Abstract

Narrow angle light scattering measurements were made for various sizes of spherical particles suspended in water. These were compared to calculated theoretical scattering values as derived from the theory of Mie (1908). Through measurements with different particle concentrations at angles between 0.2° and 0.7° the effect of the unscattered main beam light was removed. Results agreed well with Mie theory for these angles.

© 1978 Optical Society of America

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References

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  1. R. E. Morrison, “Studies on the Optical Properties of Seawater, Argus Island in the North Atlantic Ocean and in Long Island and Block Island Sounds,” Ph.D. Thesis, New York U., New York (1967).
  2. H. Hodara, AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).
  3. W. Wells, H. Hodara, O. Wilson, “Long Range Vision in Sea Water,” Final Report ARPA order 1737, Tetra Tech. Inc., Pasadena, Calif. (1972).
  4. L. Mertens, W. Wells, As described by H. Hodara, Ed., AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).
  5. S. Q. Duntley, J. Opt. Soc. Am. 53, 214 (1963).
    [CrossRef]
  6. G. Kullenberg, Deep Sea Res. 15, 423 (1968).
  7. D. Bauer, A. Morel, Ann. Geophys. 23, 109 (1967).
  8. R. N. Sokolov, F. A. Kudravitskii, G. D. Petrov, Izv. Atmos. Oceanic Phys. 7, 1015 (1971).
  9. T. J. Petzold, SIO Ref. 72–78, 79 pp. (1972).
  10. W. R. McCluney, Appl. Opt. 13, 548 (1974).
    [CrossRef] [PubMed]
  11. D. Bauer, A. Ivanoff, Compte Rend. Acad. Sci. Paris 260, 631 (1965).
  12. E. J. Softley, J. F. Dilley, in Ocean 72. IEEE International Conference of Engineering in the Ocean Environment, Newport (1972).
  13. R. C. Honey, G. P. Sorenson, AGARD Conf. Proc. No. 77, 39–39.7 (1970).
  14. A. Morel, J. Chem. Phys. 10, 1359 (1966).
  15. M. V. Kozlyaninov, Tr. Inst. Okeanol., Akad. Nauk SSR 25, 134 (1957).
  16. Y. E. Ochakovsky, U.S. Dept. Comm., Joint Publ. Res. Ser., Rep.36(816), 98–105 (1966).
  17. F. Nyfeller, AGARD Conf. Proc. No. 77, 31-1-8 (1970).
  18. A. Morel, Rapport 10, CNRS (1973).
  19. O. B. Brown, H. R. Gordon, U. MiamiPub. MIAPHOP-71.5 (1971).
  20. N. G. Jerlov, Marine Optics (Elsevier, New York, 1970), 231 pp.
  21. J. R. V. Zaneveld, H. Pak, J. Opt. Soc. Am. 63, 321 (1973).
    [CrossRef]
  22. J. R. V. Zaneveld, D. M. Roach, H. Pak, J. Geophys. Res. 79, 4536 (1974).
    [CrossRef]
  23. G. Mie, Ann. Phys. 25, 377 (1908).
    [CrossRef]
  24. I. N. Salganik, K. S. Shifrin, Light Scattering Tables (USSR Academy of Sciences, P. P. Shirskov Institute of OceanographyLeningrad, 1973).
  25. H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957, 470 pp.
  26. H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 52, 245 (1971).
    [CrossRef]

1974 (2)

W. R. McCluney, Appl. Opt. 13, 548 (1974).
[CrossRef] [PubMed]

J. R. V. Zaneveld, D. M. Roach, H. Pak, J. Geophys. Res. 79, 4536 (1974).
[CrossRef]

1973 (1)

1971 (2)

H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 52, 245 (1971).
[CrossRef]

R. N. Sokolov, F. A. Kudravitskii, G. D. Petrov, Izv. Atmos. Oceanic Phys. 7, 1015 (1971).

1970 (2)

R. C. Honey, G. P. Sorenson, AGARD Conf. Proc. No. 77, 39–39.7 (1970).

F. Nyfeller, AGARD Conf. Proc. No. 77, 31-1-8 (1970).

1968 (1)

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

1967 (1)

D. Bauer, A. Morel, Ann. Geophys. 23, 109 (1967).

1966 (1)

A. Morel, J. Chem. Phys. 10, 1359 (1966).

1965 (1)

D. Bauer, A. Ivanoff, Compte Rend. Acad. Sci. Paris 260, 631 (1965).

1963 (1)

1957 (1)

M. V. Kozlyaninov, Tr. Inst. Okeanol., Akad. Nauk SSR 25, 134 (1957).

1908 (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Bauer, D.

