Abstract

We use a Monte Carlo code that calculates the complete Stokes vector to predict the degree of polarization in the complete observable solid angle at any level in an atmosphere–ocean system. Using the Stokes vector components, we can find the positions of neutral points in a simulated plane-parallel atmosphere–ocean system for various conditions. We examine the locations and behavior of these neutral points for an observer placed directly above and beneath the air–water boundary and show how their positions are influenced by different atmospheric and oceanic conditions.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
    [CrossRef]
  2. M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
    [CrossRef]
  3. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).
  4. G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral point polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099(2002).
    [CrossRef]
  5. M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a guache de Soleil,” Compt. Rend. 107, 867–870 (1888).
  6. R. S. Fraser, “Atmospheric neutral points over water,” J. Opt. Soc. Am. 58, 1029–1031 (1968).
    [CrossRef]
  7. J. T. Adams and G. W. Kattawar, “Neutral points in an atmosphere–ocean system. 1: Upwelling light field,” Appl. Opt. 36, 1976–1986 (1997).
    [CrossRef] [PubMed]
  8. T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
    [CrossRef] [PubMed]
  9. T. H. Waterman and W. E. Westell, “Quantitative effect of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).
  10. A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).
  11. A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).
  12. B. Lundgren, “On the polarization of daylight in the sea,” Rep. 17 (Department of Physical Oceanography, University of Copenhagen, 1971), pp. 1–34.
  13. K. J. Voss and Y. Liu, “Polarized radiance distribution measurements of skylight. I. System description and characterization,” Appl. Opt. 36, 6083–6094 (1997).
    [CrossRef] [PubMed]
  14. Y. Liu and K. J. Voss, “Polarized radiance distribution measurement of skylight. II. Experiment and data,” Appl. Opt. 36, 8753–8764 (1997).
    [CrossRef]
  15. R. L. Lee Jr., “Digital imaging of clear-sky polarization,” Appl. Opt. 37, 1465–1476 (1998).
    [CrossRef]
  16. J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
    [CrossRef]
  17. S. Sabbah and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
    [CrossRef]
  18. S. Sabbah and N. Shashar, “Light polarization under water near sunrise,” J. Opt. Soc. Am. A 24, 2049–2056.
    [CrossRef]
  19. N. J. Pust and J. A. Shaw, “Digital all-sky polarization imaging of partly cloudy skies,” Appl. Opt. 47, H190–H198 (2008).
    [CrossRef] [PubMed]
  20. A. Kreuter, M. Zangerl, M. Schwarzmann, and M. Blumthaler, “All-sky imaging: a simple, versatile system for atmospheric research,” Appl. Opt. 48, 1091–1097 (2009).
    [CrossRef]
  21. A. Tonizzo, J. Zhou, A. Gilerson, M. S. Twardowski, D. J. Gray, R. A. Arnone, B. M. Gross, F. Moshary, and S. A. Ahmed, “Polarized light in coastal waters: hyperspectral and multiangular analysis,” Opt. Express 17, 5666–5683 (2009).
    [CrossRef] [PubMed]
  22. K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010).
    [CrossRef] [PubMed]
  23. C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  24. A preliminary cloudless standard atmosphere for radiation computation (International Association for Meteorology and Atmospheric Physics, Boulder, Colo., 1984).
  25. R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (100–800 nm),” Appl. Opt. 20, 177–184(1981).
    [CrossRef] [PubMed]
  26. M. Tanaka and T. Nakajima, “Effects of oceanic turbidity and index of refraction of hydrosols on the flux of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 18, 93–111 (1977).
    [CrossRef]
  27. T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1972).
  28. The average particulate phase function can be found in Chap. 3, C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  29. A. T. Young, “Revised depolarization correction for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980).
    [CrossRef] [PubMed]
  30. A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of OceanographyN.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974), pp. 1–24.
  31. Our earlier paper cites a depolarization value for seawater of ρl=0.047, which is the value for linearly polarized incident light. This is related to the natural light depolarization value, ρu, given in this paper by ρu=2ρl/(1+ρl). See, for example, p. 49 of S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  32. J. T. Adams, E. Aas, N. K. Hojerslev, and B. Lundgren, “Comparison of radiance and polarization values observed in the Mediterranean Sea and simulated in a Monte Carlo model,” Appl. Opt. 41, 2724–2733 (2002).
    [CrossRef] [PubMed]
  33. G. W. Kattawar, G. N. Plass, and S. J. Hitzfelder, “Multiple scattered radiation emerging from Rayleigh and continental haze layers. 1: Radiance, polarization, and neutral points,” Appl. Opt. 15, 632–647 (1976).
    [CrossRef] [PubMed]
  34. J. D. Dave and P. M. Furukawa, “Intensity and polarization of the radiation emerging from an optically thick Rayleigh atmosphere,” J. Opt. Soc. Am. 56, 394–400 (1966).
    [CrossRef]
  35. Y. You, P. Zhai, G. W. Kattawar, and P. Yang, “Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution,” Appl. Opt. 48, 3019–3029 (2009).
    [CrossRef] [PubMed]
  36. S. Sabbah and N. Sashar, “Underwater light polarization and radiance fluctuations induced by surface waves,” Appl. Opt. 45, 4726–4739 (2006).
    [CrossRef] [PubMed]

