Abstract

Analysis of several million particulate volume scattering functions (VSFs) from different field sites around the world’s oceans and coastlines revealed that the shape of the VSF in the backward direction was remarkably consistent (5% or less variability at angles between 90° and 170°). In agreement with theoretical models and past field measurements, the variability of the VSF shape (the VSF normalized to the backscattering coefficient) was found to be lowest between 110° and 120°. This study concludes that under most oceanic conditions, estimates of the particulate backscattering coefficient, using single angle scattering measurements near 110° to 120° and suitable conversion factors, are justified and should have a maximum uncertainty of less than a few percent once instrument noise is accounted for.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135-13142 (1995).
    [CrossRef]
  6. T. J. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. (Scripps Institution of Oceanography, 1972), pp.72-78.
  7. G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423-432 (1968).
    [CrossRef]
  8. N. G. Jerlov, “Optical measurements in the eastern North Atlantic,” Medd. Oceanogr. Inst. Göteborg 30, 1-40 (1961).
  9. M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563-571 (2003).
    [CrossRef]
  10. M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
    [CrossRef]
  11. J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189-5203(2007).
    [CrossRef]
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    [CrossRef]
  16. J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680-1690 (1992).
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    [CrossRef]
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    [CrossRef]
  19. J. M. Sullivan, M. S. Twardowski, J. R. Zaneveld, C. Moore, A. Barnard, P. L. Donaghay, and B. Rhoades, “The hyper-spectral temperature and salinity dependent absorption of pure water, salt water and heavy salt water (D2O) in the visible and near-IR wavelengths (400-750 nm),” Appl. Opt. 45, 5294-5309 (2006).
    [CrossRef]
  20. J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44-55 (1994).
    [CrossRef]
  21. M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).
  22. X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
    [CrossRef]
  23. Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
    [CrossRef]
  24. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698-5710 (2009).
    [CrossRef]
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    [CrossRef]
  26. J. L. Forand and G. R. Fournier, “Particle distribution and index of refraction estimation for Canadian waters,” Proc. SPIE 3761, 34-44 (1999).
    [CrossRef]
  27. E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam spectrum and its inversion to obtain the shape of the particle size distribution,” Appl. Opt. 40, 4885-4893(2001).
    [CrossRef]
  28. 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. 106, 14129-14142(2001).
    [CrossRef]
  29. J. M. Sullivan, M. S. Twardowski, P. L. Donaghay, and S. Freeman, “Using optical scattering to discriminate particle types in coastal waters,” Appl. Opt. 44, 1667-1680 (2005).
    [CrossRef]
  30. M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).
  31. E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
    [CrossRef]
  32. A. L. Whitmire, E. Boss, T. J. Cowles, and W. S. Pegau, “Spectral variability of the particulate backscattering ratio,” Opt. Express 15, 7019-7031 (2007).
    [CrossRef]

2009 (1)

2008 (1)

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
[CrossRef]

2007 (3)

2006 (2)

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

J. M. Sullivan, M. S. Twardowski, J. R. Zaneveld, C. Moore, A. Barnard, P. L. Donaghay, and B. Rhoades, “The hyper-spectral temperature and salinity dependent absorption of pure water, salt water and heavy salt water (D2O) in the visible and near-IR wavelengths (400-750 nm),” Appl. Opt. 45, 5294-5309 (2006).
[CrossRef]

2005 (1)

2004 (1)

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

2003 (2)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563-571 (2003).
[CrossRef]

2001 (3)

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]

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam spectrum and its inversion to obtain the shape of the particle size distribution,” Appl. Opt. 40, 4885-4893(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. 106, 14129-14142(2001).
[CrossRef]

1999 (2)

J. L. Forand and G. R. Fournier, “Particle distribution and index of refraction estimation for Canadian waters,” Proc. SPIE 3761, 34-44 (1999).
[CrossRef]

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691-707 (1999).
[CrossRef]

1997 (2)

1995 (2)

A. Morel, K. Voss, and B. Gentilli, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143-13150(1995).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135-13142 (1995).
[CrossRef]

1994 (2)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194-201 (1994).
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44-55 (1994).
[CrossRef]

1993 (1)

1992 (1)

J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680-1690 (1992).