D. Bauer, A. Morel, Ann. Geophys. 23, 109 (1967).

D. Bauer, A. Ivanoff, Compte Rend. Acad. Sci. Paris 260, 631 (1965).

Brown, O. B.

H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 52, 245 (1971).
[CrossRef]

O. B. Brown, H. R. Gordon, U. MiamiPub. MIAPHOP-71.5 (1971).

Dilley, J. F.

E. J. Softley, J. F. Dilley, in Ocean 72. IEEE International Conference of Engineering in the Ocean Environment, Newport (1972).

Duntley, S. Q.

Gordon, H. R.

H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 52, 245 (1971).
[CrossRef]

O. B. Brown, H. R. Gordon, U. MiamiPub. MIAPHOP-71.5 (1971).

Hodara, H.

H. Hodara, AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).

W. Wells, H. Hodara, O. Wilson, “Long Range Vision in Sea Water,” Final Report ARPA order 1737, Tetra Tech. Inc., Pasadena, Calif. (1972).

Honey, R. C.

R. C. Honey, G. P. Sorenson, AGARD Conf. Proc. No. 77, 39–39.7 (1970).

Ivanoff, A.

D. Bauer, A. Ivanoff, Compte Rend. Acad. Sci. Paris 260, 631 (1965).

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, New York, 1970), 231 pp.

Kozlyaninov, M. V.

M. V. Kozlyaninov, Tr. Inst. Okeanol., Akad. Nauk SSR 25, 134 (1957).

Kudravitskii, F. A.

R. N. Sokolov, F. A. Kudravitskii, G. D. Petrov, Izv. Atmos. Oceanic Phys. 7, 1015 (1971).

Kullenberg, G.

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

McCluney, W. R.

Mertens, L.

L. Mertens, W. Wells, As described by H. Hodara, Ed., AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).

Mie, G.

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Morel, A.

D. Bauer, A. Morel, Ann. Geophys. 23, 109 (1967).

A. Morel, J. Chem. Phys. 10, 1359 (1966).

A. Morel, Rapport 10, CNRS (1973).

Morrison, R. E.

R. E. Morrison, “Studies on the Optical Properties of Seawater, Argus Island in the North Atlantic Ocean and in Long Island and Block Island Sounds,” Ph.D. Thesis, New York U., New York (1967).

Nyfeller, F.

F. Nyfeller, AGARD Conf. Proc. No. 77, 31-1-8 (1970).

Ochakovsky, Y. E.

Y. E. Ochakovsky, U.S. Dept. Comm., Joint Publ. Res. Ser., Rep.36(816), 98–105 (1966).

Pak, H.

J. R. V. Zaneveld, D. M. Roach, H. Pak, J. Geophys. Res. 79, 4536 (1974).
[CrossRef]

J. R. V. Zaneveld, H. Pak, J. Opt. Soc. Am. 63, 321 (1973).
[CrossRef]

Petrov, G. D.

R. N. Sokolov, F. A. Kudravitskii, G. D. Petrov, Izv. Atmos. Oceanic Phys. 7, 1015 (1971).

Petzold, T. J.

T. J. Petzold, SIO Ref. 72–78, 79 pp. (1972).

Roach, D. M.

J. R. V. Zaneveld, D. M. Roach, H. Pak, J. Geophys. Res. 79, 4536 (1974).
[CrossRef]

Salganik, I. N.

I. N. Salganik, K. S. Shifrin, Light Scattering Tables (USSR Academy of Sciences, P. P. Shirskov Institute of OceanographyLeningrad, 1973).

