Abstract

Simultaneous measurements of the size distribution and volume scattering function of particles in clear coastal water are used to estimate a particle size–refractive index distribution. Various possibilities of the refractive index distribution and the observed particle distribution are studied systematically using Mie theory. The resulting model has minerals in mid-sizes and organic material in large and small sizes, but does not yield the correct dependence of scattering on wavelength. By assuming the existence of minerals or organics in sizes too small to be measured by the particle counter, two other models are developed, both of which yield acceptable wavelength dependence of scattering. The results of the three models are combined to provide limits on the size–refractive index distribution of the particles. Within these limits, volume scattering functions computed for the particles show good agreement with the measurements.

© 1974 Optical Society of America

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References

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  1. H. R. Gordon, O. B. Brown, Limnol. Oceanog. 17, 826 (1972).
    [CrossRef]
  2. G. Kullenberg, Deep-Sea Res. 15, 423 (1968).
  3. The volume scattering function is defined by β(θ) = dI(θ)/Edυ, where dI(θ) is the intensity of light scattered by a volume dυ in a direction θ with respect to an incident parallel beam of irradiance E.
  4. O. B. Brown, H. G. Gordon, Appl. Opt. 12, 2461 (1973).
    [CrossRef] [PubMed]
  5. H. Bader, J. Geophys. Res. 75, 2822 (1970).
    [CrossRef]
  6. H. R. Gordon, O. B. Brown, H. Bader, An Experimental Study of Suspended Particulate Matter in the Tongue of the Ocean and Its Influence on Underwater Visibility. Final Report, Contract F08605-7-C-0028, Air Force Eastern Test Range Measurements Laboratory, 1972.
  7. The volume scattering matrix M(θ) is defined by S(θ) = M(θ) So where So and S are the Stokes vectors of the incident and scattered light respectively in the I, O, U, V representation of Born, Wolf, Principles of OpticsPergamon, New York, 1965). The volume scattering function β(θ) is M11.
  8. L. E. Mertens, D. L. Phillips, Measurements of the Volume Scattering Function of Sea Water. Tech. Rep. 334 Range Measurements Laboratory, Patrick Air Force Base, Florida, 1972.
  9. L. E. Mertens, W. H. Manning, RCA Engineer 17, 38 (191).
  10. K. Kalle, Oceanogr. Mar. Biol. 14, 91 (1966).
  11. J. E. Tyler, R. C. Smith, W. H. Wilson, J. Opt. Soc. Am. 62, 83 (1972).
    [CrossRef]
  12. N. J. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968), p. 58.
  13. The results of such model calculations will depend on the size limits assumed for the fractions. It is felt that the divisions used in this paper are natural, and furthermore the general conclusions arrived at will not depend greatly on the precise values of the size limits of the divisions.
  14. The Mie intensity functions ij(θ) (j = 1–4) have been generated for the 12 indices used in this study and stored on disk and tape. The integrals of dN/dD weighted by ij(θ) are computed in terms of the size parameter x = πD/λ, where λ is the wavelength. The ij(θ)’s were computed for x = 0.1(0.01) 2(0.1) 210, hence the above integrals are based on approximately 2000 samples of ij(θ). All the Mie calculations presented here were carried out from a remote demand terminal tied to a Univac 1106 computer. Calculation of M(θ), bp, and ap for a given distribution and index at 18 scattering angles requires a total of about 20 sec of computation time. A total of about 175 volume scattering matrices M were computed for the present study.
  15. O. B. Brown, A Study of Light Scattering by Ocean Borne Particulates. Ph.D. thesis, University of Miami (1973).
  16. G. N. Plass, G. W. Kattawar, Appl. Opt. 8, 455 (1969).
    [CrossRef] [PubMed]
  17. G. Kullenberg, N. B. Olsen, A Comparison Between Observed and Computed Light Scattering Functions-II. Report 19, Kobenhavns Universitet, Institut for Fysisk Oceanografi. (1972).
  18. R. E. Morrison, J. Geophys. Res. 75, 629 (1970).
    [CrossRef]
  19. T. J. Petzold, Volume Scattering Functions For Selected Ocean Waters. Scripps Institution of Oceanography, Visibility Laboratory, San Diego, Calif; SIO Ref. 72–78 (1972).
  20. H. Bader, University of Miami, Coral Gables, Fla. personal communication.
  21. W. R. McCluney, Small-Angle Light Scattering Studies of Marine Phytoplankton, Ph.D. thesis, University of Miami (1973).
  22. J. R. V. Zaneveld, H. Pak, J. Opt. Soc. Am. 63, 321 (1973).
    [CrossRef]
  23. R. P. Chesslet, Centre National de la Recherche Scientific, 91-GIF-sur-YVETTE, FRANCE, personal communication.
  24. J. E. Harris, National Oceanographic Data Center, Washington, D.C., personal communication.

