Abstract

The sensitivity of the polarization of water-leaving radiance to the microphysical parameters of oceanic hydrosols, specifically to the real part of the bulk refractive index (nbulk) and to the hyperbolic slope of the Junge-type particle size distribution (PSD, ξ) is analyzed using in situ measurements of the underwater polarized light, in both Case I and Case II waters, and multiple scattering computations. Based on comparisons of experimental and simulated data, estimations of the real part of the refractive index and of the slope of the PSD are given. The study yielded results that generally agreed with expectations and that have accuracies comparable to previously published techniques. The analysis also demonstrates that the inclusion of polarization in addition to traditional radiance measurements can be expected to provide complementary information on the nature of particle populations in the ocean.

© 2011 Optical Society of America

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  33. M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
    [CrossRef]
  34. J. Zhou, A. Gilerson, I. Ioannou, S. Hlaing, J. Schalles, B. Gross, F. Moshary, and S. Ahmed, “Retrieving quantum yield of sun-induced chlorophyll fluorescence near surface from hyperspectral in-situ measurement in productive water,” Opt. Express 16, 17468–17483 (2008).
    [CrossRef]
  35. A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
    [CrossRef] [PubMed]
  36. E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
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    [CrossRef]
  40. J. M. Sullivan, M. Twardowski, P. L. Donaghay, and S. Freeman, “Use of optical backscattering to discriminate particle types in coastal waters,” Appl. Opt. 44, 1667–1680 (2005).
    [CrossRef]

2010

J. K. Lotsberg and J. J. Stamnes, “Impact of particulate oceanic composition on the radiance and polarization of underwater and backscattered light,” Opt. Express 18, 10432–10445(2010).
[CrossRef] [PubMed]

A. Tonizzo, A. Ibrahim, J. Zhou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Estimation of the polarized water leaving radiance from above water measurements,” Proc. SPIE 7678, 767803 (2010).
[CrossRef] [PubMed]

C. J. Buonassissi and H. M. Dierssen, “A regional comparison of particle size distributions and the power law approximation in oceanic and estuarine surface waters,” J. Geophys. Res. 115, C10028 (2010).
[CrossRef]

2009

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, 5666–5682 (2009).
[CrossRef] [PubMed]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
[CrossRef]

2008

2007

2006

2005

2002

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002).
[CrossRef] [PubMed]

2001

1998

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. Geosci. Remote Sens. 36, 51–60 (1998).

1996

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).

1994

Y. C. Agrawal and H. C. Pottsmith, “Laser diffraction particle sizing in STRESS,” Cont. Shelf Res. 14, 1101–1121 (1994).
[CrossRef]

1991

D. Stramski and D. A. Kiefer, “Light-scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383(1991).

1989

G. W. Kattawar and 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]

1974

J. E. Hansen and L. D. Travis, “Light-scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1970

V. A. Timofeeva, “The degree of light polarization in turbid media,” Izv. Atmos. Ocean Phys. 6, 513–522 (1970).

1969

V. A. Timofeeva, “Plane of vibrations of polarized light in turbid media,” Izv. Atmos. Ocean Phys. 10, 1049–1057 (1969).

1966

V. A. Timofeeva, A. A. Vostroknutov, and L. A. Koveshnikova, “Influence of asymmetrical illumination on the light field inside a turbid medium,” Izv. Atmos. Ocean Phys. 12, 1259–1266(1966).

1958

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

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).

Adams, C. N.

G. W. Kattawar and 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]

Agrawal, Y. C.

Y. C. Agrawal and H. C. Pottsmith, “Laser diffraction particle sizing in STRESS,” Cont. Shelf Res. 14, 1101–1121 (1994).
[CrossRef]

Ahmed, S.