Shifrin, K. S.

I. N. Salganik, K. S. Shifrin, Light Scattering Tables (USSR Academy of Sciences, P. P. Shirskov Institute of OceanographyLeningrad, 1973).

Softley, E. J.

E. J. Softley, J. F. Dilley, in Ocean 72. IEEE International Conference of Engineering in the Ocean Environment, Newport (1972).

Sokolov, R. N.

R. N. Sokolov, F. A. Kudravitskii, G. D. Petrov, Izv. Atmos. Oceanic Phys. 7, 1015 (1971).

Sorenson, G. P.

R. C. Honey, G. P. Sorenson, AGARD Conf. Proc. No. 77, 39–39.7 (1970).

Van De Hulst, H. C.

H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957, 470 pp.

Wells, W.

L. Mertens, W. Wells, As described by H. Hodara, Ed., AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).

W. Wells, H. Hodara, O. Wilson, “Long Range Vision in Sea Water,” Final Report ARPA order 1737, Tetra Tech. Inc., Pasadena, Calif. (1972).

Wilson, O.

W. Wells, H. Hodara, O. Wilson, “Long Range Vision in Sea Water,” Final Report ARPA order 1737, Tetra Tech. Inc., Pasadena, Calif. (1972).

Zaneveld, J. R. V.

J. R. V. Zaneveld, D. M. Roach, H. Pak, J. Geophys. Res. 79, 4536 (1974).
[CrossRef]

J. R. V. Zaneveld, H. Pak, J. Opt. Soc. Am. 63, 321 (1973).
[CrossRef]

AGARD Conf. Proc. No. 77 (2)

R. C. Honey, G. P. Sorenson, AGARD Conf. Proc. No. 77, 39–39.7 (1970).

F. Nyfeller, AGARD Conf. Proc. No. 77, 31-1-8 (1970).

Ann. Geophys. (1)

D. Bauer, A. Morel, Ann. Geophys. 23, 109 (1967).

Ann. Phys. (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Appl. Opt. (1)

Compte Rend. Acad. Sci. Paris (1)

D. Bauer, A. Ivanoff, Compte Rend. Acad. Sci. Paris 260, 631 (1965).

Deep Sea Res. (1)

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

Izv. Atmos. Oceanic Phys. (1)

R. N. Sokolov, F. A. Kudravitskii, G. D. Petrov, Izv. Atmos. Oceanic Phys. 7, 1015 (1971).

J. Chem. Phys. (1)

A. Morel, J. Chem. Phys. 10, 1359 (1966).

J. Geophys. Res. (1)

J. R. V. Zaneveld, D. M. Roach, H. Pak, J. Geophys. Res. 79, 4536 (1974).
[CrossRef]

J. Opt. Soc. Am. (2)

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

M. V. Kozlyaninov, Tr. Inst. Okeanol., Akad. Nauk SSR 25, 134 (1957).

Trans. Am. Geophys. Union (1)

H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 52, 245 (1971).
[CrossRef]

Other (12)

I. N. Salganik, K. S. Shifrin, Light Scattering Tables (USSR Academy of Sciences, P. P. Shirskov Institute of OceanographyLeningrad, 1973).

H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957, 470 pp.

E. J. Softley, J. F. Dilley, in Ocean 72. IEEE International Conference of Engineering in the Ocean Environment, Newport (1972).

Y. E. Ochakovsky, U.S. Dept. Comm., Joint Publ. Res. Ser., Rep.36(816), 98–105 (1966).

A. Morel, Rapport 10, CNRS (1973).

O. B. Brown, H. R. Gordon, U. MiamiPub. MIAPHOP-71.5 (1971).

N. G. Jerlov, Marine Optics (Elsevier, New York, 1970), 231 pp.

T. J. Petzold, SIO Ref. 72–78, 79 pp. (1972).

R. E. Morrison, “Studies on the Optical Properties of Seawater, Argus Island in the North Atlantic Ocean and in Long Island and Block Island Sounds,” Ph.D. Thesis, New York U., New York (1967).

