Abstract

It is convenient to measure the optical attenuation A of the combination of a layer of atmospheric particulate matter and the quartz fiber filter on which it has been collected. The problem of relating A to the absorption and scattering coefficients k and s of the particulate matter itself is treated as a problem in diffuse reflectance spectroscopy using the Kubelka–Munk theory. The results show that although, in general, A is a nonlinear function strongly dependent on both s and k, for a limited range of s and sample thickness d, A can be a practically linear function of k. Fortunately, this range includes that common to atmospheric particulate samples. Furthermore, it is shown that if the filter’s reflectance is sufficiently high, A can be nearly independent of s. This is in agreement with experimental and, for the limiting case when the substrate filter reflectance is unity, theoretical results obtained by other researchers. Use of such measurements of A as a means of determining the black carbon mass loading C on a filter is also investigated. It is shown that when the black carbon mass fraction f c is high, as it is for samples collected in large urban areas, A is a predictable and practically linear function of C. However, when f c is low, as it is for many rural locations, then the slope of the function A(C) is strongly dependent on f c, leading to possible overestimates of C. This problem can be alleviated by making the measurement of A at near-infrared wavelengths rather than in the visible spectrum.

© 1999 Optical Society of America

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References

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  1. J. D. Lindberg, “The composition and optical absorption coefficient of atmospheric particulate matter,” Opt. Quantum Electron. 7, 131–139 (1975).
    [CrossRef]
  2. H. Rosen, A. D. A. Hansen, L. Gundel, T. Novakov, “Identification of the graphitic carbon component of source and ambient particulates by Raman spectroscopy and an optical attenuation technique,” Appl. Opt. 17, 3859–3862 (1978).
    [CrossRef] [PubMed]
  3. Z. Yasa, N. M. Amer, H. Rosen, A. D. A. Hansen, T. Novakov, “Photoacoustic investigation of urban aerosol particles,” Appl. Opt. 18, 2528–2530 (1979).
    [CrossRef] [PubMed]
  4. J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Carbon and the optical properties of atmospheric dust,” Appl. Opt. 32, 6077–6081 (1993).
    [CrossRef] [PubMed]
  5. Z. Levin, J. D. Lindberg, “Size distribution, chemical composition, and optical properties of urban and desert aerosols in Israel,” J. Geophys. Res. 84, 6941–6950 (1979).
    [CrossRef]
  6. J. Gillespie, J. D. Lindberg, “Seasonal and geographic variations in imaginary refractive index of atmospheric particulate matter,” Appl. Opt. 31, 2107–2111 (1992).
    [CrossRef] [PubMed]
  7. C. Liousse, H. Cachier, S. G. Jennings, “Optical and thermal measurements of black carbon aerosol content in different environments: variation of the specific attenuation cross-section, sigma (σ),” Atmos. Environ. Part A 27, 1203–1211 (1993).
    [CrossRef]
  8. A. Petzold, C. Kopp, R. Niessner, “The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size,” Atmos. Environ. 31, 661–672 (1997).
    [CrossRef]
  9. Chin-I Lin, M. Baker, R. J. Charlson, “Absorption coefficient of atmospheric aerosol: a method for measurement,” Appl. Opt. 12, 1356–1363 (1973).
    [CrossRef] [PubMed]
  10. H. Rosen, T. Novakov, “Lawrence Berkeley Laboratory Laser Transmission Method,” in Light Absorption by Aerosol Particles, H. E. Gerber, E. E. Hindman, eds. (Spectrum, Hampton, Va., 1982), pp. 321–334.
  11. H. Rosen, T. Novakov, “Optical transmission through aerosol deposits on diffusely reflective filters: a method for measuring the absorbing component of aerosol particles,” Appl. Opt. 22, 1265–1267 (1983).
    [CrossRef] [PubMed]
  12. L. A. Gundel, R. L. Dod, H. Rosen, T. Novakov, “The relationship between optical attenuation and black carbon concentration for ambient and source particles,” Sci. Total Environ. 36, 197–202 (1984).
    [CrossRef]
  13. A. D. A. Hansen, H. Rosen, T. Novakov, “Real-time measurement of the absorption coefficient of aerosol particles,” Appl. Opt. 21, 3060–3062 (1982).
    [CrossRef] [PubMed]
  14. J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Absorption-coefficient-determination method for particulate materials,” Appl. Opt. 33, 4314–4319 (1994).
    [CrossRef] [PubMed]
  15. W. W. Wendtland, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).
  16. G. Kortum, Reflectance Spectroscopy (Springer-Verlag, New York, 1969).
    [CrossRef]
  17. In the notation used in the original development of the KM theory, both lower- and upper-case symbols are used for the coefficients, with the definition 2k = K and 2s = S. This was done to eliminate a factor of 2 in the final equations and frequently causes confusion. In our research we use the lower-case symbols exclusively. For more detail on these specific expressions, see Ref. 16, pp. 106–120.
  18. Our definition of attenuation does not include the arbitrary factor of 100 that was used in Refs. 10, 11, and 12.
  19. H. A. Gray, G. R. Cass, “Characteristics of atmospheric organic and elemental carbon particle concentrations in Los Angeles,” Envon. Sci. Technol. 20, 580–589 (1986).
    [CrossRef]
  20. R. McCarthy, C. E. Moore, “Determination of free carbon in atmospheric dust,” Anal. Chem. 24, 411–412 (1952).
    [CrossRef]
  21. Laboratory measurement of fc is necessarily done on a mixture of carbon soot and a diluent powder. Because of the extremely high value of fc it is difficult to obtain a laboratory carbon sample reduced sufficiently in particle size to meet the requirements of the KM theory. This leads to an underestimate of fc. A value of 240,000 cm-1 rather than our value of 210,000 cm-1 would be more consistent with the research of Ref. 12.
  22. R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
    [CrossRef]
  23. There is a further reason for making the measurements at near-IR wavelengths. Some laboratory methods determining carbon composition of samples involve burning the sample to remove carbon while using the LTM for monitoring black carbon content. Iron compounds, abundant in aerosols as trace materials, all result in Fe2O3 when completely oxidized. This iron oxide is a strong absorber in the visible spectrum where it adds absorption that may not be properly accounted for. This does not occur for near-IR wavelengths (see Refs. 4 and 14).