A. Tonizzo, A. Ibrahim, J. Zhou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Estimation of the polarized water leaving radiance from above water measurements,” Proc. SPIE 7678, 767803 (2010).
[CrossRef] [PubMed]

J. Zhou, A. Gilerson, I. Ioannou, S. Hlaing, J. Schalles, B. Gross, F. Moshary, and S. Ahmed, “Retrieving quantum yield of sun-induced chlorophyll fluorescence near surface from hyperspectral in-situ measurement in productive water,” Opt. Express 16, 17468–17483 (2008).
[CrossRef]

A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Ahmed, S. A.

Arnone, R. A.

Barnard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
[CrossRef]

J. R. V. Zaneveld, C. Moore, A. H. Barnard, M. Twardowski, and G. C. Chang, “Correction and analysis of spectral absorption data taken with the WET Labs ac-s,” presented at Ocean Optics XXVII, Fremantle, Australia, Oct. 25–29, 2004.

Boss, E.

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
[CrossRef]

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution,” Appl. Opt. 40, 4885–4893 (2001).
[CrossRef]

Bricaud, A.

Buonassissi, C. J.

C. J. Buonassissi and H. M. Dierssen, “A regional comparison of particle size distributions and the power law approximation in oceanic and estuarine surface waters,” J. Geophys. Res. 115, C10028 (2010).
[CrossRef]

Cairns, B.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).

Carder, K. L.

Chami, M.

Chang, G. C.

J. R. V. Zaneveld, C. Moore, A. H. Barnard, M. Twardowski, and G. C. Chang, “Correction and analysis of spectral absorption data taken with the WET Labs ac-s,” presented at Ocean Optics XXVII, Fremantle, Australia, Oct. 25–29, 2004.

Chowdhary, J.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).

A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

J. Chowdhary, “Incorporation of a smooth water-air interface in multiple scattering calculations using the adding method for polarized light,” Master’s thesis (Columbia University, 1999).

Ciotti, A. M.

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef] [PubMed]

Cullen, J. J.

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef] [PubMed]

Czerski, H.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

DeFoin-Platel, M.

M. DeFoin-Platel and C. Malik, “Ambiguities in the inversion of the ocean colour: Problems and solutions,” in Proceedings: Eighteenth Annual Colloquium of the Spatial Information Research Centre (Otago Univ. Press, 2006).
[CrossRef]

Dessailly, D.

Dierssen, H. M.

C. J. Buonassissi and H. M. Dierssen, “A regional comparison of particle size distributions and the power law approximation in oceanic and estuarine surface waters,” J. Geophys. Res. 115, C10028 (2010).
[CrossRef]

Dilligeard, E.

Donaghay, P. L.

Dubuisson, P.

Duforet, L.

Freeman, S.

J. M. Sullivan, M. Twardowski, P. L. Donaghay, and S. Freeman, “Use of optical backscattering to discriminate particle types in coastal waters,” Appl. Opt. 44, 1667–1680 (2005).
[CrossRef]

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Gilerson, A.

A. Tonizzo, A. Ibrahim, J. Zhou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Estimation of the polarized water leaving radiance from above water measurements,” Proc. SPIE 7678, 767803 (2010).
[CrossRef] [PubMed]

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, 5666–5682 (2009).
[CrossRef] [PubMed]

J. Zhou, A. Gilerson, I. Ioannou, S. Hlaing, J. Schalles, B. Gross, F. Moshary, and S. Ahmed, “Retrieving quantum yield of sun-induced chlorophyll fluorescence near surface from hyperspectral in-situ measurement in productive water,” Opt. Express 16, 17468–17483 (2008).
[CrossRef]

A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Gray, D. J.

Gross, B.

Gross, B. M.

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light-scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Harmel, T.

Herring, S.

Hlaing, S.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000), pp. xxx, 690.

Ibrahim, A.

A. Tonizzo, A. Ibrahim, J. Zhou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Estimation of the polarized water leaving radiance from above water measurements,” Proc. SPIE 7678, 767803 (2010).
[CrossRef] [PubMed]

A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Ioannou, I.

