Abstract

A methodology is developed to derive the backscattering cross section of individual particles as measured with the CytoSense (CytoBuoy b.v., NL). This in situ flow cytometer detects light scatter in forward and sideward directions and fluorescence in various spectral bands for a wide range of particles. First, the weighting functions are determined for the forward and sideward detectors to take into account their instrumental response as a function of the scattering angle. The CytoSense values are converted into forward and sideward scattering cross sections. The CytoSense estimates of uniform polystyrene microspheres from 1 to 90 μm are compared with Mie computations. The mean absolute relative differences ΔE are around 33.7% and 23.9% for forward and sideward scattering, respectively. Then, a theoretical relationship is developed to convert sideward scattering into backscattering cross section, from a synthetic database of 495,900 simulations including homogeneous and multi-layered spheres. The relationship follows a power law with a coefficient of determination of 0.95. To test the methodology, a laboratory experiment is carried out on a suspension of silica beads to compare backscattering cross section as measured by the WET Labs ECO-BB9 and derived from CytoSense. Relative differences are between 35% and 60%. They are of the same order of magnitude as the instrumental variability. Differences can be partly explained by the fact that the two instruments do not measure exactly the same parameter: the cross section of individual particles for the CytoSense and the bulk cross section for the ECO-BB9.

© 2015 Optical Society of America

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References

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2012 (1)

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

2011 (2)

D.W. Mackowski and M.I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transfer 112, 2182–2192 (2011).
[Crossref]

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

2010 (1)

2009 (4)

O. Pena and U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180(11), 2348–2354 (2009).
[Crossref]

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1497–1563 (2009).
[Crossref]

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009).
[Crossref] [PubMed]

X. Zhang, H. Lianbo, and M. X. He, “Scattering by pure water: effect of salinity,” Opt. Express,  17, 5698–5710 (2009).
[Crossref] [PubMed]

2008 (1)

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

2007 (3)

2006 (1)

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

2004 (2)

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

G. B. Dubelaar, P. J. Geerders, and R. R. Jonker, “High frequency monitoring reveals phytoplankton dynamics,” J. Environ. Monit. 6(12), 946–952 (2004).
[Crossref] [PubMed]

2003 (5)

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

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42(3), 526–540 (2003).
[Crossref] [PubMed]

R. E. Green, H. M. Sosik, and R. J. Olson, “Contributions of phytoplankton and other particles to inherent optical properties in New England continental shelf waters,” Limnol. Oceanogr. 48(6), 2377–2391 (2003).
[Crossref]

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

W. Yang, “Improved recursive algorithm for light scattering by a multilayered sphere,” Appl. Opt. 42(9), 1710–1720 (2003).
[Crossref] [PubMed]

2001 (2)

2000 (1)

1998 (2)

D. A. Siegel, “Resource competition in a discrete environment: Why are plankton distributions paradoxical?” Limonol. Oceanogr. 43, 1133–1146 (1998).
[Crossref]

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,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

1997 (2)

A. Quirantes and A. V. Delgado, “The scattering of light by a suspension of coated spherical particles: effects of polydispersity on cross sections,” J. Phys. D: Appl. Phys. 30, 2123–2131 (1997).
[Crossref]

R. A. Maffione and D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36(24), 6057–6067 (1997).
[Crossref] [PubMed]

1992 (3)

A. Cunningham and G. A. Buonaccorsi, “Narrow-angle forward light scattering from individual algal cells: implications for size and shape discrimination in flow cytometry,” J. Plankton. Res. 14, 223–234 (1992).
[Crossref]

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

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

1991 (1)

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

1990 (1)

1989 (1)

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

1988 (1)

1986 (1)

1981 (1)

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep Sea Res. 28, 1375–1393 (1981).
[Crossref]

Aas, E.

E. Aas, “Influence of shape and structure on light scattering by marine particles,” Report of Department of Geophysics(University of Oslo, Norway, (1984), Vol.53.

Ackleson, S. G.

Ahn, Y. H.

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

Balch, W. M.

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

Bernard, S.

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1497–1563 (2009).
[Crossref]

Berthon, J. F.

Bi, L.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Blanchot, J.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Boss, E.

Bricaud, A.

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[Crossref]

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

A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
[Crossref] [PubMed]

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep Sea Res. 28, 1375–1393 (1981).
[Crossref]

Brown, C. W.

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

Brown, S.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Buonaccorsi, G. A.

