Abstract

A theoretical basis is presented for a new method for determining the aerosol size distribution from aureole measurements around a point source. The method involves the determination of the angular scattering coefficient from radiance measurements at different observation angles between 1° and 10° around a source in the solar blind spectral region. The results are used to determine the aerosol size distribution by applying the Twomey-Chahine inversion algorithm. The derived size distribution has the desirable features of being accurate for large particles up to radii of 10 μm and being insensitive to their complex refractive index.

© 1984 Optical Society of America

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References

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  1. E. Trakhovsky, S. G. Lipson, A. D. Devir, Appl. Opt. 21, 3005 (1982).
    [Crossref] [PubMed]
  2. J. M. Shluph, C. R. Dickson, M. E. Neer, “Seasonal Variations in Ultra-Violet Single Scattering Phase Functions,” Technical Report ARAP-383 (Aeronautical Research Associates of Princeton, Inc., N.J., 1979).
  3. E. Thomalla, H. Quenzel, Appl. Opt. 21, 3170 (1982).
    [Crossref] [PubMed]
  4. A. Deepak, G. P. Box, M. A. Box, Appl. Opt. 21, 2236 (1982).
    [Crossref] [PubMed]
  5. E. Trakhovsky, U. P. Oppenheim, Appl. Opt. 22, 1633 (1983).
    [Crossref] [PubMed]
  6. E. Trakhovsky, U. P. Oppenheim, Appl. Opt. to be published.
  7. A. S. Zachor, Appl. Opt. 17, 1911 (1978).
    [Crossref] [PubMed]
  8. F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).
  9. J. R. Hodkinson, I. Greenleaves, J. Opt. Soc. Am. 53, 577 (1963).
    [Crossref]
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  11. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (American Elsevier, New York, 1977).
  12. M. Z. Hansen, Appl. Opt. 19, 3441 (1980).
    [Crossref] [PubMed]

1983 (1)

1982 (3)

1980 (1)

1978 (1)

1963 (1)

Abrew, L. W.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Box, G. P.

Box, M. A.

Callery, W. P.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Deepak, A.

Devir, A. D.

Dickson, C. R.

J. M. Shluph, C. R. Dickson, M. E. Neer, “Seasonal Variations in Ultra-Violet Single Scattering Phase Functions,” Technical Report ARAP-383 (Aeronautical Research Associates of Princeton, Inc., N.J., 1979).

Fenn, R. W.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Greenleaves, I.

Hansen, M. Z.

Hodkinson, J. R.

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Lipson, S. G.

McClatchey, R. A.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Neer, M. E.

J. M. Shluph, C. R. Dickson, M. E. Neer, “Seasonal Variations in Ultra-Violet Single Scattering Phase Functions,” Technical Report ARAP-383 (Aeronautical Research Associates of Princeton, Inc., N.J., 1979).

Oppenheim, U. P.

E. Trakhovsky, U. P. Oppenheim, Appl. Opt. 22, 1633 (1983).
[Crossref] [PubMed]

E. Trakhovsky, U. P. Oppenheim, Appl. Opt. to be published.

Quenzel, H.

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

Shluph, J. M.

J. M. Shluph, C. R. Dickson, M. E. Neer, “Seasonal Variations in Ultra-Violet Single Scattering Phase Functions,” Technical Report ARAP-383 (Aeronautical Research Associates of Princeton, Inc., N.J., 1979).

Thomalla, E.

Trakhovsky, E.

Twomey, S.

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (American Elsevier, New York, 1977).

van de Hulst, H. C.

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

Zachor, A. S.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Other (5)

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

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (American Elsevier, New York, 1977).

F. X. Kneizys, E. P. Shettle, W. P. Callery, J. H. Chetwynd, L. W. Abrew, J. E. A. Selby, R. W. Fenn, R. A. McClatchey “Atmospheric Transmittance/Radiance: Computer Codelowtran-5,” AFGL-TR-80-0067 (1980).

J. M. Shluph, C. R. Dickson, M. E. Neer, “Seasonal Variations in Ultra-Violet Single Scattering Phase Functions,” Technical Report ARAP-383 (Aeronautical Research Associates of Princeton, Inc., N.J., 1979).

E. Trakhovsky, U. P. Oppenheim, Appl. Opt. to be published.

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Figures (8)

Fig. 1
Fig. 1

Geometric description of the measurement of aureole radiance around an obscured point source.

Fig. 2
Fig. 2

Geometric description of differentiation of the radiance. Volume element between dA and dA′ is the difference between total scattering volumes for observation angles γ and γ + .

