Abstract

A ray-tracing analysis of point-source imaging in the presence of optical misalignment is used to analyze relative image shift as a source of measurement error in holographic particle image velocimetry (HPIV). Although single-reference-beam HPIV is relatively insensitive to optical misalignment, dual-reference-beam systems may suffer substantial errors because of misalignments of the order of microradians. These systems are particularly sensitive to rotations of the hologram about an axis perpendicular to the film and to reconstruction beam misalignment. In a swirling flow experiment, a proposed error-compensation scheme was able to reduce uncertainty from 130% to 10% of the mean measured velocity.

© 2000 Optical Society of America

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References

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  1. R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
    [Crossref]
  2. C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
    [Crossref]
  3. L. Lourenco, A. Krothapalli, “On the accuracy of velocity and vorticity measurements with PIV,” Exp. Fluids 18, 20–28 (1995).
    [Crossref]
  4. J. Westerweel, D. Dabiri, M. Gharib, “The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings,” Exp. Fluids 23, 20–28 (1997).
    [Crossref]
  5. R. W. Meier, “Magnification and third-order aberrations in holography,” J. Opt. Soc. Am. 55, 987–992 (1965).
  6. E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
    [Crossref]
  7. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  8. I. Banyasz, G. Kiss, P. Varga, “Holographic image of a point source in the presence of misalignment,” Appl. Opt. 27, 1293–1297 (1988).
    [Crossref] [PubMed]
  9. J. Zhang, B. Tao, J. Katz, “Turbulent flow measurement in a square duct with hybrid holographic PIV,” Exp. Fluids 23, 373–381 (1997).
    [Crossref]
  10. S. Simmons, H. Meng, F. Hussain, D. Liu, “Advances in holographic particle velocimetry,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 349–359 (1993).
  11. P. R. Hobson, J. Watson, “Accurate three-dimensional metrology of underwater objects using replayed real images from in-line and off-axis holograms,” Meas. Sci. Technol. 10, 1153–1161 (1999).
    [Crossref]
  12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  13. 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]
  14. H.-Y. S. Li, D. Psaltis, “Alignment sensitivity of holographic three-dimensional disks,” J. Opt. Soc. Am. A 12, 1902–1912 (1995).
    [Crossref]
  15. W. T. Welford, Aberrations of Optical Systems, The Adam Hilger Series on Optics and Optoelectronics (Institute of Physics, Bristol, UK, 1986).
  16. J. M. Barker, J. A. Liburdy, “Directionally sensitive double-pulsed holographic particle velocimetry,” in Laser Anemometry, 1995, T. T. Huang, ed. (American Society of Mechanical Engineers, New York, 1995), Vol. 229, pp. 45–49.
  17. N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981).

1999 (1)

P. R. Hobson, J. Watson, “Accurate three-dimensional metrology of underwater objects using replayed real images from in-line and off-axis holograms,” Meas. Sci. Technol. 10, 1153–1161 (1999).
[Crossref]

1997 (2)

J. Westerweel, D. Dabiri, M. Gharib, “The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings,” Exp. Fluids 23, 20–28 (1997).
[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]

1995 (2)

L. Lourenco, A. Krothapalli, “On the accuracy of velocity and vorticity measurements with PIV,” Exp. Fluids 18, 20–28 (1995).
[Crossref]

H.-Y. S. Li, D. Psaltis, “Alignment sensitivity of holographic three-dimensional disks,” J. Opt. Soc. Am. A 12, 1902–1912 (1995).
[Crossref]

1994 (1)

1991 (2)

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[Crossref]

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[Crossref]

1988 (1)

1967 (1)

1965 (1)

Abramson, N.

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981).

Adrian, R. J.

Banyasz, I.

Barker, J. M.

J. M. Barker, J. A. Liburdy, “Directionally sensitive double-pulsed holographic particle velocimetry,” in Laser Anemometry, 1995, T. T. Huang, ed. (American Society of Mechanical Engineers, New York, 1995), Vol. 229, pp. 45–49.