1997 (1)

A. Petzold, C. Kopp, R. Niessner, “The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size,” Atmos. Environ. 31, 661–672 (1997).
[CrossRef]

1994 (1)

1993 (3)

C. Liousse, H. Cachier, S. G. Jennings, “Optical and thermal measurements of black carbon aerosol content in different environments: variation of the specific attenuation cross-section, sigma (σ),” Atmos. Environ. Part A 27, 1203–1211 (1993).
[CrossRef]

J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Carbon and the optical properties of atmospheric dust,” Appl. Opt. 32, 6077–6081 (1993).
[CrossRef] [PubMed]

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

1992 (1)

1986 (1)

H. A. Gray, G. R. Cass, “Characteristics of atmospheric organic and elemental carbon particle concentrations in Los Angeles,” Envon. Sci. Technol. 20, 580–589 (1986).
[CrossRef]

1984 (1)

L. A. Gundel, R. L. Dod, H. Rosen, T. Novakov, “The relationship between optical attenuation and black carbon concentration for ambient and source particles,” Sci. Total Environ. 36, 197–202 (1984).
[CrossRef]

1983 (1)

1982 (1)

1979 (2)

Z. Yasa, N. M. Amer, H. Rosen, A. D. A. Hansen, T. Novakov, “Photoacoustic investigation of urban aerosol particles,” Appl. Opt. 18, 2528–2530 (1979).
[CrossRef] [PubMed]

Z. Levin, J. D. Lindberg, “Size distribution, chemical composition, and optical properties of urban and desert aerosols in Israel,” J. Geophys. Res. 84, 6941–6950 (1979).
[CrossRef]

1978 (1)

1975 (1)

J. D. Lindberg, “The composition and optical absorption coefficient of atmospheric particulate matter,” Opt. Quantum Electron. 7, 131–139 (1975).
[CrossRef]

1973 (1)

1952 (1)

R. McCarthy, C. E. Moore, “Determination of free carbon in atmospheric dust,” Anal. Chem. 24, 411–412 (1952).
[CrossRef]

Amer, N. M.

Baker, M.

Cachier, H.

C. Liousse, H. Cachier, S. G. Jennings, “Optical and thermal measurements of black carbon aerosol content in different environments: variation of the specific attenuation cross-section, sigma (σ),” Atmos. Environ. Part A 27, 1203–1211 (1993).
[CrossRef]

Cass, G. R.

H. A. Gray, G. R. Cass, “Characteristics of atmospheric organic and elemental carbon particle concentrations in Los Angeles,” Envon. Sci. Technol. 20, 580–589 (1986).
[CrossRef]

Charlson, R. J.

Dod, R. L.

L. A. Gundel, R. L. Dod, H. Rosen, T. Novakov, “The relationship between optical attenuation and black carbon concentration for ambient and source particles,” Sci. Total Environ. 36, 197–202 (1984).
[CrossRef]

Douglass, R. E.

Fernandez, G.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

Fuller, K.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

Garvey, D. M.

Gillespie, J.

Gray, H. A.

H. A. Gray, G. R. Cass, “Characteristics of atmospheric organic and elemental carbon particle concentrations in Los Angeles,” Envon. Sci. Technol. 20, 580–589 (1986).
[CrossRef]

Gundel, L.

