Abstract

We report about the determination of the axial velocity component by a laser Doppler velocity profile sensor that is based on two superposed fanlike interference fringe systems. Evaluation of the ratio of the Doppler frequencies obtained from each fringe system yields the lateral velocity component and the axial position inside the fringe system. Inclined particle trajectories result in chirped burst signals, where the change of the Doppler frequency in one burst signal is directly related to the axial velocity component. For one single tracer particle it is possible to determine (i) the lateral velocity component, (ii) the axial velocity component including the direction, and (iii) the axial position of the tracer trajectory. In this paper we present the measurement principle and report about results from simulation and experiments. An uncertainty of the axial velocity component of about 3% and a spatial resolution in the micrometer range were achieved. Possible applications of the sensor lie in three-component velocity measurements of flow fields where only one optical access is available.

© 2006 Optical Society of America

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References

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  1. H. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer, 2003).
  2. G. Byun, S. M. Ölcmen, and R. L. Simpson, "A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements," Meas. Sci. Technol. 15, 2075-2082 (2004).
    [CrossRef]
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  6. L. Büttner, J. Czarske, and H. Knuppertz, "Laser-Doppler velocity profile sensor with submicrometer spatial resolution that employs fiber optics and a diffractive lens," Appl. Opt. 44, 2274-2280 (2005).
    [CrossRef] [PubMed]
  7. J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
    [CrossRef]
  8. T. Pfister, L. Büttner, K. Shirai, and J. Czarske, "Monochromatic heterodyne fiber-optic profile sensor for spatially resolved velocity measurements with frequency division multiplexing," Appl. Opt. 44, 2501-2510 (2005).
    [CrossRef] [PubMed]
  9. T. Pfister, L. Büttner, and J. Czarske, "Laser Doppler profile sensor with sub-micrometre position resolution for velocity and absolute radius measurements of rotating objects," Meas. Sci. Technol. 16, 627-641 (2005).
    [CrossRef]
  10. P. C. Miles, "Geometry of the fringe field formed in the intersection of two Gaussian beams," Appl. Opt. 35, 5887-5895 (1996).
    [CrossRef] [PubMed]
  11. B. Lehmann, H. Nobach, and C. Tropea, "Measurement of acceleration using the laser Doppler technique," Meas. Sci. Technol. 13, 1367-1381 (2002).
    [CrossRef]

2005

2004

G. Byun, S. M. Ölcmen, and R. L. Simpson, "A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements," Meas. Sci. Technol. 15, 2075-2082 (2004).
[CrossRef]

2002

J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
[CrossRef]

B. Lehmann, H. Nobach, and C. Tropea, "Measurement of acceleration using the laser Doppler technique," Meas. Sci. Technol. 13, 1367-1381 (2002).
[CrossRef]

1996

1992

1982

1975

Aarnoudse, J. G.

Albrecht, H.

H. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer, 2003).

Benedeck, G. B.

Borys, M.

H. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer, 2003).

Büttner, L.

T. Pfister, L. Büttner, K. Shirai, and J. Czarske, "Monochromatic heterodyne fiber-optic profile sensor for spatially resolved velocity measurements with frequency division multiplexing," Appl. Opt. 44, 2501-2510 (2005).
[CrossRef] [PubMed]

L. Büttner, J. Czarske, and H. Knuppertz, "Laser-Doppler velocity profile sensor with submicrometer spatial resolution that employs fiber optics and a diffractive lens," Appl. Opt. 44, 2274-2280 (2005).
[CrossRef] [PubMed]

T. Pfister, L. Büttner, and J. Czarske, "Laser Doppler profile sensor with sub-micrometre position resolution for velocity and absolute radius measurements of rotating objects," Meas. Sci. Technol. 16, 627-641 (2005).
[CrossRef]

J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
[CrossRef]

Byun, G.

G. Byun, S. M. Ölcmen, and R. L. Simpson, "A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements," Meas. Sci. Technol. 15, 2075-2082 (2004).
[CrossRef]

Czarske, J.

T. Pfister, L. Büttner, and J. Czarske, "Laser Doppler profile sensor with sub-micrometre position resolution for velocity and absolute radius measurements of rotating objects," Meas. Sci. Technol. 16, 627-641 (2005).
[CrossRef]

L. Büttner, J. Czarske, and H. Knuppertz, "Laser-Doppler velocity profile sensor with submicrometer spatial resolution that employs fiber optics and a diffractive lens," Appl. Opt. 44, 2274-2280 (2005).
[CrossRef] [PubMed]

T. Pfister, L. Büttner, K. Shirai, and J. Czarske, "Monochromatic heterodyne fiber-optic profile sensor for spatially resolved velocity measurements with frequency division multiplexing," Appl. Opt. 44, 2501-2510 (2005).
[CrossRef] [PubMed]

J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
[CrossRef]

Damaschke, N.

H. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer, 2003).

Dassel, A. C. M.

de Mul, F. F. M.

Graaff, R.

Greve, J.

Hironaga, M.

Hoki, N.

Kajiya, F.

Kano, M.

Knuppertz, H.

Koelink, M. H.

Koyama, J.

Lehmann, B.

B. Lehmann, H. Nobach, and C. Tropea, "Measurement of acceleration using the laser Doppler technique," Meas. Sci. Technol. 13, 1367-1381 (2002).
[CrossRef]

Miles, P. C.

Müller, H.

J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
[CrossRef]

Nishihara, H.

Nobach, H.

B. Lehmann, H. Nobach, and C. Tropea, "Measurement of acceleration using the laser Doppler technique," Meas. Sci. Technol. 13, 1367-1381 (2002).
[CrossRef]

Ölcmen, S. M.

G. Byun, S. M. Ölcmen, and R. L. Simpson, "A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements," Meas. Sci. Technol. 15, 2075-2082 (2004).
[CrossRef]

Pfister, T.

