Abstract

The normalized light scattering polarization matrix has been measured for ocean water using an electrooptic light scattering polarimeter. Measurements were done on samples from the Atlantic and Pacific Oceans and the Gulf of Mexico. The polarization effects in the matrices were found to have, in general, a form which is similar to polarization effects in the Rayleigh scattering approximation; for example, all off-diagonal matrix elements except S12 and S21 were zero. Mueller matrix elements were calculated using a Mie computer code and compared to the measured matrices for ocean water. A simple one-component distribution was found to produce a reasonably good fit.

© 1984 Optical Society of America

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References

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  1. N. G. Jerlov, “Ocean Light Scattering Properties Related to Dynamic Conditions,” SPIE J. 8, 89 (1970).
  2. B. J. Price, V. H. Kollman, G. C. Salzman, “Light-Scatter Analysis of Microalgae,” Biophys. J. 22, 29 (1978).
    [CrossRef] [PubMed]
  3. R. Spinrad, “Optical Characteristics and Physiological State of Marine Phytoplankton,” AGU Ocean Sciences Meeting, 23–27 Jan. 1984, New Orleans, La.
  4. R. Reeves, Ed., Manual of Remote Sensing Vol. 2 (American Society of Photogrammetry, Va., 1975), p. 1573.
  5. G. F. Beardsley, “Mueller Scattering Matrix of Sea Water,” J. Opt. Soc. Am. 58, 52 (1968).
    [CrossRef]
  6. Y. A. Kadyshevich, Y. S. Lyubovtseva, I. N. Plakhina, “Measurement of Matrices for Light Scattered by Sea Water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 557 (1971).
  7. Y. A. Kadyshevich, Y. S. Lyubovtseva, G. V. Rozenberg, “Light-Scattering Matrices of Pacific and Atlantic Ocean Waters,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).
  8. Y. A. Kadyshevich, “Light-Scattering Matrices of Inshore Waters of the Baltic Sea,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 13, 77 (1977).
  9. H. C. van de Hulst, Light Scattering By Small Particles (Dover, New York, 1981).
  10. G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).
  11. R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M University (1978).
  12. R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
    [CrossRef] [PubMed]
  13. K. J. Voss, “Measurement of the Mueller Matrix for Ocean Water,” Ph.D. Thesis, Texas A&M University (1984).
  14. N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).
  15. J. R. Bottiger, E. S. Fry, R. C. Thompson, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1974), p. 283.
  16. A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  17. J. R. Bottiger, “Measured Light Scattering Matrices of Single Cubic Particles,” Ph.D. Thesis, Texas A&M University (1978).
  18. E. S. Fry, “Laser Intensity Regulator,” J. Opt. Soc. Am. 66, 1124 (1976).
  19. G. N. Plass, G. W. Kattawar, “Comment on: The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles. Part 1,” Appl. Opt. 10, 1172 (1971).
    [CrossRef]
  20. J. R. V. Zaneveld, D. M. Roach, H. Pak, “The Determination of the Index of Refraction Distribution of Oceanic Particulates,” J. Geophys. Res. 79, 4091 (1974).
    [CrossRef]
  21. O. B. Brown, H. R. Gordon, “Two Component Mie Scattering Models of Sargasso Sea Particles,” Appl. Opt. 12, 2461 (1973).
    [CrossRef] [PubMed]
  22. H. R. Gordon, O. B. Brown, “A Theoretical Model of Light Scattering by Sargasso Sea Particulates,” Limnol. Oceanogr. 17, 826 (1972).
    [CrossRef]
  23. E. S. Fry, G. W. Kattawar, “Relationships Between Elements of the Stokes Matrix,” Appl. Opt. 20, 2811 (1981).
    [CrossRef] [PubMed]
  24. G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep Sea Res. 15, 423 (1968).
  25. C. Houssier, K. Sauer, “Circular Dichroism and Magnetic Circular Dichroism of the Chlorophyll and Protochlorophyll Pigments,” Amer. J. Chem. Soc. 92, 779 (1970).
    [CrossRef]
  26. A. Morel, A. Bricaud, “Theoretical Results Concerning Light Absorption in a Discrete Medium, and Application to Specific Absorption of Phytoplankton,” Deep Sea Res. 28A, 1375 (1981).

1981 (2)

E. S. Fry, G. W. Kattawar, “Relationships Between Elements of the Stokes Matrix,” Appl. Opt. 20, 2811 (1981).
[CrossRef] [PubMed]

A. Morel, A. Bricaud, “Theoretical Results Concerning Light Absorption in a Discrete Medium, and Application to Specific Absorption of Phytoplankton,” Deep Sea Res. 28A, 1375 (1981).

