Abstract

Holographic particle image velocimetry (HPIV) is presently the only method that can measure at high resolution all three components of the velocity in a finite volume. In systems that are based on recording one hologram, velocity components parallel to the hologram can be measured throughout the sample volume, but elongation of the particle traces in the depth direction severely limits the accuracy of the velocity component that is perpendicular to the hologram. Previous studies overcame this limitation by simultaneously recording two orthogonal holograms, which inherently required four windows and two recording systems. This paper introduces a technique that maintains the advantages of recording two orthogonal views, but requires only one window and one recording system. Furthermore, it enables a quadruple increase in the spatial resolution. This method is based on placing a mirror in the test section that reflects the object beam at an angle of 45°. Particles located in the volume in which the incident and reflected beams from the mirror overlap are illuminated twice in perpendicular directions. Both views are recorded on the same hologram. Off-axis holography with conjugate reconstruction and high-pass filtering is used for recording and analyzing the holograms. Calibration tests show that two views reduce the uncertainty in the three-dimensional (3-D) coordinates of the particle centroids to within a few microns. The velocity is still determined plane-by-plane by use of two-dimensional particle image velocimetry procedures, but the images are filtered to trim the elongated traces based on the 3-D location of the particle. Consequently, the spatial resolution is quadrupled. Sample data containing more than 200 particles/mm3 are used for calculating the 3-D velocity distributions with interrogation volumes of 220 × 154 × 250 μm, and vector spacing of 110 × 77 × 250 μm. Uncertainty in velocity is addressed by examining how well the data satisfies the continuity equation. The results show significant improvements compared with previous procedures. Limitations of the technique are also discussed.

© 2003 Optical Society of America

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References

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  1. D. H. Barnhart, R. J. Adrian, G. C. Papen, “Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. 33, 7159–7170 (1994).
    [CrossRef] [PubMed]
  2. H. Meng, F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. 34, 1827–1840 (1995).
    [CrossRef] [PubMed]
  3. Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry system,” Exp. Fluids 29, 184–197 (1999).
    [CrossRef]
  4. J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
    [CrossRef]
  5. B. Tao, J. Katz, C. Meneveau, “Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry,” Phys. Fluids 12, 941–944 (2000).
    [CrossRef]
  6. B. Tao, J. Katz, C. Meneveau, “Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements,” J. Fluid Mech. 457, 35–78 (2002).
    [CrossRef]
  7. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography, (Academic, San Diego, Calif., 1971), pp. 232.
  8. E. Malkiel, O. Alquaddoomi, J. Katz, “Measurements of plankton distribution in the ocean using submersible holography,” Meas. Sci. Technol. 10, 1142–1152 (1999).
    [CrossRef]
  9. W. K. Pratt, Digital Image Processing, (Wiley, New York, 1992), pp. 59.
  10. G. I. Roth, J. Katz, “Five techniques for increasing the speed and accuracy of PIV interrogation,” Meas. Sci. Technol. 12, 238–245 (2001).
    [CrossRef]
  11. R. D. Keane, R. J. Adrian, Y. Zhang, “Super-resolution Particle Imaging Velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
    [CrossRef]
  12. G. I. Roth, D. T. Mascenik, J. Katz, “Measurements of the flow structure and turbulence within a ship bow wave,” Phys. Fluids. 11, 3512–3523 (1999).
    [CrossRef]
  13. G. Sridhar, J. Katz, “Lift and drag forces on microscopic bubbles entrained by a vortex,” Phys. Fluids. 7(2), 389–399 (1995).
    [CrossRef]

2002 (1)

B. Tao, J. Katz, C. Meneveau, “Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements,” J. Fluid Mech. 457, 35–78 (2002).
[CrossRef]

2001 (1)

G. I. Roth, J. Katz, “Five techniques for increasing the speed and accuracy of PIV interrogation,” Meas. Sci. Technol. 12, 238–245 (2001).
[CrossRef]