A. Cunningham and G. A. Buonaccorsi, “Narrow-angle forward light scattering from individual algal cells: implications for size and shape discrimination in flow cytometry,” J. Plankton. Res. 14, 223–234 (1992).
[Crossref]

Burkill, P.H.

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

Chami, M.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

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,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

Clavano, W. R.

W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles - from theory to observations,” Oceanogr. Mar. Biol. Ann. Rev. 45, 1–38 (2007).

Cowles, T. J.

Cunningham, A.

A. Cunningham and G. A. Buonaccorsi, “Narrow-angle forward light scattering from individual algal cells: implications for size and shape discrimination in flow cytometry,” J. Plankton. Res. 14, 223–234 (1992).
[Crossref]

Czerski, H.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

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, and 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, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

Delgado, A. V.

A. Quirantes and A. V. Delgado, “The scattering of light by a suspension of coated spherical particles: effects of polydispersity on cross sections,” J. Phys. D: Appl. Phys. 30, 2123–2131 (1997).
[Crossref]

Denis, M.

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

Dolman, V. L.

V. L. Dolman, “Meerhoff Mie Program User Guide,” in Internal Report Astronomy Dept. (Free University, 1989).

Dubelaar, G. B.

G. B. Dubelaar, P. J. Geerders, and R. R. Jonker, “High frequency monitoring reveals phytoplankton dynamics,” J. Environ. Monit. 6(12), 946–952 (2004).
[Crossref] [PubMed]

Dupouy, C.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

DuRand, M. D.

Freeman, S.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Frette, O.

Geerders, P. J.

G. B. Dubelaar, P. J. Geerders, and R. R. Jonker, “High frequency monitoring reveals phytoplankton dynamics,” J. Environ. Monit. 6(12), 946–952 (2004).
[Crossref] [PubMed]

Green, R. E.

R. E. Green, H. M. Sosik, and R. J. Olson, “Contributions of phytoplankton and other particles to inherent optical properties in New England continental shelf waters,” Limnol. Oceanogr. 48(6), 2377–2391 (2003).
[Crossref]

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42(3), 526–540 (2003).
[Crossref] [PubMed]

Grégory, G.

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

Grgori, G.

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

Guillard, R. R. L.

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

He, M. X.

Holland, R. J.

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[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, and 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, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

Hunt, A. J.

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

Jonker, R. R.

G. B. Dubelaar, P. J. Geerders, and R. R. Jonker, “High frequency monitoring reveals phytoplankton dynamics,” J. Environ. Monit. 6(12), 946–952 (2004).
[Crossref] [PubMed]

Karp-Boss, L.

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplakton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles - from theory to observations,” Oceanogr. Mar. Biol. Ann. Rev. 45, 1–38 (2007).

Kattawar, G.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Khomenko, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

Kiefer, D. A.

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

Kitchen, J. C.

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

Korotaev, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light of Small Particles (Cambridge University Press, 2002).

Landry, M.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Lebouteiller, A.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Lee, M.

Lee, M. E.

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

Lewis, M. R.

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

Lianbo, H.

Lofftus, K.

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

Loisel, H.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Mackowski, D.W.

D.W. Mackowski and M.I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transfer 112, 2182–2192 (2011).
[Crossref]

Maffione, R. A.

Malkassian, A.

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

Mante, C.

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

Marken, E.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

Mishchenko, M. I.

M. I. Mishchenko, “Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation,” Appl. Opt. 39, 1026–1031 (2000).
[Crossref]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light of Small Particles (Cambridge University Press, 2002).

Mishchenko, M.I.

D.W. Mackowski and M.I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transfer 112, 2182–2192 (2011).
[Crossref]

Moore, C.

J. M. Sullivan, M. S. Twardowski, J. R. V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” A. Kokhanovsky, ed. Light Scattering Reviews 7: Radiative Transfer and Optical Properties of Atmosphere and Underlying Surface, SpringerPraxis Books, doi:, 189–224 (2013).
[Crossref]

Morel, A.

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[Crossref]

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

A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
[Crossref] [PubMed]

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep Sea Res. 28, 1375–1393 (1981).
[Crossref]

Moulin, C.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Nerini, D.

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

Neveux, J.

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

Oishi, T.

Olson, R. J.

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42(3), 526–540 (2003).
[Crossref] [PubMed]

R. E. Green, H. M. Sosik, and R. J. Olson, “Contributions of phytoplankton and other particles to inherent optical properties in New England continental shelf waters,” Limnol. Oceanogr. 48(6), 2377–2391 (2003).
[Crossref]

Pal, U.

