Abstract

The optical properties of an aerosol of given mass concentration are derived from Mie theory. The visibility is calculated, via the optical extinction coefficient, for several log-normal distributions of carbon particles. Normalizing the optical cross sections of particles by their mass allows clear identification of the diameters at which scattering, absorption, and extinction are greatest. For highly absorbing particles this occurs in the 0.15–0.5-λ diameter range.

© 1978 Optical Society of America

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References

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  1. W. E. K. Middleton, Vision Through the Atmosphere (U. Toronto Press, Toronto, 1952).
  2. R. A. Reck, Atmos. Environ. 10, 611 (1976).
    [CrossRef]
  3. M. J. Pilat, D. S. Ensor, Atmos. Environ. 4, 163 (1970).
    [CrossRef]
  4. D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
    [CrossRef] [PubMed]
  5. R. W. Bergstrom, Beitr. Phys. Atmos. 46, 223 (1973); Atmos. Environ. 6, 247 (1972).
    [PubMed]
  6. C. N. Davies, J. Aerosol Sci. 6, 335 (1975).
    [CrossRef]
  7. F. R. Faxvog, Appl. Opt. 14, 269 (1975).
    [CrossRef] [PubMed]
  8. G. Mie, Ann. Phys. 25, 377 (1908); or see H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 119–130; or M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.
    [CrossRef]
  9. These indices of refraction were obtained from M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 621; R. P. DiNardo, A. N. Goland, J. Opt. Soc. Am. 61, 1321 (1971); Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, Ohio, 1972); and (for carbon) J. R. Hodkinson, J. Opt. Soc. Am. 54, 846 (1964).
    [CrossRef]
  10. M. Kerker, Ref. 8, p. 351.
  11. K. E. Noll, P. K. Mueller, M. Imada, Atmos. Environ. 2, 465 (1968).
    [CrossRef] [PubMed]
  12. W. H. White, P. T. Roberts, at 68th Annual Meeting of the Air Pollution Control Association, Boston (15–20 June 1975) Paper 75-28.6.
  13. R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
    [CrossRef]
  14. W. D. Conner, J. R. Hodkinson, “Optical Properties and Visual Effects of Smoke-Stack Plumes,” U.S. Dept. of Health, Education, and Welfare, Public Health Service Publication 999-AP-30 (1967), see Fig. 32.
  15. J. C. Elder, H. J. Ettinger, R. Y. Nelson, Atmos. Environ. 8, 1035 (1974).
    [CrossRef] [PubMed]

1976 (1)

R. A. Reck, Atmos. Environ. 10, 611 (1976).
[CrossRef]

1975 (2)

1974 (1)

J. C. Elder, H. J. Ettinger, R. Y. Nelson, Atmos. Environ. 8, 1035 (1974).
[CrossRef] [PubMed]

1973 (1)

R. W. Bergstrom, Beitr. Phys. Atmos. 46, 223 (1973); Atmos. Environ. 6, 247 (1972).
[PubMed]

1971 (1)

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

1970 (1)

M. J. Pilat, D. S. Ensor, Atmos. Environ. 4, 163 (1970).
[CrossRef]

1969 (1)

R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
[CrossRef]

1968 (1)

K. E. Noll, P. K. Mueller, M. Imada, Atmos. Environ. 2, 465 (1968).
[CrossRef] [PubMed]

1908 (1)

G. Mie, Ann. Phys. 25, 377 (1908); or see H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 119–130; or M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.
[CrossRef]

Ahlquist, N. C.

R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
[CrossRef]

Bergstrom, R. W.

R. W. Bergstrom, Beitr. Phys. Atmos. 46, 223 (1973); Atmos. Environ. 6, 247 (1972).
[PubMed]

Born, M.

These indices of refraction were obtained from M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 621; R. P. DiNardo, A. N. Goland, J. Opt. Soc. Am. 61, 1321 (1971); Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, Ohio, 1972); and (for carbon) J. R. Hodkinson, J. Opt. Soc. Am. 54, 846 (1964).
[CrossRef]

Charlson, R. J.

