Abstract

We present the design and the practical implementation of a polarimetric imaging system based on liquid-crystal modulators that allows generation and analysis of any polarization state on the Poincaré sphere. This system is more versatile than standard Mueller imagers that are based on optimized, but limited, sets of illumination and analysis states. Examples of benefits brought by these extra degrees of freedom are illustrated on two different applications: contrast enhancement and extraction of partial polarimetric properties of a scene.

© 2012 Optical Society of America

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    [CrossRef]
  31. Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
    [CrossRef]
  32. A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34, 1656–1658 (1995).
    [CrossRef]
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2011 (4)

2010 (5)

2009 (5)

2008 (3)

2007 (1)

2006 (2)

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

D. G. Jones, D. H. Goldstein, and J. C. Spaulding, “Reflective and polarimetric characteristics of urban materials,” Proc. SPIE 6240, 62400A (2006).
[CrossRef]

2004 (2)

2003 (1)

2002 (1)

2000 (1)

1999 (2)

1997 (1)

1996 (1)

1995 (1)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34, 1656–1658 (1995).
[CrossRef]

1993 (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

1987 (1)

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propagat. 35, 988–991 (1987).
[CrossRef]

1981 (2)

J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
[CrossRef]

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

Aas, L. M. S.

Ainouz, S.

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

Alouini, M.

Ambirajan, A.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34, 1656–1658 (1995).
[CrossRef]

Anna, G.

Antonelli, M.-R.

Azzam, R. M. A.

Benali, A.

Bénière, A.

Bigué, L.

Boerner, W. M.

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propagat. 35, 988–991 (1987).
[CrossRef]

Chipman, R. A.

Compain, E.

De, A.

De Martino, A.

Devlaminck, V.

Dolfi, D.

Drevillon, B.

Drévillon, B.

Duan, Q. Y.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Ellingsen, P. G.

Elsner, A. E.

Engheta, N.

Galland, F.

Garcia-Caurel, E.

Gayet, B.

Goldstein, D. H.

D. G. Jones, D. H. Goldstein, and J. C. Spaulding, “Reflective and polarimetric characteristics of urban materials,” Proc. SPIE 6240, 62400A (2006).
[CrossRef]

Goudail, F.

Gupta, V. K.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Hoover, B. G.

Jeune, B. L.

Johnson, S. J.

J. S. Tyo, Z. Wang, S. J. Johnson, and B. G. Hoover, “Design and optimization of partial Mueller matrix polarimeters,” Appl. Opt. 49, 2326–2333 (2010).
[CrossRef]

J. S. Tyo, S. J. Johnson, Z. Wang, and B. G. Hoover, “Designing partial Mueller matrix polarimeters,” Proc. SPIE 746174610V (2009).
[CrossRef]

Jones, D. G.

D. G. Jones, D. H. Goldstein, and J. C. Spaulding, “Reflective and polarimetric characteristics of urban materials,” Proc. SPIE 6240, 62400A (2006).
[CrossRef]

Kattawar, G. W.

Kildemo, M.

Kim, Y.-K.

Klimov, A.

S. Savenkov, R. Muttiah, E. Oberemok, and A. Klimov, “Incomplete active polarimetry: measurement of the block-diagonal scattering matrix,” J. Quant. Spectrosc. Radiat. Transfer 112, 1796–1802 (2011).
[CrossRef]

Kostinski, A. B.

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propagat. 35, 988–991 (1987).
[CrossRef]

Laude, B.

Laude-Boulesteix, B.

Lemaillet, P.

Letnes, P. A.

Liu, J.

Look, D. C.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34, 1656–1658 (1995).
[CrossRef]

Martino, A. D.

Muttiah, R.

S. Savenkov, R. Muttiah, E. Oberemok, and A. Klimov, “Incomplete active polarimetry: measurement of the block-diagonal scattering matrix,” J. Quant. Spectrosc. Radiat. Transfer 112, 1796–1802 (2011).
[CrossRef]

Nerbø, I. S.

Novikova, T.

Oberemok, E.

S. Savenkov, R. Muttiah, E. Oberemok, and A. Klimov, “Incomplete active polarimetry: measurement of the block-diagonal scattering matrix,” J. Quant. Spectrosc. Radiat. Transfer 112, 1796–1802 (2011).
[CrossRef]

Orlik, X.

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1984).

Pierangelo, A.

Poirier, S.

Pugh, E. N.

Rakovic, M. J.

Richert, M.

Rivet, S.

Rowe, M. P.

Savenkov, S.

S. Savenkov, R. Muttiah, E. Oberemok, and A. Klimov, “Incomplete active polarimetry: measurement of the block-diagonal scattering matrix,” J. Quant. Spectrosc. Radiat. Transfer 112, 1796–1802 (2011).
[CrossRef]

Schwartz, L.

Shribak, M.

Solomon, J. E.

Sorooshian, S.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Spaulding, J. C.

D. G. Jones, D. H. Goldstein, and J. C. Spaulding, “Reflective and polarimetric characteristics of urban materials,” Proc. SPIE 6240, 62400A (2006).
[CrossRef]

Stoll, M. P.

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

Takakura, Y.

Terrier, P.

Twietmeyer, K. M.

Tyo, J. S.

Validire, P.

VanNasdale, D.

Walraven, R.

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

Wang, Z.

J. S. Tyo, Z. Wang, S. J. Johnson, and B. G. Hoover, “Design and optimization of partial Mueller matrix polarimeters,” Appl. Opt. 49, 2326–2333 (2010).
[CrossRef]

J. S. Tyo, S. J. Johnson, Z. Wang, and B. G. Hoover, “Designing partial Mueller matrix polarimeters,” Proc. SPIE 746174610V (2009).
[CrossRef]

Zallat, J.