O. Pena and U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180(11), 2348–2354 (2009).
[Crossref]

Pegau, S.

Pegau, W. S.

Pena, O.

O. Pena and U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180(11), 2348–2354 (2009).
[Crossref]

Preisendorfer, R. W.

R. W. Preisendorfer, “Hydrologic optics, Vol.1: Introduction,” Springfield National Technical Information Service. Also available on CD, Office of Naval Research, (1976).

Probyn, T. A.

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1497–1563 (2009).
[Crossref]

Quinby-Hunt, M. S.

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

Quirantes, A.

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1497–1563 (2009).
[Crossref]

A. Quirantes and A. V. Delgado, “The scattering of light by a suspension of coated spherical particles: effects of polydispersity on cross sections,” J. Phys. D: Appl. Phys. 30, 2123–2131 (1997).
[Crossref]

Rune Erga, S. R.

Schreurs, R.

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,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

Shapiro, D.

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

Shybanov, E.

Siegel, D. A.

D. A. Siegel, “Resource competition in a discrete environment: Why are plankton distributions paradoxical?” Limonol. Oceanogr. 43, 1133–1146 (1998).
[Crossref]

Sosik, H. M.

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42(3), 526–540 (2003).
[Crossref] [PubMed]

R. E. Green, H. M. Sosik, and R. J. Olson, “Contributions of phytoplankton and other particles to inherent optical properties in New England continental shelf waters,” Limnol. Oceanogr. 48(6), 2377–2391 (2003).
[Crossref]

Spinrad, R. W.

Stamnes, J. J.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

Stramski, D.

Sullivan, J.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Sullivan, J. M.

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009).
[Crossref] [PubMed]

J. M. Sullivan, M. S. Twardowski, J. R. V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” A. Kokhanovsky, ed. Light Scattering Reviews 7: Radiative Transfer and Optical Properties of Atmosphere and Underlying Surface, SpringerPraxis Books, doi:, 189–224 (2013).
[Crossref]

Svensen, O.

Tarran, G. A.

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

Thyssen, M.

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light of Small Particles (Cambridge University Press, 2002).

Twardowski, M.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Twardowski, M. S.

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009).
[Crossref] [PubMed]

J. M. Sullivan, M. S. Twardowski, J. R. V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” A. Kokhanovsky, ed. Light Scattering Reviews 7: Radiative Transfer and Optical Properties of Atmosphere and Underlying Surface, SpringerPraxis Books, doi:, 189–224 (2013).
[Crossref]

Vagle, S.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Vaillancourt, R. D.

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

van Dijk, M. A.

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

Vassen, W.

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,” 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, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

Whitmire, A. L.

Wouts, R.

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,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

Yang, W.

You, Y.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

Zaneveld, J. R. V.

J. M. Sullivan, M. S. Twardowski, J. R. V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” A. Kokhanovsky, ed. Light Scattering Reviews 7: Radiative Transfer and Optical Properties of Atmosphere and Underlying Surface, SpringerPraxis Books, doi:, 189–224 (2013).
[Crossref]

Zaneveld, J.R.

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

Zhang, X.

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

X. Zhang, H. Lianbo, and M. X. He, “Scattering by pure water: effect of salinity,” Opt. Express,  17, 5698–5710 (2009).
[Crossref] [PubMed]

Zibordi, G.

Zubkov, M. V.

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

Appl. Opt. (12)

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[Crossref]

A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
[Crossref] [PubMed]

O. Svensen, O. Frette, and S. R. Rune Erga, “Scattering properties of microalgae: the effect of cell size and cell wall,” Appl. Opt. 46(23), 5762–5769 (2007).
[Crossref] [PubMed]

S. G. Ackleson and R. W. Spinrad, “Size and refractive index of individual marine particulates: a flow cytometric approach,” Appl. Opt. 27(7), 1270–1277 (1988).
[Crossref] [PubMed]

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42(3), 526–540 (2003).
[Crossref] [PubMed]

T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°,” Appl. Opt. 29(31), 4658–4665 (1990).
[Crossref] [PubMed]

R. A. Maffione and D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36(24), 6057–6067 (1997).
[Crossref] [PubMed]

E. Boss and S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40(30), 5503–5507 (2001).
[Crossref]

J. F. Berthon, E. Shybanov, M. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern adriatic sea,” Appl. Opt. 46(22), 5189–5203 (2007).
[Crossref] [PubMed]

