Abstract

An analysis of the temporal noise in the Stokes parameters computed by division of focal plane polarimeters is presented. Theoretical estimations of the Stokes parameter signal-to-noise ratios for CCD polarization imaging sensors with both 4-polarizer and 2-polarizer micropolarization filter arrays are derived. The theoretical derivation is verified with measurements from an integrated polarization imaging sensor composed of a CCD imaging array and aluminum nanowire polarization filters. The measured data obtained from the CCD polarimeters matches the theoretical derivations of the temporal noise model of the Stokes parameters.

©2010 Optical Society of America

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References

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    [Crossref]
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2010 (4)

2009 (1)

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

2008 (3)

Z Z. Wang, J. S. Tyo, and M. M. Hayat, “Generalized signal-to-noise ratio for spectral sensors with correlated bands,” J. Opt. Soc. Am. A 25(10), 2528–2534 (2008).
[Crossref]

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

2007 (1)

2006 (4)

2005 (1)

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

2002 (2)

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41(4), 619–630 (2002).
[Crossref] [PubMed]

A. Andreou and Z. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

2000 (1)

1998 (1)

1997 (1)

1992 (1)

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29, 685–689 (1982).

Andreou, A.

A. Andreou and Z. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

Azzam, R. M. A.

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29, 685–689 (1982).

Banner, M. L.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Bénière, A.

Bermak, A.

Black, W. T.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Boger, J. K.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Boussaid, F.

Bowers, D. L.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Chenault, D. B.

Chigrinov, V. G.

Corrada-Emmanuel, A.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Dereniak, E. L.

Descour, M. R.

Engheta, N.

Fetrow, M. P.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Goldstein, D. H.

Goldstein, D. L.

Goudail, F.

Gruev, V.

Hayat, M. M.

Hubbs, J. E.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Kalayjian, Z.

A. Andreou and Z. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

Kemme, S. A.

Lazarus, N.

Liu, Y.

Momeni, M.

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of Octopus retina,” IEEE Trans. Neural Netw. 17(1), 222–232 (2006).
[Crossref] [PubMed]

Ohta, J.

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

Ortega, S. E.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Ortu, A.

Perkins, R.

Pezzaniti, J. L.

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

Phipps, G. S.

Ratliff, B. M.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Sabatke, D. S.

Sasagawa, K.

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

Sato, S.

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

Schultz, H.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Shaw, J. A.

Sweatt, W. C.

Titus, A. H.

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of Octopus retina,” IEEE Trans. Neural Netw. 17(1), 222–232 (2006).
[Crossref] [PubMed]

Tokuda, T.

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

Tyo, J. S.

Van der Spiegel, J.

Voss, K. J.

Wang, Z Z.

Wei, H.

Wellems, L. D.

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Wolff, L. B.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Yalcin, J.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Yamada, H.

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

York, T.

Zappa, C. J.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Zhao, X.

Appl. Opt. (6)

Electron. Lett. (1)

T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009).
[Crossref]

IEEE Sens. J. (1)

A. Andreou and Z. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

IEEE Trans. Neural Netw. (1)

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of Octopus retina,” IEEE Trans. Neural Netw. 17(1), 222–232 (2006).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Opt. Acta (Lond.) (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29, 685–689 (1982).

Opt. Eng. (1)

D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Proc. SPIE (1)

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

Other (3)

V. Gruev, J. Van der Spiegel, and N. Engheta, “Nano-wire Dual Layer Polarization Filter,” Proc. IEEE ISCAS,561–564 (2009).

B. Razavi, Design of Analog CMOS Integrated Circuits (McGraw-Hill, New York, NY, 2001).

R. Philip, Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

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Figures (4)

Fig. 1
Fig. 1 Schematic drawings of division of focal plane polarization imaging sensors with (a) a 4-polarizer filter array and (b) a 2-polarizer filter array.

