Abstract

The Mueller phase matrices of sea water were measured at scattering angles of 20°, 30°, ⋯ 130° for ocean water, coastal water, harbor water, and river water. The measurements were made with a modified Brice–Phoenix light-scattering photometer. The measured phase matrices exhibit strong forward scattering, and the polarization is comparable in form to that due to Rayleigh scatterers but reaches a maximum value in the range 40%–70%. The matrices are also strongly diagonal and approximate the theoretical Mie scattering matrices for spheres.

© 1968 Optical Society of America

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References

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  1. T. Hatch and S. P. Choate, J. Franklin Inst. 210, 793 (1930).
    [CrossRef]
  2. A. Ivanoff, N. Jerlov, and T. H. Waterman, Limnol. Oceanog. 6, 129 (1961).
    [CrossRef]
  3. B. A. Brice, M. Halwer, and R. Speiser, J. Opt. Soc. Am. 40, 768 (1950).
    [CrossRef]
  4. B. S. Pritchard and W. G. Elliott, J. Opt. Soc. Am. 50, 191 (1960).
    [CrossRef]
  5. F. Perrin, J. Chem. Phys. 10, 415 (1942).
    [CrossRef]
  6. G. R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon Press, Ltd., London, 1965), Ch. XII.
  7. G. F. Beardsley, “The Polarization of the Near Asymptotic Light Field in Sea Water,” Ph.D. thesis, MIT, 1966.
  8. A. F. Spilhaus, “Observations of Light Scattering in Sea Water,” Ph.D. thesis, MIT, 1965.
  9. N. G. Jerlov, Oceanog. Marine Biol. Ann. Rev. 1, 89 (1963).
  10. W. R. G. Atkins and H. H. Poole, Proc. Roy. Soc. (London) B,  140, 321 (1952).
    [CrossRef]
  11. Yu. E. Ochakovsky, Tr. Inst. Okeanol., Akad. Nauk, USSR 77, 125 (1965).

1965 (1)

Yu. E. Ochakovsky, Tr. Inst. Okeanol., Akad. Nauk, USSR 77, 125 (1965).

1963 (1)

N. G. Jerlov, Oceanog. Marine Biol. Ann. Rev. 1, 89 (1963).

1961 (1)

A. Ivanoff, N. Jerlov, and T. H. Waterman, Limnol. Oceanog. 6, 129 (1961).
[CrossRef]

1960 (1)

1952 (1)

W. R. G. Atkins and H. H. Poole, Proc. Roy. Soc. (London) B,  140, 321 (1952).
[CrossRef]

1950 (1)

1942 (1)

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

1930 (1)

T. Hatch and S. P. Choate, J. Franklin Inst. 210, 793 (1930).
[CrossRef]

Atkins, W. R. G.

W. R. G. Atkins and H. H. Poole, Proc. Roy. Soc. (London) B,  140, 321 (1952).
[CrossRef]

Beardsley, G. F.

G. F. Beardsley, “The Polarization of the Near Asymptotic Light Field in Sea Water,” Ph.D. thesis, MIT, 1966.

Brice, B. A.

Choate, S. P.

T. Hatch and S. P. Choate, J. Franklin Inst. 210, 793 (1930).
[CrossRef]

Elliott, W. G.

Halwer, M.

Hatch, T.

T. Hatch and S. P. Choate, J. Franklin Inst. 210, 793 (1930).
[CrossRef]

Ivanoff, A.

A. Ivanoff, N. Jerlov, and T. H. Waterman, Limnol. Oceanog. 6, 129 (1961).
[CrossRef]

Jerlov, N.

A. Ivanoff, N. Jerlov, and T. H. Waterman, Limnol. Oceanog. 6, 129 (1961).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Oceanog. Marine Biol. Ann. Rev. 1, 89 (1963).

Ochakovsky, Yu. E.

Yu. E. Ochakovsky, Tr. Inst. Okeanol., Akad. Nauk, USSR 77, 125 (1965).

Perrin, F.

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Poole, H. H.

W. R. G. Atkins and H. H. Poole, Proc. Roy. Soc. (London) B,  140, 321 (1952).
[CrossRef]

Preisendorfer, G. R. W.

G. R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon Press, Ltd., London, 1965), Ch. XII.

Pritchard, B. S.

Speiser, R.

Spilhaus, A. F.

A. F. Spilhaus, “Observations of Light Scattering in Sea Water,” Ph.D. thesis, MIT, 1965.

Waterman, T. H.

A. Ivanoff, N. Jerlov, and T. H. Waterman, Limnol. Oceanog. 6, 129 (1961).
[CrossRef]

J. Chem. Phys. (1)

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

J. Franklin Inst. (1)

T. Hatch and S. P. Choate, J. Franklin Inst. 210, 793 (1930).
[CrossRef]

J. Opt. Soc. Am. (2)

Limnol. Oceanog. (1)

A. Ivanoff, N. Jerlov, and T. H. Waterman, Limnol. Oceanog. 6, 129 (1961).
[CrossRef]

Oceanog. Marine Biol. Ann. Rev. (1)

N. G. Jerlov, Oceanog. Marine Biol. Ann. Rev. 1, 89 (1963).

Proc. Roy. Soc. (London) B (1)

W. R. G. Atkins and H. H. Poole, Proc. Roy. Soc. (London) B,  140, 321 (1952).
[CrossRef]

Tr. Inst. Okeanol., Akad. Nauk, USSR (1)

Yu. E. Ochakovsky, Tr. Inst. Okeanol., Akad. Nauk, USSR 77, 125 (1965).

