Abstract

It is shown that the complex index of refraction of a given particle-size distribution may be calculated if the particle extinction coefficient and the particle absorption coefficient are known. If the particles are assumed to be nonabsorbing, a real index of refraction may be calculated from the ratio of light scattering at 45° from the forward for two wavelengths. Application of the method to two stations off Ecuador indicates that the particle index of refraction can be determined with sufficient accuracy to become an important parameter in the study of the oceans.

© 1973 Optical Society of America

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References

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  1. V. M. Pavlov and B. N. Grechushnikov, Some Aspects of the Theory of Daylight Polarization Indices, U. S. Dept. of Commerce, Joint Publication Research Session, Report No. 36 (U.S. Dept. of Commerce, Washington, D.C., 1966), p.25.
  2. H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
    [CrossRef]
  3. H. R. Gordon and O. B. Brown, Trans. Am. Geophys. Union 52, 245 (1971).
    [CrossRef]
  4. G. Mie, Ann. Phys. (Leipz.) 25, 377 (1908).
    [CrossRef]
  5. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 172–199.
  6. W. V. Burt, J. Mar. Res. 15, 76 (1956).
  7. K. L. Carder, Ph.D. thesis, Oregon State University, Corvallis (1970).
  8. N. G. Jerlov, Report of the Swedish Deep-Sea Expedition,1947–48, Vol. 3 (Elanders Boktryckeri Aktiebolag, Göteborg, 1953), pp. 73–97.
  9. G. D. Deirmendjian, in Electromagnetic Scattering, edited by M. Kerker, (Macmillan, New York, 1963), p. 171.
  10. G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
    [CrossRef]

1971 (1)

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

1970 (2)

H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
[CrossRef]

G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
[CrossRef]

1956 (1)

W. V. Burt, J. Mar. Res. 15, 76 (1956).

1908 (1)

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

Beardsley, G. F.

G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
[CrossRef]

H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
[CrossRef]

Brown, O. B.

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

Burt, W. V.

W. V. Burt, J. Mar. Res. 15, 76 (1956).

Carder, K. L.

G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
[CrossRef]

K. L. Carder, Ph.D. thesis, Oregon State University, Corvallis (1970).

Curl, H.

H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
[CrossRef]

Deirmendjian, G. D.

G. D. Deirmendjian, in Electromagnetic Scattering, edited by M. Kerker, (Macmillan, New York, 1963), p. 171.

Gordon, H. R.

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

Grechushnikov, B. N.

V. M. Pavlov and B. N. Grechushnikov, Some Aspects of the Theory of Daylight Polarization Indices, U. S. Dept. of Commerce, Joint Publication Research Session, Report No. 36 (U.S. Dept. of Commerce, Washington, D.C., 1966), p.25.

Heath, G. R.

H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Report of the Swedish Deep-Sea Expedition,1947–48, Vol. 3 (Elanders Boktryckeri Aktiebolag, Göteborg, 1953), pp. 73–97.

Lundgren, B.

G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
[CrossRef]

Mie, G.

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

Pak, H.

G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
[CrossRef]

H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
[CrossRef]

Pavlov, V. M.

V. M. Pavlov and B. N. Grechushnikov, Some Aspects of the Theory of Daylight Polarization Indices, U. S. Dept. of Commerce, Joint Publication Research Session, Report No. 36 (U.S. Dept. of Commerce, Washington, D.C., 1966), p.25.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 172–199.

Ann. Phys. (Leipz.) (1)

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

J. Geophys. Res. (1)

G. F. Beardsley, H. Pak, K. L. Carder, and B. Lundgren, J. Geophys. Res. 75, 2837 (1970).
[CrossRef]

J. Mar. Res. (1)

W. V. Burt, J. Mar. Res. 15, 76 (1956).

Limnol. Oceanogr. (1)

H. Pak, G. F. Beardsley, G. R. Heath, and H. Curl, Limnol. Oceanogr. 15, 683 (1970).
[CrossRef]

Trans. Am. Geophys. Union (1)

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

Other (5)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 172–199.