Gundel, L. A.

L. A. Gundel, R. L. Dod, H. Rosen, T. Novakov, “The relationship between optical attenuation and black carbon concentration for ambient and source particles,” Sci. Total Environ. 36, 197–202 (1984).
[CrossRef]

Hansen, A. D. A.

Hecht, H. G.

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

Hinds, B. D.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

Jennings, S. G.

C. Liousse, H. Cachier, S. G. Jennings, “Optical and thermal measurements of black carbon aerosol content in different environments: variation of the specific attenuation cross-section, sigma (σ),” Atmos. Environ. Part A 27, 1203–1211 (1993).
[CrossRef]

Kopp, C.

A. Petzold, C. Kopp, R. Niessner, “The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size,” Atmos. Environ. 31, 661–672 (1997).
[CrossRef]

Kortum, G.

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

Levin, Z.

Z. Levin, J. D. Lindberg, “Size distribution, chemical composition, and optical properties of urban and desert aerosols in Israel,” J. Geophys. Res. 84, 6941–6950 (1979).
[CrossRef]

Lin, Chin-I

Lindberg, J. D.

Liousse, C.

C. Liousse, H. Cachier, S. G. Jennings, “Optical and thermal measurements of black carbon aerosol content in different environments: variation of the specific attenuation cross-section, sigma (σ),” Atmos. Environ. Part A 27, 1203–1211 (1993).
[CrossRef]

Martinez-Andazola, E.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

McCarthy, R.

R. McCarthy, C. E. Moore, “Determination of free carbon in atmospheric dust,” Anal. Chem. 24, 411–412 (1952).
[CrossRef]

Moore, C. E.

R. McCarthy, C. E. Moore, “Determination of free carbon in atmospheric dust,” Anal. Chem. 24, 411–412 (1952).
[CrossRef]

Niessner, R.

A. Petzold, C. Kopp, R. Niessner, “The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size,” Atmos. Environ. 31, 661–672 (1997).
[CrossRef]

Novakov, T.

Petzold, A.

A. Petzold, C. Kopp, R. Niessner, “The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size,” Atmos. Environ. 31, 661–672 (1997).
[CrossRef]

Pinnick, R. G.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

Rosen, H.

Wendtland, W. W.

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

Yasa, Z.

Anal. Chem. (1)

R. McCarthy, C. E. Moore, “Determination of free carbon in atmospheric dust,” Anal. Chem. 24, 411–412 (1952).
[CrossRef]

Appl. Opt. (8)

Chin-I Lin, M. Baker, R. J. Charlson, “Absorption coefficient of atmospheric aerosol: a method for measurement,” Appl. Opt. 12, 1356–1363 (1973).
[CrossRef] [PubMed]

A. D. A. Hansen, H. Rosen, T. Novakov, “Real-time measurement of the absorption coefficient of aerosol particles,” Appl. Opt. 21, 3060–3062 (1982).
[CrossRef] [PubMed]

J. Gillespie, J. D. Lindberg, “Seasonal and geographic variations in imaginary refractive index of atmospheric particulate matter,” Appl. Opt. 31, 2107–2111 (1992).
[CrossRef] [PubMed]

J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Carbon and the optical properties of atmospheric dust,” Appl. Opt. 32, 6077–6081 (1993).
[CrossRef] [PubMed]

J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Absorption-coefficient-determination method for particulate materials,” Appl. Opt. 33, 4314–4319 (1994).
[CrossRef] [PubMed]

H. Rosen, A. D. A. Hansen, L. Gundel, T. Novakov, “Identification of the graphitic carbon component of source and ambient particulates by Raman spectroscopy and an optical attenuation technique,” Appl. Opt. 17, 3859–3862 (1978).
[CrossRef] [PubMed]

Z. Yasa, N. M. Amer, H. Rosen, A. D. A. Hansen, T. Novakov, “Photoacoustic investigation of urban aerosol particles,” Appl. Opt. 18, 2528–2530 (1979).
[CrossRef] [PubMed]

H. Rosen, T. Novakov, “Optical transmission through aerosol deposits on diffusely reflective filters: a method for measuring the absorbing component of aerosol particles,” Appl. Opt. 22, 1265–1267 (1983).
[CrossRef] [PubMed]

Atmos. Environ. (1)

A. Petzold, C. Kopp, R. Niessner, “The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size,” Atmos. Environ. 31, 661–672 (1997).
[CrossRef]

Atmos. Environ. Part A (1)

C. Liousse, H. Cachier, S. G. Jennings, “Optical and thermal measurements of black carbon aerosol content in different environments: variation of the specific attenuation cross-section, sigma (σ),” Atmos. Environ. Part A 27, 1203–1211 (1993).
[CrossRef]

