Abstract

In this paper we propose a model to understand the polarization patterns of skylight when reflected off the surface of waves. The semi-empirical Rayleigh model is used to analyze the polarization of scattered skylight; the Harrison and Coombes model is used to analyze light radiance distribution; and the Cox-Munk model and Mueller matrix are used to analyze reflections from wave surface. First, we calculate the polarization patterns and intensity distribution of light reflected off wave surface. Then we investigate their relationship with incident radiation, solar zenith angle, wind speed and wind direction. Our results show that the polarization patterns of reflected skylight from waves and flat water are different, while skylight reflected on both kinds of water is generally highly polarized at the Brewster angle and the polarization direction is approximately parallel to the water's surface. The backward-reflecting Brewster zone has a relatively low reflectance and a high DOP in all observing directions. This can be used to optimally diminish the reflected skylight and avoid sunglint in ocean optics measurements.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
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    [PubMed]
  6. S. P. Garaba and O. Zielinski, “Methods in reducing surface reflected glint for shipborne above-water remote sensing,” J. Europ. Opt. Soc. Rap. Public.8, 13058 (2013).
    [CrossRef]
  7. S. Kay, J. D. Hedley, and S. Lavender, “Sun glint correction of high and low spatial resolution images of aquatic scenes: a review of methods for visible and near-infrared wavelengths,” Remote Sens.1(4), 697–730 (2009).
    [CrossRef]
  8. A. Cunningham, P. Wood, and D. McKee, “Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer,” J. Opt. A, Pure Appl. Opt.4(4), S29–S33 (2002).
    [CrossRef]
  9. J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Bound.-Lay. Meteorol.18(3), 235–245 (1980).
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  10. K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
    [CrossRef]
  11. Z. P. Lee, K. L. Carder, T. G. Peacock, and R. G. Steward, “Remote sensing reflectance measured with and without a vertical polarizer,” Proc. SPIE2963, 483–488 (1997).
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A19(10), 2085–2099 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  24. X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
    [CrossRef]
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2013 (1)

S. P. Garaba and O. Zielinski, “Methods in reducing surface reflected glint for shipborne above-water remote sensing,” J. Europ. Opt. Soc. Rap. Public.8, 13058 (2013).
[CrossRef]

2011 (1)

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Philos. Trans. R. Soc. Lond. B Biol. Sci.366(1565), 671–679 (2011).
[CrossRef] [PubMed]

2010 (1)

X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
[CrossRef]

2009 (1)

S. Kay, J. D. Hedley, and S. Lavender, “Sun glint correction of high and low spatial resolution images of aquatic scenes: a review of methods for visible and near-infrared wavelengths,” Remote Sens.1(4), 697–730 (2009).
[CrossRef]

2008 (1)

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

2006 (1)

2004 (1)

2002 (3)

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A19(10), 2085–2099 (2002).
[CrossRef] [PubMed]

N. Ebuchi and S. Kizu, “Probability distribution of surface wave slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers,” J. Oceanogr.58(3), 477–486 (2002).
[CrossRef]

A. Cunningham, P. Wood, and D. McKee, “Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer,” J. Opt. A, Pure Appl. Opt.4(4), S29–S33 (2002).
[CrossRef]

2001 (2)

J. Gál, G. Horváth, and V. B. Meyer-Rochow, “Measurement of the reflection-polarization pattern of the flat water surface under a clear sky at sunset,” Remote Sens. Environ.76(1), 103–111 (2001).
[CrossRef]

L. T. Wong and W. K. Chow, “Solar radiation model,” Appl. Energy69(3), 191–224 (2001).
[CrossRef]

2000 (1)

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
[CrossRef]

1997 (2)

G. Horváth and D. Varjú, “Polarization pattern of freshwater habitats recorded by video polarimetry in red, green and blue spectral ranges and its relevance for water detection by aquatic insects,” J. Exp. Biol.200, 1155–1163 (1997).
[PubMed]

Z. P. Lee, K. L. Carder, T. G. Peacock, and R. G. Steward, “Remote sensing reflectance measured with and without a vertical polarizer,” Proc. SPIE2963, 483–488 (1997).
[CrossRef]

1995 (1)

G. Horváth, “Reflection-polarization patterns at flat water surfaces and their relevance for insect polarization vision,” J. Theor. Biol.175(1), 27–37 (1995).
[CrossRef] [PubMed]

1993 (1)

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

1988 (1)

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy40(1), 57–63 (1988).
[CrossRef]

1981 (1)

W. A. Peterson and I. Dirmhirn, “The ratio of diffuse to direct solar irradiance (perpendicular to the sun’s rays) with clear skies-a conserved quantity throughout the day,” J. Appl. Meteorol.20(7), 826–828 (1981).
[CrossRef]

1980 (1)

J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Bound.-Lay. Meteorol.18(3), 235–245 (1980).
[CrossRef]

1977 (1)

1967 (1)

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res.72(18), 4643–4649 (1967).
[CrossRef]

1954 (1)

Bai, Y.

