Abstract

The single scattering properties of hydrosols play an important role in the study of ocean optics, ocean color remote sensing, and ocean biogeochemistry research. Measurements show that hydrosols can be of various sizes and shapes, suggesting general non-spherical models should be considered for the study of single scattering properties of hydrosols. In this work, light scattering by non-spherical hydrosols are modeled by randomly oriented spheroids with the Amsterdam discrete dipole approximation (ADDA) code. We have defined two new parameters to quantify the degree of optical non-sphericity (DONS) and investigated the dependence of DONS on refractive index, size, and aspect ratio. For particles with non-unitary aspect ratios, the magnitude of DONS increases as the refractive index and particle size increase. The dependence of the backscattering fraction on the non-sphericity, size, and refractive index of hydrosols is also studied. It is found that the backscattering fraction is larger for smaller particles as well as for particles with higher refractive indices. Absorptive hydrosols generally have a lower backscattering fraction than non-absorptive hydrosols. This study of light scattering by non-spherical hydrosols would lead to better radiative transfer models in ocean waters and new remote sensing techniques of hydrosol compositions.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2017 (1)

G. Xu, B. Sun, S. D. Brooks, P. Yang, G. W. Kattawar, and X. Zhang, “Modeling the inherent optical properties of aquatic particles using an irregular hexahedral ensemble,” J. Quant. Spectrosc. Radiat. Transfer 191, 30–39 (2017)
[Crossref]

2016 (2)

B. Sun, G. W. Kattawar, P. Yang, M. S. Twardowski, and J. M. Ivan, “Simulation of the scattering properties of a chain-forming triangular prism oceanic diatom,” J. Quant. Spectrosc. Radiat. Transfer 178, 390–399 (2016).
[Crossref]

A. M. Sánchez and J. Piera, “Methods to retrieve the complex refractive index of aquatic suspended particles: going beyond simple shapes,” Biogeosciences 13(14), 4081–4098 (2016).
[Crossref]

2013 (2)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding t-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transfer 116, 169 – 183, (2013).
[Crossref]

H. R. Gordon, “Mie-theory models of light scattering by ocean,” Suspended Solids in Water 4, 73 (2013).

2012 (2)

M. Twardowski, X. D. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” Journal of Geophysical Research: Oceans 117(C7), 2012 (2012).
[Crossref]

M. Nicolet, M. Schnaiter, and O. Stetzer, “Circular depolarization ratios of single water droplets and finite ice circular cylinders: a modeling study,” Atmospheric Chemistry and Physics 12(9), 4207–4214 (2012).
[Crossref]

2011 (2)

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112(9), 1492 – 1508, (2011).
[Crossref]

T. Müller, M. Laborde, G. Kassell, and A. Wiedensohler, “Design and performance of a three-wavelength led-based total scatter and backscatter integrating nephelometer,” Atmospheric Measurement Techniques 4(6), 1291–1303 (2011).
[Crossref]

2009 (1)

Y. Hu, D. Winker, M. Vaughan, B. Lin, A. Omar, C. Trepte, D. Flittner, P. Yang, S. L. Nasiri, B. Baum, R. Holz, W. Sun, Z. Liu, Z. Wang, S. Young, K. Stamnes, J. Huang, and R. Kuehn, “CALIPSO/CALIOP Cloud Phase Discrimination Algorithm,” Journal of Atmospheric and Oceanic Technology 26(11), 2293–2309 (2009).
[Crossref]

2007 (4)

W. J. Clavano, E. S. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles-from theory to observation,” Oceanogr. Mar. Biol. 45, 11–38 (2007).

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106(1), 546–557 (2007).
[Crossref]

M. A. Yurkin and A.G. Hoekstra, “The discrete dipole approximation: An overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 558–589 (2007).
[Crossref]

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15(26), 17902–17911 (2007).
[Crossref] [PubMed]

2005 (1)

2004 (6)

T. W. Lee and S. C. Hagness, “Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials,” J. Opt. Soc. Am. B 21(2), 330–342 (2004).
[Crossref]

S. B. Woźniak and D. Stramski, “Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms,” Appl. Opt. 43(17), 3489–3503 (2004).
[Crossref]

