Abstract

We quantitatively analyze how a polarization-sensitive imager can overcome the precision of a standard intensity camera when estimating a parameter on a polarized source over an intense background. We show that the gain is maximized when the two polarimetric channels are perturbed with significantly correlated noise fluctuations. An optimal estimator is derived and compared to standard intensity and polarimetric estimators.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. J. Guan, J. Zhu, “Target detection in turbid medium using polarization-based range-gated technology,” Opt. Express 21, 14152–14158 (2013).
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  7. P. Réfrégier, M. Roche, F. Goudail, “Cramer-Rao lower bound for the estimation of the degree of polarization in active coherent imagery at low photon levels,” Opt. Lett. 31, 3565–3567 (2006).
    [CrossRef] [PubMed]
  8. A. Bénière, F. Goudail, M. Alouini, D. Dolfi, “Degree of polarization estimation in the presence of nonuniform illumination and additive gaussian noise,” J. Opt. Soc. Am. A 25, 919–929 (2008).
    [CrossRef]
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  13. N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
    [CrossRef]
  14. M. Darecki, D. Stramski, M. Sokólski, “Measurements of high-frequency light fluctuations induced by sea surface waves with an underwater porcupine radiometer system,” J. Geophys. Res. 116, C00H09 (2011).
    [CrossRef]
  15. F. A. Sadjadi, C. L. Chun, “Automatic detection of small objects from their infrared state-of-polarization vectors,” Opt. Lett. 28, 531–533 (2003).
    [CrossRef] [PubMed]
  16. B. Laude-Boulesteix, A. D. Martino, B. Drévillon, L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
    [CrossRef] [PubMed]
  17. J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
    [CrossRef]
  18. P. Garthwaite, I. Jolliffe, B. Jones, Statistical Inference (Prentice Hall, 1995).
  19. J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
    [CrossRef]

2013

2012

2011

M. Darecki, D. Stramski, M. Sokólski, “Measurements of high-frequency light fluctuations induced by sea surface waves with an underwater porcupine radiometer system,” J. Geophys. Res. 116, C00H09 (2011).
[CrossRef]

2009

2008

A. Bénière, F. Goudail, M. Alouini, D. Dolfi, “Degree of polarization estimation in the presence of nonuniform illumination and additive gaussian noise,” J. Opt. Soc. Am. A 25, 919–929 (2008).
[CrossRef]

J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

2006

2004

2003

1999

1998

H. Ramachandran, A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

1996

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

O. Emile, F. Bretenaker, A. L. Floch, “Rotating polarization imaging in turbid media,” Opt. Lett. 21, 1706–1708 (1996).
[CrossRef] [PubMed]

1995

1990

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
[CrossRef]

Alfalou, A.

Alfano, R.

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

Allais, A.-G.

Alouini, M.

Aubert, D.

N. Hautiere, D. Aubert, “Contrast restoration of foggy images through use of an onboard camera,” in Proceedings of 2005 IEEE Intelligent Transportation Systems(2005), pp 601–606.

Bénière, A.

Boffety, M.

Bretenaker, F.

Brosseau, C.

Chun, C. L.

Darecki, M.

M. Darecki, D. Stramski, M. Sokólski, “Measurements of high-frequency light fluctuations induced by sea surface waves with an underwater porcupine radiometer system,” J. Geophys. Res. 116, C00H09 (2011).
[CrossRef]

Delrot, P.

Demos, S.

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

Dogariu, A.

Dolfi, D.

Drévillon, B.

Dubreuil, M.

Emile, O.

Engheta, N.

Fabre, C.

J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

Fade, J.

J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

Floch, A. L.

Galland, F.

Garcia, R.

N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
[CrossRef]

Garthwaite, P.

P. Garthwaite, I. Jolliffe, B. Jones, Statistical Inference (Prentice Hall, 1995).

Goudail, F.

Gracias, N.

N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
[CrossRef]

Guan, J.

Hautiere, N.

N. Hautiere, D. Aubert, “Contrast restoration of foggy images through use of an onboard camera,” in Proceedings of 2005 IEEE Intelligent Transportation Systems(2005), pp 601–606.

Heerdt, A. S.

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

Jaffe, J.

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
[CrossRef]

Jolliffe, I.

P. Garthwaite, I. Jolliffe, B. Jones, Statistical Inference (Prentice Hall, 1995).

Jones, B.

P. Garthwaite, I. Jolliffe, B. Jones, Statistical Inference (Prentice Hall, 1995).

Jordan, D. L.

Laude-Boulesteix, B.

Leonard, I.

Lewis, G. D.

Martino, A. D.

Narayanan, A.

H. Ramachandran, A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

Negahdaripour, S.

N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
[CrossRef]

Neumann, L.

N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
[CrossRef]

Prados, R.

N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
[CrossRef]

Pugh, E. N.

Ramachandran, H.

H. Ramachandran, A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

Réfrégier, P.

J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

P. Réfrégier, M. Roche, F. Goudail, “Cramer-Rao lower bound for the estimation of the degree of polarization in active coherent imagery at low photon levels,” Opt. Lett. 31, 3565–3567 (2006).
[CrossRef] [PubMed]

Roberts, P. J.

Roche, M.

Rowe, M. P.

Sadjadi, F. A.

Savage, H.

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

Schantz, S.

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

Schwartz, L.

Sokólski, M.

M. Darecki, D. Stramski, M. Sokólski, “Measurements of high-frequency light fluctuations induced by sea surface waves with an underwater porcupine radiometer system,” J. Geophys. Res. 116, C00H09 (2011).
[CrossRef]

Stramski, D.

M. Darecki, D. Stramski, M. Sokólski, “Measurements of high-frequency light fluctuations induced by sea surface waves with an underwater porcupine radiometer system,” J. Geophys. Res. 116, C00H09 (2011).
[CrossRef]

Treps, N.