2000 (1)

B. Tao, J. Katz, C. Meneveau, “Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry,” Phys. Fluids 12, 941–944 (2000).
[CrossRef]

1999 (3)

G. I. Roth, D. T. Mascenik, J. Katz, “Measurements of the flow structure and turbulence within a ship bow wave,” Phys. Fluids. 11, 3512–3523 (1999).
[CrossRef]

E. Malkiel, O. Alquaddoomi, J. Katz, “Measurements of plankton distribution in the ocean using submersible holography,” Meas. Sci. Technol. 10, 1142–1152 (1999).
[CrossRef]

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry system,” Exp. Fluids 29, 184–197 (1999).
[CrossRef]

1997 (1)

J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
[CrossRef]

1995 (3)

G. Sridhar, J. Katz, “Lift and drag forces on microscopic bubbles entrained by a vortex,” Phys. Fluids. 7(2), 389–399 (1995).
[CrossRef]

R. D. Keane, R. J. Adrian, Y. Zhang, “Super-resolution Particle Imaging Velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

H. Meng, F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. 34, 1827–1840 (1995).
[CrossRef] [PubMed]

1994 (1)

Adrian, R. J.

R. D. Keane, R. J. Adrian, Y. Zhang, “Super-resolution Particle Imaging Velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

D. H. Barnhart, R. J. Adrian, G. C. Papen, “Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. 33, 7159–7170 (1994).
[CrossRef] [PubMed]

Alquaddoomi, O.

E. Malkiel, O. Alquaddoomi, J. Katz, “Measurements of plankton distribution in the ocean using submersible holography,” Meas. Sci. Technol. 10, 1142–1152 (1999).
[CrossRef]

Barnhart, D. H.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography, (Academic, San Diego, Calif., 1971), pp. 232.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography, (Academic, San Diego, Calif., 1971), pp. 232.

Hussain, F.

Katz, J.

B. Tao, J. Katz, C. Meneveau, “Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements,” J. Fluid Mech. 457, 35–78 (2002).
[CrossRef]

G. I. Roth, J. Katz, “Five techniques for increasing the speed and accuracy of PIV interrogation,” Meas. Sci. Technol. 12, 238–245 (2001).
[CrossRef]

B. Tao, J. Katz, C. Meneveau, “Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry,” Phys. Fluids 12, 941–944 (2000).
[CrossRef]

E. Malkiel, O. Alquaddoomi, J. Katz, “Measurements of plankton distribution in the ocean using submersible holography,” Meas. Sci. Technol. 10, 1142–1152 (1999).
[CrossRef]

G. I. Roth, D. T. Mascenik, J. Katz, “Measurements of the flow structure and turbulence within a ship bow wave,” Phys. Fluids. 11, 3512–3523 (1999).
[CrossRef]

J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
[CrossRef]

G. Sridhar, J. Katz, “Lift and drag forces on microscopic bubbles entrained by a vortex,” Phys. Fluids. 7(2), 389–399 (1995).
[CrossRef]

Keane, R. D.

R. D. Keane, R. J. Adrian, Y. Zhang, “Super-resolution Particle Imaging Velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography, (Academic, San Diego, Calif., 1971), pp. 232.

Malkiel, E.

E. Malkiel, O. Alquaddoomi, J. Katz, “Measurements of plankton distribution in the ocean using submersible holography,” Meas. Sci. Technol. 10, 1142–1152 (1999).
[CrossRef]

Mascenik, D. T.

G. I. Roth, D. T. Mascenik, J. Katz, “Measurements of the flow structure and turbulence within a ship bow wave,” Phys. Fluids. 11, 3512–3523 (1999).
[CrossRef]

Meneveau, C.

