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 OSA

Full Article  |  PDF Article
OSA Recommended Articles
Characterization of a visible spectrum division-of-focal-plane polarimeter

Timothy York and Viktor Gruev
Appl. Opt. 51(22) 5392-5400 (2012)

Calibration methods for division-of-focal-plane polarimeters

S. Bear Powell and Viktor Gruev
Opt. Express 21(18) 21039-21055 (2013)

CCD polarization imaging sensor with aluminum nanowire optical filters

Viktor Gruev, Rob Perkins, and Timothy York
Opt. Express 18(18) 19087-19094 (2010)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. 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(22), 5453–5469 (2006).
    [Crossref] [PubMed]
  2. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31(31), 6676–6683 (1992).
    [Crossref] [PubMed]
  3. K. J. Voss and Y. Liu, “Polarized radiance distribution measurements of skylight. I. System description and characterization,” Appl. Opt. 36(24), 6083–6094 (1997).
    [Crossref] [PubMed]
  4. 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]
  5. 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).
  6. J. S. Tyo, “Hybrid division of aperture/division of a focal-plane polarimeter for real-time polarization imagery without an instantaneous field-of-view error,” Opt. Lett. 31(20), 2984–2986 (2006).
    [Crossref] [PubMed]
  7. J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V (2005).
    [Crossref]
  8. V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18(18), 19087–19094 (2010).
    [Crossref] [PubMed]
  9. V. Gruev, J. Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18(18), 19292–19303 (2010).
    [Crossref] [PubMed]
  10. A. Andreou and Z. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
    [Crossref]
  11. 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]
  12. 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]
  13. X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18(17), 17776–17787 (2010).
    [Crossref] [PubMed]
  14. V. Gruev, A. Ortu, N. Lazarus, J. Van der Spiegel, and N. Engheta, “Fabrication of a dual-tier thin film micropolarization array,” Opt. Express 15(8), 4994–5007 (2007).
    [Crossref] [PubMed]
  15. J. S. Tyo, “Optimum linear combination strategy for an N-channel polarization-sensitive imaging or vision system,” J. Opt. Soc. Am. A 15(2), 359–366 (1998).
    [Crossref]
  16. 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(4), 683–693 (2010).
    [Crossref] [PubMed]
  17. V. Gruev, J. Van der Spiegel, and N. Engheta, “Nano-wire Dual Layer Polarization Filter,” Proc. IEEE ISCAS,561–564 (2009).
  18. B. Razavi, Design of Analog CMOS Integrated Circuits (McGraw-Hill, New York, NY, 2001).
  19. R. Philip, Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).
  20. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
    [Crossref]
  21. 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]
  22. 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]
  23. 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]
  24. J. S. Tyo and H. Wei, “Optimizing imaging polarimeters constructed with imperfect optics,” Appl. Opt. 45(22), 5497–5503 (2006).
    [Crossref] [PubMed]

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)

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]

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]

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)

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

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]

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).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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 .

Metrics