H. Hodara, AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).

W. Wells, H. Hodara, O. Wilson, “Long Range Vision in Sea Water,” Final Report ARPA order 1737, Tetra Tech. Inc., Pasadena, Calif. (1972).

L. Mertens, W. Wells, As described by H. Hodara, Ed., AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973).

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Figures (8)

Fig. 1
Fig. 1

Theoretical scattering values β(θ) for 1 particle/m3 and for diameters indicated. Values were obtained from Salganik and Shifrin.24θ is the angle from the main beam. Particles have an index of refraction of 1.15 relative to pure water.

Fig. 2
Fig. 2

Schematic drawing of the laboratory setup of the small angle scattering meter.

Fig. 3
Fig. 3

An elementary scattering volume Adx scattering light with the solid angle wθ at an angle θ from the main beam.

Fig. 4
Fig. 4

Experimental results obtained with the narrow angle scattering meter showing the maximum and minimum values of [Pr(θ)]/[Pr(θ)] for eleven values of θ and the mean value over the complete angular range. Pr(θ) is the power received at an angle θ from the main beam. Pr(0) is the power received at 0° from the main beam.

Fig. 5
Fig. 5

Theoretical and experimental scattering maxima and minima at small angles for suspended particles of 5.2-μm diam.

Fig. 6
Fig. 6

Theoretical and experimental scattering maxima and minima at small angles for suspended particles of 8-μm diam.

Fig. 7
Fig. 7

Theoretical and experimental scattering maxima and minima at small angles for suspended particles of 9.8-μm diam.

Fig. 8
Fig. 8

A qualitative comparison of mean scattering results obtained in this experiment, results of previous experiments, and the theoretical results obtained from the theory of Mie,23 normalized to β(θ) = 1m−1 at θ = 0.5°.

Equations (19)

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P r = P β + P n .
β ( θ ) = [ d I ( θ ) ] / ( E d υ ) ( Jerlov 20 ) ,
d I ( θ ) = { d P β exp [ c ( L x ) ] / w θ ,
E = [ P 0 exp ( c x ) ] / A .
β ( θ ) = d P β exp [ c ( L x ) ] w θ P 0 exp ( c x ) A A d x
d P β = β ( θ ) w θ P 0 exp ( c L ) .
P β = 0 L d P β d x = β ( θ ) w θ P 0 L exp ( c L ) .
P r = P n + β ( θ ) w θ P 0 L exp ( c L ) .
β ( θ ) = β p ( θ ) + β w ( θ ) ,
P r = P n + [ β p ( θ ) + β w ( θ ) ] w θ P 0 L exp ( c L ) .
P r 1 = P n 1 + [ β p ( θ ) + β w ( θ ) ] w θ P 0 L exp ( c 1 L ) ,
P r 2 = P n 1 exp [ ( c 2 c 1 ) L ] + [ F β p ( θ ) + β w ( θ ) ] w θ P 0 L exp ( c 2 L ) .
T 1 = exp ( c 1 L ) , T 2 = exp ( c 2 L ) , P n 2 = P n 1 exp ( c 2 L ) exp ( c 1 L ) = P n 1 exp [ ( c 2 c 1 ) L ] .
P r 1 exp [ ( c 2 c 1 ) L ] P r 2 = [ β p ( θ ) + β w ( θ ) ] w θ P 0 L exp ( c 2 L ) [ F β p ( θ ) + β w ( θ ) ] w θ P 0 L exp ( c 2 L )
= ( 1 F ) β p ( θ ) w θ P 0 L exp ( c 2 L ) ,
β p ( θ ) = P r 1 ( θ ) exp ( c 1 L ) P r 2 ( θ ) exp ( c 2 L ) ( 1 F ) w θ P 0 L .
T 1 = exp ( c 1 L ) = [ P r 1 ( ° ) ] / P 0 ,
T 2 = exp ( c 2 L ) = [ P r 2 ( 0 ) ] / P 0 .
P r 1 ( θ ) P r 1 ( 0 ) P r 2 ( θ ) P r 2 ( 0 ) ( 1 F ) w θ L .

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