1990 (1)

1989 (1)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the Sun angle,” Limnol. Oceanog. 34, 1484-1489(1989).

1975 (1)

1968 (1)

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423-432 (1968).
[CrossRef]

1961 (1)

N. G. Jerlov, “Optical measurements in the eastern North Atlantic,” Medd. Oceanogr. Inst. Göteborg 30, 1-40 (1961).

Agrawal, Y. C.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
[CrossRef]

Baratange, F.

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

Barnard, 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. 106, 14129-14142(2001).
[CrossRef]

Berthon, J.-F.

Boss, E.

A. L. Whitmire, E. Boss, T. J. Cowles, and W. S. Pegau, “Spectral variability of the particulate backscattering ratio,” Opt. Express 15, 7019-7031 (2007).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

E. Boss, M. S. Twardowski, and S. Herring, “Shape of the particulate beam spectrum and its inversion to obtain the shape of the particle size distribution,” Appl. Opt. 40, 4885-4893(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. 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]

Brock, R. S.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Brown, O. B.

Chami, M.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

Claustre, H.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).

Cowles, T. J.

Dana, D. R.

Donaghay, P. L.

Forand, J. L.

J. L. Forand and G. R. Fournier, “Particle distribution and index of refraction estimation for Canadian waters,” Proc. SPIE 3761, 34-44 (1999).
[CrossRef]

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194-201 (1994).
[CrossRef]

Fournier, G. R.

J. L. Forand and G. R. Fournier, “Particle distribution and index of refraction estimation for Canadian waters,” Proc. SPIE 3761, 34-44 (1999).
[CrossRef]

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194-201 (1994).
[CrossRef]

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).

Freeman, S.

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

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Freeman, S. A.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).

Fry, E. S.

Gentili, B.

Gentilli, B.

A. Morel, K. Voss, and B. Gentilli, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143-13150(1995).
[CrossRef]

Gordon, H. R.

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the Sun angle,” Limnol. Oceanog. 34, 1484-1489(1989).

H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties,” Appl. Opt. 14, 417-427 (1975).
[CrossRef]

He, M.-X.

Herring, S.

Hu, L.

Hu, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Huot, Y.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).

Jacobs, K. M.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Jacobs, M. M.

Jerlov, N. G.

N. G. Jerlov, “Optical measurements in the eastern North Atlantic,” Medd. Oceanogr. Inst. Göteborg 30, 1-40 (1961).

Jonasz, M.

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).

Khomenko, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

Kitchen, J. C.

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44-55 (1994).
[CrossRef]

J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680-1690 (1992).

Korotaev, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

Kullenberg, G.

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423-432 (1968).
[CrossRef]

Lee, M.

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

Lee, M. E.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563-571 (2003).
[CrossRef]

Lee, M. E.-G.

Lewis, M. R.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563-571 (2003).
[CrossRef]

Lu, J. Q.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

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. 106, 14129-14142(2001).
[CrossRef]

Maffione, R. A.

Marken, E.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

Mikkelsen, O. A.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
[CrossRef]

Moore, C.

J. M. Sullivan, M. S. Twardowski, J. R. Zaneveld, C. Moore, A. Barnard, P. L. Donaghay, and B. Rhoades, “The hyper-spectral temperature and salinity dependent absorption of pure water, salt water and heavy salt water (D2O) in the visible and near-IR wavelengths (400-750 nm),” Appl. Opt. 45, 5294-5309 (2006).
[CrossRef]

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Moore, C. C.

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44-55 (1994).
[CrossRef]

Morel, A.

