Abstract

Reflected skylight in above-water measurements of diffuse marine reflectance can be reduced substantially by viewing the surface through an analyzer transmitting the vertically polarized component of incident radiance. For maximum reduction of effects, radiometric measurements should be made at a viewing zenith angle of ∼45° (near the Brewster angle) and a relative azimuth angle between solar and viewing directions greater than 90° (backscattering), preferably 135°. In this case the residual reflected skylight in the polarized signal exhibits minimum sensitivity to the sea state and can be corrected to within a few 10-4 in reflectance units. For most oceanic waters the resulting relative error on the diffuse marine reflectance in the blue and green is less than 1%. Since the water body polarizes incident skylight, the measured polarized reflectance differs from the total reflectance. The difference, however, is small for the considered geometry. Measurements made at the Scripps Institution of Oceanography pier in La Jolla, Calif., with a specifically designed scanning polarization radiometer, confirm the theoretical findings and demonstrate the usefulness of polarization radiometry for measuring diffuse marine reflectance.

© 1999 Optical Society of America

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References

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  1. M. Viollier, “Radiometric calibration of the Coastal Zone Color Scanner on Nimbus-7: a proposed adjustment,” Appl. Opt. 21, 6142–6145 (1982).
    [CrossRef]
  2. D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
    [CrossRef]
  3. B. Fougnie, P.Y. Deschamps, R. Frouin, “Vicarious calibration of the POLDER ocean color spectral bands using in situ measurements,” IEEE Trans. Geosci. Remote Sensing, ADEOS special issue, 37, 1567–1574 (1998).
  4. J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, Revision 1,” (NASA, Goddard Space Flight Center, Greenbelt, Md., 1995).
  5. K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
    [CrossRef]
  6. Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
    [CrossRef]
  7. K. L. Carder, P. Reinersman, R. F. Chen, F. Muller-Karger, C. O. Davis, M. Hamilton, “AVIRIS calibration and application in coastal oceanic environments,” Remote Sens. Environ. 44, 205–216 (1993).
    [CrossRef]
  8. Z. P. Lee, K. L. Carder, T. G. Peacock, R. G. Steward, “Remote-sensing reflectance measured with and without a vertical polarizer,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 483–488 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. S. Chandrasekhar, Radiative Transfer, (Oxford University, Oxford, England, 1950; Dover, New York, 1960).
  14. J. Lenoble, Atmospheric Radiative Transfer, (A. Deepak, Hampton, Va., 1993).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. B. G. Mitchell, M. Kahru, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).
  20. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters 2: bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
    [CrossRef] [PubMed]
  21. A. Ivanoff, Introduction à l’océanographie: Tome II, (Vuibert, Paris, 1975).
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    [CrossRef] [PubMed]
  23. R. Frouin, E. Pouliquen, F.-M. Bréon, “Ocean color remote sensing using polarization properties of reflected sunlight,” in Proceedings of the Sixth International College on “Physical Measurements and Signatures in Remote Sensing,” 17–21 January 1994, Val d’Isère, France, ISPRS. 665-674 (Centre National d’Etudes Spatiales, Toulouse, France, 1994).

1998 (2)

B. Fougnie, P.Y. Deschamps, R. Frouin, “Vicarious calibration of the POLDER ocean color spectral bands using in situ measurements,” IEEE Trans. Geosci. Remote Sensing, ADEOS special issue, 37, 1567–1574 (1998).

M. Schwindling, P. Y. Deschamps, R. Frouin, “Validation of aerosol models for satellite ocean color remote sensing,” J. Geophys. Res. 103, 24,919–24,935 (1998).
[CrossRef]

1997 (1)

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

1993 (2)

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

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters 2: bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

1989 (1)

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 6483–6494 (1989).

1988 (2)

K. Masuda, T. Takashima, “Dependence of the radiation just above and below the ocean surface on atmospheric and oceanic parameters,” Appl. Opt. 27, 4891–4898 (1988).
[CrossRef] [PubMed]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

1985 (1)

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (1)

M. Viollier, “Radiometric calibration of the Coastal Zone Color Scanner on Nimbus-7: a proposed adjustment,” Appl. Opt. 21, 6142–6145 (1982).
[CrossRef]

1954 (1)

C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 11,838–11,850 (1954).
[CrossRef]

Austin, R. W.

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, Revision 1,” (NASA, Goddard Space Flight Center, Greenbelt, Md., 1995).

Bréon, F.-M.