Other (3)

G. R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon Press, Ltd., London, 1965), Ch. XII.

G. F. Beardsley, “The Polarization of the Near Asymptotic Light Field in Sea Water,” Ph.D. thesis, MIT, 1966.

A. F. Spilhaus, “Observations of Light Scattering in Sea Water,” Ph.D. thesis, MIT, 1965.

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Figures (5)

Fig. 1
Fig. 1

Schematic arrangement of the modified light-scattering photometer. The source H produces a ray which is fitted to the desired band by a color filter at G, attenuated to the proper level by a neutral-density filter at F, and brought to the desired polarization by a polarizer-waveplate combination at Pj. After leaving the sample X, the beam passes through a second waveplate-polarizer pair at Di, and is detected by a photomultiplier.

Fig. 2
Fig. 2

The four geometries used to calibrate the light-scattering photometer. The procedure is explained in the text. Nj is the polarized beam, Di the analyzing system, K the photomultiplier, X the seawater sample, and O the opal standard.

Fig. 3
Fig. 3

Sij(θ) in relative units, a typical record of photomultiplier output, vs θ, scattering angle. The discontinuities are produced by changing the setting of the neutral density filters at F (see Fig. 1). The input was horizontally plane polarized light, and the curves are for each of the possible detector configurations indicated by the numbers.

Fig. 4
Fig. 4

Dependence of the phase functions σ(θ) in msr−1 of five surface samples as a function of the scattering angle θ. ● Boston Harbor, ○ Charles River, ▲ Atlantic #4, △ Atlantic #6, □ Cape Cod coastal waters. Precise locations and sampling times are given in the table.

Fig. 5
Fig. 5

Inherent polarization as a function of scattering angle for the five samples described in Fig. 4. The points ⊙ show the theoretical behavior of Rayleigh scatterers.

Tables (1)

Tables Icon

Table I Phase function, inherent polarization, and scattering matrix at 30° for five types of marine water. All measurements were made with a narrow-band green (546 μ) filter at G (see Fig. 1) on surface samples. Sample #1 was taken in Boston Harbor at Thieves Ledge on 10 Feb. 1966 at 1400 h from the R/V SHROCK. Sample #2 was taken in the Charles River, Cambridge, Massachusetts, from the MIT sailing pavilion on 22 Feb. 1966 at 1300 h. Sample #4 was obtained at 39° 55′N, 70° 38′W on 27 April 1966 at 1850 h from the R/V CHAIN. Sample #6 was taken at 34° 56.5′N, 66° 29.5′W on 20 Apr. 1966 at 1200 h from the R/V CHAIN. Sample #7 was taken at 41°N, 70° 55′W on 5 May 1966 at 1410 h from the R/V CHAIN. All numbers are given in (km-sr)−1.

Equations (14)

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N = { N l , N r , U , V }
{ N 1 , N 2 , N 3 , N 4 }
P M = [ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 ]
N s ( r , ω ) = 4 π [ P M ( ω , ω , r ) ] N ( ω , r ) d ω d r ,
N s ( θ ) = [ P M ( θ ) ] N ( 0 ) Δ ω Δ r .
S i j = K ( 1 , 1 , 0 , 0 ) · [ D ι ] N j Δ ω Δ a ,
S 1 = K Δ ω Δ a ( N 1 ) S 2 = K Δ ω Δ a ( N 2 ) S 3 = K Δ ω Δ a [ 1 2 ( N 1 + N 2 ) + N 3 ] S 4 = K Δ ω Δ a [ 1 2 ( N 1 + N 2 ) - N 4 ] ,
S x i j ( 0 ) = K Δ ω s d Δ a N t 2 / F x i j .
S x i j ( θ ) = K Δ ω s x Δ ω x d l 0 Δ a t 2 F x i j sin θ { ( 1 , 1 , 0 , 0 , ) · [ D i ] [ [ P M ( θ ) ] + [ R ] [ P M ( θ ) ] + [ P M ( θ ) ] [ R ] ] N j } ,
S 0 i j = K Δ ω s d Δ a F 0 i j ( ( 1 , 1 , 0 , 0 ) · [ D ι ] N j ) .
S r i j = K Δ ω s r Δ ω r d Δ d ( ( 1 , 1 , 0 , 0 ) · [ D ι ] [ T r ] N j ) ,
σ ( θ ) = 1 2 ( a 11 + a 12 + a 21 + a 22 ) .
p ( θ ) = ( a 11 + a 12 - a 21 - a 22 ) / ( a 11 + a 12 + a 21 + a 22 ) ,
p r ( θ ) = sin 2 θ / ( 1 + cos 2 θ ) ,