R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
[CrossRef]

Conner, W. D.

W. D. Conner, J. R. Hodkinson, “Optical Properties and Visual Effects of Smoke-Stack Plumes,” U.S. Dept. of Health, Education, and Welfare, Public Health Service Publication 999-AP-30 (1967), see Fig. 32.

Davies, C. N.

C. N. Davies, J. Aerosol Sci. 6, 335 (1975).
[CrossRef]

Elder, J. C.

J. C. Elder, H. J. Ettinger, R. Y. Nelson, Atmos. Environ. 8, 1035 (1974).
[CrossRef] [PubMed]

Ensor, D. S.

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

M. J. Pilat, D. S. Ensor, Atmos. Environ. 4, 163 (1970).
[CrossRef]

Ettinger, H. J.

J. C. Elder, H. J. Ettinger, R. Y. Nelson, Atmos. Environ. 8, 1035 (1974).
[CrossRef] [PubMed]

Faxvog, F. R.

Hodkinson, J. R.

W. D. Conner, J. R. Hodkinson, “Optical Properties and Visual Effects of Smoke-Stack Plumes,” U.S. Dept. of Health, Education, and Welfare, Public Health Service Publication 999-AP-30 (1967), see Fig. 32.

Imada, M.

K. E. Noll, P. K. Mueller, M. Imada, Atmos. Environ. 2, 465 (1968).
[CrossRef] [PubMed]

Kerker, M.

M. Kerker, Ref. 8, p. 351.

MacCready, P. B.

R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
[CrossRef]

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (U. Toronto Press, Toronto, 1952).

Mie, G.

G. Mie, Ann. Phys. 25, 377 (1908); or see H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 119–130; or M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.
[CrossRef]

Mueller, P. K.

K. E. Noll, P. K. Mueller, M. Imada, Atmos. Environ. 2, 465 (1968).
[CrossRef] [PubMed]

Nelson, R. Y.

J. C. Elder, H. J. Ettinger, R. Y. Nelson, Atmos. Environ. 8, 1035 (1974).
[CrossRef] [PubMed]

Noll, K. E.

K. E. Noll, P. K. Mueller, M. Imada, Atmos. Environ. 2, 465 (1968).
[CrossRef] [PubMed]

Pilat, M. J.

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

M. J. Pilat, D. S. Ensor, Atmos. Environ. 4, 163 (1970).
[CrossRef]

Reck, R. A.

R. A. Reck, Atmos. Environ. 10, 611 (1976).
[CrossRef]

Roberts, P. T.

W. H. White, P. T. Roberts, at 68th Annual Meeting of the Air Pollution Control Association, Boston (15–20 June 1975) Paper 75-28.6.

Selvidge, H.

R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
[CrossRef]

White, W. H.

W. H. White, P. T. Roberts, at 68th Annual Meeting of the Air Pollution Control Association, Boston (15–20 June 1975) Paper 75-28.6.

Wolf, E.

These indices of refraction were obtained from M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 621; R. P. DiNardo, A. N. Goland, J. Opt. Soc. Am. 61, 1321 (1971); Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, Ohio, 1972); and (for carbon) J. R. Hodkinson, J. Opt. Soc. Am. 54, 846 (1964).
[CrossRef]

Ann. Phys. (1)

G. Mie, Ann. Phys. 25, 377 (1908); or see H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 119–130; or M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.
[CrossRef]

Appl. Opt. (1)

Atmos. Environ. (4)

R. A. Reck, Atmos. Environ. 10, 611 (1976).
[CrossRef]

M. J. Pilat, D. S. Ensor, Atmos. Environ. 4, 163 (1970).
[CrossRef]

K. E. Noll, P. K. Mueller, M. Imada, Atmos. Environ. 2, 465 (1968).
[CrossRef] [PubMed]

J. C. Elder, H. J. Ettinger, R. Y. Nelson, Atmos. Environ. 8, 1035 (1974).
[CrossRef] [PubMed]

Beitr. Phys. Atmos. (1)