Ivanoff, A.

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

Kattawar, G.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Kattawar, G. W.

G. W. Kattawar and 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]

G. W. Kattawar, “Ocean optics in the near future 5–10 years out, where we’re headed and current challenges,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Kawata, Y.

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. Geosci. Remote Sens. 36, 51–60 (1998).

Kiefer, D. A.

D. Stramski and D. A. Kiefer, “Light-scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383(1991).

Knobelspiesse, K.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
[CrossRef]

Koveshnikova, L. A.

V. A. Timofeeva, A. A. Vostroknutov, and L. A. Koveshnikova, “Influence of asymmetrical illumination on the light field inside a turbid medium,” Izv. Atmos. Ocean Phys. 12, 1259–1266(1966).

Lee, Z. P.

Lewis, M. R.

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47, 404–417 (2002).
[CrossRef] [PubMed]

Lide, D. R.

D. R. Lide, “Physical and optical properties of minerals,” in CRC Handbook of Chemistry and Physics (CRC Press, 1997).
[CrossRef]

Loisel, H.

Lotsberg, J. K.

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
[CrossRef]

Malik, C.

M. DeFoin-Platel and C. Malik, “Ambiguities in the inversion of the ocean colour: Problems and solutions,” in Proceedings: Eighteenth Annual Colloquium of the Spatial Information Research Centre (Otago Univ. Press, 2006).
[CrossRef]

Mckee, D.

Mishchenko, M.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000), pp. xxx, 690.

Moore, C.

J. R. V. Zaneveld, C. Moore, A. H. Barnard, M. Twardowski, and G. C. Chang, “Correction and analysis of spectral absorption data taken with the WET Labs ac-s,” presented at Ocean Optics XXVII, Fremantle, Australia, Oct. 25–29, 2004.

Morel, A.

Moshary, F.

Pegau, W. S.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
[CrossRef]

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

Pottsmith, H. C.

Y. C. Agrawal and H. C. Pottsmith, “Laser diffraction particle sizing in STRESS,” Cont. Shelf Res. 14, 1101–1121 (1994).
[CrossRef]

Santer, R.

Sathyendranath, S.

S. Sathyendranath, “Remote sensing of ocean colour in coastal, and other optically-complex, waters,” in Reports of the International Ocean-Colour Coordinating Group No. 3 (IOCCG, 2000).

Schalles, J.

Schmid, B.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
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Stamnes, J. J.

Stramski, D.

Sullivan, J.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

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V. A. Timofeeva, A. A. Vostroknutov, and L. A. Koveshnikova, “Influence of asymmetrical illumination on the light field inside a turbid medium,” Izv. Atmos. Ocean Phys. 12, 1259–1266(1966).

Tonizzo, A.

A. Tonizzo, A. Ibrahim, J. Zhou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Estimation of the polarized water leaving radiance from above water measurements,” Proc. SPIE 7678, 767803 (2010).
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A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Travis, L. D.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).

J. E. Hansen and L. D. Travis, “Light-scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000), pp. xxx, 690.

Twardowski, M.

J. M. Sullivan, M. Twardowski, P. L. Donaghay, and S. Freeman, “Use of optical backscattering to discriminate particle types in coastal waters,” Appl. Opt. 44, 1667–1680 (2005).
[CrossRef]

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

J. R. V. Zaneveld, C. Moore, A. H. Barnard, M. Twardowski, and G. C. Chang, “Correction and analysis of spectral absorption data taken with the WET Labs ac-s,” presented at Ocean Optics XXVII, Fremantle, Australia, Oct. 25–29, 2004.

Twardowski, M. S.

Vagle, S.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Vostroknutov, A. A.

V. A. Timofeeva, A. A. Vostroknutov, and L. A. Koveshnikova, “Influence of asymmetrical illumination on the light field inside a turbid medium,” Izv. Atmos. Ocean Phys. 12, 1259–1266(1966).