Barnhart, D. H.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Champagne, E. B.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Dabiri, D.

J. Westerweel, D. Dabiri, M. Gharib, “The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings,” Exp. Fluids 23, 20–28 (1997).
[Crossref]

Gharib, M.

J. Westerweel, D. Dabiri, M. Gharib, “The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings,” Exp. Fluids 23, 20–28 (1997).
[Crossref]

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hobson, P. R.

P. R. Hobson, J. Watson, “Accurate three-dimensional metrology of underwater objects using replayed real images from in-line and off-axis holograms,” Meas. Sci. Technol. 10, 1153–1161 (1999).
[Crossref]

Hussain, F.

S. Simmons, H. Meng, F. Hussain, D. Liu, “Advances in holographic particle velocimetry,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 349–359 (1993).

Katz, 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]

Kiss, G.

Krothapalli, A.

L. Lourenco, A. Krothapalli, “On the accuracy of velocity and vorticity measurements with PIV,” Exp. Fluids 18, 20–28 (1995).
[Crossref]

Li, H.-Y. S.

Liburdy, J. A.

J. M. Barker, J. A. Liburdy, “Directionally sensitive double-pulsed holographic particle velocimetry,” in Laser Anemometry, 1995, T. T. Huang, ed. (American Society of Mechanical Engineers, New York, 1995), Vol. 229, pp. 45–49.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Liu, D.

S. Simmons, H. Meng, F. Hussain, D. Liu, “Advances in holographic particle velocimetry,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 349–359 (1993).

Lourenco, L.

L. Lourenco, A. Krothapalli, “On the accuracy of velocity and vorticity measurements with PIV,” Exp. Fluids 18, 20–28 (1995).
[Crossref]

Meier, R. W.

Meng, H.

S. Simmons, H. Meng, F. Hussain, D. Liu, “Advances in holographic particle velocimetry,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 349–359 (1993).

Papen, G. C.

Psaltis, D.

Simmons, S.

S. Simmons, H. Meng, F. Hussain, D. Liu, “Advances in holographic particle velocimetry,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 349–359 (1993).

Tao, B.

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

Varga, P.

Watson, J.

P. R. Hobson, J. Watson, “Accurate three-dimensional metrology of underwater objects using replayed real images from in-line and off-axis holograms,” Meas. Sci. Technol. 10, 1153–1161 (1999).
[Crossref]

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems, The Adam Hilger Series on Optics and Optoelectronics (Institute of Physics, Bristol, UK, 1986).

Westerweel, J.

J. Westerweel, D. Dabiri, M. Gharib, “The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings,” Exp. Fluids 23, 20–28 (1997).
[Crossref]

Willert, C. E.

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[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]

Annu. Rev. Fluid Mech. (1)

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[Crossref]

Appl. Opt. (2)

Exp. Fluids (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]

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[Crossref]

L. Lourenco, A. Krothapalli, “On the accuracy of velocity and vorticity measurements with PIV,” Exp. Fluids 18, 20–28 (1995).
[Crossref]

J. Westerweel, D. Dabiri, M. Gharib, “The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings,” Exp. Fluids 23, 20–28 (1997).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

P. R. Hobson, J. Watson, “Accurate three-dimensional metrology of underwater objects using replayed real images from in-line and off-axis holograms,” Meas. Sci. Technol. 10, 1153–1161 (1999).
[Crossref]

Other (6)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

S. Simmons, H. Meng, F. Hussain, D. Liu, “Advances in holographic particle velocimetry,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 349–359 (1993).

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

W. T. Welford, Aberrations of Optical Systems, The Adam Hilger Series on Optics and Optoelectronics (Institute of Physics, Bristol, UK, 1986).

J. M. Barker, J. A. Liburdy, “Directionally sensitive double-pulsed holographic particle velocimetry,” in Laser Anemometry, 1995, T. T. Huang, ed. (American Society of Mechanical Engineers, New York, 1995), Vol. 229, pp. 45–49.