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009).
[Crossref] [PubMed]

W. Yang, “Improved recursive algorithm for light scattering by a multilayered sphere,” Appl. Opt. 42(9), 1710–1720 (2003).
[Crossref] [PubMed]

M. I. Mishchenko, “Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation,” Appl. Opt. 39, 1026–1031 (2000).
[Crossref]

Biogeosci. Discuss. (1)

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1497–1563 (2009).
[Crossref]

Comput. Phys. Commun. (1)

O. Pena and U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180(11), 2348–2354 (2009).
[Crossref]

Cytometry Part A (1)

A. Malkassian, D. Nerini, M. A. van Dijk, M. Thyssen, C. Mante, and G. Grégory, “Functional analysis and classification of phytoplankton based on data from an automated flow cytometer,” Cytometry Part A 79(4), 263–275 (2011), doi: .
[Crossref]

Deep Sea Res. (2)

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

A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep Sea Res. 28, 1375–1393 (1981).
[Crossref]

J. Atmosp. Oceanic Technol. (1)

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

J. Environ. Monit. (1)

G. B. Dubelaar, P. J. Geerders, and R. R. Jonker, “High frequency monitoring reveals phytoplankton dynamics,” J. Environ. Monit. 6(12), 946–952 (2004).
[Crossref] [PubMed]

J. Geophys. Res. (3)

M. Twardowski, X. 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,” J. Geophys. Res. 117, C00H17 (2012.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111(C05), C05013 (2006).

C. Dupouy, H. Loisel, J. Neveux, C. Moulin, S. Brown, J. Blanchot, A. Lebouteiller, and M. Landry, “Microbial absorption and backscattering coefficients from in situ and POLDER satellite during an El Nino-Southern Oscillation cold phase in the equatorial Pacific (180),” J. Geophys. Res. 108(C12), 8138 (2003).
[Crossref]

J. Phys. D: Appl. Phys. (1)

A. Quirantes and A. V. Delgado, “The scattering of light by a suspension of coated spherical particles: effects of polydispersity on cross sections,” J. Phys. D: Appl. Phys. 30, 2123–2131 (1997).
[Crossref]

J. Plank. Res. (1)

M. Thyssen, G. A. Tarran, M. V. Zubkov, R. J. Holland, G. Grgori, P.H. Burkill, and M. Denis, “The emergence of automated high frequency flow cytometry : revealing temporal and spatial phytoplankton variability,” J. Plank. Res. 30(3), 333–343 (2008).
[Crossref]

J. Plankton. Res. (2)

A. Cunningham and G. A. Buonaccorsi, “Narrow-angle forward light scattering from individual algal cells: implications for size and shape discrimination in flow cytometry,” J. Plankton. Res. 14, 223–234 (1992).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

D.W. Mackowski and M.I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transfer 112, 2182–2192 (2011).
[Crossref]

Limnol. Oceanogr. (3)

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,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[Crossref]

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

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[Crossref]

Limonol. Oceanogr. (2)

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[Crossref]

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[Crossref]

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Opt. Express (2)

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[Crossref]

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Figures (10)

Fig. 1
Fig. 1

CytoSense design: (a) beam shaping and light intensity distribution; (b) and (c) principle of flow cytometry.

Fig. 2
Fig. 2

Comparison of measured scattering cross sections (dots) and scattering cross sections as predicted by Mie theory (crosses) in (a) forward and (b) backward directions for the PRECYM CytoSense.

Fig. 3
Fig. 3

Same as Fig. 2 for the LOG CytoSense.

Fig. 4
Fig. 4

Backscattering cross section as a function of sideward scattering cross section. Color lines corresponds to regression slopes performed for the whole dataset (black), homogeneous spheres (yellow), two-layered spheres (red and green) and three-layered spheres (light blue)

Fig. 5
Fig. 5

Backscattering cross section as a function of sideward scattering cross section. (a) homogenous spheres (b)–(c) heterogenous spheres with 80%−20% and 60%−40% of relative proportions of cytoplasm and chloroplast (d) heterogenous spheres with 80%-18.63%-1.37% of relative proportions of cytoplasm, chloroplast and silica wall. A distinction is made between data corresponding to different diameters: 1 ≤ d < 10 μm (grey dots), 10 ≤ d < 20 μm (red dots), 20 ≤ d ≤ 40 μm (blue dots).

