Abstract

We measured the linearly polarized light scattering of pure water and seawater at various salinities and estimated the depolarization ratio using five different methods of data analysis after removing the scattering due to contamination by residual nanoparticles. The depolarization ratio values (δ) estimated for pure water using these different methods are largely consistent with each other and result in a mean value of 0.039±0.001. For seawater, our results reveal a trend of a slight linear increase of δ with salinity (S), δ=0.039+a1×S, where a1 varies in the range of 1×104 to 2×104 between the methods.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

P. J. Werdell, L. I. W. McKinna, E. Boss, S. G. Ackleson, S. E. Craig, W. W. Gregg, Z. Lee, S. Maritorena, C. S. Roesler, C. S. Rousseaux, D. Stramski, J. M. Sullivan, M. S. Twardowski, M. Tzortziou, and X. Zhang, “An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing,” Prog. Oceanogr. 160, 186–212 (2018).
[Crossref]

D. Koestner, D. Stramski, and R. A. Reynolds, “Measurements of the volume scattering function and the degree of linear polarization of light scattered by contrasting natural assemblages of marine particles,” Appl. Sci. 8, 2690 (2018).
[Crossref]

C. McElfresh, T. Harrington, and K. S. Vecchio, “Application of a novel new multispectral nanoparticle tracking technique,” Meas. Sci. Technol. 29, 065002 (2018).
[Crossref]

X. Zhang and L. Hu, “Anomalous light scattering by pure seawater,” Appl. Sci. 8, 2679 (2018).
[Crossref]

2017 (2)

B. Sun, P. Yang, G. W. Kattawar, and X. Zhang, “Physical-geometric optics method for large size faceted particles,” Opt. Express 25, 24044–24060 (2017).
[Crossref]

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]

2012 (2)

2009 (3)

2008 (1)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of standard seawater and the definition of the reference-composition salinity scale,” Deep-Sea Res. I 55, 50–72 (2008).
[Crossref]

2007 (1)

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

1998 (1)

W.-C. Chin, M. V. Orellana, and P. Verdugo, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391, 568–572 (1998).
[Crossref]

1996 (1)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).
[Crossref]

1995 (1)

1994 (1)

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183 (1994).
[Crossref]

1992 (1)

A. Proutiere, E. Megnassan, and H. Hucteau, “Refractive index and density variations in pure liquids: a new theoretical relation,” J. Phys. Chem. 96, 3485–3489 (1992).
[Crossref]

1985 (1)

Z. Niedrich, “Dispersion interactions and the refractive index of liquids,” Physica 128B, 69–75 (1985).
[Crossref]

1984 (1)

1977 (1)

P. W. Holland and R. E. Welsch, “Robust regression using iteratively reweighted least-squares,” Comm. Statist. Theory Methods 6, 813–827 (1977).
[Crossref]

1976 (1)

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65, 593–595 (1976).
[Crossref]

1975 (1)

E. R. Pike, W. R. M. Pomeroy, and J. M. Vaughan, “Measurement of Rayleigh ratio for several pure liquids using a laser and monitored photon counting,” J. Chem. Phys. 62, 3188–3192 (1975).
[Crossref]

1973 (1)

1968 (2)

A. Morel, “Note au sujet des constantes de diffusion de la lumiere pour l’eau et l’eau de mer optiquement pures,” Cah. Oceanogr. 20, 157–162 (1968).

G. F. Beardsley, “Mueller scattering matrix of sea water,” J. Opt. Soc. Am. 58, 52–56 (1968).
[Crossref]

1966 (2)

A. Morel, “Etude Experimentale de la diffusion de la lumiere par l’eau, les solutions de chlorure de sodium et l’eau de mer optiquement pures,” J. Chim. Phys. 63, 1359–1367 (1966).
[Crossref]

B. A. Pethica and C. Smart, “Light scattering of electrolyte solutions,” Trans. Faraday Soc. 62, 1890–1899 (1966).
[Crossref]

1965 (3)

G. Cohen and H. Eisenberg, “Light scattering of water, deuterium oxide, and other pure liquids,” J. Chem. Phys. 43, 3881–3887 (1965).
[Crossref]