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981).

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Figures (7)

Fig. 1
Fig. 1

Geometry for ray tracing with arbitrary hologram orientation.

Fig. 2
Fig. 2

Experimental (a) recording and (b) reconstruction geometries.

Fig. 3
Fig. 3

Pitch α and yaw β of the reference beam.

Fig. 4
Fig. 4

Image shift induced by changes in the reconstruction beam yaw angle. The squares and triangles represent experimental results. The solid lines are Eqs. (26) and (28).

Fig. 5
Fig. 5

Image shift induced by changes in the reconstruction beam pitch angle. The squares and triangles represent experimental results. The solid lines are Eqs. (25) and (27).

Fig. 6
Fig. 6

Image registration errors for 13 separate locations in the same hologram. The vertical axis is the displacement error, and the horizontal axis represents different locations.

Fig. 7
Fig. 7

Axial displacement uncertainty that is due to collimation error for R lim = 2000 m.

Equations (37)

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ux=Δsx/Δt,
nˆr×rˆI-rˆc=mμnˆr×rˆO-rˆr,
pr=1λr nˆr×rO-rr.
pc=1mλc nˆc×rˆI-rˆc.
nˆc×rˆI-rˆc=mμLnˆr×rˆO-rˆr.
nˆr=i sin θ cos Ψ + j sin Ψ+k cos θ cos Ψ,
rˆr=iηx+jηy+kηz,
rˆc=ivx+jvy+kvz,
rˆO=k; zO<0 assumed,
rˆI=iτx+jτy+kτz,
L=1-ΦΘΦ1Ψ-Θ-Ψ1,
Θ=δϕ sin Ψ+δθ cos Ψ,
Ψ=δΨ cos θ+δθ sin Ψ-δϕ cos Ψsin θ,
Φ=δΨ sin θ-δθ sin Ψ-δϕ cos Ψcos θ.
τx-vx-mμηxcos Ψ-δΨ sin Ψcos θ-δθ sin θ-τz-vz-mμ1-ηz×cos Ψ-δΨ sin Ψsin θ+δθ cos θ=-mμ cos Ψηx sin θ-1-ηzcos θ×δθ cos Ψ+δϕ sin Ψ+ηyδθ sin Ψ-δϕ cos Ψ,
τy-vy-mμnycos Ψ-δΨ sin Ψcos θ-δθ sin θ-τz-vz-mμ1-ηz×sin Ψ+δΨ cos Ψ=-mμηxδϕ-mμηx sin θ-1-ηzcos θcos Ψ+ηy sin Ψδθ sin Ψ-δϕ cos Ψsin θ+δΨ cos θ.
xI=zOμτxτz,
yI=zOμτyτz.
τx=vx-mμηx,
τy=vy-mμηy.
xI=mvx-μηxzO/μ,
yI=mvy-μηyzO/μ,
xI=δϕμyzO,
yI=-δϕμxzO.
δxIδα=δα sin αsin β-cos β tan θzO/τz,
δxIδβ=-δβ cos αcos β-sin β tan θzO/τz,
δyIδα=-δαcos α-sin α cos β tan Ψ/cos θ×zO/τz,
δyIδβ=-δβ cos α sin β tan Ψ/cos θzO/τz.
δsx=δθηz2-ηz1+δϕηy2-ηy1zO,
δsy=δΨηz2-ηz1-δϕηx2-ηx1zO.
τx=vx+mμηx+τz-vz+mμ1-ηztan θ,
τy=vy-mμηy-τz-vz+mμ1-ηztan Ψ/cos θ.
xI=vx-ηx-vz-ηztan θzO,
yI=vy+ηy+vz-ηztan Ψ/cos θzO.
δsy=2zOηy2-ηy1.
1RI=1Rc±μ1RO-1Rr.
δsR=±4RO2RlimRlim2-4RO2±4RO2Rlim.

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