1973 (2)

1972 (2)

J. E. Tyler, R. C. Smith, W. H. Wilson, J. Opt. Soc. Am. 62, 83 (1972).
[CrossRef]

H. R. Gordon, O. B. Brown, Limnol. Oceanog. 17, 826 (1972).
[CrossRef]

1970 (2)

H. Bader, J. Geophys. Res. 75, 2822 (1970).
[CrossRef]

R. E. Morrison, J. Geophys. Res. 75, 629 (1970).
[CrossRef]

1969 (1)

1968 (1)

G. Kullenberg, Deep-Sea Res. 15, 423 (1968).

1966 (1)

K. Kalle, Oceanogr. Mar. Biol. 14, 91 (1966).

Bader, H.

H. Bader, J. Geophys. Res. 75, 2822 (1970).
[CrossRef]

H. R. Gordon, O. B. Brown, H. Bader, An Experimental Study of Suspended Particulate Matter in the Tongue of the Ocean and Its Influence on Underwater Visibility. Final Report, Contract F08605-7-C-0028, Air Force Eastern Test Range Measurements Laboratory, 1972.

H. Bader, University of Miami, Coral Gables, Fla. personal communication.

Born,

The volume scattering matrix M(θ) is defined by S(θ) = M(θ) So where So and S are the Stokes vectors of the incident and scattered light respectively in the I, O, U, V representation of Born, Wolf, Principles of OpticsPergamon, New York, 1965). The volume scattering function β(θ) is M11.

Brown, O. B.

O. B. Brown, H. G. Gordon, Appl. Opt. 12, 2461 (1973).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, Limnol. Oceanog. 17, 826 (1972).
[CrossRef]

H. R. Gordon, O. B. Brown, H. Bader, An Experimental Study of Suspended Particulate Matter in the Tongue of the Ocean and Its Influence on Underwater Visibility. Final Report, Contract F08605-7-C-0028, Air Force Eastern Test Range Measurements Laboratory, 1972.

O. B. Brown, A Study of Light Scattering by Ocean Borne Particulates. Ph.D. thesis, University of Miami (1973).

Chesslet, R. P.

R. P. Chesslet, Centre National de la Recherche Scientific, 91-GIF-sur-YVETTE, FRANCE, personal communication.

Gordon, H. G.

Gordon, H. R.

H. R. Gordon, O. B. Brown, Limnol. Oceanog. 17, 826 (1972).
[CrossRef]

H. R. Gordon, O. B. Brown, H. Bader, An Experimental Study of Suspended Particulate Matter in the Tongue of the Ocean and Its Influence on Underwater Visibility. Final Report, Contract F08605-7-C-0028, Air Force Eastern Test Range Measurements Laboratory, 1972.

Harris, J. E.

J. E. Harris, National Oceanographic Data Center, Washington, D.C., personal communication.

Jerlov, N. J.

N. J. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968), p. 58.

Kalle, K.

K. Kalle, Oceanogr. Mar. Biol. 14, 91 (1966).

Kattawar, G. W.

Kullenberg, G.

G. Kullenberg, Deep-Sea Res. 15, 423 (1968).

G. Kullenberg, N. B. Olsen, A Comparison Between Observed and Computed Light Scattering Functions-II. Report 19, Kobenhavns Universitet, Institut for Fysisk Oceanografi. (1972).