Envon. Sci. Technol. (1)

H. A. Gray, G. R. Cass, “Characteristics of atmospheric organic and elemental carbon particle concentrations in Los Angeles,” Envon. Sci. Technol. 20, 580–589 (1986).
[CrossRef]

J. Geophys. Res. (2)

Z. Levin, J. D. Lindberg, “Size distribution, chemical composition, and optical properties of urban and desert aerosols in Israel,” J. Geophys. Res. 84, 6941–6950 (1979).
[CrossRef]

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid southwestern United States: measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1993).
[CrossRef]

Opt. Quantum Electron. (1)

J. D. Lindberg, “The composition and optical absorption coefficient of atmospheric particulate matter,” Opt. Quantum Electron. 7, 131–139 (1975).
[CrossRef]

Sci. Total Environ. (1)

L. A. Gundel, R. L. Dod, H. Rosen, T. Novakov, “The relationship between optical attenuation and black carbon concentration for ambient and source particles,” Sci. Total Environ. 36, 197–202 (1984).
[CrossRef]

Other (7)

There is a further reason for making the measurements at near-IR wavelengths. Some laboratory methods determining carbon composition of samples involve burning the sample to remove carbon while using the LTM for monitoring black carbon content. Iron compounds, abundant in aerosols as trace materials, all result in Fe2O3 when completely oxidized. This iron oxide is a strong absorber in the visible spectrum where it adds absorption that may not be properly accounted for. This does not occur for near-IR wavelengths (see Refs. 4 and 14).

Laboratory measurement of fc is necessarily done on a mixture of carbon soot and a diluent powder. Because of the extremely high value of fc it is difficult to obtain a laboratory carbon sample reduced sufficiently in particle size to meet the requirements of the KM theory. This leads to an underestimate of fc. A value of 240,000 cm-1 rather than our value of 210,000 cm-1 would be more consistent with the research of Ref. 12.

H. Rosen, T. Novakov, “Lawrence Berkeley Laboratory Laser Transmission Method,” in Light Absorption by Aerosol Particles, H. E. Gerber, E. E. Hindman, eds. (Spectrum, Hampton, Va., 1982), pp. 321–334.

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

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

In the notation used in the original development of the KM theory, both lower- and upper-case symbols are used for the coefficients, with the definition 2k = K and 2s = S. This was done to eliminate a factor of 2 in the final equations and frequently causes confusion. In our research we use the lower-case symbols exclusively. For more detail on these specific expressions, see Ref. 16, pp. 106–120.

Our definition of attenuation does not include the arbitrary factor of 100 that was used in Refs. 10, 11, and 12.

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Figures (5)

Fig. 1
Fig. 1

Attenuation A as a function of absorption coefficient k for samples with d = 5 µm and R 0f = 0.91, with parameter s varied; s = 5000, 2500, 1000, and 100 cm-1, respectively, in curves A, B, C, and D.

Fig. 2
Fig. 2

Attenuation A as a function of absorption coefficient k for samples with d = 0.5 µm and R 0f = 0.91, with parameter s varied; s = 5000, 2500, 1000, and 100 cm-1, respectively, in curves A, B, C, and D.

Fig. 3
Fig. 3

Attenuation A as a function of absorption coefficient k for samples with d = 5 µm and R 0f = 1, with parameter s varied; s = 5000, 2500, 1000, and 100 cm-1, respectively, in curves A, B, C, and D.

Fig. 4
Fig. 4

Ratio r of the partial derivative of A with respect to k to the partial derivative of A with respect to s as a function of sample layer thickness d. R 0f is parametrically varied; R 0f = 1, 0.999, 0.99, 0.97, and 0.91 in curves A through E, respectively.

Fig. 5
Fig. 5

Attenuation A as a function of black carbon loading C in micrograms per square centimeter for accumulation of sample thickness in aerosols of constant composition. The black carbon mass fraction f c is parametrically varied; f c = 0.5, 1, 2, 4, 8, and 16% in curves A through F, respectively.

Tables (2)

Tables Icon

Table 1 Notations and Definitions

Tables Icon

Table 2 Parameters for a Typical Atmospheric Particulate Filter Sample

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

T=T/1-R0R0f,
A=-lnT=ln1-R0R0f-lnT.
a=1+k/s,
b=a2-11/2,
R0=a+b coth2bsd-1,
T=a-R02-b21/2.
A=Ak, s, d, R0f,
kV=kcVc+k0V0.
k=gmzCkcgc-k0g0+mk0g0,
A=AR0f, kc, gc, k0, g0, C, m, z, s, g,
fc=mc/m=zC/m,
r=A/kA/s.
σATN=σabs+1-fcfcσscat,
mfckc  m1-fck0,
fc1-fckck0  1.

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