Abstract

We present an approach based on three-dimensional Monte Carlo radiative transfer simulations for estimating scattering error in measurements of light absorption by aquatic particles with a typical laboratory double-beam spectrophotometer. The scattering error is calculated by combining the weighting function describing the angular distribution of photon losses that are due to scattering on suspended particles with the volume scattering function of particles. We applied this method to absorption measurements made on marine phytoplankton, a diatom Thalassiosira pseudonana and a cyanobacterium Synechococcus. Assuming that the scattering phase function is described by the Henyey-Greenstein formula, we determined the backscatter probability of phytoplankton, which yields the best correction for scattering error at a light wavelength of 750 nm, where true absorption is null. The backscattering ratio estimated for both phytoplankton species is significantly higher than previously reported data based on Mie-scattering calculations for homogeneous spheres. Depending on the type of particles, the corrected absorption spectra obtained with our method may be similar or significantly different from spectra obtained with the null-point correction based on wavelength-independent scattering error.

© 2003 Optical Society of America

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    [CrossRef]
  3. J. T. O. Kirk, “Monte Carlo modeling of the performance of a reflective tube absorption meter,” Appl. Opt. 31, 6463–6468 (1992).
    [CrossRef] [PubMed]
  4. J. R. V. Zaneveld, J. Kitchen, C. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
    [CrossRef]
  5. J. Piskozub, P. J. Flatau, J. R. V. Zaneveld, “Monte Carlo study of the scattering error of a quartz reflective absorption tube,” J. Atmos. Oceanic Technol. 18, 438–445 (2001).
    [CrossRef]
  6. R. A. Reynolds, D. Stramski, D. A. Kiefer, “The effect of nitrogen-limitation on the absorption and scattering properties of the marine diatom Thalassiosira pseudonana,” Limnol. Oceanogr. 42, 881–892 (1997).
    [CrossRef]
  7. D. Stramski, A. Shalapyonok, R. A. Reynolds, “Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance,” J. Geophys. Res. 100, 13295–13307 (1995).
    [CrossRef]
  8. M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
    [CrossRef]
  9. D. Stramski, R. A. Reynolds, “Diel variations in the optical properties of a marine diatom,” Limnol. Oceanogr. 38, 1347–1364 (1993).
    [CrossRef]
  10. H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
    [CrossRef]
  11. W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  14. D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplankton cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
    [CrossRef] [PubMed]
  15. D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
    [CrossRef]
  16. J. Piskozub, “Effects of surface waves and sea bottom on self-shading of in-water optical instruments” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 300–308 (1994).
    [CrossRef]
  17. J. Piskozub, A. R. Weeks, J. N. Schwartz, I. S. Robinson, “Self-shading of upwelling irradiance for an instrument with sensors on a sidearm,” Appl. Opt. 39, 1872–1878 (2000).
    [CrossRef]
  18. F. M. Sogandares, E. S. Fry, “Absorption spectrum (340–640 nm) of pure water. I. Photothermal measurements,” Appl. Opt. 36, 8699–8709 (1997).
    [CrossRef]
  19. R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [CrossRef]
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  22. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).
  23. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  24. L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  25. V. I. Haltrin, “One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater,” Appl. Opt. 41, 1022–1028 (2002).
    [CrossRef] [PubMed]
  26. C. D. Mobley, L. K. Sundman, E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
    [CrossRef] [PubMed]
  27. Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
    [CrossRef]
  28. R. A. Meyer, “Light scattering from biological cells: dependence of backscatter radiation on membrane thickness and refractive index,” Appl. Opt. 18, 585–588 (1979).
    [CrossRef] [PubMed]
  29. A. Bricaud, J. R. V. Zaneveld, J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 27–33 (1992).
    [CrossRef]
  30. J. C. Kitchen, J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol Oceanogr. 37, 1680–1690 (1992).
    [CrossRef]
  31. R. D. Vaillancourt, C. Brown, R. R. L. Guillard, “A taxonomic survey of the optical properties of marine phytoplankton with special emphasis on the backscattering coefficient,” Eos Trans. Am. Geophys. Union 80, 119–120 (1999).
  32. R. A. Maffione, D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997).
    [CrossRef] [PubMed]
  33. X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
    [CrossRef]
  34. A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates. A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
    [CrossRef]
  35. D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]

2002 (4)

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

V. I. Haltrin, “One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater,” Appl. Opt. 41, 1022–1028 (2002).
[CrossRef] [PubMed]

C. D. Mobley, L. K. Sundman, E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[CrossRef] [PubMed]

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

2001 (1)

J. Piskozub, P. J. Flatau, J. R. V. Zaneveld, “Monte Carlo study of the scattering error of a quartz reflective absorption tube,” J. Atmos. Oceanic Technol. 18, 438–445 (2001).
[CrossRef]

2000 (1)

1999 (2)

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

R. D. Vaillancourt, C. Brown, R. R. L. Guillard, “A taxonomic survey of the optical properties of marine phytoplankton with special emphasis on the backscattering coefficient,” Eos Trans. Am. Geophys. Union 80, 119–120 (1999).

