Abstract

Measurements of the radiance and degree of polarization made in 1971 in the Mediterranean Sea are presented along with the simulation of all observed quantities by a Monte Carlo technique. It is shown that our independent scattering treatment utilizing a Stokes vector formalism to describe the polarization state of the light field produces remarkably good agreement with those values measured in situ.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Knudsen, “On measurement of the penetration of light into the sea,” J. Cons. Cons. Permanent Int. l’Explor. Mer 76, 1–16 (1922).
  2. E. Bartholini, Experimenta Crystalli Islandici Disdiaclastici Qvibus Mira et Insolita Refractio Detegitur (Hafniae, Sumptibus Danielis Paulli Regii Biblia, The Royal Danish Library, Copenhagen, Denmark, 1669).
  3. C. Huygens, Traité de la Luminière. Ou sont Expliquées les Causes de ce qui luy Arrive dans la Reflexion, et Particuliérement dans l’Étrange Refraction du Cristal d’Islande (1690). (Also presented in C. Huygens, Oeuvres Completes, Publication par la Société Hollandaise des Sciences, 1937, Tome 19).
  4. T. H. Waterman, “Polarization of scattered sunlight in deep waters,” in Papers in Marine Biology and Oceanography, Deep-Sea Res.3, Suppl.426–434 (1955).
  5. T. H. Waterman, “Underwater light and the orientation of animals,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 415–445.
  6. T. H. Waterman, “Polarization of marine light fields and animal orientation,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 431–437 (1988).
    [CrossRef]
  7. A. Ivanoff, “Contribution a l’étude des propriétés optiques de l’eau de mer en Bretagne et en Corse, et la théorie de la polarisation sous-marine,” Ann. Geophys. 13, 22–53 (1957).
  8. A. Ivanoff, “Polarization measurements in the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, New York, 1974), pp. 151–175.
  9. A. Ivanoff, T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).
  10. A. Ivanoff, T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).
  11. B. Lundgren, “On the polarization of daylight in the sea,” Rep. 17, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1971), pp. 1–34.
  12. J. Lenoble, “Sur l’état de polarisation du rayonnement diffus aux grandes profondeurs dans un milieu suivant la loi de Rayleigh,” Comptes Rendus 246, 924–927 (1958).
  13. J. E. Tyler, “Estimation of per cent polarization in deep oceanic water,” J. Mar. Res. 21, 102–109 (1963).
  14. V. A. Timoveeva, “Optics of turbid waters,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steeman Nielsen, eds. (Academic, London, 1974), pp. 177–218.
  15. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).
  16. G. Kullenberg, N. Berg Olsen, “A comparison between observed and computed light scattering functions—II,” Rep. 19, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1972), pp. 1–27.
  17. N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. 21, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1973).
  18. N. K. Højerslev, “Daylight measurements for photosynthetic studies in the Western Mediterranean,” Rep. 26, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1974).
  19. N. G. Jerlov, “Significant relationships between optical properties of the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974).
  20. N. G. Jerlov, “A simple method for measuring quanta irradiance in the ocean,” Rep. 24, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1974).
  21. R. C. Smith, “Structure of solar radiation in the upper layers of the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 95–119.
  22. N. K. Højerslev, N. G. Jerlov, “The use of the colour index for determining quanta irradiance in the sea,” Rep. 35, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1977).
  23. N. K. Højerslev, E. Aas, “Spectral irradiance, radiance, and polarization in blue Mediterranean waters,” Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 138–147 (1997).
    [CrossRef]
  24. E. Aas, N. K. Højerslev, B. Lundgren, “Spectral irradiance, radiance, and polarization data from the Nordic Cruise in the Mediterranean Sea during June-July 1971,” Rep. 102, Department of Geophysics (University of Oslo, Oslo, Norway, 1997).
  25. B. Lundgren, N. K. Højerslev, “Daylight measurements in the Sargasso Sea. Results from the “Dana” Expedition January-April 1966,” Rep. 14, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1971).
  26. E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
    [CrossRef]
  27. A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).
  28. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
    [CrossRef] [PubMed]
  29. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  30. H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
    [CrossRef]
  31. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
    [CrossRef] [PubMed]
  32. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [CrossRef] [PubMed]
  33. A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 1–24.
  34. R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (100–800 nm),” Appl. Opt. 20, 177–184 (1981).
    [CrossRef] [PubMed]
  35. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [CrossRef]
  36. G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
    [CrossRef]
  37. C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  38. B. R. Marshall, “Raman scattering in ocean water,” Department of Geography (University of California, Santa Barbara, Santa Barbara, Calif.1989).
  39. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  40. J. T. Adams, G. W. Kattawar, “Neutral points in an atmosphere ocean system. 1: Upwelling light field,” Appl. Opt. 36, 1976–1986 (1997).
    [CrossRef] [PubMed]

1999 (1)

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

1997 (2)

1993 (1)

1991 (1)

1989 (2)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[CrossRef]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

1981 (1)

1977 (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

1975 (1)

1963 (1)

J. E. Tyler, “Estimation of per cent polarization in deep oceanic water,” J. Mar. Res. 21, 102–109 (1963).

1958 (3)

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

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

J. Lenoble, “Sur l’état de polarisation du rayonnement diffus aux grandes profondeurs dans un milieu suivant la loi de Rayleigh,” Comptes Rendus 246, 924–927 (1958).

