Abstract

The elements of the Mueller matrix for polydisperse systems of irregular, randomly oriented particles have been measured in absolute terms as a function of scattering angle for two wavelengths. These results have been compared to the matrix elements that were calculated for assemblies of spherical particles that fit the same particle size distribution function and have the same (real) refractive index.

© 1970 Optical Society of America

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References

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  1. D. Deirmendjian, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, Potsdam, New York, 1962 (Pergamon Press Ltd., London, 1963).
  2. B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Amer. 50, 191 (1960).
    [CrossRef]
  3. J. Hodkinson, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, Potsdam, New York, 1962 (Pergamon Press Ltd., London, 1963).
  4. A. C. Holland, J. S. Draper, Appl. Opt. 6, 511 (1967).
    [CrossRef] [PubMed]
  5. F. Perrin, J. Chem. Phys. 10, 414 (1942).
    [CrossRef]
  6. H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, New York, 1957).
  7. G. V. Rozenberg, Sov. Phys.-Usp. 3, 346 (1960).
    [CrossRef]
  8. N. G. Parke, “Statistical Optics: Mueller Phenomenological Algebra,” MIT Res. Lab. of Electronics, Rept. 119, June1949.
  9. S. Chandrasekhar, Radiative Transfer (Dover Publications, New York, 1960).
  10. G. N. Abramovich, The Theory of Turbulent Jets (MIT Press, Cambridge, Mass., 1963).
  11. C. J. Cremers, R. C. Birkebak, Appl. Opt. 5, 1057 (1966).
    [CrossRef] [PubMed]
  12. G. V. Rozenberg, G. Gorchakov, Izv. Atmos. Oceanic Phys. 1, 1279 (1965).

1967 (1)

1966 (1)

1965 (1)

G. V. Rozenberg, G. Gorchakov, Izv. Atmos. Oceanic Phys. 1, 1279 (1965).

1960 (2)

G. V. Rozenberg, Sov. Phys.-Usp. 3, 346 (1960).
[CrossRef]

B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Amer. 50, 191 (1960).
[CrossRef]

1942 (1)

F. Perrin, J. Chem. Phys. 10, 414 (1942).
[CrossRef]

Abramovich, G. N.

G. N. Abramovich, The Theory of Turbulent Jets (MIT Press, Cambridge, Mass., 1963).

Birkebak, R. C.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover Publications, New York, 1960).

Cremers, C. J.

Deirmendjian, D.

D. Deirmendjian, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, Potsdam, New York, 1962 (Pergamon Press Ltd., London, 1963).

Draper, J. S.

Elliott, W. G.

B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Amer. 50, 191 (1960).
[CrossRef]

Gorchakov, G.

G. V. Rozenberg, G. Gorchakov, Izv. Atmos. Oceanic Phys. 1, 1279 (1965).

Hodkinson, J.

J. Hodkinson, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, Potsdam, New York, 1962 (Pergamon Press Ltd., London, 1963).

Holland, A. C.

Parke, N. G.

N. G. Parke, “Statistical Optics: Mueller Phenomenological Algebra,” MIT Res. Lab. of Electronics, Rept. 119, June1949.

Perrin, F.

F. Perrin, J. Chem. Phys. 10, 414 (1942).
[CrossRef]

Pritchard, B. S.

B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Amer. 50, 191 (1960).
[CrossRef]

Rozenberg, G. V.

G. V. Rozenberg, G. Gorchakov, Izv. Atmos. Oceanic Phys. 1, 1279 (1965).

G. V. Rozenberg, Sov. Phys.-Usp. 3, 346 (1960).
[CrossRef]

Van de Hulst, H. C.

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

Appl. Opt. (2)

Izv. Atmos. Oceanic Phys. (1)

G. V. Rozenberg, G. Gorchakov, Izv. Atmos. Oceanic Phys. 1, 1279 (1965).

J. Chem. Phys. (1)

F. Perrin, J. Chem. Phys. 10, 414 (1942).
[CrossRef]

J. Opt. Soc. Amer. (1)

B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Amer. 50, 191 (1960).
[CrossRef]

Sov. Phys.-Usp. (1)

G. V. Rozenberg, Sov. Phys.-Usp. 3, 346 (1960).
[CrossRef]

Other (6)

N. G. Parke, “Statistical Optics: Mueller Phenomenological Algebra,” MIT Res. Lab. of Electronics, Rept. 119, June1949.

S. Chandrasekhar, Radiative Transfer (Dover Publications, New York, 1960).

G. N. Abramovich, The Theory of Turbulent Jets (MIT Press, Cambridge, Mass., 1963).

J. Hodkinson, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, Potsdam, New York, 1962 (Pergamon Press Ltd., London, 1963).