2010 (1)

2009 (3)

2008 (1)

2007 (1)

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[CrossRef]

2006 (2)

2005 (1)

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

2002 (2)

2001 (1)

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

1998 (1)

1997 (3)

1981 (1)

1980 (1)

1977 (1)

M. Tanaka and T. Nakajima, “Effects of oceanic turbidity and index of refraction of hydrosols on the flux of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 18, 93–111 (1977).
[CrossRef]

1976 (1)

1968 (1)

1966 (1)

1958 (2)

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

1956 (1)

T. H. Waterman and W. E. Westell, “Quantitative effect of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).

1954 (2)

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef] [PubMed]

1888 (1)

M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a guache de Soleil,” Compt. Rend. 107, 867–870 (1888).

Aas, E.

Adams, J. T.

Ahmed, S. A.

Arnone, R. A.

Baker, K. S.

Barta, A.

Bernáth, B.

Blumthaler, M.

Cairns, B.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Chami, M.

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[CrossRef]

Chandrasekhar, , S.

Our earlier paper cites a depolarization value for seawater of ρl=0.047, which is the value for linearly polarized incident light. This is related to the natural light depolarization value, ρu, given in this paper by ρu=2ρl/(1+ρl). See, for example, p. 49 of S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chowdhary, J.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Cota, G. F.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Coulson, K. L.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).

Cox, C.

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Dave, J. D.

Fraser, R. S.

Furukawa, P. M.

Gál, J.

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Gilerson, A.

Gray, D. J.

Gross, B. M.

Hitzfelder, S. J.

Hobbs, P. V.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Hojerslev, N. K.

Holben, B. N.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Horváth, G.

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral point polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099(2002).
[CrossRef]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Ivanoff, A.

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

Kattawar, G. W.

Kreuter, A.

Lee, R. L.

Liu, Y.

Lundgren, B.

Meyer-Rochow, V. B.

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Mishchenko, M. I.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Mobley, C. D.

The average particulate phase function can be found in Chap. 3, C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

Morel, A.

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of OceanographyN.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974), pp. 1–24.

Moshary, F.

Munk, W.

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Nakajima, T.

M. Tanaka and T. Nakajima, “Effects of oceanic turbidity and index of refraction of hydrosols on the flux of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 18, 93–111 (1977).
[CrossRef]

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1972).

Plass, G. N.

Pust, N. J.

Redemann, J.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Russell, E.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Rutledge, K.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

Sabbah, S.

Sashar, N.

Schwarzmann, M.

Shashar, N.

Shaw, J. A.

Smith, R. C.

Soret, M. J. L.

M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a guache de Soleil,” Compt. Rend. 107, 867–870 (1888).

Souaidia, N.

Suhai, B.

Tanaka, M.

M. Tanaka and T. Nakajima, “Effects of oceanic turbidity and index of refraction of hydrosols on the flux of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 18, 93–111 (1977).
[CrossRef]

Tonizzo, A.

Twardowski, M. S.

Voss, K. J.

Waterman, T. H.

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

T. H. Waterman and W. E. Westell, “Quantitative effect of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef] [PubMed]

Wehner, R.

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral point polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099(2002).
[CrossRef]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Westell, W. E.

T. H. Waterman and W. E. Westell, “Quantitative effect of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).

Yang, P.

You, Y.

Young, A. T.

Zangerl, M.

Zhai, P.

Zhou, J.