1998 (1)

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

1997 (5)

D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
[CrossRef]

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

R. A. Reynolds, D. Stramski, D. A. Kiefer, “The effect of nitrogen-limitation on the absorption and scattering properties of the marine diatom Thalassiosira pseudonana,” Limnol. Oceanogr. 42, 881–892 (1997).
[CrossRef]

F. M. Sogandares, E. S. Fry, “Absorption spectrum (340–640 nm) of pure water. I. Photothermal measurements,” Appl. Opt. 36, 8699–8709 (1997).
[CrossRef]

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

1995 (1)

D. Stramski, A. Shalapyonok, R. A. Reynolds, “Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance,” J. Geophys. Res. 100, 13295–13307 (1995).
[CrossRef]

1993 (1)

D. Stramski, R. A. Reynolds, “Diel variations in the optical properties of a marine diatom,” Limnol. Oceanogr. 38, 1347–1364 (1993).
[CrossRef]

1992 (3)

J. T. O. Kirk, “Monte Carlo modeling of the performance of a reflective tube absorption meter,” Appl. Opt. 31, 6463–6468 (1992).
[CrossRef] [PubMed]

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

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

1991 (2)

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates. A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

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

1988 (1)

1986 (1)

1983 (1)

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 35, 562–582 (1983).
[CrossRef]

1981 (1)

1979 (1)

1941 (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Ahn, Y.-H.

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates. A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

Babin, M.

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

Baker, K. S.

Balch, W. M.

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Boss, E.

Bricaud, A.

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplankton cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 35, 562–582 (1983).
[CrossRef]

A. Bricaud, J. R. V. Zaneveld, J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 27–33 (1992).
[CrossRef]

Brown, C.

R. D. Vaillancourt, C. Brown, R. R. L. Guillard, “A taxonomic survey of the optical properties of marine phytoplankton with special emphasis on the backscattering coefficient,” Eos Trans. Am. Geophys. Union 80, 119–120 (1999).

Charlton, F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Cucci, T. L.

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

Dana, D. R.

de Haan, J. F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Dekker, A. G.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Drapeau, D. T.

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

Flatau, P. J.

J. Piskozub, P. J. Flatau, J. R. V. Zaneveld, “Monte Carlo study of the scattering error of a quartz reflective absorption tube,” J. Atmos. Oceanic Technol. 18, 438–445 (2001).
[CrossRef]

Fritz, J. J.

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

Fry, E. S.

Greenstein, J. L.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Guillard, R. R. L.

R. D. Vaillancourt, C. Brown, R. R. L. Guillard, “A taxonomic survey of the optical properties of marine phytoplankton with special emphasis on the backscattering coefficient,” Eos Trans. Am. Geophys. Union 80, 119–120 (1999).

Haltrin, V. I.

Henyey, L. C.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hoogenboom, H. J.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Hovenier, J. W.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Johnson, B.

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Kiefer, D. A.

R. A. Reynolds, D. Stramski, D. A. Kiefer, “The effect of nitrogen-limitation on the absorption and scattering properties of the marine diatom Thalassiosira pseudonana,” Limnol. Oceanogr. 42, 881–892 (1997).
[CrossRef]

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

Kilpatrick, K. A.

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

Kirk, J. T. O.

Kitchen, J.

J. R. V. Zaneveld, J. Kitchen, C. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

Kitchen, J. C.

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

A. Bricaud, J. R. V. Zaneveld, J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 27–33 (1992).
[CrossRef]

Korotaev, G.

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Lee, M.

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Lewis, M.

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Maffione, R. A.

Meyer, R. A.

Mobley, C. D.

C. D. Mobley, L. K. Sundman, E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[CrossRef] [PubMed]

D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
[CrossRef]

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

Moore, C.

J. R. V. Zaneveld, J. Kitchen, C. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

Morel, A.