T. Pfister, L. Büttner, and J. Czarske, "Laser Doppler profile sensor with sub-micrometre position resolution for velocity and absolute radius measurements of rotating objects," Meas. Sci. Technol. 16, 627-641 (2005).
[CrossRef]

T. Pfister, L. Büttner, K. Shirai, and J. Czarske, "Monochromatic heterodyne fiber-optic profile sensor for spatially resolved velocity measurements with frequency division multiplexing," Appl. Opt. 44, 2501-2510 (2005).
[CrossRef] [PubMed]

Razik, T.

J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
[CrossRef]

Shirai, K.

Simpson, R. L.

G. Byun, S. M. Ölcmen, and R. L. Simpson, "A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements," Meas. Sci. Technol. 15, 2075-2082 (2004).
[CrossRef]

Tanaka, T.

Tropea, C.

B. Lehmann, H. Nobach, and C. Tropea, "Measurement of acceleration using the laser Doppler technique," Meas. Sci. Technol. 13, 1367-1381 (2002).
[CrossRef]

H. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer, 2003).

Weijers, A. L.

Appl. Opt.

Meas. Sci. Technol.

G. Byun, S. M. Ölcmen, and R. L. Simpson, "A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements," Meas. Sci. Technol. 15, 2075-2082 (2004).
[CrossRef]

J. Czarske, L. Büttner, T. Razik, and H. Müller, "Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution," Meas. Sci. Technol. 13, 1979-1989 (2002).
[CrossRef]

T. Pfister, L. Büttner, and J. Czarske, "Laser Doppler profile sensor with sub-micrometre position resolution for velocity and absolute radius measurements of rotating objects," Meas. Sci. Technol. 16, 627-641 (2005).
[CrossRef]

B. Lehmann, H. Nobach, and C. Tropea, "Measurement of acceleration using the laser Doppler technique," Meas. Sci. Technol. 13, 1367-1381 (2002).
[CrossRef]

Other

H. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer, 2003).

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Figures (11)

Fig. 1
Fig. 1

(a) Superposed fanlike interference fringe systems of the laser-Doppler velocity profile sensor: top, convergent fringes; bottom, divergent fringes. (b) Coordinate system and parameters of the tracer particle movement.

Fig. 2
Fig. 2

Block diagram of burst signal processing. A/D, analog/digital; FFT, fast Fourier transform.

Fig. 3
Fig. 3

Simulated error of the axial velocity in dependence of the SNR for an angle between the lateral and the axial velocity components of α = 45 ° .

Fig. 4
Fig. 4

Experimental setup of the laser-Doppler velocity profile sensor for chirp detection.

Fig. 5
Fig. 5

Characterization of the laser-Doppler velocity profile sensor. (a) Fringe-spacing curves d 1 , 2 ( z ) . Both interference fringe systems exhibit a linear gradient of the fringe spacing. (b) Calibration curve q ( z ) = d 1 ( z ) d 2 ( z ) for the determination of the position.

Fig. 6
Fig. 6

(a) Burst signals directly obtained from the photodetectors. (b) Burst signals after signal preparation (bandpass filtering, normalization, and truncation to the 1 e 2 borders).

Fig. 7
Fig. 7

Period time–time functions for both channels, obtained from the ST-FFT. The momentary values at the marked point of time are used to calculate the offset position z 0 and the lateral velocity component v x , whereas the slope of the functions yields the axial v z component.

Fig. 8
Fig. 8

Test of (a) the angle and (b) the velocity component measurements for different inclination angles of the chopper. An excellent agreement between the default and the measured values occurs.

Fig. 9
Fig. 9

(a) Test of determination of the position and spatial resolution: measured position versus default position. (b) Measured velocities at different positions.

Fig. 10
Fig. 10

Influence of the SNR on the measurement accuracy. (a) The spatial resolution as well as the (b) relative uncertainty of the axial velocity exhibits an exponential decrease with rising SNR.

Fig. 11
Fig. 11

Test of (a) the angle measurement and (b) velocity component measurements for pointwise scattering particles emitted from an atomizer nozzle. The measured results agree well with the default values.

Equations (16)

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f = v x d .
q ( z ) = f 2 ( v x , z ) f 1 ( v x , z ) = v x d 2 ( z ) v x d 1 ( z ) = d 1 ( z ) d 2 ( z ) .
v x ( z ) = f 1 ( v x , z ) d 1 ( z ) = f 2 ( v x , z ) d 2 ( z ) .
v x = v cos α ,
v z = v sin α ,
tan α = v z v x .
d 1 ( z ) = d 01 + c 1 z ,
d 2 ( z ) = d 02 + c 2 z ,
r ( t ) = ( x ( t ) 0 z ( t ) ) = ( v x t 0 v z t + z 0 ) ,
f 1 , 2 ( v x , v z , z 0 , t ) = v x d 1 , 2 ( z ( t ) ) = v x d 01 , 2 + c 1 , 2 v z t + c 1 , 2 z 0 ,
T 1 , 2 ( t ) 1 f 1 , 2 ( t ) = d 01 , 2 + c 1 , 2 v z t + c 1 , 2 z 0 v x .
d T 1 , 2 ( t ) d t = c 1 , 2 v z v x .
v z = mse 2 v z , 1 + mse 1 v z , 2 mse 1 + mse 2 ,
I 1 , 2 ( x , z , t ) = I 0 exp ( 2 x 2 l x 2 ) exp ( 2 z 2 l z 2 ) cos 2 ( π x d 1 , 2 ( z ) ) ,
d 01 = 1.95 μ m , c 1 = 1.16 × 10 3 ,
d 02 = 2.70 μ m , c 2 = 1.38 × 10 3 .

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