Abstract

Single scattering characteristics of volume elements in coal clouds are discussed and computed, with the aim of developing laser diagnosis methods in dense particle-laden flows, where multiple scattering phenomena become predominant. Results are provided for extinction efficiency factors, single scattering albedos, asymmetry parameters, forward scattering ratios, and phase functions (rigorous as well as modeled). Interest is focused on coal particles because of their present importance in connection with problems linked to the crisis of energy. Computations are carried out at three wavelengths covering 3 orders of magnitude (0.5145-μm Ar-ion laser; 10.6-μm CO2 laser; 337-μm HCN laser) for diameters ranging from ~1 to ~100 μm.

© 1983 Optical Society of America

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References

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  1. G. Gouesbet, G. Grehan, “Laser-Doppler Systems for Plasma Measurements: A Review and Prospective Paper,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. 1979.
  2. G. Gouesbet, G. Grehan, “The Quasi-Elastic Scattering of Light: A Lecture with Emphasis on Particulate Diagnosis,” in Proceedings, NATO Workshop on Soot in Combustion Systems, and Its Toxic Properties, Le Bischenberg, 31 Aug.–3 Sept. 1981, to be published.
  3. R. Kleine, G. Gouesbet, Gleichzeitige lokale Optische Messungen der Teilchengeschwindigkeit, Teilchengrösse und Teilchenkonzentration. Beitrag Zur Sensor 82, Essen (Januar1982).
  4. D. Allano, G. Gouesbet, G. Grehan, D. Lisiecki, “Comparative Measurements of Calibrated Droplets Using Gabor Holography and Corrected Top-Hat Laser Beam Sizing with Discussion of Simultaneous Velocimetry,” in Proceedings, International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 5–7 July 1982.
  5. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  6. S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).
  7. H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas, and Applications, Vols. 1 and 2 (Academic, New York, 1980).
  8. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersion (American Elsevier, New York, 1969).
  9. G. Grehan, G. Gouesbet, Appl. Opt. 18, 3489 (1979).
    [CrossRef] [PubMed]
  10. G. Gouesbet, G. Grehan, J. Opt. 13, 97 (1982).
    [CrossRef]
  11. N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
    [CrossRef]
  12. W. C. Tsai, R. J. Pogorzelski, J. Opt. Soc. Am. 65, 1457 (1975).
    [CrossRef]
  13. W. G. Tam, R. Corriveau, J. Opt. Soc. Am. 68, 763 (1978).
    [CrossRef]
  14. P. Debye, Ann. Phys. (Leipzig) 4, No. 30, 57 (1909).
  15. W. M. Irvine, J. Opt. Soc. Am. 1, 16 (1965).
    [CrossRef]
  16. A. Ungut, G. Grehan, G. Gouesbet, Appl. Opt. 20, 2911 (1981).
    [CrossRef] [PubMed]
  17. G. Grehan, G. Gouesbet, C. Rabasse, Appl. Opt. 20, 796 (1981).
    [CrossRef] [PubMed]
  18. H. Kagiwada, R. Kalaba, Rand Report RM-55 37-PR, Rand Corp., Santa Monica, California (1967).
  19. L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
    [CrossRef]
  20. W. M. Irvine, Astrophys. J. 4, 1563 (1965).
    [CrossRef]
  21. G. Kortum, Reflectance Spectroscopy (Springer, Berlin, 1969).
    [CrossRef]
  22. P. Chylek, J. Opt. Soc. Am. 63, 1467 (1973).
    [CrossRef]
  23. G. Grehan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.
  24. G. Grehan, G. Gouesbet, “The Computer Program supermidi for Mie Theory Calculations, Without Practical Size nor Refractive Index Limitations,” Internal Report TTI/GG/79/03/20.
  25. J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
    [CrossRef]
  26. J. T. McCartney, J. B. Yasinsky, S. Ergun, Fuels 44, 349 (1965).
  27. C. Willis, Appl. Phys. 3, 1944 (1970).
  28. P. J. Foster, C. R. Howarth, Carbon 6, 719 (1968).
    [CrossRef]
  29. L. A. Gilbert, Fuels 41, 351 (1968).
  30. J. T. McCartney, S. Ergun, Fuels 37, 272 (1958).
  31. S. R. Broadbent, A. J. Shaw, Fuels 34, 385 (1955).
  32. K. C. Lahiri, T. N. Basu, J. Sci. Ind. Res. Sect. B, 11, 486 (1952).
  33. M. W. Williams, E. T. Arakawa, J. Appl. Phys. 43, No. 8 (1972).
  34. M. Hale, M. R. Querry, Appl. Opt. 12, 555 (1973).
    [CrossRef] [PubMed]
  35. B. H. J. McKellar, M. A. Box, J. Atmos. Sci. 38, 1063 (1981).
    [CrossRef]
  36. S. Chandrasekhar, Proc. Natl. Acad. Sci. U.S.A. 44, 933 (1958).
    [CrossRef] [PubMed]
  37. G. B. Rybicki, J. Quant. Spectrosc. Radiat. Transfer 11, 827 (1971).
    [CrossRef]
  38. P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
    [CrossRef]
  39. A. L. Crosbie, R. L. Dougherty, J. Quant. Spectrosc. Radiat. Transfer 20, 151 (1977).
    [CrossRef]
  40. D. C. Look, H. F. Nelson, A. L. Crosbie, J. Heat Transfer 103, 127 (1981).
    [CrossRef]