Fig. 3
Fig. 3

Composite phase functions for βA = 0.284 km−1βR = 0.266 km−1, f = 0.5, and (a) g = 0.9, (b) g = 0.72, (c) g = 0.5.

Fig. 4
Fig. 4

LogL as a function of observation angle for (a) g = 0.9, (b) g = 0.72, (c) g = 0.5.

Fig. 5
Fig. 5

Scattering efficiency Q(θ,r) at λ = 0.25 μm as a function of particle radius for (a) θ = 1°, (b) θ = 2°, (c) θ = 4°, (d) θ = 8°.

Fig. 6
Fig. 6

Scattering efficiency Q′(θ,r) at λ = 0.25 μm for (a) θ = 1°, (b) θ = 2°, (c) θ = 4°, (d) θ = 8°.

Fig. 7
Fig. 7

Inverted size distribution for different first guesses of the Junge slope ν: (a) original size distribution with ν = 4, (b) inverted size distribution with ν = 5, (c) inverted size distribution with ν = 3, (d) same as (b) but with R1 = 0.2 μm instead of R1 = 0.02 μm.

Fig. 8
Fig. 8

Convergence of the rms residual for different first guesses of the Junge slope ν as a function of iteration step: (a) ν = 5, (b) ν = 3.

Equations (24)

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B 1 ( γ , R ) = β I R sin γ exp ( - K R cos γ ) × γ π exp ( - K R sin γ tan θ 2 ) P ( cos θ ) d θ .
γ + ɛ π exp ( - K R sin γ tan θ 2 ) β ( θ ) d θ = B 1 ( γ , R ) R sin γ I exp ( - K R cos γ ) .
a p ( a ) g ( a ) f ( x , a ) d a = p g f a d x + f ( g , a ) d g d a - f ( p , a ) d p d a .
- τ cos γ γ + ɛ π tan θ 2 exp ( - τ sin γ tan θ 2 ) β ( θ ) d θ - exp ( - τ sin γ tan γ + ɛ 2 ) β ( γ + ɛ ) = γ [ B 1 ( γ , R ) R sin γ I exp ( - τ cos γ ) ] .
β ( γ + ɛ ) = - γ [ B 1 ( γ , R ) R sin γ I ] = - γ L ( γ , R ) ,
P C ( μ ) = [ P R ( μ ) + β A β R P A ( μ ) ] / ( 1 + β A β R ) ,
P A ( μ ) = 1 - g 2 4 π [ 1 ( 1 + g 2 - 2 g μ ) 3 / 2 + f 0.5 ( 3 μ 2 - 1 ) ( 1 + g 2 ) 3 / 2 ] .
P R ( μ ) = 3 16 π ( 1 + μ 2 ) .
L ( γ , R ) A exp ( - C γ ) ,
β ( γ + ɛ ) = A C exp ( - C γ ) ,
β ( θ ) = A C exp [ - C ( θ - ɛ ) ] = A C exp ( - C θ ) .
β A ( θ ) = β ( θ ) - β R ( θ ) ,
β R ( k ) = k 4 9.27 × 10 18 - 1.07 × 10 9 k 2 ,
β A ( θ ) = 1 k 2 r 1 r 2 d N d r · i ( θ , r ) d r ,
i ( θ , r ) = i d ( θ , r ) + i r ( θ , r ) + i t ( θ , r ) ,
i ( θ , r ) = 2 x 2 [ J 1 ( x sin θ ) sin θ ] 2 ,
β A ( θ ) = r 1 r 2 d N d r · 2 [ J 1 ( x sin θ ) sin θ ] 2 r 2 d r .
Q ( θ , r ) = 2 π [ J 1 ( x sin θ ) sin θ ] 2 .
β A ( θ ) = r 1 r 2 d N d r Q ( θ , r ) π r 2 d r .
Q ( θ , r ) = Q ( θ , r ) r .
β A ( θ ) = 2.3 r 1 r 2 d N d log r π r 2 Q ( θ , r ) d r .
d N ( n ) d r = d N ( n - 1 ) d r ( r ) i = 1 I [ 1 + ɛ i ( n - 1 ) Q ( θ i , r ) Q max ( θ i ) ] ,
d N ( 0 ) d r = { C 0 · ( R 2 ) - ν for R 1 r R 2 , C 0 · r - ν for R 2 < r R 3 .
d N ( n ) d r new = d N ( N ) d r old i = 1 I [ 1 + ɛ i ( n ) ] I .

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