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

D. Deirmendjian, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, Potsdam, New York, 1962 (Pergamon Press Ltd., London, 1963).

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Figures (10)

Fig. 1
Fig. 1

Schematic of polar nephelometer.

Fig. 2
Fig. 2

Block diagram of signal processing system.

Fig. 3
Fig. 3

Typical “5-μ minusil” particles.

Fig. 4
Fig. 4

Minusil particle frequency function.

Fig. 5
Fig. 5

Minusil particle distribution function.

Fig. 6
Fig. 6

Matrix elements S 11 ( m ˜ , x 0 , θ ) and S 11 ( m ˜ , x 0 , θ ) vs θ for λ = 5460 Å.

Fig. 7
Fig. 7

Matrix elements S 12 ( , m ˜ x , θ ) = S 21 ( m ˜ , x , θ ) vs θ for λ = 5460 Å.

Fig. 8
Fig. 8

Matrix elements S 33 ( m ˜ , x 0 , θ ) , S 44 ( m ˜ , x o , θ ) vs θ for λ = 5460 Å.

Fig. 9
Fig. 9

Matrix elements S 34 ( m ˜ , x , θ ) = S 13 ( m ˜ , x o , θ ) vs θ for λ = 5460 Å.

Fig. 10
Fig. 10

Matrix elements S 11 ( m ˜ . x 0 , θ ) and S 22 ( m ˜ , x 0 , θ ) vs θ for λ = 4860 Å.

Equations (32)