1982

G. Gouesbet, G. Grehan, J. Opt. 13, 97 (1982).
[CrossRef]

R. Kleine, G. Gouesbet, Gleichzeitige lokale Optische Messungen der Teilchengeschwindigkeit, Teilchengrösse und Teilchenkonzentration. Beitrag Zur Sensor 82, Essen (Januar1982).

1981

B. H. J. McKellar, M. A. Box, J. Atmos. Sci. 38, 1063 (1981).
[CrossRef]

D. C. Look, H. F. Nelson, A. L. Crosbie, J. Heat Transfer 103, 127 (1981).
[CrossRef]

G. Grehan, G. Gouesbet, C. Rabasse, Appl. Opt. 20, 796 (1981).
[CrossRef] [PubMed]

A. Ungut, G. Grehan, G. Gouesbet, Appl. Opt. 20, 2911 (1981).
[CrossRef] [PubMed]

1979

1978

1977

A. L. Crosbie, R. L. Dougherty, J. Quant. Spectrosc. Radiat. Transfer 20, 151 (1977).
[CrossRef]

1975

1974

P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
[CrossRef]

1973

1972

M. W. Williams, E. T. Arakawa, J. Appl. Phys. 43, No. 8 (1972).

1971

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

G. B. Rybicki, J. Quant. Spectrosc. Radiat. Transfer 11, 827 (1971).
[CrossRef]

1970

C. Willis, Appl. Phys. 3, 1944 (1970).

1968

P. J. Foster, C. R. Howarth, Carbon 6, 719 (1968).
[CrossRef]

L. A. Gilbert, Fuels 41, 351 (1968).

N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

1965

J. T. McCartney, J. B. Yasinsky, S. Ergun, Fuels 44, 349 (1965).

W. M. Irvine, J. Opt. Soc. Am. 1, 16 (1965).
[CrossRef]

W. M. Irvine, Astrophys. J. 4, 1563 (1965).
[CrossRef]

1958

S. Chandrasekhar, Proc. Natl. Acad. Sci. U.S.A. 44, 933 (1958).
[CrossRef] [PubMed]

J. T. McCartney, S. Ergun, Fuels 37, 272 (1958).

1955

S. R. Broadbent, A. J. Shaw, Fuels 34, 385 (1955).

1952

K. C. Lahiri, T. N. Basu, J. Sci. Ind. Res. Sect. B, 11, 486 (1952).

1941

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[CrossRef]

1909

P. Debye, Ann. Phys. (Leipzig) 4, No. 30, 57 (1909).

Allano, D.

D. Allano, G. Gouesbet, G. Grehan, D. Lisiecki, “Comparative Measurements of Calibrated Droplets Using Gabor Holography and Corrected Top-Hat Laser Beam Sizing with Discussion of Simultaneous Velocimetry,” in Proceedings, International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 5–7 July 1982.

Arakawa, E. T.