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Fig. 2
Fig. 2 Experimental and theoretical signal-to-noise ratios for S 0 for both the 4-polarizer and 2-polarizer filter array architectures.

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Fig. 3
Fig. 3 Experimental and theoretical signal-to noise ratios for S 1 for both the 4-polarizer and 2-polarizer filter array architectures at 3 different S 0 values. Different values of S 0 are represented by the different colors.

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Fig. 4
Fig. 4 Experimental and theoretical signal-to noise ratios for S 2 for both the 4-polarizer and 2-polarizer filter array architectures at 3 different S 0 values. Different values of S 0 are represented by the different colors.

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Equations (36)

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

S 0 = I 0 + I 90 ,
S 1 = I 0 − I 90 ,
S 2 = I 45 − I 135 .
S 0 = I t o t ,
S 1 = 2 I 0 − I t o t ,
S 2 = 2 I 45 − I t o t ,
σ s h o t = I p h o t o ,
σ S F = 4 3 k T q g m S F , m B T ,
σ S F = a I b i a s q * | f | .
σ pixel = I i + R 2 .
σ S 0 = ( ∂ ( S 0 ) ∂ ( I 0 ) ) 2 σ I 0 2 + ( ∂ ( S 0 ) ∂ ( I 90 ) ) 2 σ I 90 2 ,
σ S 1 = ( ∂ ( S 1 ) ∂ ( I 0 ) ) 2 σ I 0 2 + ( ∂ ( S 1 ) ∂ ( I 90 ) ) 2 σ I 90 2 ,
σ S 2 = ( ∂ ( S 2 ) ∂ ( I 45 ) ) 2 σ I 45 2 + ( ∂ ( S 2 ) ∂ ( I 135 ) ) 2 σ I 135 2 .
σ S 0 = I 0 + I 90 + 2 R 2 ,
σ S 1 = I 0 + I 90 + 2 R 2 ,
σ S 2 = I 45 + I 135 + 2 R 2 .
σ S 0 = σ S 1 = σ S 2 = S 0 + 2 R 2 .
S N R ( S 0 ) = S 0 S 0 + 2 R 2 ,
S N R ( S 1 ) = | S 1 | S 0 + 2 R 2 ,
S N R ( S 2 ) = | S 2 | S 0 + 2 R 2 .
σ S 0 = ( ∂ ( S 0 ) ∂ ( I t o t ) ) 2 σ I 2 ,
σ S 1 = ( ∂ ( S 1 ) ∂ ( I t o t ) ) 2 σ I t o t 2 + ( ∂ ( S 1 ) ∂ ( I 0 ) ) 2 σ I 0 2 ,
σ S 2 = ( ∂ ( S 2 ) ∂ ( I t o t ) ) 2 σ I t o t 2 + ( ∂ ( S 2 ) ∂ ( I 45 ) ) 2 σ I 45 2 .
σ S 0 = I t o t + R 2 ,
σ S 1 = 4 I 0 + I t o t + 5 R 2 ,
σ S 2 = 4 I 45 + I t o t + 5 R 2 .
σ S 0 = S 0 + R 2 ,
σ S 1 = 3 S 0 + 2 S 1 + 5 R 2 ,
σ S 2 = 3 S 0 + 2 S 2 + 5 R 2 .
S N R ( S 0 ) = S 0 S 0 + R 2 ,
S N R ( S 1 ) = | S 1 | 3 S 0 + 2 S 1 + 5 R 2 ,
S N R ( S 2 ) = | S 2 | 3 S 0 + 2 S 2 + 5 R 2 .
S 0 = 1 2 ( I 0 + I 45 + I 90 + I 135 ) .
S N R ( S 0 ) = 2 * S 0 S 0 + 2 R 2 .
S 0 = 1 2 ( I t o t , 1 + I t o t , 2 ) .
S N R ( S 0 ) = 2 * S 0 S 0 + R 2 .

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