A. Quirantes and S. Bernard, “Light scattering by marine algae: two-layer spherical and nonspherical models,” J. Quant. Spectrosc. Radiat. Transfer 89(1), 311–321 (2004).
[Crossref]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progress in Oceanography 61(1), 27–56 (2004).
[Crossref]

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” Journal of Plankton Research 26(2), 191–212 (2004).
[Crossref]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “Particulate backscattering ratio at leo 15 and its use to study particle composition and distribution,” Journal of Geophysical Research 109(C1), 2004 (2004).
[Crossref]

2003 (2)

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” Journal of Atmospheric & Oceanic Technology 20(4), 563–571 (2003).
[Crossref]

D. Stramski and J. Piskozub, “Estimation of scattering error in spectrophotometric measurements of light absorption by aquatic particles from three-dimensional radiative transfer simulations,” Appl. Opt. 42(18), 3634–3646 (2003).
[Crossref] [PubMed]

2001 (1)

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,” Journal of Geophysical Research: Oceans 106(C7), 14129–14142 (2001).
[Crossref]

1998 (1)

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnology and Oceanography 43(6), 1180–1197 (1998).
[Crossref]

1997 (2)

Q. H. Liu, “The pstd algorithm: A time-domain method requiring only two cells per wavelength,” Microwave and optical technology letters 15(3), 158–165 (1997).
[Crossref]

P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14(9), 2278–2289 (1997).
[Crossref]

1996 (4)

P. Yang and K. N. Liou, “Geometric-optics–integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35(33), 6568–6584 (1996).
[Crossref] [PubMed]

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13(10), 2072–2085 (1996).
[Crossref]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55(5), 535–575 (1996).
[Crossref]

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
[Crossref]

1994 (2)

1993 (1)

1992 (1)

J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnology and Oceanography 37(8), 1680–1690 (1992).
[Crossref]

1991 (2)

D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Progress in Oceanography 28(4), 343–383 (1991).
[Crossref]

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: A review of methods and suggested new approaches,” Journal of Geophysical Research: Atmospheres 96(D3), 5269–5277 (1991).
[Crossref]

1990 (1)

A. J Hunt, M. S Quinby-Hunt, and D. B Shapiro, “Effects of wavelength-dependent absorption on the polarization of light scattered from marine chlorella,” Proc. SPIE 1302, 269–280 (1990).
[Crossref]

1989 (3)

R. J. Olson, E. R. Zettler, and O. K. Anderson, “Discrimination of eukaryotic phytoplankton cell types from light scatter and autofluorescence properties measured by flow cytometry,” Cytometry Part A 10(5), 636–643 (1989).
[Crossref]

M. S. Quinby-Hunt, A. J. Hunt, K. Lofftus, and D. Shapiro, “Polarized-light scattering studies of marine chlorella,” Limnology and Oceanography 34(8), 1587–1600 (1989).
[Crossref]

M. Hofer and O. Glatter, “Mueller matrix calculations for randomly oriented rotationally symmetric objects with low contrast,” Appl. Opt. 28(12), 2389–2400 (1989).
[Crossref] [PubMed]

1988 (3)

B. R. Johnson, “Invariant imbedding t matrix approach to electromagnetic scattering,” Appl. Opt. 27(23), 4861–4873 (1988).
[Crossref] [PubMed]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” The Astrophysical Journal 333, 848–872 (1988).
[Crossref]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
[Crossref]

1987 (1)

M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnology and Oceanography 32(5), 1059–1065 (1987).
[Crossref]

1986 (1)

M. Jonasz and H. Prandke, “Comparison of measured and computed light scattering in the baltic,” Tellus B: Chemical and Physical Meteorology 38(2), 144–157 (1986).
[Crossref]

1985 (2)

E. S. Fry and K. J. Voss, “Measurement of the mueller matrix for phytoplankton,” Limnology and Oceanography 30(6), 1322–1326 (1985).
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P. E. Geller, T. G. Tsuei, and P. W. Barber, “Information content of the scattering matrix for spheroidal particles,” Appl. Opt. 24(15), 2391–2396 (1985).
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1984 (1)

1980 (1)

1977 (1)

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnology and Oceanography 22(4), 709–722 (1977).
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1975 (2)

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Science Reviews 16(4), 527–610 (1974).
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1973 (2)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” The Astrophysical Journal 186, 705–714 (1973).
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O. B. Brown and H. R. Gordon, “Two component mie scattering models of sargasso sea particles,” Appl. Opt. 12(10), 2461–2465 (1973).
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1972 (1)

H. R. Gordon and O. B. Brown, “A theoretical model of light scattering by sargasso sea particulates,” Limnology and Oceanography 17(6), 826–832 (1972).
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1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3(4), 825–839 (1971).
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1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation 14(3), 302–307 (1966).
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1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
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Ahlquist, N. A.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
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Anderson, O. K.