Appl. Opt. (12)

G. W. Kattawar, G. N. Plass, and S. J. Hitzfelder, “Multiple scattered radiation emerging from Rayleigh and continental haze layers. 1: Radiance, polarization, and neutral points,” Appl. Opt. 15, 632–647 (1976).
[CrossRef] [PubMed]

R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (100–800 nm),” Appl. Opt. 20, 177–184(1981).
[CrossRef] [PubMed]

J. T. Adams and G. W. Kattawar, “Neutral points in an atmosphere–ocean system. 1: Upwelling light field,” Appl. Opt. 36, 1976–1986 (1997).
[CrossRef] [PubMed]

K. J. Voss and Y. Liu, “Polarized radiance distribution measurements of skylight. I. System description and characterization,” Appl. Opt. 36, 6083–6094 (1997).
[CrossRef] [PubMed]

R. L. Lee Jr., “Digital imaging of clear-sky polarization,” Appl. Opt. 37, 1465–1476 (1998).
[CrossRef]

Y. Liu and K. J. Voss, “Polarized radiance distribution measurement of skylight. II. Experiment and data,” Appl. Opt. 36, 8753–8764 (1997).
[CrossRef]

J. T. Adams, E. Aas, N. K. Hojerslev, and B. Lundgren, “Comparison of radiance and polarization values observed in the Mediterranean Sea and simulated in a Monte Carlo model,” Appl. Opt. 41, 2724–2733 (2002).
[CrossRef] [PubMed]

A. T. Young, “Revised depolarization correction for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980).
[CrossRef] [PubMed]

N. J. Pust and J. A. Shaw, “Digital all-sky polarization imaging of partly cloudy skies,” Appl. Opt. 47, H190–H198 (2008).
[CrossRef] [PubMed]

A. Kreuter, M. Zangerl, M. Schwarzmann, and M. Blumthaler, “All-sky imaging: a simple, versatile system for atmospheric research,” Appl. Opt. 48, 1091–1097 (2009).
[CrossRef]

S. Sabbah and N. Sashar, “Underwater light polarization and radiance fluctuations induced by surface waves,” Appl. Opt. 45, 4726–4739 (2006).
[CrossRef] [PubMed]

Y. You, P. Zhai, G. W. Kattawar, and P. Yang, “Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution,” Appl. Opt. 48, 3019–3029 (2009).
[CrossRef] [PubMed]

Compt. Rend. (1)

M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a guache de Soleil,” Compt. Rend. 107, 867–870 (1888).

J. Atmos. Sci. (1)

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russell, “Retrieval of aerosol scattering and absorption properties from photopolarimetric observations over the ocean during the CLAMS experiment,” J. Atmos. Sci. 62, 1093–1117 (2005).
[CrossRef]

J. Geophys. Res. (1)

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[CrossRef]

J. Mar. Res. (4)

T. H. Waterman and W. E. Westell, “Quantitative effect of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

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

M. Tanaka and T. Nakajima, “Effects of oceanic turbidity and index of refraction of hydrosols on the flux of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 18, 93–111 (1977).
[CrossRef]

Opt. Express (2)

Proc. R. Soc. London Ser. A (1)

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Science (1)

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef] [PubMed]

Other (7)

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1972).

The average particulate phase function can be found in Chap. 3, C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).

B. Lundgren, “On the polarization of daylight in the sea,” Rep. 17 (Department of Physical Oceanography, University of Copenhagen, 1971), pp. 1–34.

A preliminary cloudless standard atmosphere for radiation computation (International Association for Meteorology and Atmospheric Physics, Boulder, Colo., 1984).

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of OceanographyN.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974), pp. 1–24.

Our earlier paper cites a depolarization value for seawater of ρl=0.047, which is the value for linearly polarized incident light. This is related to the natural light depolarization value, ρu, given in this paper by ρu=2ρl/(1+ρl). See, for example, p. 49 of S. Chandrasekhar, Radiative Transfer (Dover, 1960).

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 (20)

Fig. 1
Fig. 1

Data format for the fish-eye lens images. The center of the image is the zenith (or nadir, if the observer is looking down), and the outer edge is the horizon. The principal plane is defined by the incident sunlight direction and the zenith.

Fig. 2
Fig. 2

Example of the downwelling radiance at a wavelength of 600 nm for a solar zenith angle of 60 ° in a Rayleigh atmosphere. The images are log-scaled. In (a), the observer is just above the water surface, and in (b), the observer is just below the water surface. Note that, in image (b), the downwelling radiance from the sky is compressed into the Snel cone by refraction at the air–ocean boundary.

Fig. 3
Fig. 3

Degree of polarization for Fig. 2. The images are log-scaled to emphasize polarization values near zero.