A. Morel, K. Voss, and B. Gentilli, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143-13150(1995).
[CrossRef]

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

Oishi, T.

Pegau, W. S.

A. L. Whitmire, E. Boss, T. J. Cowles, and W. S. Pegau, “Spectral variability of the particulate backscattering ratio,” Opt. Express 15, 7019-7031 (2007).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[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. 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]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. (Scripps Institution of Oceanography, 1972), pp.72-78.

Pope, R. M.

Pottsmith, H. C.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
[CrossRef]

Rhoades, B.

Shybanov, E.

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189-5203(2007).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

Slivkoff, M.

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Stamnes, J. J.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

Stramski, D.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).

Sullivan, J. M.

J. M. Sullivan, M. S. Twardowski, J. R. Zaneveld, C. Moore, A. Barnard, P. L. Donaghay, and B. Rhoades, “The hyper-spectral temperature and salinity dependent absorption of pure water, salt water and heavy salt water (D2O) in the visible and near-IR wavelengths (400-750 nm),” Appl. Opt. 45, 5294-5309 (2006).
[CrossRef]

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

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691-707 (1999).
[CrossRef]

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Twardowski, M. S.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).

J. M. Sullivan, M. S. Twardowski, J. R. Zaneveld, C. Moore, A. Barnard, P. L. Donaghay, and B. Rhoades, “The hyper-spectral temperature and salinity dependent absorption of pure water, salt water and heavy salt water (D2O) in the visible and near-IR wavelengths (400-750 nm),” Appl. Opt. 45, 5294-5309 (2006).
[CrossRef]

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

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[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. 106, 14129-14142(2001).
[CrossRef]

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

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691-707 (1999).
[CrossRef]

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Voss, K.

A. Morel, K. Voss, and B. Gentilli, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143-13150(1995).
[CrossRef]

Whitmire, A.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
[CrossRef]

Whitmire, A. L.

Yang, P.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Zaneveld, J. R.

Zaneveld, J. R. V.

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. 106, 14129-14142(2001).
[CrossRef]

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691-707 (1999).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135-13142 (1995).
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44-55 (1994).
[CrossRef]

J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680-1690 (1992).

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Zhang, X.

Zibordi, G.

Appl. Opt. (10)

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

H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties,” Appl. Opt. 14, 417-427 (1975).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189-5203(2007).
[CrossRef]

T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°,” Appl. Opt. 29, 4658-4665 (1990).
[CrossRef]

R. A. Maffione and D. R. Dana, “Instruments and methods for measuring the backward scattering coefficient of ocean waters,” Appl. Opt. 36, 6057-6067 (1997).
[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]

R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710-8723 (1997).
[CrossRef]

J. M. Sullivan, M. S. Twardowski, J. R. Zaneveld, C. Moore, A. Barnard, P. L. Donaghay, and B. Rhoades, “The hyper-spectral temperature and salinity dependent absorption of pure water, salt water and heavy salt water (D2O) in the visible and near-IR wavelengths (400-750 nm),” Appl. Opt. 45, 5294-5309 (2006).
[CrossRef]

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

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

Biogeosciences (1)

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the “clearest” natural waters,” Biogeosciences 4, 1041-1058(2007).

Deep-Sea Res. (1)

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423-432 (1968).
[CrossRef]

J. Atmos. Ocean. Technol. (2)

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563-571 (2003).
[CrossRef]

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691-707 (1999).
[CrossRef]

J. Geophys. Res. (6)

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen, and H. C. Pottsmith, “Light scattering by random shaped particles and consequences on measuring suspended sediments by laser diffraction,” J. Geophys. Res. 113, C04023 (2008).
[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. 106, 14129-14142(2001).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. S. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “The particulate backscattering ratio at LEO-15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, C05013 (2006).
[CrossRef]

A. Morel, K. Voss, and B. Gentilli, “Bidirectional reflectance of oceanic waters: a comparison of modeled and measured upward radiance fields,” J. Geophys. Res. 100, 13143-13150(1995).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135-13142 (1995).
[CrossRef]

Limnol. Oceanog. (1)

H. R. Gordon, “Dependence of the diffuse reflectance of natural waters on the Sun angle,” Limnol. Oceanog. 34, 1484-1489(1989).