X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
[CrossRef]

Barta, A.

Bernáth, B.

Carder, K. L.

Z. P. Lee, K. L. Carder, T. G. Peacock, and R. G. Steward, “Remote sensing reflectance measured with and without a vertical polarizer,” Proc. SPIE2963, 483–488 (1997).
[CrossRef]

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

Chen, R. F.

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

Chow, W. K.

L. T. Wong and W. K. Chow, “Solar radiation model,” Appl. Energy69(3), 191–224 (2001).
[CrossRef]

Coombes, C. A.

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy40(1), 57–63 (1988).
[CrossRef]

Cox, C.

Cunningham, A.

A. Cunningham, P. Wood, and D. McKee, “Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer,” J. Opt. A, Pure Appl. Opt.4(4), S29–S33 (2002).
[CrossRef]

Davis, C. O.

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

Dirmhirn, I.

W. A. Peterson and I. Dirmhirn, “The ratio of diffuse to direct solar irradiance (perpendicular to the sun’s rays) with clear skies-a conserved quantity throughout the day,” J. Appl. Meteorol.20(7), 826–828 (1981).
[CrossRef]

Ebuchi, N.

N. Ebuchi and S. Kizu, “Probability distribution of surface wave slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers,” J. Oceanogr.58(3), 477–486 (2002).
[CrossRef]

Erlick, C.

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Philos. Trans. R. Soc. Lond. B Biol. Sci.366(1565), 671–679 (2011).
[CrossRef] [PubMed]

Gál, J.

J. Gál, G. Horváth, and V. B. Meyer-Rochow, “Measurement of the reflection-polarization pattern of the flat water surface under a clear sky at sunset,” Remote Sens. Environ.76(1), 103–111 (2001).
[CrossRef]

Garaba, S. P.

S. P. Garaba and O. Zielinski, “Methods in reducing surface reflected glint for shipborne above-water remote sensing,” J. Europ. Opt. Soc. Rap. Public.8, 13058 (2013).
[CrossRef]

Gong, F.

X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
[CrossRef]

Gower, J. F. R.

J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Bound.-Lay. Meteorol.18(3), 235–245 (1980).
[CrossRef]

Guinn, J. A.

Hamilton, M.

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

Harrison, A. W.

A. W. Harrison and C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy40(1), 57–63 (1988).
[CrossRef]

He, X. Q.

X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
[CrossRef]

Hedley, J. D.

S. Kay, J. D. Hedley, and S. Lavender, “Sun glint correction of high and low spatial resolution images of aquatic scenes: a review of methods for visible and near-infrared wavelengths,” Remote Sens.1(4), 697–730 (2009).
[CrossRef]

Horváth, G.

B. Suhai and G. Horváth, “How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study,” J. Opt. Soc. Am. A21(9), 1669–1676 (2004).
[CrossRef] [PubMed]

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A19(10), 2085–2099 (2002).
[CrossRef] [PubMed]

J. Gál, G. Horváth, and V. B. Meyer-Rochow, “Measurement of the reflection-polarization pattern of the flat water surface under a clear sky at sunset,” Remote Sens. Environ.76(1), 103–111 (2001).
[CrossRef]

G. Horváth and D. Varjú, “Polarization pattern of freshwater habitats recorded by video polarimetry in red, green and blue spectral ranges and its relevance for water detection by aquatic insects,” J. Exp. Biol.200, 1155–1163 (1997).
[PubMed]

G. Horváth, “Reflection-polarization patterns at flat water surfaces and their relevance for insect polarization vision,” J. Theor. Biol.175(1), 27–37 (1995).
[CrossRef] [PubMed]

Kattawar, G. W.

Kay, S.

S. Kay, J. D. Hedley, and S. Lavender, “Sun glint correction of high and low spatial resolution images of aquatic scenes: a review of methods for visible and near-infrared wavelengths,” Remote Sens.1(4), 697–730 (2009).
[CrossRef]

Kizu, S.

N. Ebuchi and S. Kizu, “Probability distribution of surface wave slope derived using sun glitter images from geostationary meteorological satellite and surface vector winds from scatterometers,” J. Oceanogr.58(3), 477–486 (2002).
[CrossRef]

Klemm, F. J.