Fig. 4
Fig. 4

Four-color method to determine neutral lines and the formation of neutral points for the scenario shown in Fig. 3. In (a) and (c), the observer is just above the surface, and in (b) and (d), the observer is just below the surface. The colors in (a) and (b) represent regions where Q and U are positive or negative: white (yellow), both Q and U are negative; dark (blue), Q is negative and U is positive; medium (red), Q is positive and U is negative; light (green), both Q and U are positive. Neutral lines, lines where Q = 0 or U = 0 , are the edges of the colored regions and are shown in (c) and (d). Neutral points form where neutral lines intersect—where both Q and U change sign simultaneously. In (a) and (b), this occurs where dark (blue) and medium (red) regions intersect, or where light (green) and white (yellow) intersect.

Fig. 5
Fig. 5

Positions of the neutral points as a function of solar zenith angle in (a) the principal plane and (b) at azimuth angles. The observer is just above the ocean surface. The atmosphere is Rayleigh scattering only. The solid line in (a) is the position of the Sun. Note that the 500 nm points are outside the principal plane for some solar zenith angles and in it for others.

Fig. 6
Fig. 6

Effect of aerosols on the azimuth angle of the neutral points as a function of solar zenith angle. The wavelength is 550 nm , and the observer is just above the ocean surface.

Fig. 7
Fig. 7

Effect of aerosols on the position of the neutral points in the principal plane as a function of solar zenith angle. The wavelength is 400 nm . The observer is just above the ocean surface.

Fig. 8
Fig. 8

The position of the Arago neutral point as a function of solar zenith angle. The observer is just above the ocean surface. The atmosphere is Rayleigh scattering only.

Fig. 9
Fig. 9

Same as Fig. 8 but the atmosphere now includes an aerosol haze.

Fig. 10
Fig. 10

Positions of neutral points about the Sun as a function of wind speed for an observer just above the ocean surface. The solar zenith angle is 60 ° , the wavelength is 550 nm , the atmosphere is Rayleigh scattering only, and there are no hydrosols in the ocean.

Fig. 11
Fig. 11

Position of the principal plane neutral points for an observer just below the ocean surface. The atmosphere is Rayleigh scattering only. The solid line shows the apparent position of the Sun to the underwater observer, and the dashed line shows the critical angle.

Fig. 12
Fig. 12

Same as Fig. 11, but the atmosphere now includes an aerosol haze.

Fig. 13
Fig. 13

Effect of hydrosols on the neutral points in the principal plane for an observer just below the surface. The wavelength is 400 nm . In both cases, the atmosphere includes aerosols.

Fig. 14
Fig. 14

Position of the neutral points in the principal plane facing away from the Sun as a function of solar zenith angle for an observer directly below the ocean surface. The atmosphere is Rayleigh scattering only.

Fig. 15
Fig. 15

Same as Fig. 14, but the atmosphere includes an aerosol haze.

Fig. 16
Fig. 16

Effect of hydrosols on the neutral points in the principal plane facing away from the Sun as a function of solar zenith angle for an observer just below the surface. The wavelength is 400 nm . In both cases, the atmosphere includes aerosols.

Fig. 17
Fig. 17

The polarization structure of the light field. The top row shows the 400 nm results for (a) downwelling light and (b) upwelling light, and the bottom row shows the 700 nm results for (c) downwelling light and (d) upwelling light. The solar zenith angle is 80 ° , and there are no aerosols or hydrosols present. The colors are the same as in Fig. 4. Note that the downwelling light in regions outside the Snel cone in (a) and (c) are reflections of the upwelling light field in (b) and (d).

Fig. 18
Fig. 18

Log-scaled image of the degree of linear polarization for an observer directly beneath the surface. The wavelength is 700 nm , and the solar zenith angle is 86 ° . In (a), we show the downwelling light field and four neutral points. The neutral points outside the critical angle are a result of total internal reflection of the upwelling light field, shown in (b).

Fig. 19
Fig. 19

Positions of neutral points about the Sun as a function of wind speed for an observer just below the ocean surface. The solar zenith angle is 60 ° , the wavelength is 550 nm , the atmosphere is Rayleigh scattering only, and there are no hydrosols in the ocean.

Fig. 20
Fig. 20

Effect of wind speed on the polarization structure for the conditions shown in Fig. 19. The wind speeds are (a) 0 kn and (b) 10 kn . The color scheme is the same as in Fig. 4.

Tables (2)

Tables Icon

Table 1 Aerosol Parameters for the MAR-I Model a

Tables Icon

Table 2 Optical Parameters Used in the Calculations a

Equations (2)

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

n ( r ) = d N i ( r ) d r = N i r ln σ i 2 π exp [ ( ln r ln r i ) 2 2 ( ln σ i ) 2 ] .
n ( r ) = d N ( r ) d r = k r 4 .

Metrics