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates. A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplankton cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 35, 562–582 (1983).
[CrossRef]

A. Morel, “Diffusion de la lumière par les eaux de mer: résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD Lecture Series 63 (Advisory Group for Aerospace Research and Development, Paris, 1973), Sect. 3, pp. 1–76.

Petzold, T. J.

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

Piskozub, J.

J. Piskozub, P. J. Flatau, J. R. V. Zaneveld, “Monte Carlo study of the scattering error of a quartz reflective absorption tube,” J. Atmos. Oceanic Technol. 18, 438–445 (2001).
[CrossRef]

J. Piskozub, A. R. Weeks, J. N. Schwartz, I. S. Robinson, “Self-shading of upwelling irradiance for an instrument with sensors on a sidearm,” Appl. Opt. 39, 1872–1878 (2000).
[CrossRef]

J. Piskozub, “Effects of surface waves and sea bottom on self-shading of in-water optical instruments” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 300–308 (1994).
[CrossRef]

Pope, R. M.

Prieur, L.

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 35, 562–582 (1983).
[CrossRef]

Reynolds, R. A.

R. A. Reynolds, D. Stramski, D. A. Kiefer, “The effect of nitrogen-limitation on the absorption and scattering properties of the marine diatom Thalassiosira pseudonana,” Limnol. Oceanogr. 42, 881–892 (1997).
[CrossRef]

D. Stramski, A. Shalapyonok, R. A. Reynolds, “Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance,” J. Geophys. Res. 100, 13295–13307 (1995).
[CrossRef]

D. Stramski, R. A. Reynolds, “Diel variations in the optical properties of a marine diatom,” Limnol. Oceanogr. 38, 1347–1364 (1993).
[CrossRef]

Robinson, I. S.

Schreurs, R.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Schwartz, J. N.

Shalapyonok, A.

D. Stramski, A. Shalapyonok, R. A. Reynolds, “Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance,” J. Geophys. Res. 100, 13295–13307 (1995).
[CrossRef]

Smith, R. C.

Sogandares, F. M.

Stramski, D.

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

R. A. Reynolds, D. Stramski, D. A. Kiefer, “The effect of nitrogen-limitation on the absorption and scattering properties of the marine diatom Thalassiosira pseudonana,” Limnol. Oceanogr. 42, 881–892 (1997).
[CrossRef]

D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
[CrossRef]

D. Stramski, A. Shalapyonok, R. A. Reynolds, “Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance,” J. Geophys. Res. 100, 13295–13307 (1995).
[CrossRef]

D. Stramski, R. A. Reynolds, “Diel variations in the optical properties of a marine diatom,” Limnol. Oceanogr. 38, 1347–1364 (1993).
[CrossRef]

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

D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplankton cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
[CrossRef] [PubMed]

Sundman, L. K.

Vaillancourt, R. D.

R. D. Vaillancourt, C. Brown, R. R. L. Guillard, “A taxonomic survey of the optical properties of marine phytoplankton with special emphasis on the backscattering coefficient,” Eos Trans. Am. Geophys. Union 80, 119–120 (1999).

Vassen, W.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Villancourt, R. D.

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

Volten, H.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Weeks, A. R.

Wouts, R.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Zaneveld, J. R. V.

J. Piskozub, P. J. Flatau, J. R. V. Zaneveld, “Monte Carlo study of the scattering error of a quartz reflective absorption tube,” J. Atmos. Oceanic Technol. 18, 438–445 (2001).
[CrossRef]

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

A. Bricaud, J. R. V. Zaneveld, J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 27–33 (1992).
[CrossRef]

J. R. V. Zaneveld, J. Kitchen, C. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

Zhang, X.

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Appl. Opt. (11)

J. T. O. Kirk, “Monte Carlo modeling of the performance of a reflective tube absorption meter,” Appl. Opt. 31, 6463–6468 (1992).
[CrossRef] [PubMed]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

D. Stramski, A. Morel, A. Bricaud, “Modeling the light attenuation and scattering by spherical phytoplankton cells: a retrieval of the bulk refractive index,” Appl. Opt. 27, 3954–3956 (1988).
[CrossRef] [PubMed]

J. Piskozub, A. R. Weeks, J. N. Schwartz, I. S. Robinson, “Self-shading of upwelling irradiance for an instrument with sensors on a sidearm,” Appl. Opt. 39, 1872–1878 (2000).
[CrossRef]

F. M. Sogandares, E. S. Fry, “Absorption spectrum (340–640 nm) of pure water. I. Photothermal measurements,” Appl. Opt. 36, 8699–8709 (1997).
[CrossRef]