1957 (1)

A. Ivanoff, “Contribution a l’étude des propriétés optiques de l’eau de mer en Bretagne et en Corse, et la théorie de la polarisation sous-marine,” Ann. Geophys. 13, 22–53 (1957).

1954 (1)

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

1939 (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

1922 (1)

M. Knudsen, “On measurement of the penetration of light into the sea,” J. Cons. Cons. Permanent Int. l’Explor. Mer 76, 1–16 (1922).

Aas, E.

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

E. Aas, N. K. Højerslev, B. Lundgren, “Spectral irradiance, radiance, and polarization data from the Nordic Cruise in the Mediterranean Sea during June-July 1971,” Rep. 102, Department of Geophysics (University of Oslo, Oslo, Norway, 1997).

N. K. Højerslev, E. Aas, “Spectral irradiance, radiance, and polarization in blue Mediterranean waters,” Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 138–147 (1997).
[CrossRef]

Adams, C. N.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Adams, J. T.

Baker, K. S.

Bartholini, E.

E. Bartholini, Experimenta Crystalli Islandici Disdiaclastici Qvibus Mira et Insolita Refractio Detegitur (Hafniae, Sumptibus Danielis Paulli Regii Biblia, The Royal Danish Library, Copenhagen, Denmark, 1669).

Berg Olsen, N.

G. Kullenberg, N. Berg Olsen, “A comparison between observed and computed light scattering functions—II,” Rep. 19, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1972), pp. 1–27.

Brown, O. B.

Cox, C.

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

Fry, E. S.

Gentili, B.

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

Gordon, H. R.

Højerslev, N. K.

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

E. Aas, N. K. Højerslev, B. Lundgren, “Spectral irradiance, radiance, and polarization data from the Nordic Cruise in the Mediterranean Sea during June-July 1971,” Rep. 102, Department of Geophysics (University of Oslo, Oslo, Norway, 1997).

N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. 21, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1973).

N. K. Højerslev, “Daylight measurements for photosynthetic studies in the Western Mediterranean,” Rep. 26, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1974).

N. K. Højerslev, N. G. Jerlov, “The use of the colour index for determining quanta irradiance in the sea,” Rep. 35, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1977).

N. K. Højerslev, E. Aas, “Spectral irradiance, radiance, and polarization in blue Mediterranean waters,” Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 138–147 (1997).
[CrossRef]

B. Lundgren, N. K. Højerslev, “Daylight measurements in the Sargasso Sea. Results from the “Dana” Expedition January-April 1966,” Rep. 14, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1971).

Huygens, C.

C. Huygens, Traité de la Luminière. Ou sont Expliquées les Causes de ce qui luy Arrive dans la Reflexion, et Particuliérement dans l’Étrange Refraction du Cristal d’Islande (1690). (Also presented in C. Huygens, Oeuvres Completes, Publication par la Société Hollandaise des Sciences, 1937, Tome 19).

Ivanoff, A.

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

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

A. Ivanoff, “Contribution a l’étude des propriétés optiques de l’eau de mer en Bretagne et en Corse, et la théorie de la polarisation sous-marine,” Ann. Geophys. 13, 22–53 (1957).

A. Ivanoff, “Polarization measurements in the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, New York, 1974), pp. 151–175.

Jacobs, M. M.

Jerlov, N. G.

N. G. Jerlov, “A simple method for measuring quanta irradiance in the ocean,” Rep. 24, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1974).

N. G. Jerlov, “Significant relationships between optical properties of the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974).

N. K. Højerslev, N. G. Jerlov, “The use of the colour index for determining quanta irradiance in the sea,” Rep. 35, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1977).

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

Kattawar, G. W.

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

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Knudsen, M.

M. Knudsen, “On measurement of the penetration of light into the sea,” J. Cons. Cons. Permanent Int. l’Explor. Mer 76, 1–16 (1922).

Kullenberg, G.

G. Kullenberg, N. Berg Olsen, “A comparison between observed and computed light scattering functions—II,” Rep. 19, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1972), pp. 1–27.

Lenoble, J.

J. Lenoble, “Sur l’état de polarisation du rayonnement diffus aux grandes profondeurs dans un milieu suivant la loi de Rayleigh,” Comptes Rendus 246, 924–927 (1958).