R. Frouin, E. Pouliquen, F.-M. Bréon, “Ocean color remote sensing using polarization properties of reflected sunlight,” in Proceedings of the Sixth International College on “Physical Measurements and Signatures in Remote Sensing,” 17–21 January 1994, Val d’Isère, France, ISPRS. 665-674 (Centre National d’Etudes Spatiales, Toulouse, France, 1994).

Broenkow, W.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

Carder, K. L.

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

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

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

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer, (Oxford University, Oxford, England, 1950; Dover, New York, 1960).

Chen, R. F.

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

Clark, D. K.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

Cox, C.

C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 11,838–11,850 (1954).
[CrossRef]

Davis, C. O.

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

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Deschamps, P. Y.

M. Schwindling, P. Y. Deschamps, R. Frouin, “Validation of aerosol models for satellite ocean color remote sensing,” J. Geophys. Res. 103, 24,919–24,935 (1998).
[CrossRef]

P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
[CrossRef] [PubMed]

Deschamps, P.Y.

B. Fougnie, P.Y. Deschamps, R. Frouin, “Vicarious calibration of the POLDER ocean color spectral bands using in situ measurements,” IEEE Trans. Geosci. Remote Sensing, ADEOS special issue, 37, 1567–1574 (1998).

Deuzé, J. L.

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 6483–6494 (1989).

Fougnie, B.

B. Fougnie, P.Y. Deschamps, R. Frouin, “Vicarious calibration of the POLDER ocean color spectral bands using in situ measurements,” IEEE Trans. Geosci. Remote Sensing, ADEOS special issue, 37, 1567–1574 (1998).

Frouin, R.

B. Fougnie, P.Y. Deschamps, R. Frouin, “Vicarious calibration of the POLDER ocean color spectral bands using in situ measurements,” IEEE Trans. Geosci. Remote Sensing, ADEOS special issue, 37, 1567–1574 (1998).

M. Schwindling, P. Y. Deschamps, R. Frouin, “Validation of aerosol models for satellite ocean color remote sensing,” J. Geophys. Res. 103, 24,919–24,935 (1998).
[CrossRef]

R. Frouin, E. Pouliquen, F.-M. Bréon, “Ocean color remote sensing using polarization properties of reflected sunlight,” in Proceedings of the Sixth International College on “Physical Measurements and Signatures in Remote Sensing,” 17–21 January 1994, Val d’Isère, France, ISPRS. 665-674 (Centre National d’Etudes Spatiales, Toulouse, France, 1994).

Ge, Y.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

Gentili, B.

Gordon, H. R.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

Hamilton, M.

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

Herman, M.

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 6483–6494 (1989).

P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
[CrossRef] [PubMed]

Ivanoff, A.

A. Ivanoff, Introduction à l’océanographie: Tome II, (Vuibert, Paris, 1975).

Kahru, M.

B. G. Mitchell, M. Kahru, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).

Koepke, P.

Lee, Z. P.

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

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Lenoble, J.

J. Lenoble, Atmospheric Radiative Transfer, (A. Deepak, Hampton, Va., 1993).

Masuda, K.

Mitchell, B. G.

T. Moisan, B. G. Mitchell, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).

B. G. Mitchell, M. Kahru, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).

Moisan, T.

T. Moisan, B. G. Mitchell, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).

Morel, A.

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters 2: bidirectional aspects,” Appl. Opt. 32, 6864–6879 (1993).
[CrossRef] [PubMed]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

A. Morel, “Optical properties of oceanic case 1 waters, revisited,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 108–114 (1997).
[CrossRef]

Mueller, J. L.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, Revision 1,” (NASA, Goddard Space Flight Center, Greenbelt, Md., 1995).

Muller-Karger, F.

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

Munk, W.

C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 11,838–11,850 (1954).
[CrossRef]

Peacock, T. G.

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

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

Pouliquen, E.

R. Frouin, E. Pouliquen, F.-M. Bréon, “Ocean color remote sensing using polarization properties of reflected sunlight,” in Proceedings of the Sixth International College on “Physical Measurements and Signatures in Remote Sensing,” 17–21 January 1994, Val d’Isère, France, ISPRS. 665-674 (Centre National d’Etudes Spatiales, Toulouse, France, 1994).

Reinersman, P.

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

Santer, R.

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 6483–6494 (1989).

Schwindling, M.

M. Schwindling, P. Y. Deschamps, R. Frouin, “Validation of aerosol models for satellite ocean color remote sensing,” J. Geophys. Res. 103, 24,919–24,935 (1998).
[CrossRef]

Steward, R. G.

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

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

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

Takashima, T.