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{ Γ i } = const [ S i j ] { Γ j } .
I = E l E l * + E r E r * , Q = E l E l * E r E r * , U = 2 Re ( E l E r * ) = E l E r * + E r E l * , V = 2 Im ( E l E r * ) = i ( E l E r * + E r E l * ) .
I 2 Q 2 + U 2 + V 2 .
[ I s Q s U s V s ] = 1 k 2 [ S i j ] [ I 0 Q 0 U 0 V 0 ] .
[ S i j ] = [ S 11 S 12 0 0 S 12 S 22 0 0 0 0 S 33 S 34 0 0 S 34 S 44 ] .
S 11 ( m ˜ , x , θ ) = S 22 ( m ˜ , x , θ ) = 1 2 [ i 2 ( m ˜ , x , θ ) + i 1 ( m ˜ , x , θ ) ] , S 12 ( m ˜ , x , θ ) = S 21 ( m ˜ , x , θ ) = 1 2 [ i 2 ( m ˜ , x , θ ) i 1 ( m ˜ , x , θ ) ] , S 33 ( m ˜ , x , θ ) = S 44 ( m ˜ , x , θ ) = i 3 ( m ˜ , x , θ ) , S 43 = S 34 = i 4 ( m ˜ , x , θ ) .
P j ( m ˜ , x 0 , θ ) 4 π = 1 k 2 β s ( m ˜ , x ) x a x M f ( x ) i j ( m ˜ , x , θ ) d x ( j = 1,2,3,4 ) .
β s ( m ˜ , x 0 ) = λ 2 4 π x a x M f ( x ) Q s ( m ˜ , x ) d x .
[ S i j ] = β s ( m ˜ , x 0 ) [ 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) + P 1 ( m ˜ , x 0 , θ ) ] 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) P 1 ( m ˜ , x 0 , θ ) ] 0 0 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) P 1 ( m ˜ , x 0 , θ ) ] 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) + P 1 ( m ˜ , x 0 , θ ) ] 0 0 0 0 P 3 ( m ˜ , x 0 , θ ) / 4 π P 4 ( m ˜ , x 0 , θ / 4 π 0 0 P 4 ( m ˜ , x 0 , θ ) / 4 π P 3 ( m ˜ , x 0 , θ ) / 4 π ] .
1 2 [ P 2 ( m ˜ , x 0 , θ ) 4 π + P 1 ( m ˜ , x 0 , θ ) 4 π ] d ω = 1.0.
f ( D ) d D = [ N δ / ( D a ) ( π ) 1 2 ] exp ( δ 2 { ln [ ( D a ) / ( D 0 a ) ] } ) 2 d D ( particles / cm 3 )
N = 6 M / π ρ E ( a , δ ) .
E ( a , δ ) = a 3 + 3 a 2 ( D 0 a ) exp ( 1 / 4 δ 2 ) + 3 a ( D 0 a ) 2 exp ( 1 / δ 2 ) + ( D 0 a ) 3 exp ( 9.0 / 4 δ 2 ) .
E ( a , δ ) = D 0 3 exp ( 9.0 / 4 δ 2 ) and N = ( M / M 0 ) exp ( 9 / 4 δ 2 ) ,
P j ( m ˜ , x 0 , θ ) = 1 k 2 β s ( m ˜ , x 0 ) · 6 M π ρ E ( a , δ ) · δ ( π ) 1 2 × x a x M i j ( m ˜ , x , θ ) ( x x a ) exp { δ 2 [ ln ( x x a x 0 x a ) ] 2 } d x ,
β s ( m ˜ , x 0 ) = 3 2 D 0 2 x 0 2 · M δ ρ E ( a , δ ) ( π ) 1 2 x a x M x 2 Q s ( m ˜ , x ) ( x x a ) × exp { δ 2 [ ln ( x x a x 0 x a ) ] 2 } d x .
[ S i j ] = k s ( m ˜ , x 0 ) [ 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) + P 1 ( m ˜ , x 0 , θ ) ] 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) P 1 ( m ˜ , x 0 , θ ) ] 0 0 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) P 1 ( m ˜ , x 0 , θ ) ] 1 / 8 π [ P 2 ( m ˜ , x 0 , θ ) + P 1 ( m ˜ , x 0 , θ ) ] 0 0 0 0 P 3 ( m ˜ , x 0 , θ ) / 4 π P 4 ( m ˜ , x 0 , θ ) / 4 π 0 0 P 4 ( m ˜ , x 0 , θ ) / 4 π P 3 ( m ˜ , x 0 , θ ) / 4 π ] .
β s ( P , A , θ ; λ ) = K ( P , A , θ ; λ ) × W s c ( P , A , θ ; λ ) ,
const × W s c ( P , A , θ ) / W M ( P , A , θ M ) .
V 0 T W M ( P , A , θ M , t ) d t .
k s ( P , A , θ M ) β s ( P , A , θ M ) / ρ ˜ ( θ M , t ) = W M ( P , A , θ M , t ) K ( P , A , θ M ) / ρ ˜ ( θ M , t ) ,
V = k s ( P , A , θ M ) K ( P , A , θ M ) 0 T ρ ˜ ( θ M , t ) d t .
ρ ˜ ( θ , t ) = C ( θ ) M ˙ ( t ) .
V = k s ( P , A , θ M ) K ( P , A , θ M ) × C ( θ M ) 0 T M ˙ ( t ) d t = k s ( P , A , θ M ) K ( P , A , θ M ) × C ( θ M ) × M ,
k s ( P , A , θ M ) = V × K ( P , A , θ M ) / M × C ( θ M ) c m 2 / g-sr .
W s c ( P , A , θ , t ) W M ( P , A , θ M , t ) k s ( P , A , θ ) k s ( P , A , θ M ) × K ( P , A , θ M ) K ( P , A , θ ) × ρ ˜ ( θ , t ) ρ ˜ ( θ M , t )
k s ( P , A , θ ) k s ( P , A , θ M ) = const × W s c ( P , A , θ , t ) W M ( P , A , θ M , t ) × K ( P , A , θ ) K ( P , A , θ M ) × C ( θ M ) C ( θ ) .
[ I s Q s U s V s ] = const [ A i j ] [ S i j ] [ P i j ] [ I 0 0 0 0 ] .
U U , H H , V V , V H , H V , D D , d d , D d , d D , R R , R d , d R , D R , R D , H D , D H , H R , and R H .
k s ( U , U , θ ) = ( I s / I 0 ) ( U , U , θ ) = S 11 ( m ˜ , x 0 , θ ) ,
S 11 ( m ˜ , x 0 , θ ) = 1 4 [ k s ( H , H , θ ) + k s ( V , V , θ ) + k s ( H , V , θ ) + k s ( V , H , θ ) ] .
[ E s l E s r ] = const x [ A 2 A 3 A 4 A 1 ] [ E 0 l E 0 r ]

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