Abstract

We have designed an image sensor that can capture the first three Stokes parameters at 648 by 488 spatial resolution at 260 frames per second. The sensor consists of a CCD image sensor monolithically integrated with pixel pitch-matched aluminum nanowire polarization filters. The sensor demonstrates a Malus law response over all pixels, and has a relatively uniform diattenuation over the visible spectrum. We demonstrate two potential applications for the sensor. The first uses circular polarization in transmission mode to observe high-speed stress failure in polycarbonate. The second uses polarization in reflected mode to track high speed automobile traffic.

© 2016 Optical Society of America

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References

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  1. A. El Gamal and H. Eltoukhy, “CMOS image sensors,” IEEE Circuits Devices Mag. 21(3), 6–20 (2005).
    [Crossref]
  2. D. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2011).
  3. H. Zhan, D. G. Voelz, S.-Y. Cho, and X. Xiao, “Complex index of refraction estimation from degree of polarization with diffuse scattering consideration,” Appl. Opt. 54(33), 9889–9895 (2015).
    [Crossref] [PubMed]
  4. N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
    [Crossref] [PubMed]
  5. T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
    [Crossref] [PubMed]
  6. S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind Haze Separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006) pp. 1984–1991.
  7. 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]
  8. J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
    [Crossref]
  9. 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]
  10. W. L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, and S. Pau, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22(3), 3063–3074 (2014).
    [Crossref] [PubMed]
  11. Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
    [Crossref]
  12. X. Zhao, X. Pan, X. Fan, P. Xu, A. Bermak, and V. G. Chigrinov, “Patterned dual-layer achromatic micro-quarter-wave-retarder array for active polarization imaging,” Opt. Express 22(7), 8024–8034 (2014).
    [Crossref] [PubMed]
  13. G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16(5), 1168–1174 (1999).
    [Crossref]
  14. Z. Wu, P. E. Powers, A. M. Sarangan, and Q. Zhan, “Optical characterization of wiregrid micropolarizers designed for infrared imaging polarimetry,” Opt. Lett. 33(15), 1653–1655 (2008).
    [Crossref] [PubMed]
  15. S. B. Powell and V. Gruev, “Calibration methods for division-of-focal-plane polarimeters,” Opt. Express 21(18), 21039–21055 (2013).
    [Crossref] [PubMed]
  16. G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–410 (1852).
  17. 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]
  18. R. Perkins and V. Gruev, “Signal-to-noise analysis of Stokes parameters in division of focal plane polarimeters,” Opt. Express 18(25), 25815–25824 (2010).
    [Crossref] [PubMed]
  19. V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19(24), 24361–24369 (2011).
    [Crossref] [PubMed]
  20. T. York and V. Gruev, “Characterization of a visible spectrum division-of-focal-plane polarimeter,” Appl. Opt. 51(22), 5392–5400 (2012).
    [Crossref] [PubMed]

2015 (2)

2014 (4)

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

W. L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, and S. Pau, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22(3), 3063–3074 (2014).
[Crossref] [PubMed]

X. Zhao, X. Pan, X. Fan, P. Xu, A. Bermak, and V. G. Chigrinov, “Patterned dual-layer achromatic micro-quarter-wave-retarder array for active polarization imaging,” Opt. Express 22(7), 8024–8034 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2011 (1)

2010 (2)

2008 (2)

Z. Wu, P. E. Powers, A. M. Sarangan, and Q. Zhan, “Optical characterization of wiregrid micropolarizers designed for infrared imaging polarimetry,” Opt. Lett. 33(15), 1653–1655 (2008).
[Crossref] [PubMed]

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

2006 (1)

2005 (1)

A. El Gamal and H. Eltoukhy, “CMOS image sensors,” IEEE Circuits Devices Mag. 21(3), 6–20 (2005).
[Crossref]

2002 (1)

1999 (1)

1852 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–410 (1852).

Achilefu, S.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Balakrishnan, K.

Bermak, A.

Brock, N.

Charanya, T.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Chenault, D.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Chenault, D. B.

Chigrinov, V. G.

Cho, S.-Y.

Cronin, T. W.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

de Erausquin, I.

Deguzman, P. C.

Edmiston, C.

El Gamal, A.

A. El Gamal and H. Eltoukhy, “CMOS image sensors,” IEEE Circuits Devices Mag. 21(3), 6–20 (2005).
[Crossref]

Eltoukhy, H.

A. El Gamal and H. Eltoukhy, “CMOS image sensors,” IEEE Circuits Devices Mag. 21(3), 6–20 (2005).
[Crossref]

Engheta, N.

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

Fan, X.

Gao, S.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Garcia, N. M.

Goldstein, D. L.

Gruev, V.