K. L. Carder, Ph.D. thesis, Oregon State University, Corvallis (1970).

N. G. Jerlov, Report of the Swedish Deep-Sea Expedition,1947–48, Vol. 3 (Elanders Boktryckeri Aktiebolag, Göteborg, 1953), pp. 73–97.

G. D. Deirmendjian, in Electromagnetic Scattering, edited by M. Kerker, (Macmillan, New York, 1963), p. 171.

V. M. Pavlov and B. N. Grechushnikov, Some Aspects of the Theory of Daylight Polarization Indices, U. S. Dept. of Commerce, Joint Publication Research Session, Report No. 36 (U.S. Dept. of Commerce, Washington, D.C., 1966), p.25.

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Figures (3)

F. 1
F. 1

The total scattering coefficient per particle bp/Nπ×10−6 m−1 as a function of the index-of-refraction parameter k = (2π/λ)|npmw|×10−6 m−1 and the parameter A of the exponential particle-size distribution for the case of nonabsorbing particles (np = 0).

F. 2
F. 2

The exponential particle-size distribution parameter A as a function of the ratio of light scattered at 45° for two wavelengths β451)/β452) with the difference between the particulate and water indices of refraction |npmw| as a parameter. Dots and circles mark samples taken off the coast of Ecuador from stations 4-2 and 4-8, respectively. λ1 = 436 nm, λ2 = 546 nm.

F. 3
F. 3

The difference between the particulate and water indices of refraction |npmw| as a function of depth for the two stations of Fig. 2.

Equations (20)

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| m 1 | 1 ,
Q ext = 2 4 e ρ tan β cos β ρ sin ( ρ β ) 4 e ρ tan β ( cos β ρ ) 2 cos ( ρ 2 β ) + 4 ( cos β ρ ) 2 cos 2 β
Q abs = 1 + e 2 ρ tan β ρ tan β + e 2 ρ tan β 1 2 ( ρ tan β ) 2 ,
ρ = 2 π D λ | n p m w 1 | ,
ρ = 2 π D λ vac | n p m w | .
k = 2 π λ vac | n p m w |
tan β = n p / ( n p m w ) .
c p = 0 f ( D ) Q ext ( k , D , β ) π D 2 4 d D .
a p = 0 f ( D ) Q abs ( k , D , β ) π D 2 4 d D .
f ( D ) d D = N A e A D d D .
g ( D ) = D N A e A D d D = N e A D .
c p = 0 N A e A D π D 2 4 { 2 4 e k D tan β cos β k D sin ( k D β ) 4 e k D tan β ( cos β k D ) 2 cos ( k D 2 β ) + 4 ( cos β k D ) 2 cos 2 β } d D .
c p = N A π { 1 A 3 2 cos 2 β A + k tan β [ ( A + k tan β ) 2 + k 2 ] 2 + sin 2 β 2 k [ ( A + k tan β ) 2 k 2 ] [ ( A + k tan β ) 2 + k 2 ] 2 ( cos β k ) 2 cos 2 β A + k tan β ( A + k tan β ) 2 + k 2 cos 2 β sin 2 β k 1 ( A + k tan β ) 2 + k 2 + ( cos β k ) 2 cos 2 β A } .
a p = 0 N A e A D π D 2 4 [ 1 + e 2 k D tan β k D tan β + e 2 k D tan β 1 2 ( k D tan β ) 2 ] d D
a p = N π 2 [ 1 A 2 1 ( A + 2 k tan β ) 2 ] .
k tan β = 2 π λ n p
k = 2 π λ | n p m w |
b p ( λ 1 ) b p ( λ 2 ) = β 45 ( λ 1 ) β 45 ( λ 2 ) .
b p ( λ 1 ) b p ( λ 2 ) = β 45 ( λ 1 ) β 45 ( λ 2 ) = 1 / A 2 + ( k 1 2 A 2 ) / ( A 2 + k 1 2 ) 2 1 / A 2 + ( k 2 2 A 2 ) / ( A 2 + k 2 2 ) 2 ,
k 1 = 2 π λ 1 | n p m w | and k 2 = 2 π λ 2 | n p m w | .