Kotchenova, S. Y.

Labhart, T.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
[CrossRef]

Lambrinos, D.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
[CrossRef]

Lavender, S.

S. Kay, J. D. Hedley, and S. Lavender, “Sun glint correction of high and low spatial resolution images of aquatic scenes: a review of methods for visible and near-infrared wavelengths,” Remote Sens.1(4), 697–730 (2009).
[CrossRef]

Lee, Z. P.

Z. P. Lee, K. L. Carder, T. G. Peacock, and R. G. Steward, “Remote sensing reflectance measured with and without a vertical polarizer,” Proc. SPIE2963, 483–488 (1997).
[CrossRef]

Lerner, A.

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Philos. Trans. R. Soc. Lond. B Biol. Sci.366(1565), 671–679 (2011).
[CrossRef] [PubMed]

Li, W.

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

Matarrese, R.

McKee, D.

A. Cunningham, P. Wood, and D. McKee, “Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer,” J. Opt. A, Pure Appl. Opt.4(4), S29–S33 (2002).
[CrossRef]

Meyer-Rochow, V. B.

J. Gál, G. Horváth, and V. B. Meyer-Rochow, “Measurement of the reflection-polarization pattern of the flat water surface under a clear sky at sunset,” Remote Sens. Environ.76(1), 103–111 (2001).
[CrossRef]

Möller, R.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
[CrossRef]

Muller-Karger, F.

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

Munk, W.

Ottaviani, M.

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

Peacock, T. G.

Z. P. Lee, K. L. Carder, T. G. Peacock, and R. G. Steward, “Remote sensing reflectance measured with and without a vertical polarizer,” Proc. SPIE2963, 483–488 (1997).
[CrossRef]

Peterson, W. A.

W. A. Peterson and I. Dirmhirn, “The ratio of diffuse to direct solar irradiance (perpendicular to the sun’s rays) with clear skies-a conserved quantity throughout the day,” J. Appl. Meteorol.20(7), 826–828 (1981).
[CrossRef]

Pfeifer, R.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
[CrossRef]

Plass, G. N.

Reinersrnan, P.

K. L. Carder, P. Reinersrnan, R. F. Chen, F. Muller-Karger, C. O. Davis, and M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ.44(2-3), 205–216 (1993).
[CrossRef]

Sabbah, S.

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Philos. Trans. R. Soc. Lond. B Biol. Sci.366(1565), 671–679 (2011).
[CrossRef] [PubMed]

Saunders, P. M.

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res.72(18), 4643–4649 (1967).
[CrossRef]

Shashar, N.

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Philos. Trans. R. Soc. Lond. B Biol. Sci.366(1565), 671–679 (2011).
[CrossRef] [PubMed]

Spurr, R.

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

Stamnes, K.

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

Steward, R. G.

Z. P. Lee, K. L. Carder, T. G. Peacock, and R. G. Steward, “Remote sensing reflectance measured with and without a vertical polarizer,” Proc. SPIE2963, 483–488 (1997).
[CrossRef]

Su, W.

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

Suhai, B.

Varjú, D.

G. Horváth and D. Varjú, “Polarization pattern of freshwater habitats recorded by video polarimetry in red, green and blue spectral ranges and its relevance for water detection by aquatic insects,” J. Exp. Biol.200, 1155–1163 (1997).
[PubMed]

Vermote, E. F.

Wehner, R.

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A19(10), 2085–2099 (2002).
[CrossRef] [PubMed]

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst.30(1-2), 39–64 (2000).
[CrossRef]

Wiscombe, W.

M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
[CrossRef]

Wong, L. T.

L. T. Wong and W. K. Chow, “Solar radiation model,” Appl. Energy69(3), 191–224 (2001).
[CrossRef]

Wood, P.

A. Cunningham, P. Wood, and D. McKee, “Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer,” J. Opt. A, Pure Appl. Opt.4(4), S29–S33 (2002).
[CrossRef]

Zhu, Q. K.

X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
[CrossRef]

Zielinski, O.