M. W. Williams, E. T. Arakawa, J. Appl. Phys. 43, No. 8 (1972).

Backett, P.

P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
[CrossRef]

Basu, T. N.

K. C. Lahiri, T. N. Basu, J. Sci. Ind. Res. Sect. B, 11, 486 (1952).

Box, M. A.

B. H. J. McKellar, M. A. Box, J. Atmos. Sci. 38, 1063 (1981).
[CrossRef]

Broadbent, S. R.

S. R. Broadbent, A. J. Shaw, Fuels 34, 385 (1955).

Chandrasekhar, S.

S. Chandrasekhar, Proc. Natl. Acad. Sci. U.S.A. 44, 933 (1958).
[CrossRef] [PubMed]

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).

Chylek, P.

Corriveau, R.

Crosbie, A. L.

D. C. Look, H. F. Nelson, A. L. Crosbie, J. Heat Transfer 103, 127 (1981).
[CrossRef]

A. L. Crosbie, R. L. Dougherty, J. Quant. Spectrosc. Radiat. Transfer 20, 151 (1977).
[CrossRef]

Debye, P.

P. Debye, Ann. Phys. (Leipzig) 4, No. 30, 57 (1909).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersion (American Elsevier, New York, 1969).

Dougherty, R. L.

A. L. Crosbie, R. L. Dougherty, J. Quant. Spectrosc. Radiat. Transfer 20, 151 (1977).
[CrossRef]

Ergun, S.

J. T. McCartney, J. B. Yasinsky, S. Ergun, Fuels 44, 349 (1965).

J. T. McCartney, S. Ergun, Fuels 37, 272 (1958).

Foster, P. J.

P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
[CrossRef]

P. J. Foster, C. R. Howarth, Carbon 6, 719 (1968).
[CrossRef]

Gilbert, L. A.

L. A. Gilbert, Fuels 41, 351 (1968).

Gouesbet, G.

G. Gouesbet, G. Grehan, J. Opt. 13, 97 (1982).
[CrossRef]

R. Kleine, G. Gouesbet, Gleichzeitige lokale Optische Messungen der Teilchengeschwindigkeit, Teilchengrösse und Teilchenkonzentration. Beitrag Zur Sensor 82, Essen (Januar1982).

G. Grehan, G. Gouesbet, C. Rabasse, Appl. Opt. 20, 796 (1981).
[CrossRef] [PubMed]

A. Ungut, G. Grehan, G. Gouesbet, Appl. Opt. 20, 2911 (1981).
[CrossRef] [PubMed]

G. Grehan, G. Gouesbet, Appl. Opt. 18, 3489 (1979).
[CrossRef] [PubMed]

G. Grehan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

G. Gouesbet, G. Grehan, “Laser-Doppler Systems for Plasma Measurements: A Review and Prospective Paper,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. 1979.

G. Gouesbet, G. Grehan, “The Quasi-Elastic Scattering of Light: A Lecture with Emphasis on Particulate Diagnosis,” in Proceedings, NATO Workshop on Soot in Combustion Systems, and Its Toxic Properties, Le Bischenberg, 31 Aug.–3 Sept. 1981, to be published.

D. Allano, G. Gouesbet, G. Grehan, D. Lisiecki, “Comparative Measurements of Calibrated Droplets Using Gabor Holography and Corrected Top-Hat Laser Beam Sizing with Discussion of Simultaneous Velocimetry,” in Proceedings, International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 5–7 July 1982.

G. Grehan, G. Gouesbet, “The Computer Program supermidi for Mie Theory Calculations, Without Practical Size nor Refractive Index Limitations,” Internal Report TTI/GG/79/03/20.

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[CrossRef]

Grehan, G.

G. Gouesbet, G. Grehan, J. Opt. 13, 97 (1982).
[CrossRef]

G. Grehan, G. Gouesbet, C. Rabasse, Appl. Opt. 20, 796 (1981).
[CrossRef] [PubMed]

A. Ungut, G. Grehan, G. Gouesbet, Appl. Opt. 20, 2911 (1981).
[CrossRef] [PubMed]

G. Grehan, G. Gouesbet, Appl. Opt. 18, 3489 (1979).
[CrossRef] [PubMed]

G. Grehan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

G. Gouesbet, G. Grehan, “Laser-Doppler Systems for Plasma Measurements: A Review and Prospective Paper,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. 1979.