Tanre, D.

Trees, C.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

Viollier, M.

M. Viollier, “Radiometric calibration of the Coastal Zone Color Scanner on Nimbus-7: a proposed adjustment,” Appl. Opt. 21, 6142–6145 (1982).
[CrossRef]

Voss, K. J.

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

Appl. Opt. (5)

IEEE Trans. Geosci. Remote Sensing (1)

B. Fougnie, P.Y. Deschamps, R. Frouin, “Vicarious calibration of the POLDER ocean color spectral bands using in situ measurements,” IEEE Trans. Geosci. Remote Sensing, ADEOS special issue, 37, 1567–1574 (1998).

J. Geophys. Res. (1)

M. Schwindling, P. Y. Deschamps, R. Frouin, “Validation of aerosol models for satellite ocean color remote sensing,” J. Geophys. Res. 103, 24,919–24,935 (1998).
[CrossRef]

J. Geophys. Res. (2)

D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102, 17,209–17,217 (1997).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 11,838–11,850 (1954).
[CrossRef]

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

J. L. Deuzé, M. Herman, R. Santer, “Fourier series expansion of the transfer equation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 41, 6483–6494 (1989).

Limnol. Oceanogr. (1)

K. L. Carder, R. G. Steward, “A remote-sensing reflectance model of a red tide dinoflagellate off West Florida,” Limnol. Oceanogr. 30, 286–298 (1985).
[CrossRef]

Remote Sens. Environ. (1)

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

Other (10)

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

S. Chandrasekhar, Radiative Transfer, (Oxford University, Oxford, England, 1950; Dover, New York, 1960).

J. Lenoble, Atmospheric Radiative Transfer, (A. Deepak, Hampton, Va., 1993).

J. L. Mueller, R. W. Austin, “Ocean optics protocols for SeaWiFS validation, Revision 1,” (NASA, Goddard Space Flight Center, Greenbelt, Md., 1995).

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 160–166 (1997).
[CrossRef]

T. Moisan, B. G. Mitchell, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).

A. Ivanoff, Introduction à l’océanographie: Tome II, (Vuibert, Paris, 1975).

R. Frouin, E. Pouliquen, F.-M. Bréon, “Ocean color remote sensing using polarization properties of reflected sunlight,” in Proceedings of the Sixth International College on “Physical Measurements and Signatures in Remote Sensing,” 17–21 January 1994, Val d’Isère, France, ISPRS. 665-674 (Centre National d’Etudes Spatiales, Toulouse, France, 1994).

A. Morel, “Optical properties of oceanic case 1 waters, revisited,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 108–114 (1997).
[CrossRef]

B. G. Mitchell, M. Kahru, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California (personal communication, 1997).

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Figures (12)

Fig. 1
Fig. 1

Parallel-polarized (dots) and total (circles) reflectances of the ocean at 443 nm computed as a function of the viewing zenith angle for three relative azimuth angles: (a) 90°, (b) 135°; and (c) 180°. The solar zenith angle is 47°. The water-body reflectance is assumed to equal zero and the atmosphere contains only molecules. The error bar represents the minimum and the maximum values for varied wind speeds from 2 to 12.5 m s-1.

Fig. 2
Fig. 2

Same as Fig. 1 but for a relative azimuth angle of 135° and for three solar zenith angles: (a) 32°, (b) 47°, and (c) 58°.

Fig. 3
Fig. 3

Same as Fig. 1 but for a relative azimuth angle of 135°, a solar zenith angle of 47°, and for three wavelengths: (a) 443 nm, (b) 565 nm, and (c) 865 nm.

Fig. 4
Fig. 4

(a) Total and (b) parallel-polarized reflectances of the ocean at 443 nm as a function of the viewing zenith angle for a solar zenith angle of 47° and a relative azimuth angle of 135°. The atmosphere contains maritime aerosols characterized by their optical depth at 865 nm (0.0.1 and 0.2) and the atmospheric relative humidity (90%).

Fig. 5
Fig. 5

Same as Fig. 4 but for a coastal aerosol with an atmospheric relative humidity of 70%.

Fig. 6
Fig. 6

Spectral response of the Refpol interference filters.

Fig. 7
Fig. 7

Rotating wheel characteristics: two polarizers (VIS for 443, 550, and 670 nm and IR for 870 nm) and an optically black area. In the depicted configuration, L 3 is acquired at 550 nm and L 1 at 670 and 870 nm. Data at 443 nm are rejected because the polarizer sheet is not in the right position (443 nm must correspond to VIS).