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

S. B. Powell and V. Gruev, “Calibration methods for division-of-focal-plane polarimeters,” Opt. Express 21(18), 21039–21055 (2013).
[Crossref] [PubMed]

T. York and V. Gruev, “Characterization of a visible spectrum division-of-focal-plane polarimeter,” Appl. Opt. 51(22), 5392–5400 (2012).
[Crossref] [PubMed]

V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19(24), 24361–24369 (2011).
[Crossref] [PubMed]

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]

R. Perkins and V. Gruev, “Signal-to-noise analysis of Stokes parameters in division of focal plane polarimeters,” Opt. Express 18(25), 25815–25824 (2010).
[Crossref] [PubMed]

Hsu, W. L.

Ibn-Elhaj, M.

Jones, M. W.

Kahan, L.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Lake, S. P.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Marshall, J.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Meier, J. T.

Milin, Z.

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

Myhre, G.

Namer, E.

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind Haze Separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006) pp. 1984–1991.

Nan, C.

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

Nordin, G. P.

Pan, X.

Pau, S.

Perkins, R.

Pezzaniti, J. L.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Pezzaniti, J. P.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Powell, S. B.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

S. B. Powell and V. Gruev, “Calibration methods for division-of-focal-plane polarimeters,” Opt. Express 21(18), 21039–21055 (2013).
[Crossref] [PubMed]

Powers, P. E.

Raman, B.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Reinhardt, J.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Roberts, N. W.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Roche, M.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Saha, D.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Sarangan, A. M.

Schechner, Y. Y.

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind Haze Separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006) pp. 1984–1991.

Schultz, H.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Shaw, J. A.

Shwartz, S.

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind Haze Separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006) pp. 1984–1991.

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–410 (1852).

Tyo, J. S.

Van der Spiegel, J.

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

Voelz, D. G.

Wu, Z.

Xiao, X.

Xiaotie, W.

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

Xu, P.

York, T.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

T. York and V. Gruev, “Characterization of a visible spectrum division-of-focal-plane polarimeter,” Appl. Opt. 51(22), 5392–5400 (2012).
[Crossref] [PubMed]

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]

Zhan, H.

Zhan, Q.

Zhao, X.

Appl. Opt. (4)

IEEE Circuits Devices Mag. (1)

A. El Gamal and H. Eltoukhy, “CMOS image sensors,” IEEE Circuits Devices Mag. 21(3), 6–20 (2005).
[Crossref]

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

Opt. Express (7)

Opt. Lett. (1)

Proc IEEE Inst Electr Electron Eng (1)

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Proc. IEEE (1)

Z. Milin, W. Xiaotie, C. Nan, N. Engheta, and J. Van der Spiegel, “Bioinspired focal-plane polarization image sensor design: from application to implementation,” Proc. IEEE 102(10), 1435–1449 (2014).
[Crossref]

Proc. SPIE (1)

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, J. P. Pezzaniti, and H. Schultz, “Four camera complete Stokes imaging polarimeter,” Proc. SPIE 6972, 69720J (2008).
[Crossref]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–410 (1852).

Other (2)

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind Haze Separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006) pp. 1984–1991.

D. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2011).

Supplementary Material (3)

NameDescription
» Visualization 1: MP4 (2607 KB)      Visualization 1
» Visualization 2: MP4 (1789 KB)      Visualization 2
» Visualization 3: MP4 (5253 KB)      Visualization 3

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Figures (10)

Fig. 1
Fig. 1 Optical setup for optical evaluation of the high frame rate sensor.

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Fig. 2
Fig. 2 Uncalibrated pixel response averaged over the image sensor.

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Fig. 3
Fig. 3 Calibrated pixel response averaged over the image sensor.

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Fig. 4
Fig. 4 Monochromator setup for measuring spectral response of image sensor.

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Fig. 5
Fig. 5 Diattenuation of the polarization filters over the visible spectrum.

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Fig. 6
Fig. 6 Scanning electron microscope image of pixelated, nanowire polarization filters.

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Fig. 7
Fig. 7 High speed (top row) and low speed (bottom row) capture of polycarbonate square cracking. Blue indicates areas of low strain (DoLP = 0) and red of high strain (DoLP = 1). See supplementary video online (see Visualization 1).

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Fig. 8
Fig. 8 Capture of polycarbonate failure at 1000 frames-per-second (see Visualization 2).

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Fig. 9
Fig. 9 Comparison of high frame rate video (top) and normal rate (bottom) for vehicular tracking. The high frame rate video maintains a strong polarization signature in the reflected windshield, while the normal speed video shows erroneous measurments in the DoLP and AoP (see Visualization 3).

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Fig. 10
Fig. 10 Another comparison of of high frame rate video (top) and normal rate (bottom) for vehicular tracking (see Visualization 3).

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Equations (6)

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

I( θ,ϕ )= 1 2 ( S 0 + S 1 cos2θ+ S 2 sin2θcosϕ+ S 3 sin2θsinϕ )
S 0 = 1 2 [ I(0°,0°)+I(45°,0°)+I(90°,0°)+I(135°,0°) ]
S 1 =I(0°,0°)−I(90°,0°)
S 2 =I(45°,0°)−I(135°,0°)
DoLP= S 1 2 + S 2 2 S 0
AoP= 1 2 tan −1 ( S 2 S 1 )

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