Abstract

A typical integrating sphere configuration for measuring backscatter includes a conventional cuvette with flat windows. This arrangement results in a significant amount of total internal reflection, preventing a large portion of the backscattered flux from entering the integrating sphere–detector system. Use of a semispherical cuvette overcomes this problem. Monte Carlo simulations of a semispherical cuvette window demonstrate that the detected signal varies monotonically with the attenuation, depending only on the probability of backscattering for a given single scattering albedo. That is, only the total backscattering probability matters, regardless of subtle differences in the scattering phase function in the backward direction. The system is calibrated by use of standard microspheres for which the size distribution and the refractive index are known; this makes it possible to compute the exact phase function based on Mie theory. We have performed Monte Carlo simulations for various measured volume scattering functions and for computed phase functions, using particle scattering codes. All the results indicate that the backscattering measurement errors are likely to be less than 10%.

© 2005 Optical Society of America

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References

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  1. D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
    [CrossRef]
  2. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, 1983).
    [CrossRef]
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  4. M. Kerker, Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).
  5. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  6. M. E. Lee, 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.
  7. R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
    [CrossRef]
  8. 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]
  9. A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
    [CrossRef]
  10. A. Morel, Y. H. Ahn, “Optical efficiency factors of free-living marine bacteria: influence of bacterioplankton upon the optical properties and particulate organic carbon in oceanic waters,” J. Mar. Res. 48, 145–175 (1990).
    [CrossRef]
  11. Y. H. Ahn, A. Bricaud, A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep-Sea Res. 39, 1835–1855 (1992).
    [CrossRef]
  12. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, 1972).
  13. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  14. E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

2004 (3)

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
[CrossRef]

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

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]

1992 (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]

1990 (1)

A. Morel, Y. H. Ahn, “Optical efficiency factors of free-living marine bacteria: influence of bacterioplankton upon the optical properties and particulate organic carbon in oceanic waters,” J. Mar. Res. 48, 145–175 (1990).
[CrossRef]

1983 (1)

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[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, “Optical efficiency factors of free-living marine bacteria: influence of bacterioplankton upon the optical properties and particulate organic carbon in oceanic waters,” J. Mar. Res. 48, 145–175 (1990).
[CrossRef]

Balch, W. M.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[CrossRef]

Baratange, F.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Bohren, C. F.

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

Boss, E.

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

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]

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

Brown, C. W.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[CrossRef]

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]

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]

Gordon, H. R.

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, 1983).
[CrossRef]

Guillard, R. R. L.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[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, 1983).

Kerker, M.

M. Kerker, Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

Korotaev, G.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

Lee, M.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

Lee, M. E.

M. E. Lee, 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.

Lewis, M. R.

M. E. Lee, 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.

Mobley, C. D.

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

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, “Optical efficiency factors of free-living marine bacteria: influence of bacterioplankton upon the optical properties and particulate organic carbon in oceanic waters,” J. Mar. Res. 48, 145–175 (1990).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

Morel, A. Y.

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, 1983).
[CrossRef]

Pegau, W. S.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, 1972).

Prieur, L.

A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

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]

Shybanov, E.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

Stramski, D.

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Twardowski, M.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

Vaillancourt, R. D.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

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]

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]

Voss, K. J.

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
[CrossRef]

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]

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]

J. Atmos. Ocean. Technol. (1)

M. E. Lee, 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.

J. Geophys. Res. (1)

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, F. Baratange, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109(C1), C01014 (2004).

J. Mar. Res. (1)

A. Morel, Y. H. Ahn, “Optical efficiency factors of free-living marine bacteria: influence of bacterioplankton upon the optical properties and particulate organic carbon in oceanic waters,” J. Mar. Res. 48, 145–175 (1990).
[CrossRef]

J. Plankton Res. (1)

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212 (2004).
[CrossRef]

Limnol. Oceanogr. (2)

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. 28, 816–832 (1983).
[CrossRef]

Progr. Oceanogr. (1)

D. Stramski, E. Boss, D. Bogucki, K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progr. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Other (6)

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review, Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, 1983).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

M. Kerker, Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

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

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, 1972).

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

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Figures (13)

Fig. 1
Fig. 1

(a) Design of Ahn et al.11 with a flat cuvette window; (b) new design with a spherical cuvette window. Note the angular range of backscattered flux contribution.