H. Eisenberg, “Equation for the refractive index of water,” J. Chem. Phys. 43, 3887–3892 (1965).
[Crossref]

J. P. Kratohvil, M. Kerker, and L. E. Oppenheimer, “Light scattering by pure water,” J. Chem. Phys. 43, 914–921 (1965).
[Crossref]

1963 (1)

V. S. R. Rao and J. F. Foster, “Depolarization of scattered light in solutions of linear and branched polysaccharides,” J. Polym. Sci. Part A Gen. Pap. 1, 289–300 (1963).
[Crossref]

1961 (1)

A. Ivanoff, N. Jerlov, and T. H. Waterman, “A comparative study of irradiance, beam transmittance and scattering in the sea near Bermuda,” Limnol. Oceanogr. 6, 129–148 (1961).
[Crossref]

1959 (1)

1956 (1)

W. Prins and J. J. Hermans, “Light-scattering by solutions of some sodium alkyl-1-sulfates,” Proc. K. Ned. Akad. Wet. B59, 298–311 (1956).

1955 (2)

J. Kraut and W. B. Dandliker, “Light scattering by water,” J. Chem. Phys. 23, 1544–1545 (1955).
[Crossref]

A. Rousset and R. Lochet, “Sur la diffusion anisotrope des solutions aqueuses d’ions isotrope,” C. R. Acad. Sci. 240, 70–73 (1955).

1942 (1)

C. R. Hoover, F. W. Putnam, and E. G. Wittenberg, “The depolarization of the Tyndall-scattered light of bentonite and ferric oxide sols,” J. Phys. Chem. 46, 81–93 (1942).
[Crossref]

1941 (1)

1938 (3)

W. Lotmar, “Über die Lichtstreuung in Lösungen von Hochmolekularen,” Helv. Chim. Acta 21, 953–984 (1938).
[Crossref]

M. Peyrot, “Nouvelles recherches expérimentales sur la diffusion de la lumière dans les liquides,” Ann. Phys. 11, 335–407 (1938).
[Crossref]

H. Hogrebe, “The depolarisation of molecular diffused light of watery electrolytic solutions,” Phys. Z. 39, 23–36 (1938).

1926 (1)

C. W. Sweitzer, “Light-scattering of aqueous salt solutions,” J. Phys. Chem. 31, 1150–1191 (1926).
[Crossref]

1925 (3)

K. S. Krishnan, “LXXV. On the molecular scattering of light in liquids,” Philos. Mag. 50(298), 697–715 (1925).
[Crossref]

M. Y. Rocard, “Diffusion de la lumiere dans les fluides,” C. R. Acad. Sci. 180, 212–213 (1925).

M. Y. Rocard, “Sur la diffusion de la lumiere dans les fluides,” C. R. Acad. Sci. 179, 52–53 (1925).

1923 (2)

C. V. Raman and K. S. Rao, “LXIII. On the molecular scattering and extinction of light in liquids and the determination of the Avogadro constant,” London Edinburgh Dublin Philos. Mag. J. Sci. 45(267), 625–640 (1923).
[Crossref]

R. Gans, “Das Tyndallphänomen in Flüssigkeiten,” Z. Phys. 17, 353–397 (1923).
[Crossref]

1922 (1)

J. Cabannes, “Considérations théoriques sur la diffusion de la lumière par les liquides transparents. Polarisation de la lumière diffusée latéralement,” J. Phys. Radium 3, 429–442 (1922).
[Crossref]

1921 (1)

W. H. Martin and S. Lehrman, “The scattering of light by dust-free liquids. II,” J. Phys. Chem. 26, 75–88 (1921).
[Crossref]

1918 (1)

R. J. L. R. Strutt, “The light scattered by gases: its polarisation and intensity,” Proc. R. Soc. London Ser. A 95, 155–176 (1918).
[Crossref]

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249 (1996).
[Crossref]

Ackleson, S. G.

P. J. Werdell, L. I. W. McKinna, E. Boss, S. G. Ackleson, S. E. Craig, W. W. Gregg, Z. Lee, S. Maritorena, C. S. Roesler, C. S. Rousseaux, D. Stramski, J. M. Sullivan, M. S. Twardowski, M. Tzortziou, and X. Zhang, “An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing,” Prog. Oceanogr. 160, 186–212 (2018).
[Crossref]

Babin, M.

Beardsley, G. F.