Waquet, F.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
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M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Y. You, Department of Physics and Astronomy, Texas A&M University (personal communication, 2010).
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M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
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J. R. V. Zaneveld, C. Moore, A. H. Barnard, M. Twardowski, and G. C. Chang, “Correction and analysis of spectral absorption data taken with the WET Labs ac-s,” presented at Ocean Optics XXVII, Fremantle, Australia, Oct. 25–29, 2004.

Zhang, X.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition and dynamics at the near-surface in the surf zone and open ocean,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

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J. M. Sullivan, M. Twardowski, P. L. Donaghay, and S. Freeman, “Use of optical backscattering to discriminate particle types in coastal waters,” Appl. Opt. 44, 1667–1680 (2005).
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J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).

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IEEE Trans. Geosci. Remote Sens.

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. Geosci. Remote Sens. 36, 51–60 (1998).

Izv. Atmos. Ocean Phys.

V. A. Timofeeva, “The degree of light polarization in turbid media,” Izv. Atmos. Ocean Phys. 6, 513–522 (1970).

V. A. Timofeeva, A. A. Vostroknutov, and L. A. Koveshnikova, “Influence of asymmetrical illumination on the light field inside a turbid medium,” Izv. Atmos. Ocean Phys. 12, 1259–1266(1966).

V. A. Timofeeva, “Plane of vibrations of polarized light in turbid media,” Izv. Atmos. Ocean Phys. 10, 1049–1057 (1969).

J. Atmos. Ocean Technol.

G. Zibordi, “Immersion factor of in-water radiance sensors: Assessment for a class of radiometers,” J. Atmos. Ocean Technol. 23, 302–313 (2006).
[CrossRef]

J. Geophys. Res.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206(2009).
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C. J. Buonassissi and H. M. Dierssen, “A regional comparison of particle size distributions and the power law approximation in oceanic and estuarine surface waters,” J. Geophys. Res. 115, C10028 (2010).
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J. Geophys. Res. Oceans

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. Oceans 106, 14129–14142 (2001).
[CrossRef]

J. Mar. Res.

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

J. Plankton Res.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).

Limnol. Oceanogr.

G. W. Kattawar and 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).
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M. Chami and D. Mckee, “Determination of biogeochemical properties of marine particles using above water measurements of the degree of polarization at the Brewster angle,” Opt. Express 15, 9494–9509 (2007).
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A. Tonizzo, A. Ibrahim, J. Zhou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Estimation of the polarized water leaving radiance from above water measurements,” Proc. SPIE 7678, 767803 (2010).
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D. Stramski and D. A. Kiefer, “Light-scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383(1991).

Space Sci. Rev.

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Other

G. W. Kattawar, “Ocean optics in the near future 5–10 years out, where we’re headed and current challenges,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000), pp. xxx, 690.

J. R. V. Zaneveld, C. Moore, A. H. Barnard, M. Twardowski, and G. C. Chang, “Correction and analysis of spectral absorption data taken with the WET Labs ac-s,” presented at Ocean Optics XXVII, Fremantle, Australia, Oct. 25–29, 2004.

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J. Chowdhary, “Incorporation of a smooth water-air interface in multiple scattering calculations using the adding method for polarized light,” Master’s thesis (Columbia University, 1999).

A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010.

Y. You, Department of Physics and Astronomy, Texas A&M University (personal communication, 2010).
[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

The underwater polarimeter in clear oceanic waters. For this deployment, a fourth radiance sensor (measuring circular polarization, not discussed in this analysis) was installed on the scanning system (photo courtesy of Erich Schlegel).

Fig. 2
Fig. 2

(a) In-water scattering angle versus above-water viewing angle, θ v , and Sun elevation, θ Sun . θ v = 0 ° corresponds to an observer looking along the nadir direction and θ v = ± 90 ° corresponds to the horizontal directions. (b) Geometry of observation and relevant angles. The thick gray lines indicate the borders of Snell’s window.