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

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981)∼.
[CrossRef] [PubMed]

V. I. Haltrin, “One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater,” Appl. Opt. 41, 1022–1028 (2002).
[CrossRef] [PubMed]

C. D. Mobley, L. K. Sundman, E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050 (2002).
[CrossRef] [PubMed]

R. A. Meyer, “Light scattering from biological cells: dependence of backscatter radiation on membrane thickness and refractive index,” Appl. Opt. 18, 585–588 (1979).
[CrossRef] [PubMed]

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

Astrophys. J. (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Deep-Sea Res. (1)

Y.-H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
[CrossRef]

Eos Trans. Am. Geophys. Union (1)

R. D. Vaillancourt, C. Brown, R. R. L. Guillard, “A taxonomic survey of the optical properties of marine phytoplankton with special emphasis on the backscattering coefficient,” Eos Trans. Am. Geophys. Union 80, 119–120 (1999).

J. Atmos. Oceanic Technol. (1)

J. Piskozub, P. J. Flatau, J. R. V. Zaneveld, “Monte Carlo study of the scattering error of a quartz reflective absorption tube,” J. Atmos. Oceanic Technol. 18, 438–445 (2001).
[CrossRef]

J. Geophys. Res. (2)

W. M. Balch, D. T. Drapeau, T. L. Cucci, R. D. Villancourt, K. A. Kilpatrick, J. J. Fritz, “Optical backscattering by calcifying algae: separating the contribution of particulate inorganic and organic carbon fractions,” J. Geophys. Res. 104, 1541–1558 (1999).
[CrossRef]

D. Stramski, A. Shalapyonok, R. A. Reynolds, “Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance,” J. Geophys. Res. 100, 13295–13307 (1995).
[CrossRef]

J. Mar. Res. (1)

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates. A tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

Limnol Oceanogr. (1)

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

Limnol. Oceanogr. (7)

X. Zhang, M. Lewis, M. Lee, B. Johnson, G. Korotaev, “The volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

D. Stramski, R. A. Reynolds, “Diel variations in the optical properties of a marine diatom,” Limnol. Oceanogr. 38, 1347–1364 (1993).
[CrossRef]

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 35, 562–582 (1983).
[CrossRef]

R. A. Reynolds, D. Stramski, D. A. Kiefer, “The effect of nitrogen-limitation on the absorption and scattering properties of the marine diatom Thalassiosira pseudonana,” Limnol. Oceanogr. 42, 881–892 (1997).
[CrossRef]

D. Stramski, C. D. Mobley, “Effects of microbial particles on oceanic optics: a database of single-particle optical properties,” Limnol. Oceanogr. 42, 538–549 (1997).
[CrossRef]

Prog. Oceanogr. (1)

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

Other (8)

A. Bricaud, J. R. V. Zaneveld, J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 27–33 (1992).
[CrossRef]

A. Morel, “Diffusion de la lumière par les eaux de mer: résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD Lecture Series 63 (Advisory Group for Aerospace Research and Development, Paris, 1973), Sect. 3, pp. 1–76.

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

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

J. Piskozub, “Effects of surface waves and sea bottom on self-shading of in-water optical instruments” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 300–308 (1994).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge U. Press, Cambridge, UK, 1994).
[CrossRef]

J. R. V. Zaneveld, J. Kitchen, C. Moore, “The scattering error correction of reflecting-tube absorption meters,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 44–55 (1994).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Absorption spectra of (a) T. pseudonana and (b) Synechococcus measured with a Uvikon-860 spectrophotometer. No correction for scattering error was applied to these spectra.

Fig. 2
Fig. 2

Beam attenuation spectra of (a) T. pseudonana and (b) Synechococcus measured with a Uvikon-860 spectrophotometer.

Fig. 3
Fig. 3

Schematic diagram of the experimental setup for measuring absorption with a Uvikon-860 spectrophotometer. Example trajectories of photons scattered within the sample cuvette at an angle of 45° are shown. For simplicity of illustration, some reflection events were omitted. This graph is in 1:1 scale, so it shows the actual size of the beam, cuvette, and the entrance port of the integrating sphere (in two dimensions).

Fig. 4
Fig. 4

Scattering phase functions obtained from Mie calculations at three example wavelengths, 350, 550, and 750 nm, for (a) T. pseudonana and (b) Synechococcus.