Fig. 8
Fig. 8

Above-water Refpol measurements of parallel-polarized (dots) and unpolarized (circles) reflectances as a function of the viewing zenith angle for four wavelengths (443, 550, 665, and 870 nm). The solar zenith angle is 27°, and the relative azimuth angle is 180°. Two successive scans separated by ∼4 min are presented. The measurements were performed at the SIO pier on 8 April 1996 at 18H55 Greenwich mean time (GMT).

Fig. 9
Fig. 9

Same as Fig. 8, but for a relative azimuth angle of 135° and for a solar zenith angle of 36°. The measurements were performed on 10 April 1996 at 17H53 GMT.

Fig. 10
Fig. 10

Same as Fig. 8 but for a relative azimuth angle of 90° and a solar zenith angle of 34°. The measurements were performed on 10 April 1996 at 18H04 GMT.

Fig. 11
Fig. 11

Same as Fig. 8 but for a relative azimuth angle of 135° and a solar zenith angle of 55°. The measurements were performed on 8 April 1996 at 23H23 GMT.

Fig. 12
Fig. 12

Diffuse marine reflectance derived from the parallel-polarized (dots) and unpolarized (circles) Refpol measurements of Fig. 9 as a function of the viewing zenith angle for the four wavelengths [(a) 443 nm, (b) 550 nm, (c) 665 nm, and (d) 870 nm]. The solar zenith angle is 36° and the relative azimuth angle is 135°.

Tables (6)

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Table 1 Error Budget (in Reflectance Units) on Diffuse Marine Reflectance Derived from Two Types of Measurement, at 443 and 565 nm, and for Several Solar Zenith Angles θs

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Table 2 Characteristics of Refpol

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Table 3 Sequence of Refpol Measurements for the Eight Positions of the Rotating Wheel

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Table 4 Refpol Calibration Coefficients in Reflectance Units (×106)

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Table 5 Mean and Standard Deviation of Marine Reflectance Estimated from the Above-Water Refpol Measurements

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Table 6 Mean and Standard Deviation of Marine Reflectance Measured by the Underwater MER Radiometer

Equations (22)

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L 0 λ ,   θ s ,   θ v ,   φ = L w + λ ,   θ s ,   θ v ,   φ + L c λ ,   θ s ,   θ v ,   φ ,
L c θ s ,   θ v ,   φ = L s θ s ,   θ v ,   φ + L g θ s ,   θ v ,   φ ,
L s θ s ,   θ v ,   φ = 0 2 π 0 π / 2   L s d θ ,   θ s ,   φ p V ,   θ v ,   θ ,   φ × p V ,   θ v ,   θ ,   φ r θ v ,   θ ,   φ sin θ cos θ d θ d φ ,
L g θ s ,   θ v ,   φ = E so   cos θ s exp - δ cos θ s × p V ,   θ v ,   θ s ,   φ r θ v ,   θ s ,   φ ,
ρ 0 , c θ s ,   θ v ,   φ = π L 0 , c θ s ,   θ v ,   φ d 2 cos θ s E so d 0 2 ,
ρ o , c / / , θ s ,   θ v ,   φ = 2 π L 0 , c / / , θ s ,   θ v ,   φ d 2 cos θ s E s 0 d 0 2 .
ρ 0 θ s ,   θ v ,   φ = ρ c / / θ s ,   θ v ,   φ + ρ c θ s ,   θ v ,   φ + t a θ s ρ w + θ s ,   θ v ,   φ ,
ρ w + θ s ,   θ v ,   φ = ρ o θ s ,   θ v ,   φ - ρ c θ s ,   θ v ,   φ t a θ s
ρ w + θ s ,   θ v ,   φ = ρ o / / θ s ,   θ v ,   φ - ρ c / / θ s ,   θ v ,   φ t a θ s ,
Δ ρ w + θ s ,   θ v ,   φ = Δ ρ c θ s ,   θ v ,   φ t a θ s ,
t a θ s exp - 0.48 δ r cos θ s ,
I = L 3 + L 1 ,
Q = L 3 - L 1 ,
U = 2 L 2 - L 1 - L 3 .
I = I ,
Q = Q   cos 2 α + U   sin 2 α ,
U = - Q   sin 2 α + U   cos 2 α ,
L / / = I + Q / 2 ,
L = I - Q / 2 .
ρ = π L E so = K NC - NC 0 ,
ρ i = K NC i - NC 0 i d 2 cos θ s d 0 2 .
α pol = 2   cos 2   χ 1 + cos 2   χ ,

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