D. Allano, G. Gouesbet, G. Grehan, D. Lisiecki, “Comparative Measurements of Calibrated Droplets Using Gabor Holography and Corrected Top-Hat Laser Beam Sizing with Discussion of Simultaneous Velocimetry,” in Proceedings, International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 5–7 July 1982.

G. Gouesbet, G. Grehan, “The Quasi-Elastic Scattering of Light: A Lecture with Emphasis on Particulate Diagnosis,” in Proceedings, NATO Workshop on Soot in Combustion Systems, and Its Toxic Properties, Le Bischenberg, 31 Aug.–3 Sept. 1981, to be published.

G. Grehan, G. Gouesbet, “The Computer Program supermidi for Mie Theory Calculations, Without Practical Size nor Refractive Index Limitations,” Internal Report TTI/GG/79/03/20.

Hale, M.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[CrossRef]

Howarth, C. R.

P. J. Foster, C. R. Howarth, Carbon 6, 719 (1968).
[CrossRef]

Hutson, V.

P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
[CrossRef]

Irvine, W. M.

W. M. Irvine, J. Opt. Soc. Am. 1, 16 (1965).
[CrossRef]

W. M. Irvine, Astrophys. J. 4, 1563 (1965).
[CrossRef]

Kagiwada, H.

H. Kagiwada, R. Kalaba, Rand Report RM-55 37-PR, Rand Corp., Santa Monica, California (1967).

Kalaba, R.

H. Kagiwada, R. Kalaba, Rand Report RM-55 37-PR, Rand Corp., Santa Monica, California (1967).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kleine, R.

R. Kleine, G. Gouesbet, Gleichzeitige lokale Optische Messungen der Teilchengeschwindigkeit, Teilchengrösse und Teilchenkonzentration. Beitrag Zur Sensor 82, Essen (Januar1982).

Kortum, G.

G. Kortum, Reflectance Spectroscopy (Springer, Berlin, 1969).
[CrossRef]

Lahiri, K. C.

K. C. Lahiri, T. N. Basu, J. Sci. Ind. Res. Sect. B, 11, 486 (1952).

Lisiecki, D.

D. Allano, G. Gouesbet, G. Grehan, D. Lisiecki, “Comparative Measurements of Calibrated Droplets Using Gabor Holography and Corrected Top-Hat Laser Beam Sizing with Discussion of Simultaneous Velocimetry,” in Proceedings, International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 5–7 July 1982.

Look, D. C.

D. C. Look, H. F. Nelson, A. L. Crosbie, J. Heat Transfer 103, 127 (1981).
[CrossRef]

McCartney, J. T.

J. T. McCartney, J. B. Yasinsky, S. Ergun, Fuels 44, 349 (1965).

J. T. McCartney, S. Ergun, Fuels 37, 272 (1958).

McKellar, B. H. J.

B. H. J. McKellar, M. A. Box, J. Atmos. Sci. 38, 1063 (1981).
[CrossRef]

Morita, N.

N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Moss, R. L.

P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
[CrossRef]

Nelson, H. F.

D. C. Look, H. F. Nelson, A. L. Crosbie, J. Heat Transfer 103, 127 (1981).
[CrossRef]

Pogorzelski, R. J.

Querry, M. R.

Rabasse, C.

G. Grehan, G. Gouesbet, C. Rabasse, Appl. Opt. 20, 796 (1981).
[CrossRef] [PubMed]

G. Grehan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

Rybicki, G. B.

G. B. Rybicki, J. Quant. Spectrosc. Radiat. Transfer 11, 827 (1971).
[CrossRef]

Shaw, A. J.

S. R. Broadbent, A. J. Shaw, Fuels 34, 385 (1955).

Tam, W. G.

Tanaka, T.

N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Tomohisa, T.

N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Tsai, W. C.

Twitty, J. T.

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

Ungut, A.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas, and Applications, Vols. 1 and 2 (Academic, New York, 1980).

Weinman, J. A.

