Abstract

Based on the theory by Aden and Kerker, computations of the scattering and absorption properties for concentric spherical water and soot particles have been performed for visible and infrared wavelengths. The complex dielectric constant for the kernel was assumed to be frequency independent; for the water shell it was assumed to be constant over the visible range only. Computations were performed for size parameter values up to 250. Results indicate that, for compound particles with a nucleus smaller than about one-tenth of the total diameter of the particle, the optical properties are almost completely determined by the outer shell.

© 1965 Optical Society of America

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References

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  1. A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
    [Crossref]
  2. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. M. Kerker, J. P. Kratohvil, E. Matijevic, J. Opt. Soc. Am. 52, 551 (1962).
    [Crossref]
  4. K. S. Shifrin, Dokl. Akad. Nauk SSSR 94, 673 (1954).
  5. K. S. Shifrin, Scattering of Light in a Turbid Medium (State Publishing House of Theoretical and Technical Literature, Moscow, 1951).

1962 (1)

1954 (1)

K. S. Shifrin, Dokl. Akad. Nauk SSSR 94, 673 (1954).

1951 (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[Crossref]

Aden, A. L.

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[Crossref]

Kerker, M.

Kratohvil, J. P.

Matijevic, E.

Shifrin, K. S.

K. S. Shifrin, Dokl. Akad. Nauk SSSR 94, 673 (1954).

K. S. Shifrin, Scattering of Light in a Turbid Medium (State Publishing House of Theoretical and Technical Literature, Moscow, 1951).

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Dokl. Akad. Nauk SSSR (1)

K. S. Shifrin, Dokl. Akad. Nauk SSSR 94, 673 (1954).

J. Appl. Phys. (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[Crossref]

J. Opt. Soc. Am. (1)

Other (2)

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

K. S. Shifrin, Scattering of Light in a Turbid Medium (State Publishing House of Theoretical and Technical Literature, Moscow, 1951).

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Figures (5)

Fig. 1
Fig. 1

(a)–(f) Efficiency factors of absorption, scattering, and extinction for concentric soot-water particles of specific ratios b/a = 1, 1.1, 1.2, 1.5, 2,5, respectively, as function of the size parameter, for visible light.

Fig. 2
Fig. 2

Efficiency factor for absorption for constant total particle size as function of the specific ratio.

Fig. 3
Fig. 3

(a)–(d). Angular scattering intensities for concentric particles of various specific ratios b/a and various total size parameters.

Fig. 4
Fig. 4

Degree of polarization for concentric particles of various specific ratios and size parameters.

Fig. 5
Fig. 5

Efficiency factor of absorption for concentric soot–water particles as function of wavelength in the infrared region.

Tables (2)

Tables Icon

Table I Absorption Efficiency Factor Qaa

Tables Icon

Table II Complex Refractive Index for Water in the Infrared Regiona

Equations (13)

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i λ = i λ 0 λ 2 4 π 2 ( i λ 1 + i λ 2 2 ) ,
i 1 = | I 1 | 2 = | m = 1 2 m + 1 m ( m + 1 ) [ a m π m + b m τ m ] 2 , i 2 = | I 2 | 2 = | m = 1 2 m + 1 m ( m + 1 ) [ a m τ m + b m π m ] 2 .
Q e = 2 ν 2 m = 1 ( 2 m + 1 ) R e ( a m + b m ) , Q s = 2 ν 2 m = 1 ( 2 m + 1 ) ( | a m | 2 + | b m | 2 ) .
z m ( 1 ) ( y ) = ( π 2 y ) ½ J m + 1 2 ( y ) , spherical Besel function of first kind , z m ( 3 ) ( y ) = ( π 2 y ) ½ H ( 2 ) m + 1 2 ( y ) , spherical Hankel function of second kind .
z m ( y ) = 2 m 1 y z m 1 ( y ) z m 2 ( y ) .
η m ( 1 ) ( y ) = d [ y z m ( 1 ) ( y ) ] y d y ; η m ( 3 ) ( y ) = d [ yz m ( 3 ) ( y ) ] ydy ,
η m ( y ) = m y z m ( y ) + z m 1 ( y )
B 1 = η m ( 1 ) ( x 1 ) [ z m ( 3 ) ( x 2 ) z m ( 1 ) ( x 3 ) z m ( 1 ) ( x 2 ) z m ( 3 ) ( x 3 ) ] , B 2 = z m ( 1 ) ( x 1 ) [ η m ( 1 ) ( x 2 ) z m ( 3 ) ( x 3 ) η m ( 3 ) ( x 2 ) z m ( 1 ) ( x 3 ) ] , B 3 = η m ( 1 ) ( x 1 ) [ z m ( 1 ) ( x 2 ) η m ( 1 ) ( x 3 ) z m ( 3 ) ( x 2 ) η m ( 1 ) ( x 3 ) ] , B 4 = z m ( 1 ) ( x 1 ) [ η m ( 1 ) ( x 3 ) η m ( 3 ) ( x 2 ) η m ( 1 ) ( x 2 ) η m ( 3 ) ( x 3 ) ] ,
A 1 = Y 2 2 B 1 + Y 1 Y 2 B 2 , A 2 = Y 2 B 3 + Y 1 B 4 , A 3 = Y 2 2 B 4 + Y 1 Y 2 B 3 , A 4 = Y 2 B 2 + Y 1 B 1 .
a m = A 1 η m ( 1 ) ( x 4 ) + Y 3 A 2 z m ( 1 ) ( x 4 ) A 1 η m ( 3 ) ( x 4 ) + Y 3 A 2 z m ( 3 ) ( x 4 ) , b m = A 3 η m ( 1 ) ( x 4 ) + Y 3 A 4 η m ( 1 ) ( x 4 ) A 3 z m ( 3 ) ( x 4 ) + Y 3 A 4 η m ( 3 ) ( x 4 ) .
π m ( cos θ ) = d P m ( cos θ ) d ( cos θ ) , τ m ( cos θ ) = ( cos θ ) π m ( 1 cos 2 θ ) d 2 P m ( cos θ ) d ( cos θ ) 2
π 0 = 0 ; π 1 = 1 , π m ( cos θ ) = 2 m 1 m 1 ( cos θ ) π m 1 m m 1 π m 2 , τ m ( cos θ ) = m ( cos θ ) π m ( m + 1 ) π m 1 .
θ = 0 ° ( 5 ° ) 180 ° for all ν < 2 , θ = 0 ° ( 1 ° ) 20 ° ( 10 ° ) 160 ° ( 1 ° ) 180 ° for ν 2 .

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