Abstract

A method is presented for determining the optical absorption coefficient, or the imaginary refractive index, of particulate material that has been collected from aerosols or hydrosols by means of filtration. The method, based on the Kubelka–Munk theory of diffuse reflectance, is nondestructive and requires no other knowledge of the sample than the amount present, the specific gravity, and an estimate of the real index of refraction. The theoretical development of the method is discussed along with an analysis of photometric and gravimetric errors. We test the method by comparing results obtained for powdered didymium glass with measurements made before the glass was crushed. An example of the method’s application to the determination of the absorption coefficient of atmospheric dust at UV, visible, and near-IR wavelengths is also presented.

© 1994 Optical Society of America

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References

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  1. G. Kortum, Reflectance Spectroscopy (Springer-Verlag, New York, 1969).
    [Crossref]
  2. W. W. Wendtland, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).
  3. The standard used here was SPECTRALON, manufactured by Labsphere, Inc., North Sutton, N.H.; another is the Eastman White Reflectance Standard, a powdered barium sulfate standard produced by Eastman Kodak Corporation.
  4. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485–1502 (1971).
    [Crossref] [PubMed]
  5. B. J. Brinkworth, “Interpretation of the Kubelka–Munk coefficients in reflection theory,” Appl. Opt. 11, 1434–1435 (1972).
    [Crossref] [PubMed]
  6. E. L. Simmons, “Diffuse reflectance spectroscopy: a comparison of the theories,” Appl. Opt. 14, 1380–1386 (1975).
    [Crossref] [PubMed]
  7. J. D. Lindberg, R. E. Douglass, D. Garvey, “Carbon and the optical properties of atmospheric dust,” Appl. Opt. 32, 6077–6081 (1993).
    [Crossref] [PubMed]
  8. J. D. Lindberg, L. S. Laude, “Measurement of the absorption coefficient of atmospheric dust,” Appl. Opt. 13, 1923–1927 (1974); J. D. Lindberg, “Absorption coefficient of atmospheric dust and other strongly absorbing powders: improvement on the method of measurement,” Appl. Opt. 14, 2813–2815 (1975).
    [Crossref] [PubMed]

1993 (1)

1975 (1)

1974 (1)

1972 (1)

1971 (1)

Brinkworth, B. J.

Douglass, R. E.

Garvey, D.

Hecht, H. G.

W. W. Wendtland, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

Kortum, G.

G. Kortum, Reflectance Spectroscopy (Springer-Verlag, New York, 1969).
[Crossref]

Laude, L. S.

Lindberg, J. D.

Mudgett, P. S.

Richards, L. W.

Simmons, E. L.

Wendtland, W. W.

W. W. Wendtland, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

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Figures (2)

Fig. 1
Fig. 1

Absorption coefficient k′ as determined by direct transmission through plates of didymium glass (solid lower curve) and by diffuse reflectance methods applied to the powdered form of the same glass plates (dotted upper curve). The error bars are discussed in the text.

Fig. 2
Fig. 2

Absorption coefficient k′ for a sample of atmospheric dust collected at a remote location on White Sands Missile Range in New Mexico. The error bars are discussed in the text.

Tables (1)

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Table 1 Definitions of Symbols

Equations (15)

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T = T s ( 1 - R 0 f R 0 ) T f ,
A R 0 2 + B R 0 + C = 0 ,
A = R g ,
B = - ( 1 + R R g ) ,
C = R - T 2 R g .
Q = - ( 1 / 2 ) [ B - ( B 2 - 4 A C ) 1 / 2 ] ,
R 0 = C / Q .
R = a - b ,
a = ( 1 + R 0 2 - T 2 ) / ( 2 R 0 ) ,
b = ( a 2 - 1 ) 1 / 2 .
k s = ( 1 - R ) 2 2 R .
s = 1 2 b d coth - 1 [ ( 1 - a R 0 ) / ( b R 0 ) ] .
k = ( 1 - R ) 2 coth - 1 [ ( 1 - a R 0 ) b R 0 ] 4 b d R .
k = ( 3 k ) / ( 2 n 2 ) ,
i = ( λ / 4 π ) k ,

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