Limnol. Oceanogr. (1)

J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680-1690 (1992).

Medd. Oceanogr. Inst. Göteborg (1)

N. G. Jerlov, “Optical measurements in the eastern North Atlantic,” Medd. Oceanogr. Inst. Göteborg 30, 1-40 (1961).

Opt. Express (2)

Phys. Med. Biol. (1)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Proc. SPIE (3)

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194-201 (1994).
[CrossRef]

J. L. Forand and G. R. Fournier, “Particle distribution and index of refraction estimation for Canadian waters,” Proc. SPIE 3761, 34-44 (1999).
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, and C. C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE 2258, 44-55 (1994).
[CrossRef]

Other (3)

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. (Scripps Institution of Oceanography, 1972), pp.72-78.

M. S. Twardowski, WET Labs, Inc., Department of Research, 70 Dean Knauss Drive, Narragansett, Rhode Island, 02882, USA, and C. Moore, J. M. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

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Figures (5)

Fig. 1
Fig. 1

Mechanical drawing of the MASCOT. The MASCOT has a semicircular array of 17 detector windows with a laser source and beam stop at each edge of the semicircle of detectors. The MASCOT has a length × width × height of 86 cm × 38 cm × 15 cm .

Fig. 2
Fig. 2

(a) VSF in the backward angles from all field sites. (b) Phase functions in the backward direction ( β ˜ b p ) from all field sites. (c) Average β ˜ b p from each of the ten field sites.

Fig. 3
Fig. 3

(a) Average and standard deviation (σ) of β ˜ b p using MASCOT data from all field sites [open circles with error bars (σ) and dotted curve] compared to the β ˜ b p of Petzold’s [6] three water types (turbid, coastal, and clear). (b) Average and σ of β ˜ b p using MASCOT data from all field sites [open circles with error bars (σ) and dotted curve] compared to the β ˜ F F analytical model values (shaded area). The solid curve through the center of the shaded area represents the average β ˜ F F with the width of the shading equal to the σ of the β ˜ F F values.

Fig. 4
Fig. 4

(a) Average and standard deviations (σ) of χ p factors using MASCOT data from all field sites [open circles with error bars (σ) and dotted curve]. The χ p factors of Boss and Pegau [15] (solid curve marked “BP”), Chami et al. [10] (dashed curve marked “C”) and Berthon et al. [11] (dashed–dotted curve marked “B”) are plotted for comparison. (b) Average of χ p factors using MASCOT data from all field sites over the full angular range of the instrument.

Fig. 5
Fig. 5

(a) Percent variability (σ as %) in χ p in the backward direction (open circles with error bars) compared to the random noise error of the MASCOT determined from dark count profiles (dotted curves). (b) Percent variability (σ as %) in χ p over the full angular range of the MASCOT (open circles with error bars) compared to the random noise error of the MASCOT determined from dark count profiles (dotted curves).

Tables (3)

Tables Icon

Table 1 Average, Standard Deviation (σ), and Percent Variability (σ as %) of β ˜ bp Yielded from the Combined Data of All Field Sites

Tables Icon

Table 2 Coefficients for a Fourth-Order Polynomial Fit of the Average Data a

Tables Icon

Table 3 Average and Standard Deviation (σ) of χ p Yielded from the Combined Data of All Field Sites

Equations (3)

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

β ( θ ¯ i ) = [ Φ i D i ] f i e L [ b p ϵ + a p g + a w ] ,
β ˜ b p = β p ( θ ) / b b p .
χ p ( θ ) = b b p / 2 π β p ( θ ) = 1 / 2 π β ˜ b p ( θ ) .

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