S. P. Garaba and O. Zielinski, “Methods in reducing surface reflected glint for shipborne above-water remote sensing,” J. Europ. Opt. Soc. Rap. Public.8, 13058 (2013).
[CrossRef]

Appl. Energy (1)

L. T. Wong and W. K. Chow, “Solar radiation model,” Appl. Energy69(3), 191–224 (2001).
[CrossRef]

Appl. Opt. (2)

Bound.-Lay. Meteorol. (1)

J. F. R. Gower, “Observations of in situ fluorescence of chlorophyll-a in Saanich Inlet,” Bound.-Lay. Meteorol.18(3), 235–245 (1980).
[CrossRef]

J. Appl. Meteorol. (1)

W. A. Peterson and I. Dirmhirn, “The ratio of diffuse to direct solar irradiance (perpendicular to the sun’s rays) with clear skies-a conserved quantity throughout the day,” J. Appl. Meteorol.20(7), 826–828 (1981).
[CrossRef]

J. Europ. Opt. Soc. Rap. Public. (1)

S. P. Garaba and O. Zielinski, “Methods in reducing surface reflected glint for shipborne above-water remote sensing,” J. Europ. Opt. Soc. Rap. Public.8, 13058 (2013).
[CrossRef]

J. Exp. Biol. (1)

G. Horváth and D. Varjú, “Polarization pattern of freshwater habitats recorded by video polarimetry in red, green and blue spectral ranges and its relevance for water detection by aquatic insects,” J. Exp. Biol.200, 1155–1163 (1997).
[PubMed]

J. Geophys. Res. (1)

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res.72(18), 4643–4649 (1967).
[CrossRef]

J. Oceanogr. (1)

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J. Opt. A, Pure Appl. Opt. (1)

A. Cunningham, P. Wood, and D. McKee, “Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer,” J. Opt. A, Pure Appl. Opt.4(4), S29–S33 (2002).
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M. Ottaviani, R. Spurr, K. Stamnes, W. Li, W. Su, and W. Wiscombe, “Improving the description of sunglint for accurate prediction of remotely sensed radiances,” J. Quant. Spectr. Rad. Tr.109(14), 2364–2375 (2008).
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X. Q. He, Y. Bai, Q. K. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectr. Rad. Tr.111(10), 1426–1448 (2010).
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J. Theor. Biol. (1)

G. Horváth, “Reflection-polarization patterns at flat water surfaces and their relevance for insect polarization vision,” J. Theor. Biol.175(1), 27–37 (1995).
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Philos. Trans. R. Soc. Lond. B Biol. Sci. (1)

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Philos. Trans. R. Soc. Lond. B Biol. Sci.366(1565), 671–679 (2011).
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Remote Sens. (1)

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Figures (15)

Fig. 1
Fig. 1

(a) Geometry of wave facet reflectance; (b) Sketch map of reference plane rotation.

Fig. 2
Fig. 2

DOP patterns of clear sky at solar zenith angle θs = 0°, 30°, 60°, 90°. Here and in the following figures, the celestial hemisphere and its reflection patterns are represented in a two dimensional coordinate system. The zenith and the nadir are at the origin and the horizon is represented by the outermost circle. The zenith angle and azimuth angle are measured radially and tangentially, respectively. The solar azimuth angle is always set to 0.

Fig. 3
Fig. 3

AOP patterns of clear sky at solar zenith angle θs = 0°, 30°, 60°, 90°, where the reference plane is the meridian of each observing direction.

Fig. 4
Fig. 4

Polarization patterns calculated by semi-empirical Rayleigh model and that calculated by 6SV. (a1) and (b1) are DOP and AOP patterns calculated by Rayleigh model, (a2) and (b2) are DOP and AOP patterns calculated by 6SV. Other parameters: SZA is 30°, aerosol optical depth of 550nm is 0.2, wind speed is 5 m/s, wind direction is 0°, the Midlatitude Summer atmosphere model and Maritime aerosol model are used.

Fig. 5
Fig. 5

DOP patterns of reflected clear skylight off a flat water surface at solar zenith angle θs = 0°, 30°, 60°, 90°, the DOPs range from 0 to 1.

Fig. 6
Fig. 6

AOP patterns reflected clear skylight off flat water surface at solar zenith angle θs = 0°, 30°, 60°, 90°, the AOP ranges from 0° to 90°, the reference plane is the meridian of each observing direction.

Fig. 7
Fig. 7

Reflectivity patterns reflected clear skylight off flat water surface at solar zenith angle θs = 0°, 30°, 60°, 90°.

Fig. 8
Fig. 8

Polarization and intensity patterns of reflected light from wave water under clear sky (a1,b1,c1) and overcast skylight (a2,b2,c2). (a1) and (a2) refer to AOP patterns. (b1) and (b2) refer to DOP patterns. (c1) and (c2) refer to intensity patterns. Other parameters: SZA is 30°, wind direction is 0°, wind speed is 5m/s, intensity ratio of sunlight to scattered skylight is 9:1.