Fig. 6
Fig. 6

Same as Fig. 5. A distinction is made between data corresponding to different volume equivalent refractive indices (real part): 1.03 ≤ mr ≤ 1.05 (grey dots); 1.05 < mr ≤ 1.07 (red dots) and 1.07 < mr ≤ 1.09 (blue dots).

Fig. 7
Fig. 7

Same as Fig. 5. A distinction is made between data corresponding to different different volume equivalent refractive indices (imaginary part) : 0.001 ≤ mi < 0.005 (grey dots); 0.006 ≤ mi < 0.01 (red dots) and 0.01 ≤ mi ≤ 0.015 (blue dots).

Fig. 8
Fig. 8

Flowchart showing how CytoSense measurements and ECO-BB9 are converted into backscattering cross section to be compared

Fig. 9
Fig. 9

Optical backscattering cross section of silica beads (5 μm in diameter) from ECOBB9 (black dots), CytoSense (open squares) and Mie theory with mr = 1.07 (blue lines), and 1.09 (green lines). Dotted and dashed lines correspond to simulations for perfect monodispersion and gaussian PSD with a CV of 30%, respectively. Error bars stand for the standard deviation over the mean C sca b b ( B B 9 ). Standard deviation over the mean C sca b b ( cyto ) are not represented as it is small compared to standard deviation over the BB9 cross section. ECOBB9 signal was converted using (a) χp of 1.1 (b) χp of 1.27

Fig. 10
Fig. 10

Same as Fig. 9 but for 3 μm beads. ECO-BB9 signal was converted using (a) χp of 1.26 (b) χp of 1.33

Tables (3)

Tables Icon

Table 1 Statistical relationship between the sideward and the backward cross sections, C sca b b ( 488 n m ) = 10 B × [ C sca SWS ( 488 n m ) ] A, calculated from theoretical computations for homogeneous and two or three-layered spheres.

Tables Icon

Table 2 Estimates from CytoSense - Silica beads of 3μm

Tables Icon

Table 3 Estimates from CytoSense - Silica beads of 5μm

Equations (19)

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C sca ( λ ) = r 2 I inc ( λ , n inc ) 4 π d n sca I sca ( λ , n sca )
I sca = 1 r 2 ( Z 11 I inc + Z 12 Q inc + Z 13 U inc + Z 14 V inc ) ,
Z ˜ ( λ , n sca , n inc ) = F ˜ ( λ , θ ) L ˜ ( ϕ ) = ( F 11 ( λ , θ ) F 12 ( λ , θ ) cos 2 ϕ F 12 ( λ , θ ) sin 2 ϕ 0 F 12 ( λ , θ ) F 22 ( λ , θ ) cos 2 ϕ F 22 ( λ , θ ) sin 2 ϕ 0 0 F 33 ( λ , θ ) sin 2 ϕ F 33 ( λ , θ ) cos 2 ϕ F 34 ( λ , θ ) 0 F 34 ( λ , θ ) sin 2 ϕ F 34 ( λ , θ ) cos 2 ϕ F 44 ( λ , θ ) )
C sca b b ( λ ) = 2 π π / 2 π F 11 ( λ , θ ) sin ( θ ) d θ
< X > = d min d max n ( d ) × X ( d ) d d ,
β ( λ , θ ) = < F 11 ( λ , θ ) > × N V
b b p ( λ ) = < C sca b b ( λ ) > × N V ,
b b = 2 π χ ( θ s ) β ( θ s )
b b p = 2 π χ p [ β ( θ s ) β w ( θ s ) ]
W FWS ( θ ) = π × [ d 1 tan ( θ ) + d 2 tan ( β ) + d 3 tan ( γ ) ] 2
β = sin 1 ( m w m H S sin θ )
γ = sin 1 ( m w sin θ )
W SWS ( θ ) = sin [ π 2 sin 1 ( m w sin θ ) ]
FWS Mie = θ = 20 ° θ = 15 ° W FWS ( θ ) F 11 ( θ ) sin ( θ ) d θ
SWS Mie = θ = 45 ° θ = 135 ° W SWS ( θ ) F 11 ( θ ) sin ( θ ) d θ
FWS ( d ) = FWS Mie ( RF ) FWS cyto ( RF ) × FWS cyto ( d ) .
j m r j V j = m r j V j
C sca b b ( 488 n m ) = 10 B × [ C sca SWS ( 488 n m ) ] A ,
Δ E ( % ) = C sca b b ( B B 9 ) C sca b b ( cyto ) C sca b b ( B B 9 ) .

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