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

Zhao, Y.

Appl. Opt. (12)

J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, “Target detection in optical scattering media by polarization-difference imaging,” Appl. Opt. 35, 1855–1870 (1996).
[CrossRef]

J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
[CrossRef]

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (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. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
[CrossRef]

B. G. Hoover and J. S. Tyo, “Polarization components analysis for invariant discrimination,” Appl. Opt. 46, 8364–8373 (2007).
[CrossRef]

B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
[CrossRef]

F. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. Devlaminck, “Target detection with a liquid crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282(2004).
[CrossRef]

A. Bénière, F. Goudail, M. Alouini, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
[CrossRef]

J. Liu and R. M. A. Azzam, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36, 1553–1559 (1997).
[CrossRef]

J. S. Tyo, Z. Wang, S. J. Johnson, and B. G. Hoover, “Design and optimization of partial Mueller matrix polarimeters,” Appl. Opt. 49, 2326–2333 (2010).
[CrossRef]

F. Goudail and A. Bénière, “Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise,” Appl. Opt. 49, 683–693 (2010).
[CrossRef]

IEEE Trans. Antennas Propagat. (1)

A. B. Kostinski and W. M. Boerner, “On the polarimetric contrast optimization,” IEEE Trans. Antennas Propagat. 35, 988–991 (1987).
[CrossRef]

J. Opt. A (1)

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

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

J. Optim. Theory Appl. (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

S. Savenkov, R. Muttiah, E. Oberemok, and A. Klimov, “Incomplete active polarimetry: measurement of the block-diagonal scattering matrix,” J. Quant. Spectrosc. Radiat. Transfer 112, 1796–1802 (2011).
[CrossRef]

Opt. Eng. (2)

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34, 1656–1658 (1995).
[CrossRef]

Opt. Express (6)

Opt. Lett. (7)

Proc. SPIE (2)

D. G. Jones, D. H. Goldstein, and J. C. Spaulding, “Reflective and polarimetric characteristics of urban materials,” Proc. SPIE 6240, 62400A (2006).
[CrossRef]

J. S. Tyo, S. J. Johnson, Z. Wang, and B. G. Hoover, “Designing partial Mueller matrix polarimeters,” Proc. SPIE 746174610V (2009).
[CrossRef]

Other (1)

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1984).

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of the imaging system: white-light fiber source; Sl, spotlight reducing the aperture angle at the output of the fiber; d, diffuser; FD, field diaphragm; AD, aperture diaphragm; P1, P2, polarizers; LC1,,4, liquid crystals; F, spectral filter; C, camera.

Fig. 2.
Fig. 2.

Scheme of a PSG consisting of one linear polarizer followed by two fixed retarders. The orientations of the fast axes of the two variable retarders are given by the angles γ and θ with respect to the direction of the polarizer. ϕ1 and ϕ2 are the phase shifts introduced respectively by LCVR 1 and 2.

Fig. 3.
Fig. 3.

Comparison between the polarization states theoretically expected and effectively generated using the PSG presented Fig. 2 with the angles γ=45° and θ=90°

Fig. 4.
Fig. 4.

(a) Mueller matrix of a scene composed of some polygonal chunks of sandpaper glued on a sandpaper of different roughness, the whole scene being cover with the same paint. The integration time for the acquisition of each image used to compute the Mueller matrix is t0/16. (b) Optimal image obtained by using the set of polarization states in illumination and analysis maximizing the contrast. The integration time for the acquisition is t0.

Tables (3)

Tables Icon

Table 1. Set of Optimal States in Illumination and Analysis, Respectively, of Azimuth And Ellipticity (αs,εs), (αt,εt), Minimizing the Condition Number of the QT,SΩ Matrix in the Case of a Mueller Matrix of the Form in Eq. (13)

Tables Icon

Table 2. Optimal States Used to Acquire the Four Images that Enable Extraction of the Four Relevant Coefficients of the Mueller Matrix of the Piece of Wood

Tables Icon

Table 3. Standard Deviation (std) of the Coefficients Computed from the Acquisition of the Full Mueller Matrix or from the Acquisition of Four Optimized Imagesa

Equations (16)

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

i=ητI02TTMS,
D=cos1[sin(2ε1).sin(2ε2)+cos(2ε1).cos(2ε2).cos(2(α1α2))].
Bt,b=18(x¯tx¯b)T[Γt+Γb2]1(x¯tx¯b)+12log[det(Γt+Γb2)det(Γt)det(Γb)],
Bmueller=4.6,Bopt=18.6.
TnTMSn=In;n{1,,N},
Sn(αnS,εnS)=[1cos(2αnS)cos(2εnS)sin(2αnS)cos(2εnS)sin(2εnS)]Tn(αnT,εnT)=[1cos(2αnT)cos(2εnT)sin(2αnT)cos(2εnT)sin(2εnT)],
n{1,,16},WnTVM=In ⇔ QT,SVM=I,
VM=QT,S1I.
cond(Q)=σmaxσmin,
M=[M00M01000M11M1200M21M220M3000M33].
QT,SΩVMΩ=IΩ,
(S,T)=argmin(Sn,Tn),n{1,,NΩ}{cond[QT,SΩ]},
M=[M00M0100M10M110000M22M2300M32M33]
C=trace[([QT,SΩ]TQT,SΩ)1].
[1.000.000.020.010.000.180.000.010.010.010.180.000.010.010.000.09].
M00=1;M11=0.18;M22=0.16;M33=0.09.

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