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

Williams, M. W.

M. W. Williams, E. T. Arakawa, J. Appl. Phys. 43, No. 8 (1972).

Willis, C.

C. Willis, Appl. Phys. 3, 1944 (1970).

Yasinsky, J. B.

J. T. McCartney, J. B. Yasinsky, S. Ergun, Fuels 44, 349 (1965).

Yoshiro, N.

N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Ann. Phys. (Leipzig)

P. Debye, Ann. Phys. (Leipzig) 4, No. 30, 57 (1909).

Appl. Opt.

Appl. Phys.

C. Willis, Appl. Phys. 3, 1944 (1970).

Astrophys. J.

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[CrossRef]

W. M. Irvine, Astrophys. J. 4, 1563 (1965).
[CrossRef]

Carbon

P. J. Foster, C. R. Howarth, Carbon 6, 719 (1968).
[CrossRef]

Fuels

L. A. Gilbert, Fuels 41, 351 (1968).

J. T. McCartney, S. Ergun, Fuels 37, 272 (1958).

S. R. Broadbent, A. J. Shaw, Fuels 34, 385 (1955).

J. T. McCartney, J. B. Yasinsky, S. Ergun, Fuels 44, 349 (1965).

Gleichzeitige lokale Optische Messungen der Teilchengeschwindigkeit, Teilchengrösse und Teilchenkonzentration. Beitrag Zur Sensor

R. Kleine, G. Gouesbet, Gleichzeitige lokale Optische Messungen der Teilchengeschwindigkeit, Teilchengrösse und Teilchenkonzentration. Beitrag Zur Sensor 82, Essen (Januar1982).

IEEE Trans. Antennas Propag.

N. Morita, T. Tanaka, T. Tomohisa, N. Yoshiro, IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

J. Appl. Meteorol.

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

J. Appl. Phys.

M. W. Williams, E. T. Arakawa, J. Appl. Phys. 43, No. 8 (1972).

J. Atmos. Sci.

B. H. J. McKellar, M. A. Box, J. Atmos. Sci. 38, 1063 (1981).
[CrossRef]

J. Heat Transfer

D. C. Look, H. F. Nelson, A. L. Crosbie, J. Heat Transfer 103, 127 (1981).
[CrossRef]

J. Opt.

G. Gouesbet, G. Grehan, J. Opt. 13, 97 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

G. B. Rybicki, J. Quant. Spectrosc. Radiat. Transfer 11, 827 (1971).
[CrossRef]

P. Backett, P. J. Foster, V. Hutson, R. L. Moss, J. Quant. Spectrosc. Radiat. Transfer 14, 1115 (1974).
[CrossRef]

A. L. Crosbie, R. L. Dougherty, J. Quant. Spectrosc. Radiat. Transfer 20, 151 (1977).
[CrossRef]

J. Sci. Ind. Res. Sect. B

K. C. Lahiri, T. N. Basu, J. Sci. Ind. Res. Sect. B, 11, 486 (1952).

Proc. Natl. Acad. Sci. U.S.A.

S. Chandrasekhar, Proc. Natl. Acad. Sci. U.S.A. 44, 933 (1958).
[CrossRef] [PubMed]

Other

G. Kortum, Reflectance Spectroscopy (Springer, Berlin, 1969).
[CrossRef]

G. Grehan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

G. Grehan, G. Gouesbet, “The Computer Program supermidi for Mie Theory Calculations, Without Practical Size nor Refractive Index Limitations,” Internal Report TTI/GG/79/03/20.

H. Kagiwada, R. Kalaba, Rand Report RM-55 37-PR, Rand Corp., Santa Monica, California (1967).

G. Gouesbet, G. Grehan, “Laser-Doppler Systems for Plasma Measurements: A Review and Prospective Paper,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. 1979.

G. Gouesbet, G. Grehan, “The Quasi-Elastic Scattering of Light: A Lecture with Emphasis on Particulate Diagnosis,” in Proceedings, NATO Workshop on Soot in Combustion Systems, and Its Toxic Properties, Le Bischenberg, 31 Aug.–3 Sept. 1981, to be published.