R. J. Olson, E. R. Zettler, and O. K. Anderson, “Discrimination of eukaryotic phytoplankton cell types from light scatter and autofluorescence properties measured by flow cytometry,” Cytometry Part A 10(5), 636–643 (1989).
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Anderson, T. L.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
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Atkinson, R. J. A.

R. N. Gibson, R. J. A. Atkinson, and J. D. M. Gordon, Oceanography and Marine Biology: An Annual Review, 6, Volume 45 (CRC Press, 2007).
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Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
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Balch, W. M.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” Journal of Plankton Research 26(2), 191–212 (2004).
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Baratange, F.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “Particulate backscattering ratio at leo 15 and its use to study particle composition and distribution,” Journal of Geophysical Research 109(C1), 2004 (2004).
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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,” Journal of Geophysical Research: Oceans 106(C7), 14129–14142 (2001).
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Bates, T. S.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
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Y. Hu, D. Winker, M. Vaughan, B. Lin, A. Omar, C. Trepte, D. Flittner, P. Yang, S. L. Nasiri, B. Baum, R. Holz, W. Sun, Z. Liu, Z. Wang, S. Young, K. Stamnes, J. Huang, and R. Kuehn, “CALIPSO/CALIOP Cloud Phase Discrimination Algorithm,” Journal of Atmospheric and Oceanic Technology 26(11), 2293–2309 (2009).
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Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112(9), 1492 – 1508, (2011).
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A. Quirantes and S. Bernard, “Light scattering by marine algae: two-layer spherical and nonspherical models,” J. Quant. Spectrosc. Radiat. Transfer 89(1), 311–321 (2004).
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Bi, L.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding t-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transfer 116, 169 – 183, (2013).
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M. Twardowski, X. D. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” Journal of Geophysical Research: Oceans 117(C7), 2012 (2012).
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L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112(9), 1492 – 1508, (2011).
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D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progress in Oceanography 61(1), 27–56 (2004).
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E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “Particulate backscattering ratio at leo 15 and its use to study particle composition and distribution,” Journal of Geophysical Research 109(C1), 2004 (2004).
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D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Progress in Oceanography 61(1), 27–56 (2004).
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M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case i and case ii waters,” Journal of Geophysical Research: Oceans 106(C7), 14129–14142 (2001).
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Boss, E. S.

W. J. Clavano, E. S. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles-from theory to observation,” Oceanogr. Mar. Biol. 45, 11–38 (2007).

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J. R. Bottiger, E. S. Fry, and R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” Light scattering by irregularly shaped particles, 283–290 (Springer,1980).
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Brock, R. S.

Brooks, S. D.

G. Xu, B. Sun, S. D. Brooks, P. Yang, G. W. Kattawar, and X. Zhang, “Modeling the inherent optical properties of aquatic particles using an irregular hexahedral ensemble,” J. Quant. Spectrosc. Radiat. Transfer 191, 30–39 (2017)
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Brown, C. W.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” Journal of Plankton Research 26(2), 191–212 (2004).
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Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
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H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
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H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427, (1975).
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O. B. Brown and H. R. Gordon, “Two component mie scattering models of sargasso sea particles,” Appl. Opt. 12(10), 2461–2465 (1973).
[Crossref] [PubMed]

H. R. Gordon and O. B. Brown, “A theoretical model of light scattering by sargasso sea particulates,” Limnology and Oceanography 17(6), 826–832 (1972).
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Caldow, R.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
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Charlson, R. J.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
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Charlton, F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnology and Oceanography 43(6), 1180–1197 (1998).
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Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
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Clavano, W. J.

W. J. Clavano, E. S. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles-from theory to observation,” Oceanogr. Mar. Biol. 45, 11–38 (2007).

Covert, D. S.