Manning, W. H.

L. E. Mertens, W. H. Manning, RCA Engineer 17, 38 (191).

McCluney, W. R.

W. R. McCluney, Small-Angle Light Scattering Studies of Marine Phytoplankton, Ph.D. thesis, University of Miami (1973).

Mertens, L. E.

L. E. Mertens, W. H. Manning, RCA Engineer 17, 38 (191).

L. E. Mertens, D. L. Phillips, Measurements of the Volume Scattering Function of Sea Water. Tech. Rep. 334 Range Measurements Laboratory, Patrick Air Force Base, Florida, 1972.

Morrison, R. E.

R. E. Morrison, J. Geophys. Res. 75, 629 (1970).
[CrossRef]

Olsen, N. B.

G. Kullenberg, N. B. Olsen, A Comparison Between Observed and Computed Light Scattering Functions-II. Report 19, Kobenhavns Universitet, Institut for Fysisk Oceanografi. (1972).

Pak, H.

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions For Selected Ocean Waters. Scripps Institution of Oceanography, Visibility Laboratory, San Diego, Calif; SIO Ref. 72–78 (1972).

Phillips, D. L.

L. E. Mertens, D. L. Phillips, Measurements of the Volume Scattering Function of Sea Water. Tech. Rep. 334 Range Measurements Laboratory, Patrick Air Force Base, Florida, 1972.

Plass, G. N.

Smith, R. C.

Tyler, J. E.

Wilson, W. H.

Wolf,

The volume scattering matrix M(θ) is defined by S(θ) = M(θ) So where So and S are the Stokes vectors of the incident and scattered light respectively in the I, O, U, V representation of Born, Wolf, Principles of OpticsPergamon, New York, 1965). The volume scattering function β(θ) is M11.

Zaneveld, J. R. V.

Appl. Opt. (2)

Deep-Sea Res. (1)

G. Kullenberg, Deep-Sea Res. 15, 423 (1968).

J. Geophys. Res. (2)

H. Bader, J. Geophys. Res. 75, 2822 (1970).
[CrossRef]

R. E. Morrison, J. Geophys. Res. 75, 629 (1970).
[CrossRef]

J. Opt. Soc. Am. (2)

Limnol. Oceanog. (1)

H. R. Gordon, O. B. Brown, Limnol. Oceanog. 17, 826 (1972).
[CrossRef]

Oceanogr. Mar. Biol. (1)

K. Kalle, Oceanogr. Mar. Biol. 14, 91 (1966).

RCA Engineer (1)

L. E. Mertens, W. H. Manning, RCA Engineer 17, 38 (191).

Other (14)

The volume scattering function is defined by β(θ) = dI(θ)/Edυ, where dI(θ) is the intensity of light scattered by a volume dυ in a direction θ with respect to an incident parallel beam of irradiance E.

H. R. Gordon, O. B. Brown, H. Bader, An Experimental Study of Suspended Particulate Matter in the Tongue of the Ocean and Its Influence on Underwater Visibility. Final Report, Contract F08605-7-C-0028, Air Force Eastern Test Range Measurements Laboratory, 1972.

The volume scattering matrix M(θ) is defined by S(θ) = M(θ) So where So and S are the Stokes vectors of the incident and scattered light respectively in the I, O, U, V representation of Born, Wolf, Principles of OpticsPergamon, New York, 1965). The volume scattering function β(θ) is M11.

L. E. Mertens, D. L. Phillips, Measurements of the Volume Scattering Function of Sea Water. Tech. Rep. 334 Range Measurements Laboratory, Patrick Air Force Base, Florida, 1972.

N. J. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968), p. 58.

The results of such model calculations will depend on the size limits assumed for the fractions. It is felt that the divisions used in this paper are natural, and furthermore the general conclusions arrived at will not depend greatly on the precise values of the size limits of the divisions.