D. Allano, G. Gouesbet, G. Grehan, D. Lisiecki, “Comparative Measurements of Calibrated Droplets Using Gabor Holography and Corrected Top-Hat Laser Beam Sizing with Discussion of Simultaneous Velocimetry,” in Proceedings, International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, Lisbon, Portugal, 5–7 July 1982.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).

H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas, and Applications, Vols. 1 and 2 (Academic, New York, 1980).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersion (American Elsevier, New York, 1969).

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Figures (22)

Fig. 1
Fig. 1

n(coal) vs λ,λ ranging from 0.2 to 0.6 μm.

Fig. 2
Fig. 2

nk(coal) vs λ,λ ranging from 0.2 to 0.6 μm.

Fig. 3
Fig. 3

n(coal) vs λ,λ ranging from 1 to 10 μm.

Fig. 4
Fig. 4

nk(coal) vs λ,λ ranging from 1 to 10 μm.

Fig. 5
Fig. 5

a, g, ζ, and Qext vs d for λ = 0.5145 μm and m = 1.7–0.1i.

Fig. 6
Fig. 6

a, g, ζ, and Qext vs d for λ = 0.5145 μm and m = 2.0–0.6i.

Fig. 7
Fig. 7

a, g, ζ, and Qext vs d for λ = 10.6 μm and m = 1.7–0.7i.

Fig. 8
Fig. 8

a, g, ζ, and Qext vs d for λ = 10.6 μm and m = 2.6–1.2i.

Fig. 9
Fig. 9

a, g, ζ, and Qext vs d for λ = 337 μm and m = 2.0–5.0i.

Fig. 10
Fig. 10

a, g, ζ, and Qext vs d for λ = 337 μm and m = 4.0–10.0i.

Fig. 11
Fig. 11

Comparisons between pLMT and pHG for d = 5 μm, m = 1.7–0.1i, and λ = 0.5145 μm.

Fig. 12
Fig. 12

Comparisons between pLMT and pHG for d = 25 μm, m = 1.7–0.1i, and λ = 0.5145 μm.

Fig. 13
Fig. 13

Comparisons between pLMT and pHG for d = 100 μm, m = 1.7–0.1i, and λ = 0.5145 μm.

Fig. 14
Fig. 14

Comparisons between pLMT and pHG for d = 5 μm, m = 1.7–0.7i, and λ = 10.6 μm.

Fig. 15
Fig. 15

Comparisons between pLMT and pHG for d = 25 μm, m = 1.7–0.7i, and λ = 10.6 μm.

Fig. 16
Fig. 16

Comparisons between pLMT and pHG for d = 100 μm, m = 1.7–0.7i, and λ = 10.6 μm.

Fig. 17
Fig. 17

Comparisons between pLMT, pHG, and isotropic scattering, for λ = 337 μm, m = 2.0–5.0i, and d = 5, 25, and 100 μm.

Fig. 18
Fig. 18

Comparisons between pLMT, p R C, pE, and pKK for d = 5 μm, m = 2.0–5.0i, and λ = 337 μm.

Fig. 19
Fig. 19

Comparisons between pLMT, p R C, pE, and pKK for d = 25 μm, m = 2.0–5.0i, and λ = 337 μm.

Fig. 20
Fig. 20

Comparisons between pLMT, p R C, pE, and pKK for d = 100 μm, m = 2.0–5.0i, and λ = 337 μm.

Fig. 21
Fig. 21

Different p LMT av for d = 24.95 μm, m = 1.7–0.7i, and λ = 10.6 μm.

Fig. 22
Fig. 22

Reflectance for a completely opaque atmosphere for m = 4.0–10.0i and λ = 337 μm.

