Abstract

A laser technique for simultaneous determination of particle size and velocity is proposed and the requisite theoretical analysis presented. The method utilizes light scattering or fluorescence signatures from individual particles passing through parallel laser beams to specify completely the particle trajectory, including two velocity components and the traverse position, in the plane perpendicular to the laser beams. The incident-laser-intensity history of the particle can then be calculated, which allows the particle size to be unambiguously determined from absolute light-scattering or fluorescence measurements.

© 1978 Optical Society of America

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References

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  1. E. D. Hirleman, S. L. K. Wittig, Sixteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1977), p. 245.
    [CrossRef]
  2. F. R. Faxvog, Appl. Opt. 13, 1913 (1974).
    [CrossRef] [PubMed]
  3. W. M. Farmer, Appl. Opt. 11, 2603 (1972).
    [CrossRef] [PubMed]
  4. R. Schodl, “Laser Two-Focus Velocimetry for Use in Aero Engines,” AGARD Lecture Series No. 90, Trenton, N.J., August 25–26, 1977.
  5. K. G. Bartlett, C. Y. She, Opt. Lett. 1, 175 (1977).
    [CrossRef] [PubMed]
  6. M. J. Rudd, in Proceedings of the Second International Workshop on Laser Velocimetry, Eng. Exp. Station, Bull. No. 144 (Purdue U. P., Lafayette, Ind., 1974), Vol. II, p. 300.
  7. E. D. Hirleman, W. H. Stevenson, Appl. Opt., to be published (1978).
    [PubMed]
  8. E. D. Hirleman, Optical Technique for Particulate Characterization in Combustion Environments: The Multiple Ratio Single Particle Counter, Ph.D. dissertation, (Purdue U. P., Lafayette, Ind., August, 1977).
  9. C. C. Gravatt, J. Air Pollut. Control Assoc. 23, 1035 (1973).
    [CrossRef] [PubMed]
  10. J. Heyder, C. Roth, W. Stahlhofen, J. Aerosol Sci. 2, 341 (1971).
    [CrossRef]
  11. R. G. Kollenberg, in Aerosol Measurements, National Bureau of Standards Special Publication No. 412 (U.S. Government Printing Office, Washington, D.C., 1974), p. 57.
  12. W. H. Stevenson, R. dos Santos, S. C. Mettler, Appl. Phys. Lett. 27, 395 (1975).
    [CrossRef]
  13. R. dos Santos, W. Stevenson, Appl. Phys. Lett. 30, 236 (1977).
    [CrossRef]
  14. F. Durst, H. Umhauer, in The Accuracy of Flow Measurements by Laser Doppler Methods (Proceedings LDA Symposium, Copenhagen, Denmark, 1975), p. 430.

1977 (2)

R. dos Santos, W. Stevenson, Appl. Phys. Lett. 30, 236 (1977).
[CrossRef]

K. G. Bartlett, C. Y. She, Opt. Lett. 1, 175 (1977).
[CrossRef] [PubMed]

1975 (1)

W. H. Stevenson, R. dos Santos, S. C. Mettler, Appl. Phys. Lett. 27, 395 (1975).
[CrossRef]

1974 (1)

1973 (1)

C. C. Gravatt, J. Air Pollut. Control Assoc. 23, 1035 (1973).
[CrossRef] [PubMed]

1972 (1)

1971 (1)

J. Heyder, C. Roth, W. Stahlhofen, J. Aerosol Sci. 2, 341 (1971).
[CrossRef]

Bartlett, K. G.

dos Santos, R.

R. dos Santos, W. Stevenson, Appl. Phys. Lett. 30, 236 (1977).
[CrossRef]

W. H. Stevenson, R. dos Santos, S. C. Mettler, Appl. Phys. Lett. 27, 395 (1975).
[CrossRef]

Durst, F.

F. Durst, H. Umhauer, in The Accuracy of Flow Measurements by Laser Doppler Methods (Proceedings LDA Symposium, Copenhagen, Denmark, 1975), p. 430.

Farmer, W. M.

Faxvog, F. R.

Gravatt, C. C.

C. C. Gravatt, J. Air Pollut. Control Assoc. 23, 1035 (1973).
[CrossRef] [PubMed]

Heyder, J.

J. Heyder, C. Roth, W. Stahlhofen, J. Aerosol Sci. 2, 341 (1971).
[CrossRef]

Hirleman, E. D.

E. D. Hirleman, W. H. Stevenson, Appl. Opt., to be published (1978).
[PubMed]

E. D. Hirleman, Optical Technique for Particulate Characterization in Combustion Environments: The Multiple Ratio Single Particle Counter, Ph.D. dissertation, (Purdue U. P., Lafayette, Ind., August, 1977).

E. D. Hirleman, S. L. K. Wittig, Sixteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1977), p. 245.
[CrossRef]

Kollenberg, R. G.

R. G. Kollenberg, in Aerosol Measurements, National Bureau of Standards Special Publication No. 412 (U.S. Government Printing Office, Washington, D.C., 1974), p. 57.