1980 (1)

1978 (1)

B. J. Price, V. H. Kollman, G. C. Salzman, “Light-Scatter Analysis of Microalgae,” Biophys. J. 22, 29 (1978).
[CrossRef] [PubMed]

1977 (1)

Y. A. Kadyshevich, “Light-Scattering Matrices of Inshore Waters of the Baltic Sea,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 13, 77 (1977).

1976 (2)

Y. A. Kadyshevich, Y. S. Lyubovtseva, G. V. Rozenberg, “Light-Scattering Matrices of Pacific and Atlantic Ocean Waters,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

E. S. Fry, “Laser Intensity Regulator,” J. Opt. Soc. Am. 66, 1124 (1976).

1974 (1)

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The Determination of the Index of Refraction Distribution of Oceanic Particulates,” J. Geophys. Res. 79, 4091 (1974).
[CrossRef]

1973 (1)

1972 (1)

H. R. Gordon, O. B. Brown, “A Theoretical Model of Light Scattering by Sargasso Sea Particulates,” Limnol. Oceanogr. 17, 826 (1972).
[CrossRef]

1971 (2)

G. N. Plass, G. W. Kattawar, “Comment on: The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles. Part 1,” Appl. Opt. 10, 1172 (1971).
[CrossRef]

Y. A. Kadyshevich, Y. S. Lyubovtseva, I. N. Plakhina, “Measurement of Matrices for Light Scattered by Sea Water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 557 (1971).

1970 (3)

N. G. Jerlov, “Ocean Light Scattering Properties Related to Dynamic Conditions,” SPIE J. 8, 89 (1970).

A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113 (1970).
[CrossRef] [PubMed]

C. Houssier, K. Sauer, “Circular Dichroism and Magnetic Circular Dichroism of the Chlorophyll and Protochlorophyll Pigments,” Amer. J. Chem. Soc. 92, 779 (1970).
[CrossRef]

1968 (2)

G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep Sea Res. 15, 423 (1968).

G. F. Beardsley, “Mueller Scattering Matrix of Sea Water,” J. Opt. Soc. Am. 58, 52 (1968).
[CrossRef]

1853 (1)

G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).

Beardsley, G. F.

Bottiger, J. R.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
[CrossRef] [PubMed]

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1974), p. 283.

J. R. Bottiger, “Measured Light Scattering Matrices of Single Cubic Particles,” Ph.D. Thesis, Texas A&M University (1978).

Bricaud, A.

A. Morel, A. Bricaud, “Theoretical Results Concerning Light Absorption in a Discrete Medium, and Application to Specific Absorption of Phytoplankton,” Deep Sea Res. 28A, 1375 (1981).

Brown, O. B.

O. B. Brown, H. R. Gordon, “Two Component Mie Scattering Models of Sargasso Sea Particles,” Appl. Opt. 12, 2461 (1973).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “A Theoretical Model of Light Scattering by Sargasso Sea Particulates,” Limnol. Oceanogr. 17, 826 (1972).
[CrossRef]

Fry, E. S.

E. S. Fry, G. W. Kattawar, “Relationships Between Elements of the Stokes Matrix,” Appl. Opt. 20, 2811 (1981).
[CrossRef] [PubMed]

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
[CrossRef] [PubMed]

E. S. Fry, “Laser Intensity Regulator,” J. Opt. Soc. Am. 66, 1124 (1976).

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1974), p. 283.

Gagne, G.

Gordon, H. R.

O. B. Brown, H. R. Gordon, “Two Component Mie Scattering Models of Sargasso Sea Particles,” Appl. Opt. 12, 2461 (1973).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, “A Theoretical Model of Light Scattering by Sargasso Sea Particulates,” Limnol. Oceanogr. 17, 826 (1972).
[CrossRef]

Holland, A. C.

Houssier, C.

C. Houssier, K. Sauer, “Circular Dichroism and Magnetic Circular Dichroism of the Chlorophyll and Protochlorophyll Pigments,” Amer. J. Chem. Soc. 92, 779 (1970).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, “Ocean Light Scattering Properties Related to Dynamic Conditions,” SPIE J. 8, 89 (1970).

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

Kadyshevich, Y. A.

Y. A. Kadyshevich, “Light-Scattering Matrices of Inshore Waters of the Baltic Sea,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 13, 77 (1977).

Y. A. Kadyshevich, Y. S. Lyubovtseva, G. V. Rozenberg, “Light-Scattering Matrices of Pacific and Atlantic Ocean Waters,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

Y. A. Kadyshevich, Y. S. Lyubovtseva, I. N. Plakhina, “Measurement of Matrices for Light Scattered by Sea Water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 557 (1971).

Kattawar, G. W.

Kollman, V. H.