Fig. 2
Fig. 2

Weighting functions of a semispherical cuvette at the scattering volume along the incident beam path. The Y axis represents the distance of the infinitesimal scattering volume from the tip of the semisphere along the incident light path. For each scattering volume, the scattering contribution to the integrating sphere (Z axis) is calculated over the scattering angle (X axis). The weighting functions are calculated based on the single-scattering assumption, which is sufficient to illustrate the overall properties of the semispherical cuvette system.

Fig. 3
Fig. 3

(a) Scattering contributions to the integrating sphere by the semispherical cuvette for a Petzold phase function. (b) At each distance of the scattering volume, Qbf and Qbb are the areas under the scattering contribution curves at forward and backward angles (left-hand axis). Qbf_cumulative and Qbb_cumulative are the line integrals of Qbf and Qbb, respectively, in arbitrary relative units.

Fig. 4
Fig. 4

Scattering phase functions used to test the backscattering loss.

Fig. 5
Fig. 5

Left, cuvette shift toward light trap; right, no shift.

Fig. 6
Fig. 6

Effect of the cuvette shift when Petzold’s average particle phase function was used. The top two figures show the relative contributions of forward and backward scattering into the integrating sphere: (a) no shift, (b) 3 mm shift. (c) Integrated flux over the forward and backward angular regions at each distance along the illuminating beam in the scattering volume; (d) the corresponding cumulative scattering fluxes, in arbitrary relative units.

Fig. 7
Fig. 7

Effects of the cuvette shift for a mixture of silica and polystyrene microspheres: (a) scattering plot for the unshifted cuvette, (b) scattering plot for a cuvette shifted by 3 mm, (c) integrated flux over the forward and backward angular regions at each distance along the illuminating beam in the scattering volume, and (d) the corresponding cumulative scattering fluxes, in arbitrary relative units.

Fig. 8
Fig. 8

(a) Characteristic detected flux curves of various values of ω0 and B. Solid curves, ω0 = 0.5; dashed curves, ω0 = 0.8. The backscattering probability ranges from 0.001 (bottom curve) to 0.05 (top curve) for both curve groups. (b) Two groups of bb/c: 0.004 for all thin curves, 0.0025 for all thick curves. (c) Total detected fluxes for four values of bb/c: 0.001, 0.002, 0.003, and 0.004. Each group consists of a pair of curves: solid, B = 0.005; dotted, B = 0.01. High B has smaller ω0 and low B has larger ω0, so bb/c values are identical. For instance, a pair of curves at the bottom has a bb/c value of 0.001. In that case, the solid curve is for ω0 = 0.2 and the dashed curve is for ω0 = 0.1. The top pair of lines has a bb/c value of 0.004. In that case, the solid curve is for ω0 = 0.8 and the dashed curve is for ω0 = 0.4. (d) Detected portion of the initially backscattered flux. The description for Fig. 11(c) below applies here as well. (e) Flux entering the integrating sphere and total detected flux. Qbb_IS indicates the part of initially backscattered (bb) flux that enters the integrating sphere (IS). Qdet indicates the total detected flux. (f) Amount of initially backscattered flux that is absorbed by the sample (Qbb_abs) and absorbed by the integrating sphere surface (Qbb_IS_abs).

Fig. 9
Fig. 9

Probability of backscattering of Mie particles as a function of size at a wavelength of 590 nm. Each curve represents scattering from a sphere with a specific relative refractive index ranging from 1.02 (bottom) to 1.2 (top) in intervals of 0.02.

Fig. 10
Fig. 10

Standard particle phase functions used for system calibration.

Fig. 11
Fig. 11

(a) Petzold’s two phase functions, the corresponding Fournier–Forand (FF) phase functions, and standard silica-polystyrene phase functions. (b) System response for Petzold’s clear water. (c) System response for Petzold’s turbid water. Simulations were made with ω0 = 0.8. Reference dashed curves for other ω0 values are also shown.

Fig. 12
Fig. 12

Result of simulation with VSM data: (a) VSM phase functions and (b) system response. In each figure the backscattering probabilities are (top to bottom) 0.0042, 0.0084, 0.0133, and 0.026. Standard responses of the same backscattering probabilities are shown as dashed curves in (b).

Fig. 13
Fig. 13

(a) Phase functions and (b) system response of five phase functions compared with those of the standard phase function for calibration. The average size and refractive index of the particle are shown in (a) for each phase function.

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