T. L. Anderson, D. S. Covert, S. F. Marshall, M. L. Laucks, R. J. Charlson, A. P. Waggoner, J. A. Ogren, R. Caldow, R. L. Holm, F. R. Quant, G. J. Sem, A. Wiedensohler, N. A. Ahlquist, and T. S. Bates, “Performance Characteristics of a High-Sensitivity, Three-wavelength, Total Scatter/Backscatter Nephelometer,” Journal Of Atmospheric and Oceanic Technology 13(5), 967–986 (1996).
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Czerski, H.

M. Twardowski, X. D. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” Journal of Geophysical Research: Oceans 117(C7), 2012 (2012).
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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, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnology and Oceanography 43(6), 1180–1197 (1998).
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Dekker, A. G.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnology and Oceanography 43(6), 1180–1197 (1998).
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Donaghay, P. L.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” The Astrophysical Journal 333, 848–872 (1988).
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Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
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Flittner, D.

Y. Hu, D. Winker, M. Vaughan, B. Lin, A. Omar, C. Trepte, D. Flittner, P. Yang, S. L. Nasiri, B. Baum, R. Holz, W. Sun, Z. Liu, Z. Wang, S. Young, K. Stamnes, J. Huang, and R. Kuehn, “CALIPSO/CALIOP Cloud Phase Discrimination Algorithm,” Journal of Atmospheric and Oceanic Technology 26(11), 2293–2309 (2009).
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Freeman, S.

M. Twardowski, X. D. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” Journal of Geophysical Research: Oceans 117(C7), 2012 (2012).
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Fry, E. S.

E. S. Fry and K. J. Voss, “Measurement of the mueller matrix for phytoplankton,” Limnology and Oceanography 30(6), 1322–1326 (1985).
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K. J. Voss and E. S. Fry, “Measurement of the mueller matrix for ocean water,” Appl. Opt. 23(23), 4427–4439 (1984).
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J. R. Bottiger, E. S. Fry, and R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” Light scattering by irregularly shaped particles, 283–290 (Springer,1980).
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Gibson, R. N.

R. N. Gibson, R. J. A. Atkinson, and J. D. M. Gordon, Oceanography and Marine Biology: An Annual Review, 6, Volume 45 (CRC Press, 2007).
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Gordon, H. R.

H. R. Gordon, “Mie-theory models of light scattering by ocean,” Suspended Solids in Water 4, 73 (2013).

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” Journal of Geophysical Research: Atmospheres 93(D9), 10909–10924 (1988).
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H. R. Gordon and W. R. McCluney, “Estimation of the depth of sunlight penetration in the sea for remote sensing,” Appl. Opt. 14(2), 413–416 (1975).
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H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427, (1975).
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O. B. Brown and H. R. Gordon, “Two component mie scattering models of sargasso sea particles,” Appl. Opt. 12(10), 2461–2465 (1973).
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H. R. Gordon and O. B. Brown, “A theoretical model of light scattering by sargasso sea particulates,” Limnology and Oceanography 17(6), 826–832 (1972).
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Gordon, J. D. M.

R. N. Gibson, R. J. A. Atkinson, and J. D. M. Gordon, Oceanography and Marine Biology: An Annual Review, 6, Volume 45 (CRC Press, 2007).
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Guillard, R. R. L.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” Journal of Plankton Research 26(2), 191–212 (2004).
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Hagness, S. C.

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Science Reviews 16(4), 527–610 (1974).
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M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106(1), 546–557 (2007).
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Holm, R. L.

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Y. Hu, D. Winker, M. Vaughan, B. Lin, A. Omar, C. Trepte, D. Flittner, P. Yang, S. L. Nasiri, B. Baum, R. Holz, W. Sun, Z. Liu, Z. Wang, S. Young, K. Stamnes, J. Huang, and R. Kuehn, “CALIPSO/CALIOP Cloud Phase Discrimination Algorithm,” Journal of Atmospheric and Oceanic Technology 26(11), 2293–2309 (2009).
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H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnology and Oceanography 43(6), 1180–1197 (1998).
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H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnology and Oceanography 43(6), 1180–1197 (1998).
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L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112(9), 1492 – 1508, (2011).
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Huang, J.