J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

Tyo, J. S.

Zhu, J.

Appl. Opt.

Eur. Phys. J. D

J. Fade, N. Treps, C. Fabre, P. Réfrégier, “Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations,” Eur. Phys. J. D 50, 215–227 (2008).
[CrossRef]

IEEE J. Oceanic Eng.

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
[CrossRef]

J. Geophys. Res.

M. Darecki, D. Stramski, M. Sokólski, “Measurements of high-frequency light fluctuations induced by sea surface waves with an underwater porcupine radiometer system,” J. Geophys. Res. 116, C00H09 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. Demos, H. Savage, A. S. Heerdt, S. Schantz, R. Alfano, “Time resolved degree of polarization for human breast tissue,” Opt. Commun. 124, 439–442 (1996).
[CrossRef]

H. Ramachandran, A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Other

P. Garthwaite, I. Jolliffe, B. Jones, Statistical Inference (Prentice Hall, 1995).

N. Hautiere, D. Aubert, “Contrast restoration of foggy images through use of an onboard camera,” in Proceedings of 2005 IEEE Intelligent Transportation Systems(2005), pp 601–606.

N. Gracias, S. Negahdaripour, L. Neumann, R. Prados, R. Garcia, “A motion compensated filtering approach to remove sunlight flicker in shallow water images,” in OCEANS 2008, (2008), pp. 1–7.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Sketch of the image formation model: a polarization-splitting analyzing device (PSAD) can be any suitable birefringent crystal in case of simultaneous acquisitions of images X// and X [11], or a rotating polarizer or liquid crystal device for sequential acquisitions. Image formation optics are not represented for the sake of clarity.

Fig. 2
Fig. 2

Evolution of μ(ω, P, β, ρ) for P = 0.4 and β = 0.1 as a function of ρ for ω = {10−3, 1, 5, 104}.

Fig. 3
Fig. 3

Contour plots of ρ lim K for various values of K as a function of P and β. Additional contour plots of ρmin and μ ,min are provided when relations (7) and (8) hold. The yellow circles correspond to the situation addressed in Fig. 2 (P = 0.4 and β = 0.1).

Tables (1)

Tables Icon

Table 1 List and description of symbols and acronyms. Dependency in scene location i has been omitted for the sake of concision.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

X i P = [ 1 + P 2 s i + 1 + β 2 b i 1 P 2 s i + 1 β 2 b i ] .
Γ i = [ σ / / , i 2 c i c i σ , i 2 ] = [ 1 + β 2 ε i 2 + σ 0 2 ρ 1 β 2 2 ε i 2 ρ 1 β 2 2 ε i 2 1 β 2 ε i 2 + σ 0 2 ] .
I F ( y ) = 2 ln P X ( X ) y 2 .
μ ( ω , P , β , ρ ) = I F P ( s ) I F I ( s ) = ( 1 + ω 2 ) [ 1 + P 2 2 + Q 4 ω 2 ] 1 + ω 2 + ( 1 ρ 2 ) ( 1 β 2 ) 4 ω 4 ,
Q = ( 1 2 β P + P 2 ) ρ ( 1 P 2 ) 1 β 2 ,
μ ( P , β , ρ ) = μ ( ω 1 , P , β , ρ ) = Q ( 1 ρ 2 ) ( 1 β 2 ) ,
{ μ , min = ( 1 + P ) 2 2 ( 1 + β ) and ρ min = 1 P 1 + P 1 + β 1 β , if β 2 P 1 + P 2 μ , min = ( 1 P ) 2 2 ( 1 β ) and ρ min = 1 + P 1 P 1 β 1 + β , otherwise
β ( 1 + P ) 2 2 K 1 , if β P ,
β 1 ( 1 P ) 2 2 K if β P .
ρ ρ lim K = 1 P 2 2 K 1 β 2 + Φ ,
Φ = [ 1 1 2 K ( 1 P ) 2 1 β ] × [ 1 1 2 K ( 1 + P ) 2 1 + β ] .
s ^ M L P = U X ^ / / + V X ^ + Z W ,
Γ = δ X δ X T = c 2 [ ε 2 + ς 2 ρ γ ε 2 ρ γ ε 2 γ 2 ε 2 + ς 2 ] ,
I F P ( s ) = a 2 c 2 ε 2 ( α 2 2 ρ α γ + γ 2 ) + ( 1 + α 2 ) u 2 γ 2 ( 1 ρ 2 ) + ( 1 + γ 2 ) u 2 + u 4 ,
I F I ( s ) = a 2 c 2 ε 2 ( 1 + α 2 ) ( 1 + γ 2 ) + u 2 = σ 2 1 + ω 2 .
μ ( u , α , γ , ρ ) = A u 2 + B D u 4 + C u 2 + 1 × C u 2 + 1 E ,
[ μ ( u , α , γ , ρ ) ] u = 2 u ( u ) [ 1 + C u 2 + D u 4 ] 2 E ,
Δ = 4 D ( A 2 + D B 2 A B C ) = 4 γ 2 ( 1 ρ 2 ) [ α ( 1 γ 2 ) ρ γ ( 1 α 2 ) ] 2 ,
μ ( α , γ , ρ ) = ( α 2 2 ρ α γ + γ 2 ) ( 1 + γ 2 ) γ 2 ( 1 ρ 2 ) ( 1 + α 2 )
γ 2 K ( 1 + α ) 2 1 when γ α
γ 2 α 2 / [ K ( 1 + α ) 2 α 2 ] when γ α .
γ 2 K ( 1 + α ) 2 1 , if α γ 2 , and
γ 2 α 2 / [ K ( 1 + α ) 2 α 2 ] , if α γ 2 ,

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