Tables (9)

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Table I For 0.5145-μm Wavelength and 1.7–0.1i Index

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Table II For 0.5145-μm Wavelength and 2.0–0.6i Index

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Table III For 10.6-μm Wavelength and 1.7–0.7i Index

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Table IV For 10.6-μm Wavelength and 2.6–1.2i Index

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Table V For 337-μm Wavelength and 2.0–5.0i Index

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Table VI For 337-μm Wavelength and 2.0–5.0i Index

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Table VII For 337-μm Wavelength and 4.0–10.0i Index

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Table VIII For 337-μm Wavelength and 4.0–10.0i Index

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Table IX Comparison Between Values Obtained from van de Hulst and Our Computations for Various α and m

Equations (34)

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p LMT ( cos θ ) = 2 α 2 Q ext ( S 1 2 + S 2 2 ) ,
ϕ LMT ( cos θ ) = 1 a p LMT ( cos θ ) = 2 α 2 Q sca = 2 α 2 Q sca ( S 1 2 + S 2 2 ) ,
N ^ = 4 π · d ω 4 π ,
g = cos θ = 1 2 a 0 π p ( cos θ ) sin θ cos θ d θ
g = 0 π p ( cos θ ) sin θ cos θ d θ 0 π p ( cos θ ) sin θ d θ = 1 2 - 1 + 1 ϕ ( μ ) μ d μ ,
g LMT = 4 α 2 Q sca n = 1 × [ n ( n + 2 ) n + 1 Re ( a n * a n + 1 + b n * b n + 1 ) + 2 n + 1 n ( n + 1 ) Re ( a n * b n ) ] ,
g LMT = 4 α 2 Q sca n = 1 { n ( n + 2 ) n + 1 [ Re ( a n ) Re ( a n + 1 ) + Im ( a n ) Im ( a n + 1 ) + Re ( b n ) Re ( b n + 1 ) + Im ( b n ) Im ( b n + 1 ) ] + 2 n + 1 n ( n + 1 ) [ Re ( a n ) Re ( b n ) + Im ( a n ) Im ( b n ) ] } .
g LMT = Q ext - Q pr Q sca ,
F = A c Q pr ,
p L ( cos θ ) = n = 0 N ω n P n ( cos θ ) ,
ω n = ( 2 n + 1 ) 2 - 1 + 1 p ( cos θ ) P n ( cos θ ) d ( cos θ ) .
ω 0 = a ,
ω 1 = 3 a g .
p L ( cos θ ) = a ( 1 + 3 g cos θ ) + n = 2 N ω n P n ( cos θ ) ,
p II ( cos θ ) = a ( 1 + 3 g cos θ ) .
p E ( cos θ ) = a ( 1 + ξ cos θ ) ,
p I = a .
p R ( cos θ ) = ¾ ( 1 + cos 2 θ ) .
p R C ( cos θ ) = a p R ( cos θ ) .
p KK ( cos θ ) = a k b - cos θ ,
k = 2 [ ln ( b + 1 b - 1 ) ] - 1 ,
b = r FB + 1 r FB - 1 ,
b = 1 / ( 2 ζ - 1 ) .
p HG ( cos θ ) = a ( 1 - g 2 ) ( 1 + g 2 - 2 g cos θ ) 3 / 2 .
p HG ( cos θ ) = a n = 0 ( 2 n + 1 ) g n P n ( cos θ ) .
p ( θ , g 1 , g 2 , ) = p HG ( θ , g 1 ) + ( 1 - ) p HG ( θ , g 2 ) .
1 2 λ d - λ d + λ · d d ,
p LMT av ( cos θ ) = 1 2 β λ d - β λ d + β λ p LMT ( cos θ ) · d d ,
4 π p LMT av ( cos θ ) d ω 4 π = a av .
a av = 1 2 β λ d - β λ d + β λ a ( d ) · d d .
ζ = C sca f / C sca ,
C sca f = 1 2 C sca - λ 2 2 π { n = 1 o m = 2 e ( 2 n + 1 ) ( 2 m + 1 ) [ m ( m + 1 ) - n ( n + 1 ) ] ( - 1 ) n + m - 1 2 · n ? ? ( m - 1 ) ? ? ( n - 1 ) ? ? m ? ? × Re ( a n a m * + b n b m * ) + n = 1 o m = 1 o 2 n + 1 n ( n + 1 ) · 2 m + 1 m ( m + 1 ) ( - 1 ) n + m - 1 2 n ? ? m ? ? ( n - 1 ) ? ? ( m - 1 ) ? ? Re ( a n b m * ) }
0 ? ? = 1 ? ? = 1 , n ? ? = ( n - 2 ) ? ? n , }
R = 1 - 1 - a 1 + 1 - a ,

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