Abstract

A dual-beam differential-type laser Doppler velocimeter using variable fringe spacing is proposed to measure the number density as well as the velocity of homogeneous monodisperse particles. The main function of the system is to investigate the variation in the visibility of the photodetector signal as a function of the crossing angle of the two beams. A preliminary experimental study was conducted to verify the theory. Good agreement between the theoretical and experimental results was obtained.

© 1984 Optical Society of America

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References

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  1. H. Mishina, T. Asakura, S. Nagai, “A Laser Doppler Microscope,” Opt. Commun. 11, 99 (1974).
    [Crossref]
  2. E. O. Schulz-Dubois, H. Koppe, P. Brummer, “Signal Statistics of Laser Light Scattering,” Appl. Phys. 21, 369 (1980).
    [Crossref]
  3. W. M. Farmer, “Measurement of Particle Size, Number Density, and Velocity Using a Laser Interferometer,” Appl. Opt. 11, 2603 (1972).
    [Crossref] [PubMed]
  4. M. J. Rudd, “A New Theoretical Model for the Laser Dopplermeter,” J. Phys. E 2, 55 (1969).
    [Crossref]
  5. T. S. Durrani, C. A. Greated, Laser Systems in Flow Measurements (Plenum, New York, 1977).
    [Crossref]
  6. K. Tedjojuwono, Y. Kawase, T. Asakura, “Effect of Particle Density on the Photodetector Signal of Differential-Type Laser Doppler Velocimetry,” Optik, (1984), in press.

1980 (1)

E. O. Schulz-Dubois, H. Koppe, P. Brummer, “Signal Statistics of Laser Light Scattering,” Appl. Phys. 21, 369 (1980).
[Crossref]

1974 (1)

H. Mishina, T. Asakura, S. Nagai, “A Laser Doppler Microscope,” Opt. Commun. 11, 99 (1974).
[Crossref]

1972 (1)

1969 (1)

M. J. Rudd, “A New Theoretical Model for the Laser Dopplermeter,” J. Phys. E 2, 55 (1969).
[Crossref]

Asakura, T.

H. Mishina, T. Asakura, S. Nagai, “A Laser Doppler Microscope,” Opt. Commun. 11, 99 (1974).
[Crossref]

K. Tedjojuwono, Y. Kawase, T. Asakura, “Effect of Particle Density on the Photodetector Signal of Differential-Type Laser Doppler Velocimetry,” Optik, (1984), in press.

Brummer, P.

E. O. Schulz-Dubois, H. Koppe, P. Brummer, “Signal Statistics of Laser Light Scattering,” Appl. Phys. 21, 369 (1980).
[Crossref]

Durrani, T. S.

T. S. Durrani, C. A. Greated, Laser Systems in Flow Measurements (Plenum, New York, 1977).
[Crossref]

Farmer, W. M.

Greated, C. A.

T. S. Durrani, C. A. Greated, Laser Systems in Flow Measurements (Plenum, New York, 1977).
[Crossref]

Kawase, Y.

K. Tedjojuwono, Y. Kawase, T. Asakura, “Effect of Particle Density on the Photodetector Signal of Differential-Type Laser Doppler Velocimetry,” Optik, (1984), in press.

Koppe, H.

E. O. Schulz-Dubois, H. Koppe, P. Brummer, “Signal Statistics of Laser Light Scattering,” Appl. Phys. 21, 369 (1980).
[Crossref]

Mishina, H.

H. Mishina, T. Asakura, S. Nagai, “A Laser Doppler Microscope,” Opt. Commun. 11, 99 (1974).
[Crossref]

Nagai, S.

H. Mishina, T. Asakura, S. Nagai, “A Laser Doppler Microscope,” Opt. Commun. 11, 99 (1974).
[Crossref]

Rudd, M. J.

M. J. Rudd, “A New Theoretical Model for the Laser Dopplermeter,” J. Phys. E 2, 55 (1969).
[Crossref]

Schulz-Dubois, E. O.

E. O. Schulz-Dubois, H. Koppe, P. Brummer, “Signal Statistics of Laser Light Scattering,” Appl. Phys. 21, 369 (1980).
[Crossref]

Tedjojuwono, K.