Boss, E.

P. J. Werdell, L. I. W. McKinna, E. Boss, S. G. Ackleson, S. E. Craig, W. W. Gregg, Z. Lee, S. Maritorena, C. S. Roesler, C. S. Rousseaux, D. Stramski, J. M. Sullivan, M. S. Twardowski, M. Tzortziou, and X. Zhang, “An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing,” Prog. Oceanogr. 160, 186–212 (2018).
[Crossref]

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).
[Crossref]

Buiteveld, H.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183 (1994).
[Crossref]

Cabannes, J.

J. Cabannes, “Considérations théoriques sur la diffusion de la lumière par les liquides transparents. Polarisation de la lumière diffusée latéralement,” J. Phys. Radium 3, 429–442 (1922).
[Crossref]

Chin, W.-C.

W.-C. Chin, M. V. Orellana, and P. Verdugo, “Spontaneous assembly of marine dissolved organic matter into polymer gels,” Nature 391, 568–572 (1998).
[Crossref]

Claustre, H.

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

Cohen, G.

G. Cohen and H. Eisenberg, “Light scattering of water, deuterium oxide, and other pure liquids,” J. Chem. Phys. 43, 3881–3887 (1965).
[Crossref]

Craig, S. E.

P. J. Werdell, L. I. W. McKinna, E. Boss, S. G. Ackleson, S. E. Craig, W. W. Gregg, Z. Lee, S. Maritorena, C. S. Roesler, C. S. Rousseaux, D. Stramski, J. M. Sullivan, M. S. Twardowski, M. Tzortziou, and X. Zhang, “An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing,” Prog. Oceanogr. 160, 186–212 (2018).
[Crossref]

Dandliker, W. B.

J. Kraut and W. B. Dandliker, “Light scattering by water,” J. Chem. Phys. 23, 1544–1545 (1955).
[Crossref]

Dawson, L. H.

Donze, M.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183 (1994).
[Crossref]

Einstein, A.

A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Books on Physics (Dover, 1956).

Eisenberg, H.

H. Eisenberg, “Equation for the refractive index of water,” J. Chem. Phys. 43, 3887–3892 (1965).
[Crossref]

G. Cohen and H. Eisenberg, “Light scattering of water, deuterium oxide, and other pure liquids,” J. Chem. Phys. 43, 3881–3887 (1965).
[Crossref]

Farinato, R. S.

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65, 593–595 (1976).
[Crossref]

Feistel, R.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of standard seawater and the definition of the reference-composition salinity scale,” Deep-Sea Res. I 55, 50–72 (2008).
[Crossref]

Foster, J. F.

V. S. R. Rao and J. F. Foster, “Depolarization of scattered light in solutions of linear and branched polysaccharides,” J. Polym. Sci. Part A Gen. Pap. 1, 289–300 (1963).
[Crossref]

Fournier, G. R.

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007), p. 704.

Freeman, S. A.

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

Fry, E. S.

Gans, R.

R. Gans, “Das Tyndallphänomen in Flüssigkeiten,” Z. Phys. 17, 353–397 (1923).
[Crossref]

Gregg, W. W.

P. J. Werdell, L. I. W. McKinna, E. Boss, S. G. Ackleson, S. E. Craig, W. W. Gregg, Z. Lee, S. Maritorena, C. S. Roesler, C. S. Rousseaux, D. Stramski, J. M. Sullivan, M. S. Twardowski, M. Tzortziou, and X. Zhang, “An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing,” Prog. Oceanogr. 160, 186–212 (2018).
[Crossref]

Hakvoort, J. H. M.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183 (1994).
[Crossref]

Harrington, T.

C. McElfresh, T. Harrington, and K. S. Vecchio, “Application of a novel new multispectral nanoparticle tracking technique,” Meas. Sci. Technol. 29, 065002 (2018).
[Crossref]

Havlik, A. J.

He, M.-X.

Hermans, J. J.

W. Prins and J. J. Hermans, “Light-scattering by solutions of some sodium alkyl-1-sulfates,” Proc. K. Ned. Akad. Wet. B59, 298–311 (1956).

Hogrebe, H.

H. Hogrebe, “The depolarisation of molecular diffused light of watery electrolytic solutions,” Phys. Z. 39, 23–36 (1938).