B. J. Price, V. H. Kollman, G. C. Salzman, “Light-Scatter Analysis of Microalgae,” Biophys. J. 22, 29 (1978).
[CrossRef] [PubMed]

Kullenberg, G.

G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep Sea Res. 15, 423 (1968).

Lyubovtseva, Y. S.

Y. A. Kadyshevich, Y. S. Lyubovtseva, G. V. Rozenberg, “Light-Scattering Matrices of Pacific and Atlantic Ocean Waters,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

Y. A. Kadyshevich, Y. S. Lyubovtseva, I. N. Plakhina, “Measurement of Matrices for Light Scattered by Sea Water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 557 (1971).

Morel, A.

A. Morel, A. Bricaud, “Theoretical Results Concerning Light Absorption in a Discrete Medium, and Application to Specific Absorption of Phytoplankton,” Deep Sea Res. 28A, 1375 (1981).

Pak, H.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The Determination of the Index of Refraction Distribution of Oceanic Particulates,” J. Geophys. Res. 79, 4091 (1974).
[CrossRef]

Plakhina, I. N.

Y. A. Kadyshevich, Y. S. Lyubovtseva, I. N. Plakhina, “Measurement of Matrices for Light Scattered by Sea Water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 557 (1971).

Plass, G. N.

Price, B. J.

B. J. Price, V. H. Kollman, G. C. Salzman, “Light-Scatter Analysis of Microalgae,” Biophys. J. 22, 29 (1978).
[CrossRef] [PubMed]

Roach, D. M.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The Determination of the Index of Refraction Distribution of Oceanic Particulates,” J. Geophys. Res. 79, 4091 (1974).
[CrossRef]

Rozenberg, G. V.

Y. A. Kadyshevich, Y. S. Lyubovtseva, G. V. Rozenberg, “Light-Scattering Matrices of Pacific and Atlantic Ocean Waters,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

Salzman, G. C.

B. J. Price, V. H. Kollman, G. C. Salzman, “Light-Scatter Analysis of Microalgae,” Biophys. J. 22, 29 (1978).
[CrossRef] [PubMed]

Sauer, K.

C. Houssier, K. Sauer, “Circular Dichroism and Magnetic Circular Dichroism of the Chlorophyll and Protochlorophyll Pigments,” Amer. J. Chem. Soc. 92, 779 (1970).
[CrossRef]

Spinrad, R.

R. Spinrad, “Optical Characteristics and Physiological State of Marine Phytoplankton,” AGU Ocean Sciences Meeting, 23–27 Jan. 1984, New Orleans, La.

Stokes, G. G.

G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).

Thompson, R. C.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
[CrossRef] [PubMed]

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1974), p. 283.

R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M University (1978).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering By Small Particles (Dover, New York, 1981).

Voss, K. J.

K. J. Voss, “Measurement of the Mueller Matrix for Ocean Water,” Ph.D. Thesis, Texas A&M University (1984).

Zaneveld, J. R. V.

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The Determination of the Index of Refraction Distribution of Oceanic Particulates,” J. Geophys. Res. 79, 4091 (1974).
[CrossRef]

Amer. J. Chem. Soc. (1)

C. Houssier, K. Sauer, “Circular Dichroism and Magnetic Circular Dichroism of the Chlorophyll and Protochlorophyll Pigments,” Amer. J. Chem. Soc. 92, 779 (1970).
[CrossRef]

Appl. Opt. (5)

Biophys. J. (1)

B. J. Price, V. H. Kollman, G. C. Salzman, “Light-Scatter Analysis of Microalgae,” Biophys. J. 22, 29 (1978).
[CrossRef] [PubMed]

Deep Sea Res. (2)

G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep Sea Res. 15, 423 (1968).

A. Morel, A. Bricaud, “Theoretical Results Concerning Light Absorption in a Discrete Medium, and Application to Specific Absorption of Phytoplankton,” Deep Sea Res. 28A, 1375 (1981).

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (3)

Y. A. Kadyshevich, Y. S. Lyubovtseva, I. N. Plakhina, “Measurement of Matrices for Light Scattered by Sea Water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 557 (1971).

Y. A. Kadyshevich, Y. S. Lyubovtseva, G. V. Rozenberg, “Light-Scattering Matrices of Pacific and Atlantic Ocean Waters,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

Y. A. Kadyshevich, “Light-Scattering Matrices of Inshore Waters of the Baltic Sea,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 13, 77 (1977).