B. Tao, J. Katz, C. Meneveau, “Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements,” J. Fluid Mech. 457, 35–78 (2002).
[CrossRef]

B. Tao, J. Katz, C. Meneveau, “Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry,” Phys. Fluids 12, 941–944 (2000).
[CrossRef]

Meng, H.

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry system,” Exp. Fluids 29, 184–197 (1999).
[CrossRef]

H. Meng, F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. 34, 1827–1840 (1995).
[CrossRef] [PubMed]

Papen, G. C.

Pratt, W. K.

W. K. Pratt, Digital Image Processing, (Wiley, New York, 1992), pp. 59.

Pu, Y.

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry system,” Exp. Fluids 29, 184–197 (1999).
[CrossRef]

Roth, G. I.

G. I. Roth, J. Katz, “Five techniques for increasing the speed and accuracy of PIV interrogation,” Meas. Sci. Technol. 12, 238–245 (2001).
[CrossRef]

G. I. Roth, D. T. Mascenik, J. Katz, “Measurements of the flow structure and turbulence within a ship bow wave,” Phys. Fluids. 11, 3512–3523 (1999).
[CrossRef]

Sridhar, G.

G. Sridhar, J. Katz, “Lift and drag forces on microscopic bubbles entrained by a vortex,” Phys. Fluids. 7(2), 389–399 (1995).
[CrossRef]

Tao, B.

B. Tao, J. Katz, C. Meneveau, “Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements,” J. Fluid Mech. 457, 35–78 (2002).
[CrossRef]

B. Tao, J. Katz, C. Meneveau, “Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry,” Phys. Fluids 12, 941–944 (2000).
[CrossRef]

J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
[CrossRef]

Zhang, J.

J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
[CrossRef]

Zhang, Y.

R. D. Keane, R. J. Adrian, Y. Zhang, “Super-resolution Particle Imaging Velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

Appl. Opt. (2)

Exp. Fluids (2)

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry system,” Exp. Fluids 29, 184–197 (1999).
[CrossRef]

J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
[CrossRef]

J. Fluid Mech. (1)

B. Tao, J. Katz, C. Meneveau, “Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements,” J. Fluid Mech. 457, 35–78 (2002).
[CrossRef]

Meas. Sci. Technol. (3)

G. I. Roth, J. Katz, “Five techniques for increasing the speed and accuracy of PIV interrogation,” Meas. Sci. Technol. 12, 238–245 (2001).
[CrossRef]

R. D. Keane, R. J. Adrian, Y. Zhang, “Super-resolution Particle Imaging Velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

E. Malkiel, O. Alquaddoomi, J. Katz, “Measurements of plankton distribution in the ocean using submersible holography,” Meas. Sci. Technol. 10, 1142–1152 (1999).
[CrossRef]

Phys. Fluids (1)

B. Tao, J. Katz, C. Meneveau, “Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry,” Phys. Fluids 12, 941–944 (2000).
[CrossRef]

Phys. Fluids. (2)

G. I. Roth, D. T. Mascenik, J. Katz, “Measurements of the flow structure and turbulence within a ship bow wave,” Phys. Fluids. 11, 3512–3523 (1999).
[CrossRef]

G. Sridhar, J. Katz, “Lift and drag forces on microscopic bubbles entrained by a vortex,” Phys. Fluids. 7(2), 389–399 (1995).
[CrossRef]

Other (2)

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography, (Academic, San Diego, Calif., 1971), pp. 232.

W. K. Pratt, Digital Image Processing, (Wiley, New York, 1992), pp. 59.

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Figures (12)

Fig. 1
Fig. 1

Principle of the single beam two-view holographic particle image velocimetry system: (a) Recording phase, (b) reconstruction phase.

Fig. 2
Fig. 2

Optical layout of holographic recording (solid lines) and reconstruction setup (dashed lines) by use of a near-forward scattering off-axis scheme.

Fig. 3
Fig. 3

Reconstructed image of a single particle and its model as a cylindrical line: (a) Iso-surface of an identified particle with 1.5 mm length in the depth direction, (b) Line fitting process. 2-D slices are contour plots of cross sections of the particle.

