).
[CrossRef]

J. Cariou, B. Le Jeune, J. Lotrian, and Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt. 29, 1689–1695 (1990).
[CrossRef]

A. Kouzoubov, M. J. Brennan, and J. C. Thomas, “Treatment of polarization in laser remote sensing of ocean water,” Appl. Opt. 37, 3873–3885 (1998).
[CrossRef]

P. C. Miller and R. S. Caprari, “Demonstration of improved automatic target-recognition performance by moment analysis of correlation peaks,” Appl. Opt. 38, 1325–1331 (1999).
[CrossRef]

G. D. Lewis, D. L. Jordan, and P. J. Roberts, “Backscattering target detection in a turbid medium by polarization discrimination,” Appl. Opt. 38, 3937–3944 (1999).
[CrossRef]

G. W. Kattawar and M. J. Rakovic, “Virtues of Mueller matrix imaging for underwater target detection,” Appl. Opt. 38, 6431–6438 (1999).
[CrossRef]

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, “Visibility depth improvement in active polarization imaging in scattering media,” Appl. Opt. 39, 4933–4941 (2000).
[CrossRef]

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. L. Jordan, and J. G. Walker, “Improving visibility depth in passive underwater imaging by use of polarization,” Appl. Opt. 42, 2794–2803 (2003).
[CrossRef]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[CrossRef]

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
[CrossRef]

C. S. Weaver and J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef]

L. Mullen, B. Cochenour, W. Rabinovich, R. Mahon, and J. Muth, “Backscatter suppression for underwater modulating retroreflector links using polarization discrimination,” Appl. Opt. 48, 328–337 (2009).
[CrossRef]

Y. You, A. Tonizzo, A. A. Gilerson, M. E. Cummings, P. Brady, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, S. A. Ahmed, and G. W. Kattawar, “Measurements and simulations of polarization states of underwater light in clear oceanic waters,” Appl. Opt. 50, 4873–4893 (2011).
[CrossRef]

I. Leonard, A. Alfalou, and C. Brosseau, “Spectral optimized asymmetric segmented phase-only correlation filter,” Appl. Opt. 51, 2638–2650 (2012).
[CrossRef]

D. A. Miller and E. L. Dereniak, “Selective polarization imager for contrast enhancements in remote scattering media,” Appl. Opt. 51, 4092–4102 (2012).
[CrossRef]

EURASIP J. Adv. Signal Process.

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Signal Process. 2010, 746052 (2010).
[CrossRef]

IEEE J. Oceanic Eng.

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[CrossRef]

IEEE Ocean. Eng.

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE Ocean. Eng. 15, 101–110 (1990).
[CrossRef]

IEEE Trans. Inf. Theory

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

IEEE Trans. PAMI

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. PAMI 31, 385–399 (2009).
[CrossRef]

Intel. Serv. Robotics

S. Bazeille, I. Quidu, and L. Jaulin, “Color-based underwater object recognition using water light attenuation,” Intel. Serv. Robotics 5, 109–118 (2012).
[CrossRef]

J. Mar. Res.

F. Bonin, A. Burguera, and G. Olivier, “Imaging systems for advanced underwater vehicles,” J. Mar. Res. 13, 65–86 (2011).

Mar. Technol. Soc. J.

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Figures (7)

Fig. 1.
Fig. 1.

Synoptic diagram of VLC architecture. FT denotes the Fourier transform.

Fig. 2.
Fig. 2.

Experimental setup for underwater target detection. Pol denotes a linear polarizer. QWP is a quarter wave plates. L1, L2, L3, L4 are plano-convex convergent lenses. The detecting angle was set to θ=10°.

Fig. 3.
Fig. 3.

Images of the plastic plug when 20 ml of skimmed milk were added to 10L of tap water. (a) Intensity image. (b) Cross linear image. (c) Signal estimation image. (d) Clear water (no milk) image. The red square indicates the area where the DOP of the backscatter was measured for target estimation. (e) Photograph of the plastic plug.

Fig. 4.
Fig. 4.

Correlation plane and PCE values (×104) corresponding to the correlation of images displayed in Fig. 3 with reference image (image in pure water). (a) Intensity image I. (b) Cross linear image (CRL). (c) Target estimation image. (d) Pure water (no milk) image.

Fig. 5.
Fig. 5.

(a), (d) PCE versus optical thickness τ0 for the plastic plug and different imaging modes showed in the inset. (b), (e) Same as in (a), (d) for the painted metal. (c), (f) Same as in (a), (d) for the rusted metal. The scattering medium is composed of skimmed milk (a), (b), and (c) and semi-skimmed milk (d), (e), and (f) diluted in tap water.

Fig. 6.
Fig. 6.

DOP of the backscatter (pscat) versus optical thickness for experiments in skimmed milk.

Fig. 7.
Fig. 7.

(a) PCE as a function of target depth for painted metal in ocean water. (b) Same as in (a) for lake water.

Equations (11)

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I(x,y)=S(x,y)+B(x,y),
Imax(x,y)=Smax(x,y)+Bmax(x,y)
Imin(x,y)=Smin(x,y)+Bmin(x,y).
ptarg(x,y)=Smax(x,y)Smin(x,y)Smax(x,y)+Smin(x,y),
pscat(x,y)=Bmax(x,y)Bmin(x,y)Bmax(x,y)+Bmin(x,y).
S(x,y)=Smax(x,y)+Smin(x,y),
B(x,y)=Bmax(x,y)+Bmin(x,y),
S^=1pscatptarg[Imin(1+pscat)Imax(1pscat)],
B^=1pscatptarg[Imax(1ptarg)Imin(1+ptarg)].
H(μ,ν)=R*(μ,ν)|R(μ,ν)|,
PCE=i,jMEpeak(i,j)i,jNEcorrelation plane(i,j),

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