Fig. 5
Fig. 5

Weighting function versus scattering angle as obtained from 3-D Monte Carlo radiative transfer simulations of our absorption measurement geometry. The results for various values of the particulate beam attenuation c p , absorption a p , and scattering b p coefficients (units are m-1) of the particulate sample are shown. The average weighting function is also shown (dotted curve). In these simulations, the values of the absorption a w and scattering b w coefficients of pure seawater were 0.00663 and 0.0076 m-1, respectively (λ = 400 nm). Note that these values are small compared with a p and b p .

Fig. 6
Fig. 6

Same as Fig. 5 but the results are shown for different scattering phase functions of the particulate sample as indicated.

Fig. 9
Fig. 9

Relationship between the backscattering ratio and the asymmetry parameter for the HG phase function.

Fig. 7
Fig. 7

Product of the weighting function, the Petzold (coastal ocean) scattering phase function, and the sine of the scattering angle as a function of scattering angle. This plot illustrates the contribution of light scattering at different angles to the scattering error in our instrument for the sample with the Petzold phase function.

Fig. 8
Fig. 8

(a) Example of the measured absorption spectrum of T. pseudonana and the corrected absorption spectrum that we obtained by using the scattering phase functions from Mie calculations. (b) The measured absorption spectrum and the corrected spectra that we obtained by using the HG phase functions with the λ-independent parameter g as indicated. Note that g = 0.9766 produces a perfect correction at 750 nm because the corrected absorption at this wavelength is null.

Fig. 14
Fig. 14

(a) Spectra of the backscattering ratio of T. pseudonana obtained from the scattering correction procedure involving the λ-dependent HG asymmetry parameter for 30 absorption measurements shown in Fig. 1(a). (b) As above but for 7 measurements of Synechococcus from Fig. 1(b). The backscattering ratio from Mie calculations is also shown (dotted curves).

Fig. 10
Fig. 10

Comparison of the spectral backscattering ratio of T. pseudonana obtained from Mie phase functions and the adjusted ratio obtained from the scattering correction procedure that utilized the λ-dependent HG phase functions. The value of the adjusted backscattering ratio at 750 nm, b bp (750)/b p (750) = 0.00496, satisfies the condition that the corrected absorption at this wavelength is null. The relative shape of the adjusted spectrum is the same as that for the Mie-based spectrum. The spectrum of the HG asymmetry parameter g corresponding to the adjusted b bp (λ)/b p (λ) is also shown. The adjusted b bp (λ)/b p (λ) and g(λ) spectra correspond to the example absorption measurement shown in Fig. 8.

Fig. 11
Fig. 11

Example of the measured absorption spectrum of T. pseudonana (same as in Fig. 8) and the corrected absorption spectra as obtained with the procedures that utilized the HG scattering phase functions with the λ-dependent asymmetry parameter g (dotted curve) and the spectrally constant g of 0.9766 (dashed curve). The result of the null-point correction is also shown (dashed-dotted-dotted curve).

Fig. 12
Fig. 12

Same as Fig. 11 but the results are shown for example measurement of absorption by Synechococcus. This graph also includes the corrected spectrum obtained with the Mie-scattering phase functions. Note that the null-point correction and the procedure involving the λ-dependent asymmetry parameter g produce nearly identical results.

Fig. 13
Fig. 13

Same as Fig. 10 but the results are shown for Synechococcus. The adjusted b bp (λ)/b p (λ) and g(λ) spectra correspond to the example absorption measurement shown in Fig. 12.

Equations (15)

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ελ=amλ-apλ=2π 0π WΨβpΨ, λsin ΨdΨ,
ελ=amλ-apλ=fλbpλ,
fλ=2π 0π WΨβ˜pλ, Ψsin ΨdΨ,
bpλ=cpλ-amλ1-fλ.
β˜pλ, Ψ=βpΨ, λbpλ,
apλ=amλ-fλcpλ1-fλ,
amλ=1dlnF0λFλ,
W1Ψ=NSΨ-NRΨ-NS*Ψ-NR*ΨNSΨ-NRΨ,
limΨ0° WΨ=0,
1-WΨ=p1-W1Ψ,
WΨ=1-p+pW1Ψ.
1dlnF0λFλ=apλ+2π 0π WΨβpΨ, λsin ΨdΨ.
p=bpλ-1dlnF0λFλ-apλbpλ-2π 0π W1ΨβpΨ, λsin ΨdΨ.
β˜HGg, Ψ=14π1-g21+g2-2g cos Ψ3/2.
b˜b=1-g2g1+g1+g21/2-1,

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