K. Tedjojuwono, Y. Kawase, T. Asakura, “Effect of Particle Density on the Photodetector Signal of Differential-Type Laser Doppler Velocimetry,” Optik, (1984), in press.

Appl. Opt. (1)

Appl. Phys. (1)

E. O. Schulz-Dubois, H. Koppe, P. Brummer, “Signal Statistics of Laser Light Scattering,” Appl. Phys. 21, 369 (1980).
[Crossref]

J. Phys. E (1)

M. J. Rudd, “A New Theoretical Model for the Laser Dopplermeter,” J. Phys. E 2, 55 (1969).
[Crossref]

Opt. Commun. (1)

H. Mishina, T. Asakura, S. Nagai, “A Laser Doppler Microscope,” Opt. Commun. 11, 99 (1974).
[Crossref]

Other (2)

T. S. Durrani, C. A. Greated, Laser Systems in Flow Measurements (Plenum, New York, 1977).
[Crossref]

K. Tedjojuwono, Y. Kawase, T. Asakura, “Effect of Particle Density on the Photodetector Signal of Differential-Type Laser Doppler Velocimetry,” Optik, (1984), in press.

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Figures (6)

Fig. 1
Fig. 1

Variations of probe volume size, fringe spacing, and fringe number as a function of the crossing angle 2θ of two beams.

Fig. 2
Fig. 2

Visibility variations of the photodetector signal as a function of the crossing angle 2θ of two beams for (a) three values, s = 7.5, 15, and 22 μm, of the particle separation and (b) three values, w = 5, 7.5, and 15 μm, of the beam radius.

Fig. 3
Fig. 3

Computer simulation result for the visibility variation of the photodetector signal as a function of the crossing angle 2θ of two beams.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup with the optical arrangement used to vary the fringe spacing together with photographs of four different fringe spacings experimentally obtained.

Fig. 5
Fig. 5

Visibility variations of the photodetector signal as a function of the crossing angle 2θ of two beams for the two cases of the regular particle separation: (a) s = 3 mm and (b) 4 mm. The solid curve indicates the theoretical result, and the dots show the experimental values.

Fig. 6
Fig. 6

Experimental result for the visibility variation of the photodetector signal as a function of the crossing angle 2θ of two beams: 1,2, positions of two neighboring peaks; 3,4, those of two neighboring valleys.

Equations (10)

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i θ ( t ) = 4 η A 2 exp [ - 2 ( v t cos θ ) 2 w 0 2 ] · cos 2 ( 2 π v t d ) ,
I θ ( f ) = π 2 η A 2 w 0 v cos θ { 2 exp ( - π 2 w 0 2 f 2 2 v 2 cos 2 θ ) + exp [ - π 2 w 0 2 ( f - f D ) 2 2 v 2 cos 2 θ ] + exp [ - π 2 w 0 2 ( f - f D ) 2 2 v 2 cos 2 θ ] } ,
I m , θ ( f ) = π 2 η A 2 w 0 v cos θ { 2 exp ( - π 2 w 0 2 f 2 2 v 2 cos 2 θ ) + exp [ - π 2 w 0 2 ( f - f D ) 2 2 v 2 cos 2 θ ] + exp [ - π 2 w 0 2 ( f - f D ) 2 2 v 2 cos 2 θ ] } · T ˜ ( s t f ) ,
T ( t / s t ) = m = - δ ( t - m s t ) = m = - exp ( i 2 π m t s t ) .
V ( θ ) = 2 m = 0 exp [ - π 2 w 0 2 2 v 2 cos 2 θ ( m v s - 2 v sin θ λ ) 2 ] m = 0 exp ( - m π 2 w 0 2 2 s v 2 cos 2 θ ) .
N = 4 w 0 λ tan θ .
m s = 2 sin θ m λ o r θ m = sin - 1 ( m λ 2 s ) .
s = λ 2 ( sin θ m + 1 - sin θ m ) .
ρ ( s ) = 1 2 π σ exp [ ( s - s ¯ ) 2 2 σ 2 ] ,
v = i beat i pedestal .

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