Holland, P. W.

P. W. Holland and R. E. Welsch, “Robust regression using iteratively reweighted least-squares,” Comm. Statist. Theory Methods 6, 813–827 (1977).
[Crossref]

Hoover, C. R.

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Figures (9)

Fig. 1.
Fig. 1. Effect of the depolarization ratio ( δ = 0.03 , 0.05, and 0.09) on the angular variation of light scattering by pure water simulated using the Zhang and Hu [33] model for scattering angle ( θ ) from 0 to 180° at a light wavelength of 532 nm and 25°C temperature. (a)  β h (solid lines) and β v (dotted lines); (b)  β h / β v , i.e., Eq. (15); and (c)  β h ( δ ) / β h ( δ = 0.039 ) .
Fig. 2.
Fig. 2. Variations of the depolarization ratio ( δ p ) at a light wavelength of 532 nm as a function of particle diameter D calculated for particles of two different shapes, sphere and hexahedron (Hexa), and of relative refractive index ( n ), 1.02 and 1.20. For hexahedron, the particle size is surface-area equivalent diameter. The field of view (FOV) of the DAWN detectors is 2.2°; the legends including FOV indicate the results are an average within the FOV assuming the detector response function F ( θ ) = 1 .
Fig. 3.
Fig. 3. Particle size distributions (PSD) measured by the ViewSizer of residual nanoparticles in ultrapure water (UP), 20 nm filtered ultrapure water (20-nm UP), master salt solution (SS), and 20 nm filtered master salt solution (20-nm SS). The value in each legend entry is the total particle concentration ( mL 1 ) over particle diameter ( D ) range from 0.05 to 1 μm.
Fig. 4.
Fig. 4. The FOV-averaged (a) vertical and (b) horizontal components of particulate volume scattering function computed at a light wavelength of 532 nm for ultrapure water (solid lines) and the 20 nm filtered master salt solution (dotted lines) using the measured particle size distributions shown in Fig. 3 and assuming a hexahedral shape and relative refractive index of 1.02, 1.08, and 1.20 for particles suspended in water.
Fig. 5.
Fig. 5. Examples illustrating the correction of scattering by residual nanoparticles for the vertical (first row) and horizontal (second row) components of the volume scattering functions measured at three salinities in the first experiment. Blue: the measured scattering (before); red: estimated scattering attributable to nanoparticles (nano); yellow: the difference between the blue and red curves (after). In the legend, S , salinity ( g kg 1 ); mr, mixing ratio of salt solution, e.g., 0.4 means 8 mL ( = 0.4 × 20 ) salt solution and 12 mL water for a total of 20 mL of final salt solution. All data are for a light wavelength of 532 nm.
Fig. 6.
Fig. 6. Comparison of the depolarization ratio at a light wavelength of 532 nm estimated from five methods (M1 to M5) listed in Table 1 for all samples prepared in experiments 1 and 2.
Fig. 7.
Fig. 7. (a) Box and whisker plot of the depolarization ratio ( δ ) estimated for pure water in the two experiments using the five methods listed in Table 2. (b)–(d) Comparisons of the volume scattering function ( β ) and its horizontal ( β h ) and vertical ( β v ) components for pure water between the measurements and the Zhang and Hu [33] model using δ = 0.039 at a light wavelength of 532 nm. All values are scaled to a temperature of 25°C. The results from the first and second experiments are represented with blue and green circles, respectively; the crosses represent the median values.
Fig. 8.
Fig. 8. (a)–(e) The depolarization ratio ( δ ) at a light wavelength of 532 nm estimated using the five methods listed in Table 2 for samples prepared at various salinities ( S ) in the two experiments. Three least-squares linear fit (LS fit) schemes were applied to the combined two datasets: (1) the ordinary LS fit including all the data points; (2) the weighted LS fit that identifies outliers (open symbols) and assigns them with less weight in regression; and (3) the ordinary LS fit excluding the outliers. The linear model ( y = a 0 + a 1 x , where y is the depolarization ratio, x is the salinity in g kg 1 , and a 0 and a 1 are the best-fit coefficients obtained from the regression analysis) shown in each panel is the result of the third LS linear regression scheme.
Fig. 9.
Fig. 9. Scattering functions (a)  β ( 90 ) , (b)  β v ( 90 ) , and (c)  β h ( 90 ) calculated at a light wavelength of 532 nm and 25°C temperature as a function of salinity ( S ) using the Zhang et al. [42] model with three different depolarization ratio values: a constant value = 0.039 and variable values following Eq. (20) with a 1 = 0.0001 and a 1 = 0.0002 . The circles represent the measured values. The black cross and error bar in (a) represent the range of the estimates ( mean ± standard deviation) of β ( 90 ) at 532 nm interpolated from Morel’s measurements [26,44] for pure water and for seawater at S = 38.4 .

