Abstract

A comparison has been made between (1) the computed angular scattering coefficient for a polydisperse cloud of small, spherical (Mie) particles and (2) the measured angular scattering coefficient for a polydisperse cloud of irregular, randomly oriented (Mie) particles fitting the same distribution function and having the same material properties. The comparison has been made for eight wavelengths covering the visible range.

© 1967 Optical Society of America

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References

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  1. D. Deirmendjian, Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press Ltd., London, 1963).
  2. B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Am. 50, 191 (1960).
    [CrossRef]
  3. J. Raymond Hodkinson, in Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press Ltd., London, 1963).
  4. H. C. Van der Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  5. D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Am. 51, 620 (1961).
    [CrossRef]
  6. R. A. Mugele, H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).
    [CrossRef]
  7. Shea L. Valley, Ed., Handbook of Geophysics and Space Environments (McGraw-Hill Book Co., Inc., New York, 1965).

1961 (1)

1960 (1)

1951 (1)

R. A. Mugele, H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).
[CrossRef]

Clasen, R.

Deirmendjian, D.

D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Am. 51, 620 (1961).
[CrossRef]

D. Deirmendjian, Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press Ltd., London, 1963).

Elliott, W. G.

Evans, H. D.

R. A. Mugele, H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).
[CrossRef]

Mugele, R. A.

R. A. Mugele, H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).
[CrossRef]

Pritchard, B. S.

Raymond Hodkinson, J.

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

Van der Hulst, H. C.

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

Viezee, W.

Ind. Eng. Chem. (1)

R. A. Mugele, H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (4)

Shea L. Valley, Ed., Handbook of Geophysics and Space Environments (McGraw-Hill Book Co., Inc., New York, 1965).

D. Deirmendjian, Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press Ltd., London, 1963).

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

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

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Figures (9)

Fig. 1
Fig. 1

Scattering geometry. E E o r 2 + E o l 2 , I s E s r 2 + E s l 2 .

Fig. 2
Fig. 2

Schematic of polar nephelometer.

Fig. 3
Fig. 3

Block diagram of signal processing system.

Fig. 4
Fig. 4

Schematic of apparatus with calibration card.

Fig. 5
Fig. 5

Absolute spectral reflectance of calibration card. ΔMg O, Φ card.

Fig. 6
Fig. 6

Differential mass scattering coefficients vs scattering angle θ. Talc: λ ¯= 4700 Å; ○, □, and △ are experimental data.

Fig. 7
Fig. 7

Differential mass scattering coefficients vs scattering angle θ. Talc: λ ¯ = 5150 Å; ○, □, and △ are experimental data.

Fig. 8
Fig. 8

Differential mass scattering coefficients vs scattering angle θ. Talc: λ ¯ = 5450 Å; ○, □, ◇, and △ are experimental data.

Fig. 9
Fig. 9

Differential mass scattering coefficients vs scattering angle θ. Talc: λ ¯ = 6000 Å; ○, experimental data.

Equations (21)