Lundgren, B.

B. Lundgren, N. K. Højerslev, “Daylight measurements in the Sargasso Sea. Results from the “Dana” Expedition January-April 1966,” Rep. 14, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1971).

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

E. Aas, N. K. Højerslev, B. Lundgren, “Spectral irradiance, radiance, and polarization data from the Nordic Cruise in the Mediterranean Sea during June-July 1971,” Rep. 102, Department of Geophysics (University of Oslo, Oslo, Norway, 1997).

Marshall, B. R.

B. R. Marshall, “Raman scattering in ocean water,” Department of Geography (University of California, Santa Barbara, Santa Barbara, Calif.1989).

Morel, A.

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 1–24.

Munk, W.

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

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78Scripps Institution of Oceanography, La Jolla, Calif., 1972).

Pope, R. M.

Prieur, L.

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Smith, R. C.

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

R. C. Smith, “Structure of solar radiation in the upper layers of the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 95–119.

Timoveeva, V. A.

V. A. Timoveeva, “Optics of turbid waters,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steeman Nielsen, eds. (Academic, London, 1974), pp. 177–218.

Tyler, J. E.

J. E. Tyler, “Estimation of per cent polarization in deep oceanic water,” J. Mar. Res. 21, 102–109 (1963).

Waterman, T. H.

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

A. Ivanoff, 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, “Polarization of marine light fields and animal orientation,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 431–437 (1988).
[CrossRef]

T. H. Waterman, “Polarization of scattered sunlight in deep waters,” in Papers in Marine Biology and Oceanography, Deep-Sea Res.3, Suppl.426–434 (1955).

T. H. Waterman, “Underwater light and the orientation of animals,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 415–445.

Ann. Geophys. (1)

A. Ivanoff, “Contribution a l’étude des propriétés optiques de l’eau de mer en Bretagne et en Corse, et la théorie de la polarisation sous-marine,” Ann. Geophys. 13, 22–53 (1957).

Appl. Opt. (6)

Comptes Rendus (1)

J. Lenoble, “Sur l’état de polarisation du rayonnement diffus aux grandes profondeurs dans un milieu suivant la loi de Rayleigh,” Comptes Rendus 246, 924–927 (1958).

J. Cons. Cons. Permanent Int. l’Explor. Mer (1)

M. Knudsen, “On measurement of the penetration of light into the sea,” J. Cons. Cons. Permanent Int. l’Explor. Mer 76, 1–16 (1922).

J. Geophys. Res. (1)

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

J. Mar. Res. (4)

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

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

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

J. E. Tyler, “Estimation of per cent polarization in deep oceanic water,” J. Mar. Res. 21, 102–109 (1963).

J. Math. Phys. (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

Limnol. Oceanogr. (3)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the sun angle,” Limnol. Oceanogr. 34, 1484–1489 (1989).
[CrossRef]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Other (22)

B. R. Marshall, “Raman scattering in ocean water,” Department of Geography (University of California, Santa Barbara, Santa Barbara, Calif.1989).

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78Scripps Institution of Oceanography, La Jolla, Calif., 1972).

A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 1–24.

V. A. Timoveeva, “Optics of turbid waters,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steeman Nielsen, eds. (Academic, London, 1974), pp. 177–218.

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

G. Kullenberg, N. Berg Olsen, “A comparison between observed and computed light scattering functions—II,” Rep. 19, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1972), pp. 1–27.

N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. 21, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1973).

N. K. Højerslev, “Daylight measurements for photosynthetic studies in the Western Mediterranean,” Rep. 26, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1974).

N. G. Jerlov, “Significant relationships between optical properties of the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974).

N. G. Jerlov, “A simple method for measuring quanta irradiance in the ocean,” Rep. 24, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1974).

R. C. Smith, “Structure of solar radiation in the upper layers of the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 95–119.

N. K. Højerslev, N. G. Jerlov, “The use of the colour index for determining quanta irradiance in the sea,” Rep. 35, Department of Physical Oceanography, (University of Copenhagen, Copenhagen, Denmark, 1977).

N. K. Højerslev, E. Aas, “Spectral irradiance, radiance, and polarization in blue Mediterranean waters,” Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 138–147 (1997).
[CrossRef]

E. Aas, N. K. Højerslev, B. Lundgren, “Spectral irradiance, radiance, and polarization data from the Nordic Cruise in the Mediterranean Sea during June-July 1971,” Rep. 102, Department of Geophysics (University of Oslo, Oslo, Norway, 1997).

B. Lundgren, N. K. Højerslev, “Daylight measurements in the Sargasso Sea. Results from the “Dana” Expedition January-April 1966,” Rep. 14, Department of Physical Oceanography (University of Copenhagen, Copenhagen, Denmark, 1971).

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

A. Ivanoff, “Polarization measurements in the sea,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, New York, 1974), pp. 151–175.