Fig. 4
Fig. 4

Particle trimming process used in velocity calculation: (a) Single 2-D image is left in the plane that is closest to the particle centroid, preserved from the image, (b) same sample area of 192 μm2 (64 × 64 pixel) containing the particle in (a) before filtering, (c) the same area after filtering.

Fig. 5
Fig. 5

Sketch of experimental setup. The He-Ne laser and a photodiode are used to detect the passage of a rising bubble.

Fig. 6
Fig. 6

Reconstructed double-exposure images of the same bubble in the two perpendicular views.

Fig. 7
Fig. 7

Results of tests with sparse particle concentration containing 174 particles, identified and matched within a cube of 8 mm × 8 mm × 8 mm. The particles are represented as ellipsoids with major and minor axes determined by experiment: (a) a 3-D plot of matched particles from the 1st and 2nd views overlapped, showing also a magnified subsection of the cube. (b), (c), and (d) are projections of the same data.

Fig. 8
Fig. 8

Probability density function of distance (mainly Δy) between the matched traces in the two views. (a) Absolute distance (b) Distance normalized by the measured particle diameter.

Fig. 9
Fig. 9

Two typical perpendicular filtered particle image pairs (a and b) and their corresponding velocity maps analyzed by autocorrelation 2-D PIV algorithm. Interrogation window size is 64 × 44 pixel (220 μm × 154 μm), and the vector spacing is 110 μm in x and 78 μm in y.

Fig. 10
Fig. 10

A 3-D volumetric velocity distribution in the wake of the rising bubble. Total number of vectors is 96 × 110 × 61 over a 10 × 10 × 20 mm3 test volume.

Fig. 11
Fig. 11

Cumulative distribution of σ̅ defined in Eq. 13. The numbers in legend indicate the length scales over which the data was averaged prior to calculating σ̅. Filled symbols indicate the present data, open symbols present the data by Zhang et al. The insert shows the 90th percentile of F(σ̅) as a function of averaging length scale.

Fig. 12
Fig. 12

Optional optical setup for recording a single-beam two-views hologram with a cubic sample volume located away from the wall.

Equations (14)

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

sin θc=λcλrsin θr,
x˜i-x˜0i=cijxj xj=c˜ijx˜i-x˜0i
cij=c-1n1sn1s+1c-1n1sn2sc-1n1sn3sc-1n1sn2sc-1n2sn2s+1c-1n2sn3sc-1n1sn3sc-1n2sn3sc-1n3sn3s+1.
c=nair λrecordnwater λrecon.
nxmx+nymy+nzmz+d=0,
x˜s, x˜e, D˜pc˜xs, xe, Dp,xs,er=xs,e-2nm · xs,e+dnm,xsr, xer, Dpcx˜sr, x˜er, D˜p,
0λr|x˜er-x˜sr|,0λo|x˜e-x˜s|,|D|D˜pr+D˜p2,
x˜e-x˜s|x˜e-x˜s|x˜er-x˜sr|x˜er-x˜sr|x˜e-x˜s|x˜e-x˜s|×x˜er-x˜sr|x˜er-x˜sr| · λo-λr-D=x˜sr-x˜s.
R12τ=Rssτ  i,jN1,N2 δτ-xi+xj,
UxmUymUxoUyo=1-2nxm2-2nxmnym-2nxmnzm-2nxmnym1-2nym2-2nymnzm100010UxUyUz,
x˜i-x˜jT·A·x˜i-x˜j=Dij,
Δx˜=Δz˜·K
KAKT·Δz˜2+KAΔx˜ijT+KAΔx˜ijTT·Δz˜+Δx˜ij·A·Δx˜ijT-Dij=0,
σ¯=u¯x+v¯y+w¯z2u¯x2+v¯y2+w¯z2,

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