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I s ( m ˜ , x , θ ) = ( E / 2 k 2 ) { i 1 ( m ˜ , x , θ ) + i 2 ( m ˜ , x , θ ) } .
i 1 ( m ˜ , x , θ ) = S 1 ( m ˜ , x , θ 2 = n = 1 2 n + 1 n ( n + 1 ) [ a n ( m ˜ , x ) π n ( θ ) + b n ( m ˜ , x ) τ n ( θ ) ] 2 i 2 ( m ˜ , x , θ ) = S 2 ( m ˜ , x , θ ) 2 = n = 1 2 n + 1 n ( n + 1 ) [ a n ( m ˜ , x ) τ n ( θ ) + b n ( m ˜ , x ) π n ( θ ) ] 2 ,
Q ext = σ ext π r 2 = 2 x 2 n = 1 ( 2 n + 1 ) R e ( a n + b n ) Q sca = σ sca π r 2 = 2 x 2 n = 1 ( 2 n + 1 ) [ a n 2 + b n 2 ] ,
β s ( m ˜ , x ) = σ s ( m ˜ , x ) n = π D 2 4 Q s ( m ˜ , x ) n ,
β s ( m , θ , x ) = n I s ( m ˜ , x , θ ) E = n 2 k 2 [ i 1 ( m ˜ , θ , x ) + i 2 ( m ˜ , θ , x ) ] ,
f ( D ) d D = ( ρ / M 0 ) [ s b / s 4 / Γ ( 4 / s ) ] { exp [ - b ( D / D 0 ) s ] } d D / D 0 ,
f ( x ) d x = ( ρ / M 0 ) [ s b / s 4 / Γ ( 4 / s ) ] { exp [ - b ( x / x 0 ) s ] } d x / x 0
β s ( m ˜ , x 0 , x 1 ) = ρ             s b / s 4 M 0 Γ ( 4 / s ) o x 1 π D 2 4 Q s ( m ˜ , x ) exp [ - b ( x / x 0 ) s ] d x / x 0 = π 4 ρ M 0 × s b / s 4 Γ ( 4 / s ) D o x 0 3 o x 1 x 2 Q s ( m ˜ , x ) exp [ - b ( x / x 0 ) s ] d x .
β s ( m ˜ , x 0 , θ ; x 1 ) = [ I s ( m ˜ , x 0 , θ ; x 1 ) ] / E ρ             s b / s 4 M 0 Γ ( 4 / s ) × D 0 2 8 x 0 3 o x 1 [ i 1 ( m ˜ , x , θ ) + i 2 ( m ˜ , x , θ ) ] exp [ - b ( x / x 0 ) s ] d x .
I s ( m ˜ , x o , θ ) = m E K s ( m ˜ , x o , θ ) = ρ ( S Δ E / sin θ ) K s ( m ˜ , x o , θ ) ,
K s ( m ˜ , x o , θ ) = I s ( θ ) E sin θ ρ S Δ = ( V R 1 V M ) s K M K R 1 × sin θ ρ S Δ ;
K s ( m ˜ , x o , θ ) = ( V R 1 / V M ) s [ I r ( θ ) / E × V M / V R 1 ] × sin θ / ρ S Δ = [ V R 1 / V M ] s [ R ( λ ) cos θ / π × V M / V R 1 ] × sin θ / ρ Δ ,
K s ( m ˜ , x o , θ ) = ( V R 1 / V M ) s × K 1 ( λ ) sin θ / ρ Δ .
K s ( m ˜ , x o , θ ) = K 1 ( λ ) × ( sin θ / ρ Δ ) ( V R 1 / V M ) s ,
V R 2 = K s ( m ˜ , x o , θ 2 ) [ ρ ( t ) Δ V M / K 2 ( λ ¯ ) sin θ 2 ] .
V R 1 V R 2 = K s ( m ¯ , x o , θ ) K s ( m ˜ , x o , θ 2 ) × K 2 ( λ ¯ ) K 1 ( λ ¯ ) sin θ 2 sin θ .
V = o T V R 2 ( t ) d t = K s ( m ˜ , x o , θ 2 ) Δ V M K 2 ( λ ¯ ) sin θ 2 o T ρ ( t ) d t .
V / W = [ C 1 K s ( m ˜ , x o , θ 2 ) Δ V M ] / K 2 ( λ ¯ ) sin θ 2 ] .
K s ( m ˜ , x o , θ ) = ( V R 1 / V R 2 ) [ K 1 ( λ ¯ ) sin θ / V M Δ C 1 ] V / W .
I s ( m ˜ , x , ) I s ( m ˜ , x , 180° ) = 1 + 4 x 2 15 ( m ˜ 2 + 4 ) ( m ˜ 2 + 2 ) 2 m ¯ 2 + 3 + ,
E E o r 2 + E o l 2 , I s E s r 2 + E s l 2 .

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