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References

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  1. K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951), NASA Technical Translation TT477, 1968.
  2. K. S. Shifrin, V. F. Raskin, “Average indicatrice corresponding gamma-distribution,” in Proceedings, Voyekov’s Main Geophysical Observatory (Leningrad, 1961), Vol. 109.
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Raskin, V. F.

K. S. Shifrin, V. F. Raskin, “Average indicatrice corresponding gamma-distribution,” in Proceedings, Voyekov’s Main Geophysical Observatory (Leningrad, 1961), Vol. 109.

Shifrin, K. S.

K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951), NASA Technical Translation TT477, 1968.

K. S. Shifrin, V. F. Raskin, “Average indicatrice corresponding gamma-distribution,” in Proceedings, Voyekov’s Main Geophysical Observatory (Leningrad, 1961), Vol. 109.

van de Hulst, H. C.

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

Other (3)

K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951), NASA Technical Translation TT477, 1968.

K. S. Shifrin, V. F. Raskin, “Average indicatrice corresponding gamma-distribution,” in Proceedings, Voyekov’s Main Geophysical Observatory (Leningrad, 1961), Vol. 109.

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

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Equations (24)

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f ( a ) = A a m exp ( - p a ) ,
a ¯ = 0 a A a m exp ( - p a ) d a 0 A a m exp ( - p a ) d a = m + 1 P .
A = N P m + 1 m ! ,
f ( a ) = N P m + 1 m ! a m exp ( - p a ) .
I ¯ ( β ) = 0 I ( β , a ) · f ( a ) d a ,
I ( β , a ) = L a 6 f 2 ( q ) ,
L = I 0 α 2 128 π 6 9 λ 4 ( 1 + cos 2 β ) ,
f ( q ) = 3 q 3 · ( sin q - q cos q ) ,
α = 3 4 π n 2 - 1 n 2 + 2 ,
q = K a             K = 4 π λ sin β 2 .
I ¯ ( β ) = I R ( a ¯ ) ζ m ( U ) ,
I R ( a ¯ ) = I 0 α 2 128 9 π a ¯ 6 λ 4 ( 1 + cos 2 β ) ,
U = 2 q ¯ m + 1 ;             q ¯ = 4 π a ¯ λ sin β 2 ,
ζ m ( U ) = 288 ( m + 1 ) 6 u 6 [ 1 - S ( m + 1 ) F + u 2 4 ( m + 1 ) ( m + 2 ) ] ,
F = cos ( m + 1 ) r + u s ( m + 1 ) sin ( m + 2 ) r - u 2 s 2 × ( m + 1 ) ( m + 2 ) 4 cos ( m + 3 ) r ; ζ m ( U ) = Γ ( m + 6 ) Γ ( m + 1 ) · ( m + 1 ) 6 .             for u 1.
K ¯ ( λ ) = 0 K ( λ , a ) f ( a ) d a ,
K ( λ , a ) = 2 π a 2 ( 1 - sin 2 δ δ + 1 - cos 2 δ 2 δ 2 ) ,
δ = 2 π a λ ( n - 1 ) .
K ¯ ( λ ) = K ¯ θ m ( t ) ,
θ m ( t ) = 1 + 2 Γ ( 1 ) Γ ( 1 + 2 ) cotan 2 t { 1 - cos 1 t × [ cos l t + l sin t · sin ( l + 1 ) t ] }
t = arctan 2 δ ¯ l ;             l = m + 1 ;             δ ¯ = 2 π a ¯ λ ( n - 1 )
K ¯ = 2 π a 2 ¯ = 2 π a ¯ 2 m + 2 m + 1 .
I ¯ n ( β ) = I ¯ ( β ) K ¯ ( λ ) .
I ¯ n ( β ) = 64 π 5 a ¯ 4 α 2 9 λ 4 · ζ m ( U ) · ( m + 1 ) · ( 1 + cos 2 β ) θ m ( t ) · ( m + 2 ) .

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