The Mie intensity functions ij(θ) (j = 1–4) have been generated for the 12 indices used in this study and stored on disk and tape. The integrals of dN/dD weighted by ij(θ) are computed in terms of the size parameter x = πD/λ, where λ is the wavelength. The ij(θ)’s were computed for x = 0.1(0.01) 2(0.1) 210, hence the above integrals are based on approximately 2000 samples of ij(θ). All the Mie calculations presented here were carried out from a remote demand terminal tied to a Univac 1106 computer. Calculation of M(θ), bp, and ap for a given distribution and index at 18 scattering angles requires a total of about 20 sec of computation time. A total of about 175 volume scattering matrices M were computed for the present study.

O. B. Brown, A Study of Light Scattering by Ocean Borne Particulates. Ph.D. thesis, University of Miami (1973).

T. J. Petzold, Volume Scattering Functions For Selected Ocean Waters. Scripps Institution of Oceanography, Visibility Laboratory, San Diego, Calif; SIO Ref. 72–78 (1972).

H. Bader, University of Miami, Coral Gables, Fla. personal communication.

W. R. McCluney, Small-Angle Light Scattering Studies of Marine Phytoplankton, Ph.D. thesis, University of Miami (1973).

R. P. Chesslet, Centre National de la Recherche Scientific, 91-GIF-sur-YVETTE, FRANCE, personal communication.

J. E. Harris, National Oceanographic Data Center, Washington, D.C., personal communication.

G. Kullenberg, N. B. Olsen, A Comparison Between Observed and Computed Light Scattering Functions-II. Report 19, Kobenhavns Universitet, Institut for Fysisk Oceanografi. (1972).

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Figures (8)

Fig. 1
Fig. 1

Average cumulative size distributions for TOTO.

Fig. 2
Fig. 2

Particle scattering functions of the small, mid, and large fractions for various refractive indices.

Fig. 3
Fig. 3

Comparison of the measured and computed values of M11 (θ) and M22 (θ) for TMC1.

Fig. 4
Fig. 4

Small fraction particle scattering function with the addition of particles smaller than 0.65 μm. Left panel: N>D ~ Dc below 0.65 μm, and the parameter on each curve is c. Right panel: N>D ~ D−6.5 below 0.65 μm; parameter is the lower limit of the distribution in microns.

Fig. 5
Fig. 5

Particle scattering functions for minerals below 1.25 μm distributed according to N>D ~ Dc, and the parameter on figure is c.

Fig. 6
Fig. 6

Comparison between experimental and computed values of the particle scattering function for TCM2 (lower θ scale) and TCM3 (upper θ scale).

Fig. 7
Fig. 7

Comparison between observed and computed values of M33 (θ) for TCM1, TCM2, and TCM3.

Fig. 8
Fig. 8

Limitations on the size–refractive index distribution of the particles as summarized in the text.

Tables (2)

Tables Icon

Table I Particle Scattering and Absorption Coefficients of the Components for Various Refractive Indices (m−1)

Tables Icon

Table II Size–Refractive Index Parameters for the Various Three-Component Models

Equations (9)

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N > D = [ ( 11 × 10 3 ) / D 3 ] m l 1 , 0.08 D 10 μ m ,
N > D ( organic ) = [ ( 16.1 × 10 3 ) / D 3 ] m l 1 , 0.1 D 2.5 μ m , and N > D ( inorganic ) = [ ( 16.1 × 10 3 ) / D 3 ] m l 1 , 2.5 D 10 μ m .
N > D = [ ( 1.6 × 10 3 ) / D 1 / 2 ] m l 1 0 < D 2.5 μ m .
c = 0.175 0.22 ± 0.01 m 1 a = 0.075 0.080 ± 0.02 m 1 .
b = 0.1 0.14 ± 0.03 m 1 ,
2 π 0 π β ( θ ) sin θ d θ ,
m = 1.01 m = 1.15 m = 1.03 0.01 i ; 0.65 < D < 1.25 μ m , ; 1.25 < D < 3.75 μ m , ; 3.75 < D < 17.0 μ m ,
N > D = K / D c , 2.7 c 3.5 ,
c max c 6.5 , and 0.012 D min 0.65 μ m .

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