Tables (3)

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Table 1. Measured Values of the Depolarization Ratio of Pure Water ( δ )a

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Table 2. Summary of Five Different Methods Used to Estimate the Depolarization Ratio ( δ ) of Seawater and Estimates of the Associated Uncertainty

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Table 3. Uncertainty of Measurements (Ratio of Standard Deviation to Mean Value in Percent) Estimated from the Six Pure Water Measurements and the Comparison Results (Median Difference in Percent) for Pure Water between the Measurements and the Zhang and Hu [33] Modela

Equations (20)

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M = β ( 90 , δ ) [ 1 + 1 δ 1 + δ cos 2 ( θ ) 1 δ 1 + δ sin 2 ( θ ) 0 0 1 δ 1 + δ sin 2 ( θ ) 2 ( 1 δ ) 1 + δ 1 δ 1 + δ sin 2 ( θ ) 0 0 0 0 2 1 δ 1 + δ cos ( θ ) 0 0 0 0 2 1 δ 1 + δ cos ( θ ) ] ,
[ I ( θ ) Q ( θ ) U ( θ ) V ( θ ) ] = V r 2 M [ I 0 Q 0 U 0 V 0 ] ,
I ( θ ) = V r 2 I 0 β ( 90 , δ ) ( 1 + 1 δ 1 + δ cos 2 θ ) ,
β ( θ , δ ) = I ( θ ) r 2 V I 0 = β ( 90 , δ ) ( 1 + 1 δ 1 + δ cos 2 θ ) .
I v ( θ ) = V r 2 I 0 β ( 90 , δ ) 2 1 + δ .
I h ( θ ) = V r 2 I 0 β ( 90 , δ ) ( 1 + 1 δ 1 + δ cos 2 θ ) .
δ = I h ( 90 ) I v ( 90 ) .
I v ( θ ) = V r 2 I 0 β ( 90 , δ ) 2 1 + δ
I h ( θ ) = V r 2 I 0 β ( 90 , δ ) ( 1 + 1 δ 1 + δ cos 2 θ ) .
β ( θ , δ ) = ( I h ( θ ) + I v ( θ ) ) r 2 2 V I 0 = β ( 90 , δ ) ( 1 + 1 δ 1 + δ cos 2 θ ) ,
β v ( θ , δ ) = I v ( θ ) r 2 V I 0 = β ( 90 , δ ) 2 1 + δ
β h ( θ , δ ) = I h ( θ ) r 2 V I 0 = β ( 90 , δ ) ( 1 + 1 δ 1 + δ cos 2 θ ) .
β = ( β h + β v ) / 2 .
δ = I h ( 90 ) I v ( 90 ) = β h ( 90 ) β v ( 90 ) .
f ( θ , δ ) = β h ( θ , δ ) β v ( θ , δ ) = 1 + δ + ( 1 δ ) cos 2 θ 2 ,
δ = f ( θ , δ ) cos 2 θ sin 2 θ .
δ 0 = θ 0 α θ 0 + α F ( θ ) ( 1 + 1 δ 1 + δ cos 2 θ ) d θ θ 0 α θ 0 + α F ( θ ) 2 1 + δ d θ cos 2 θ 0 sin 2 θ 0 .
δ 0 δ 1 + cot 2 θ 0 ( cot 2 θ 0 1 ) cos α 2 ( cot 2 θ 0 1 ) ( 1 cos α ) δ .
δ = β h , m ( 90 ) β h , p ( 90 ) β v , m ( 90 ) β v , p ( 90 ) = 1 1 r v ( 90 ) δ m r v ( 90 ) 1 r v ( 90 ) δ p ,
δ ( S ) = 0.039 + a 1 × S ,

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