J. Geophys. Res. (1)

J. R. V. Zaneveld, D. M. Roach, H. Pak, “The Determination of the Index of Refraction Distribution of Oceanic Particulates,” J. Geophys. Res. 79, 4091 (1974).
[CrossRef]

J. Opt. Soc. Am. (2)

E. S. Fry, “Laser Intensity Regulator,” J. Opt. Soc. Am. 66, 1124 (1976).

G. F. Beardsley, “Mueller Scattering Matrix of Sea Water,” J. Opt. Soc. Am. 58, 52 (1968).
[CrossRef]

Limnol. Oceanogr. (1)

H. R. Gordon, O. B. Brown, “A Theoretical Model of Light Scattering by Sargasso Sea Particulates,” Limnol. Oceanogr. 17, 826 (1972).
[CrossRef]

SPIE J. (1)

N. G. Jerlov, “Ocean Light Scattering Properties Related to Dynamic Conditions,” SPIE J. 8, 89 (1970).

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).

Other (8)

R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M University (1978).

J. R. Bottiger, “Measured Light Scattering Matrices of Single Cubic Particles,” Ph.D. Thesis, Texas A&M University (1978).

K. J. Voss, “Measurement of the Mueller Matrix for Ocean Water,” Ph.D. Thesis, Texas A&M University (1984).

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1974), p. 283.

R. Spinrad, “Optical Characteristics and Physiological State of Marine Phytoplankton,” AGU Ocean Sciences Meeting, 23–27 Jan. 1984, New Orleans, La.

R. Reeves, Ed., Manual of Remote Sensing Vol. 2 (American Society of Photogrammetry, Va., 1975), p. 1573.

H. C. van de Hulst, Light Scattering By Small Particles (Dover, New York, 1981).

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Figures (7)

Fig. 1
Fig. 1

(a) The average Mueller matrix of the Pacific and Atlantic Oceans. The x axis of each graph corresponds to the scattering angle, the y axis corresponds to the normalized matrix element value. (b) The calculated Mueller matrix of particles in the Rayleigh-Gans approximation.

Fig. 2
Fig. 2

Volume scattering function for three samples.

Fig. 3
Fig. 3

Samples from the Atlantic Ocean at a position 40° 08.46′N, 70° 56.68′W: (a) 28-m depth, (b) 143-m depth.

Fig. 4
Fig. 4

Mueller matrix of calculation with index of refraction 1.05–0.01i and size distribution dN/dD = KD4

Fig. 5
Fig. 5

Solid line, Mueller matrix elements of Fig. 4 modified to conform with S22 for ocean water; dashed line, ocean water data of Fig. 1(a).

Fig. 6
Fig. 6

Mueller matrix of calculation with index of refraction and size distribution after Zaneveld et al.20

Fig. 7
Fig. 7

Calculation of Mueller matrix elements for Platymonas suecica.

Tables (6)

Tables Icon

Table I Mean Data Points and Standard Deviations of the Mueller Matrix for Ocean Water Samples from the Pacific and Atlantic Oceans, First Row

Tables Icon

Table II Mean Data Points and Standard Deviations of the Mueller Matrix for Ocean Water Samples from the Pacific and Atlantic Oceans, Second Row

Tables Icon

Table III Mean Data Points and Standard Deviations of the Mueller Matrix for Ocean Water Samples from the Pacific and Atlantic Oceans, Third Row

Tables Icon

Table IV Mean Data Points and Standard Deviations of the Mueller Matrix for Ocean Water Samples from the Pacific and Atlantic Oceans, Fourth Row

Tables Icon

Table V Mean Data Points and Standard Deviations of the S32 Element for Rayleigh Standards

Tables Icon

Table VI Average Nonzero Matrix Elements and Standard Deviations for the Ensemble of Samples

Equations (13)

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

I = E l 2 + E r 2 , U = 2 E l E r cos δ , Q = E l 2 - E r 2 , V = 2 E l E r sin δ ,
E = E l cos ( k z - w t + ɛ l ) l ^ + E r cos ( k z - w t + ɛ r ) r ^ , δ = ɛ l - ɛ r ,
[ I Q U V ] = [ M 11 M 12 M 13 M 11 M21 M22 M23 M24 M31 M32 M33 M34 M41 M42 M43 M44 ] [ I Q U V ] ,
[ 1 S 12 S 13 S 14 S21 S22 S23 S24 S31 S32 S33 S34 S41 S42 S43 S44 ] ,
i s = AneN ,
i n = A 2 e 2 n ( l - n ) N B ,
N A = K ,
i n = 2 A e 2 n ( l - n ) B K .
1 1.59 1.92 1 2.32 3.70 4.46 1.59 3.70 5.88 7.09 1.92 4.46 7.09 8.62
[ 1 - d 0 0 - e 1 - a 0 0 0 0 b f 0 0 - g c ] ,
( M 11 + M 21 ) 2 - ( M 12 + M 22 ) 2 > ( M 13 + M 23 ) 2 + ( M 14 + M2 4 ) 2 .
d < 1 - a / 2.
d 2 + c 2 < ( 1 - a / 2 ) 2 .

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