Fig. 3
Fig. 3

Total absorption and total scattering coefficients (without the water contributions) used in the radiative transfer computations.

Fig. 4
Fig. 4

Color contour diagrams of the DOP versus viewing (and scattering) angle and bulk refractive index for a Junge-type size distribution with hyperbolic slope ξ = 3.5 , 4, 4.5; λ = 440 , 510, and 650 nm .

Fig. 5
Fig. 5

Color contour diagrams of the DOP versus viewing (and scattering) angle and hyperbolic slope for hydrosols with bulk refractive index n bulk = 1.02 , 1.12, 1.22; λ = 440 , 510, and 650 nm .

Fig. 6
Fig. 6

Color contour diagram of the RMSD versus n bulk and ξ. The solid lines are the initial outputs of the radiative transfer computations, which are then linearly interpolated with respect to n bulk and ξ.

Fig. 7
Fig. 7

Left panels: PSDs. The solid curve is obtained from LISST measurements, and the dashed line is the result of the fitting. Right panels: absorption spectra of the various water constituents. (a) Case I, (b) Case II—Coastal, (c) Case II—Coastal high [NAP].

Fig. 8
Fig. 8

DOP t versus viewing angle and scattering angle. (a) Case I, (b) Case II—Coastal, (c) Case II—Coastal high [NAP]. The vertical black line indicates the position of the specular reflection of sunlight. Computations are the solid curves.

Fig. 9
Fig. 9

Scatterplot of the measured values of DOP t versus the corresponding calculated values ( DOP calc ). N is the total number of comparisons.

Fig. 10
Fig. 10

Backscattering ratio as a function of the hyperbolic slope of the PSD. The solid black curves are the results of Mie theory calculations, and each curve represents a different bulk refractive index (between 1.02 and 1.22, at steps of 0.02), from Twardowski et al. [33]. The blue squares are the estimated values using Eq. (11), and the red circles are the estimated values obtained using polarimetric measurements.

Tables (1)

Tables Icon

Table 1 Concentrations and Inherent Optical Properties Estimated from the Absorption/Scattering Spectra for the Sites Considered in this Study

Equations (11)

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

I α = T χ 2 [ I + Q cos ( 2 α ) + U sin ( 2 α ) ] , α = 0 ° , 90 ° , 45 ° ,
DOP = Q 2 + U 2 I ,
t wai * = 2 μ m 2 ( λ ) T F * ( μ t * ( μ ) ) T F * ( μ t * ( μ ) ) = 1 4 m ( λ ) μ [ t * 2 ( μ ) + t * 2 ( μ ) t * 2 ( μ ) t * 2 ( μ ) 0 0 t * 2 ( μ ) t * 2 ( μ ) t * 2 ( μ ) + t * 2 ( μ ) 0 0 0 0 2 t * ( μ ) t * ( μ ) 0 0 0 0 2 t * ( μ ) t * ( μ ) ] ,
t * ( μ ) = 2 m ( λ ) μ μ + m ( λ ) μ t * , t * ( μ ) = 2 m ( λ ) μ m ( λ ) μ + μ t * , μ t * ( μ ) = 1 + ( μ 2 1 ) m 2 ( λ ) , μ = | cos ( θ t ) | ,
S t = t wai * · S i .
DOP t = Q t 2 + U t 2 I t ,
n ( r ) = k r ξ ,
0 n ( r ) d r = 1 .
DOP = Q I .
RMSD ( n bulk , ξ ) = 1 N θ N λ k = 1 N θ j = 1 N λ [ D O P t ( θ v , k , λ j , n bulk , ξ ) DOP calc ( θ v , k , λ j , n bulk , ξ ) ] 2 .
n bulk ( b ^ bp , γ ) = 1 + b ^ bp 0.5377 + 0.4867 γ 2 ( 1.4676 + 2.2950 γ 2 + 2.3113 γ 4 ) ,

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