R. W. Bergstrom, Beitr. Phys. Atmos. 46, 223 (1973); Atmos. Environ. 6, 247 (1972).
[PubMed]

J. Aerosol Sci. (1)

C. N. Davies, J. Aerosol Sci. 6, 335 (1975).
[CrossRef]

J. Air Pollut. Control Assoc. (2)

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

R. J. Charlson, N. C. Ahlquist, H. Selvidge, P. B. MacCready, J. Air Pollut. Control Assoc. 19, 937 (1969).
[CrossRef]

Other (5)

W. D. Conner, J. R. Hodkinson, “Optical Properties and Visual Effects of Smoke-Stack Plumes,” U.S. Dept. of Health, Education, and Welfare, Public Health Service Publication 999-AP-30 (1967), see Fig. 32.

W. H. White, P. T. Roberts, at 68th Annual Meeting of the Air Pollution Control Association, Boston (15–20 June 1975) Paper 75-28.6.

W. E. K. Middleton, Vision Through the Atmosphere (U. Toronto Press, Toronto, 1952).

These indices of refraction were obtained from M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 621; R. P. DiNardo, A. N. Goland, J. Opt. Soc. Am. 61, 1321 (1971); Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, Ohio, 1972); and (for carbon) J. R. Hodkinson, J. Opt. Soc. Am. 54, 846 (1964).
[CrossRef]

M. Kerker, Ref. 8, p. 351.

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Figures (7)

Fig. 1
Fig. 1

The calculated scattering cross section per unit mass Rscat at a wavelength of 0.55 μm for absorbing and nonabsorbing materials as a function of diameter for single-sized particles. The following refractive indices and densities (g/cm3) were used: carbon (m = 1.96–0.66i, ρ = 2.0), iron (m = 3.51–3.95i, ρ = 7.86), silica (m = 1.55, ρ = 2.66), and water (m = 1.33, ρ = 1.0).

Fig. 2
Fig. 2

The calculated absorption cross section per unit mass Rabs at 0.55 μm for single-sized particles of carbon and iron.

Fig. 3
Fig. 3

The calculated extinction cross section per unit mass Rext at 0.55 μm for single-sized particles of carbon, iron, silica, and water.

Fig. 4
Fig. 4

The number and mass distributions for an aerosol of mass concentration 20 μg/m3, geometric mean standard deviation σg = 0.3, and mean particle diameter D1 = 0.02 μm.

Fig. 5
Fig. 5

The optical extinction coefficient γext, for a carbon particle mass concentration of 20 μg/m3 as a function of the mean particle diameter D1, for several log-normal distributions.

Fig. 6
Fig. 6

Visibility vs mean particle diameter for carbon particles with a mass concentration of 20 μg/m3 and the standard deviations shown.

Fig. 7
Fig. 7

Visibility through a carbon aerosol as a function of mass concentration for several mean particle diameters.

Equations (12)

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R scat = C scat / ρ 4 3 π ( D / 2 ) 3 ,
R abs = C abs / ρ 4 3 π ( D / 2 ) 3 .
R abs = 6 π λ ρ Im ( m 2 1 m 2 + 2 ) ,
γ = 0 C ext ( D ) N f ( D ) d D ,
0 f ( D ) d D = 1 ,
m ( D ) = ρ 4 3 π ( D 2 ) 3 N f ( D ) .
R ext = C ext / ρ 4 3 π ( D / 2 ) 3 .
γ = 0 R e x t ( D ) m ( D ) d D .
n ( D ) = d [ N f ( D ) ] d log D = N σ g ( 2 π ) 1 / 2 D exp [ ( log D log D 1 ) 2 2 σ g 2 ] .
log D 3 = log D 1 + 3 σ g 2 log e .
I = I 0 exp ( γ L ) ,
V = ln 50 / γ .

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