E. Bartholini, Experimenta Crystalli Islandici Disdiaclastici Qvibus Mira et Insolita Refractio Detegitur (Hafniae, Sumptibus Danielis Paulli Regii Biblia, The Royal Danish Library, Copenhagen, Denmark, 1669).

C. Huygens, Traité de la Luminière. Ou sont Expliquées les Causes de ce qui luy Arrive dans la Reflexion, et Particuliérement dans l’Étrange Refraction du Cristal d’Islande (1690). (Also presented in C. Huygens, Oeuvres Completes, Publication par la Société Hollandaise des Sciences, 1937, Tome 19).

T. H. Waterman, “Polarization of scattered sunlight in deep waters,” in Papers in Marine Biology and Oceanography, Deep-Sea Res.3, Suppl.426–434 (1955).

T. H. Waterman, “Underwater light and the orientation of animals,” in Optical Aspects of Oceanography, N. G. Jerlov, E. Steemann Nielsen, eds. (Academic, London, 1974), pp. 415–445.

T. H. Waterman, “Polarization of marine light fields and animal orientation,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 431–437 (1988).
[CrossRef]

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 (10)

Fig. 1
Fig. 1

Geometry of data collection in the ocean. The angle θsol shows the solar position below the water surface, and θobs shows the orientation of the polarimeter and radiometer system. θ+ marks directions in the solar half of the principal plane, and θ- marks directions in the antisolar half of the principal plane.

Fig. 2
Fig. 2

Map of the Mediterranean Sea with data locations denoted by crosses at A2, D2, E2, and J2A.

Fig. 3
Fig. 3

Radiance as a function of θobs at E2. The depth is 5 m and h sol = 41°, θsol = 34°. Circles represent the experimental data and the crosses represent the Monte Carlo simulations.

Fig. 4
Fig. 4

Radiance as a function of θobs at D2. The depth is 25 m and h sol = 40°, θsol = 35°. Symbols are as in Fig. 3.

Fig. 5
Fig. 5

Radiance as a function of θobs at J2A. The depth is 50 m and h sol = 56°, θsol = 25°. Symbols are as in Fig. 3.

Fig. 6
Fig. 6

Radiance as a function of θobs at A2. The depth is 100 m and h sol = 69°, θsol = 16°. Symbols are as in Fig. 3.

Fig. 7
Fig. 7

Polarization as a function of θobs at E2. The depth is 5 m and h sol = 41°, θsol = 34°. Symbols are as in Fig. 3.

Fig. 8
Fig. 8

Polarization as a function of θobs at D2. The depth is 25 m and h sol = 40°, θsol = 35°. Symbols are as in Fig. 3.

Fig. 9
Fig. 9

Polarization as a function of θobs at J2A. The depth is 50 m and h sol = 56°, θsol = 25°. Symbols are as in Fig. 3.

Fig. 10
Fig. 10

Polarization as a function of θobs at A2. The depth is 100 m and h sol = 69°, θsol = 16°. Symbols are as in Fig. 3.

Tables (4)

Tables Icon

Table 1 Station Information from Locations Where Data Were Collected

Tables Icon

Table 2 Optical Coefficients Derived from Radiance Data

Tables Icon

Table 3 Optical Coefficients Used in the Simulation

Tables Icon

Table 4 Error Estimates for Comparison of Observed and Simulated Quantities

Equations (19)

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

Lθ=Lθ-1+ε1-ε cosϕ,
εz, θε Lθ+-Lθ-Lθ++Lθ-.
Lθ+=Lθ-1+ε1-ε.
Lθ¯= 12π02π Lz, θ, ϕdϕ=Lθ+Lθ-1/2=Lθ-1+ε1-ε1/2.
Ed=2π 0π/2Lθ+Lθ-1/2 cos θ sin θ dθ,
Eu=2π π/2πLθ+Lθ-1/2|cos θ|sin θdθ.
E0d=2π 0π/2Lθ+Lθ-1/2sin θdθ,
E0u=2π π/2πLθ+Lθ-1/2sin θdθ.
E=dEdz =-aE0,
E=Ed-Eu;
E0=E0d+E0u.
K0=- 1E0dE0dz=- 1ΔzlnE0z2E0z1,
a=K0Ed1-Ed2-Eu1+Eu2E01-E02,
R= EuEd
R=0.33 bba.
bbb= π/2π βθsin θdθ0π βθsin θdθ.
b=χR.
Kd=- 1EddEddz=- 1ΔzlnEdz2Edz1.
m=11-ρμ2-11+μ2+3-μ2ρ001-ρμ2-11+μ2+3-μ2ρ1-ρμ2+11+μ2+3-μ2ρ00002-2ρμ1+μ2+3-μ2ρ00002-6ρμ1+μ2+3-μ2ρ,

Metrics