Mettler, S. C.

W. H. Stevenson, R. dos Santos, S. C. Mettler, Appl. Phys. Lett. 27, 395 (1975).
[CrossRef]

Roth, C.

J. Heyder, C. Roth, W. Stahlhofen, J. Aerosol Sci. 2, 341 (1971).
[CrossRef]

Rudd, M. J.

M. J. Rudd, in Proceedings of the Second International Workshop on Laser Velocimetry, Eng. Exp. Station, Bull. No. 144 (Purdue U. P., Lafayette, Ind., 1974), Vol. II, p. 300.

Schodl, R.

R. Schodl, “Laser Two-Focus Velocimetry for Use in Aero Engines,” AGARD Lecture Series No. 90, Trenton, N.J., August 25–26, 1977.

She, C. Y.

Stahlhofen, W.

J. Heyder, C. Roth, W. Stahlhofen, J. Aerosol Sci. 2, 341 (1971).
[CrossRef]

Stevenson, W.

R. dos Santos, W. Stevenson, Appl. Phys. Lett. 30, 236 (1977).
[CrossRef]

Stevenson, W. H.

W. H. Stevenson, R. dos Santos, S. C. Mettler, Appl. Phys. Lett. 27, 395 (1975).
[CrossRef]

E. D. Hirleman, W. H. Stevenson, Appl. Opt., to be published (1978).
[PubMed]

Umhauer, H.

F. Durst, H. Umhauer, in The Accuracy of Flow Measurements by Laser Doppler Methods (Proceedings LDA Symposium, Copenhagen, Denmark, 1975), p. 430.

Wittig, S. L. K.

E. D. Hirleman, S. L. K. Wittig, Sixteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1977), p. 245.
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

W. H. Stevenson, R. dos Santos, S. C. Mettler, Appl. Phys. Lett. 27, 395 (1975).
[CrossRef]

R. dos Santos, W. Stevenson, Appl. Phys. Lett. 30, 236 (1977).
[CrossRef]

J. Aerosol Sci. (1)

J. Heyder, C. Roth, W. Stahlhofen, J. Aerosol Sci. 2, 341 (1971).
[CrossRef]

J. Air Pollut. Control Assoc. (1)

C. C. Gravatt, J. Air Pollut. Control Assoc. 23, 1035 (1973).
[CrossRef] [PubMed]

Opt. Lett. (1)

Other (7)

M. J. Rudd, in Proceedings of the Second International Workshop on Laser Velocimetry, Eng. Exp. Station, Bull. No. 144 (Purdue U. P., Lafayette, Ind., 1974), Vol. II, p. 300.

E. D. Hirleman, W. H. Stevenson, Appl. Opt., to be published (1978).
[PubMed]

E. D. Hirleman, Optical Technique for Particulate Characterization in Combustion Environments: The Multiple Ratio Single Particle Counter, Ph.D. dissertation, (Purdue U. P., Lafayette, Ind., August, 1977).

E. D. Hirleman, S. L. K. Wittig, Sixteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1977), p. 245.
[CrossRef]

R. Schodl, “Laser Two-Focus Velocimetry for Use in Aero Engines,” AGARD Lecture Series No. 90, Trenton, N.J., August 25–26, 1977.

R. G. Kollenberg, in Aerosol Measurements, National Bureau of Standards Special Publication No. 412 (U.S. Government Printing Office, Washington, D.C., 1974), p. 57.

F. Durst, H. Umhauer, in The Accuracy of Flow Measurements by Laser Doppler Methods (Proceedings LDA Symposium, Copenhagen, Denmark, 1975), p. 430.

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Figures (4)

Fig. 1
Fig. 1

Laser-beam properties and linear-particle traverses in a plane normal to a laser beam with the axis at (0,0).

Fig. 2
Fig. 2

Time dependence of laser intensity incident on particle moving along the linear, constant-velocity traverses of Fig. 1. Time referenced to x-axis crossings.

Fig. 3
Fig. 3

Particle traverse in plane normal to two parallel laser beams with axes at (±xb, 0).

Fig. 4
Fig. 4

Time dependence of incident intensity (and scattered-light-detector response) for linear, constant-velocity traverse of Fig. 3.

Equations (9)

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I ( r ) = I 0 exp ( - 2 r 2 / w 2 ) ,
I ( x t , y ) = I o exp ( - 2 x t 2 / w 2 ) exp ( - 2 y 2 / w 2 ) .
I ( x t , t ) = I 0 exp ( - 2 x t 2 / w 2 ) exp ( - 2 V 2 t 2 / w 2 ) .
V = w / t i ,
t t = 2 x b cos θ / V .
I 1 I 2 = exp ( 8 x b y c w 2 sin θ cos θ ) .
r min = x b sin θ ± y c cos θ
S max = σ ( d , n , g ) I max .
S max = σ ( d , n , g ) I 0 exp ( - 2 r min 2 / w 2 ) .

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