Y. Hu, D. Winker, M. Vaughan, B. Lin, A. Omar, C. Trepte, D. Flittner, P. Yang, S. L. Nasiri, B. Baum, R. Holz, W. Sun, Z. Liu, Z. Wang, S. Young, K. Stamnes, J. Huang, and R. Kuehn, “CALIPSO/CALIOP Cloud Phase Discrimination Algorithm,” Journal of Atmospheric and Oceanic Technology 26(11), 2293–2309 (2009).
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B. Sun, G. W. Kattawar, P. Yang, M. S. Twardowski, and J. M. Ivan, “Simulation of the scattering properties of a chain-forming triangular prism oceanic diatom,” J. Quant. Spectrosc. Radiat. Transfer 178, 390–399 (2016).
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W. J. Clavano, E. S. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles-from theory to observation,” Oceanogr. Mar. Biol. 45, 11–38 (2007).

Kassell, G.

T. Müller, M. Laborde, G. Kassell, and A. Wiedensohler, “Design and performance of a three-wavelength led-based total scatter and backscatter integrating nephelometer,” Atmospheric Measurement Techniques 4(6), 1291–1303 (2011).
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M. Twardowski, X. D. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” Journal of Geophysical Research: Oceans 117(C7), 2012 (2012).
[Crossref]

Kattawar, G. W.

G. Xu, B. Sun, S. D. Brooks, P. Yang, G. W. Kattawar, and X. Zhang, “Modeling the inherent optical properties of aquatic particles using an irregular hexahedral ensemble,” J. Quant. Spectrosc. Radiat. Transfer 191, 30–39 (2017)
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B. Sun, G. W. Kattawar, P. Yang, M. S. Twardowski, and J. M. Ivan, “Simulation of the scattering properties of a chain-forming triangular prism oceanic diatom,” J. Quant. Spectrosc. Radiat. Transfer 178, 390–399 (2016).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding t-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transfer 116, 169 – 183, (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112(9), 1492 – 1508, (2011).
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E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, G. Korotaev, and F. Baratange, “Particulate backscattering ratio at leo 15 and its use to study particle composition and distribution,” Journal of Geophysical Research 109(C1), 2004 (2004).
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Figures (9)

Fig. 1
Fig. 1 The spheroid is centered at origin O with semi-axes a and b aligned along coordinate axes and x is the symmetry axis. The light is incident along the z-axis.
Fig. 2
Fig. 2 The phase function P11 and reduced Mueller matrix elements −P12/P11, 1 − P22/P11, and (P44P33)/P11 of spheroidal shaped hydrosols with the refractive index m=1.02 and the aspect ratio of 1.5. The legend in Fig. 2(d) applies to all four subplots in Fig. 2. The red lines represent absorptive cases, while the black lines represent non-absorptive cases. This color code applies to all other figures.
Fig. 3
Fig. 3 The same as Fig. 2 except for the refractive index m=1.11
Fig. 4
Fig. 4 Relationship between χ and ϵ.
Fig. 5
Fig. 5 DONS (ϵ) as a function of with the volume equivalent size parameter.
Fig. 6
Fig. 6 The depolarization ratio δ as a function of the volume equivalent size parameter.
Fig. 7
Fig. 7 Relationship between δ and ϵ.
Fig. 8
Fig. 8 Backscattering fraction as a function of the volume equivalent size parameter.
Fig. 9
Fig. 9 Backscattering fraction versus DONS (ϵ).

Equations (7)

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

[ I s Q s U s V s ] = C s c a ¯ 4 π r 2 [ P 11 ( θ ) P 12 ( θ ) 0 0 P 12 ( θ ) P 22 ( θ ) 0 0 0 0 P 33 ( θ ) P 34 ( θ ) 0 0 P 34 ( θ ) P 44 ( θ ) ] [ I i Q i U i V i ] ,
1 2 0 π P 11 ( θ ) sin θ d θ = 1 .
δ = P 11 ( π ) P 22 ( π ) P 11 ( π ) + P 22 ( π ) ,
ϵ = 0 π ( 1 P 22 ( θ ) P 11 ( θ ) ) sin θ d θ ,
χ = 0 π ( P 44 ( θ ) P 33 ( θ ) P 11 ( θ ) ) sin θ d θ ,
B = π / 2 π P 11 ( θ ) sin θ d θ 0 π P 11 ( θ ) sin θ d θ ,
x = 2 π r λ ,

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