Fig. 9
Fig. 9

Polarization and intensity patterns of reflected light from wave water when the ratio of sunlight to skylight is 9:1 (a1,b1,c1) and 6:1 (a2,b2,c2). (a1) and (a2) refer to AOP patterns. (b1) and (b2) refer to DOP patterns. (c1) and (c2) refer to intensity patterns. Other parameters: SZA is 30°, wind direction is 0°, wind speed is 5m/s.

Fig. 10
Fig. 10

DOP patterns of reflected skylight under different SZAs. Other parameters: wind direction is 0°, wind speed is 5m/s, intensity ratio of sunlight to skylight is 9:1.

Fig. 11
Fig. 11

DOP patterns of reflected skylight in (A) solar meridian (positive and negative zenith angle refers to solar and anti-solar meridian, respectively) and (B) vertical meridian (positive and negative zenith angle refers to 90° direction and 270° direction, respectively.).

Fig. 12
Fig. 12

AOP patterns of reflected full skylight under different SZAs. Other parameters: wind direction is 0°, wind speed is 5m/s, intensity ratio of sunlight to scattered skylight is 9:1.

Fig. 13
Fig. 13

Intensity patterns of reflected full skylight under different SZAs. Other parameters: wind direction is 0°, wind speed is 5m/s, intensity ratio of sunlight to scattered skylight is 9:1.

Fig. 14
Fig. 14

Patterns of reflected light from wave water under different wind speed. Other parameters: SZA = 30°, wind direction is 0°, intensity ratio of sunlight to skylight is 9:1.

Fig. 15
Fig. 15

Patterns of reflected light from wave water under different wind directions. Other parameters: SZA = 30°, wind speed is 5m/s, intensity ratio of sunlight to skylight is 9:1.

Equations (19)

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N(γ, θ s , θ v )=(A+B e mγ +C cos 2 γcos θ s )(1 e 1.90sec θ v )(1 e 0.53sec θ s ).
DOP=DO P max sin 2 γ 1+ cos 2 γ .
cosγ=cos θ s cos θ v +sin θ s sin θ v cosφ.
AOP=arccos( sinφ sinγ sin θ s )
{ r s = n 1 cos θ 1 n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 r p = n 2 cos θ 1 n 1 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2 .
DO P r = r s 2 r p 2 r s 2 + r p 2 .
[ I r Q r U r V r ]=M[ I i Q i U i V i ]= 1 2 ( r s 2 + r p 2 r p 2 r s 2 0 0 r p 2 r s 2 r s 2 + r p 2 0 0 0 0 2 r s r p 0 0 0 0 2 r s r p )[ I i Q i U i V i ].
DOP= Q 2 + U 2 + V 2 I .
AOP= 1 2 tan 1 ( U Q ).
{ z x = z / x = sin α tan β = sin θ s sin φ s + sin θ o sin φ o cos θ s + cos θ o z y = z / y = cos α tan β = sin θ s cos φ s + sin θ o cos φ o cos θ s + cos θ o .
{ z x = cos χ z x + sin χ z y z y = sin χ z x + cos χ z y .
p ( z x , z y ) = 1 2 π σ u σ c e ξ 2 + η 2 2 [ 1 1 2 C 21 η ( ξ 2 1 ) 1 6 C 03 ( η 3 3 η ) + 1 24 C 40 ( ξ 4 6 ξ 2 + 3 ) + 1 4 C 22 ( ξ 2 1 ) ( η 2 1 ) + 1 24 C 04 ( η 4 6 η 2 + 3 ) ] .
{ σ u = 0.0053 + 6.71 × 10 4 W σ c = 0.0048 + 1.52 × 10 4 W .
cos Θ = cos θ s cos θ o + sin θ s sin θ o cos Δ φ .
S ( θ s , θ o , σ 2 ) = 1 1 + Λ ( cot ( θ s ) ) + Λ ( cot ( θ o ) ) Λ ( x ) = 1 2 [ 2 π σ x exp ( x 2 2 σ 2 ) erfc ( x 2 σ ) ] .
ρ g ( θ s , θ o , Δ φ ) = π r ( ω ) 4 cos θ s cos θ o cos 4 β p ( z x , z y ) S ( θ s , θ o , σ 2 ) .
R f ( θ s , θ o ,Δφ)=C(π i 2 ) F r (ω)C( i 1 ).
C(i)=[ 1 0 0 0 0 cos2i sin2i 0 0 sin2i cos2i 0 0 0 0 1 ].
R( θ s , θ o ,Δφ)= π 4cos θ s cos θ o cos 4 β p( z x , z y )S( θ s , θ o , σ 2 ) R f ( θ s , θ o ,Δφ).

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