Abstract

Digital holography appears to be a strong contender as the next-generation technology for holographic diagnostics of particle fields and holographic particle image velocimetry for flow field measurement. With the digital holographic approach, holograms are directly recorded by a digital camera and reconstructed numerically. This not only eliminates wet chemical processing and mechanical scanning, but also enables the use of complex amplitude information inaccessible by optical reconstruction, thereby allowing flexible reconstruction algorithms to achieve optimization of specific information. However, owing to the inherently low pixel resolution of solid-state imaging sensors, digital holography gives poor depth resolution for images, a problem that severely impairs the usefulness of digital holography especially in densely populated particle fields. This paper describes a technique that significantly improves particle axial-location accuracy by exploring the reconstructed complex amplitude information, compared with other numerical reconstruction schemes that merely mimic traditional optical reconstruction. This novel method allows accurate extraction of particle locations from forward-scattering particle holograms even at high particle loadings.

© 2003 Optical Society of America

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References

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  1. A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
    [CrossRef] [PubMed]
  2. M. Virant, T. Dracos, “3D PTV and its application on Lagrangian motion,” Meas. Sci. Technol. 8, 1539–1552 (1997).
    [CrossRef]
  3. F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
    [CrossRef]
  4. B. Ovryn, “Three-dimensional forward scattering particle image velocimetry applied to a microscopic field-of-view,” Exp. Fluids 29, S175–S184 (2000).
    [CrossRef]
  5. Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. Fluids 29, 184–197 (2000).
    [CrossRef]
  6. Y. Pu, X. Song, H. Meng, “Off-axis holographic particle image velocimetry for diagnosing particulate flows,” Exp. Fluids 29, S117–S128 (2000).
    [CrossRef]
  7. H. Meng, F. Hussain, “Holographic particle velocimetry, a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
    [CrossRef]
  8. M. Adams, T. Kreis, W. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
    [CrossRef]
  9. R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
    [CrossRef]
  10. S. Murata, S. N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
    [CrossRef]
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    [CrossRef]
  12. L. Onural, M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. of Am. A 9, 252–260 (1992).
    [CrossRef]
  13. B. Ovryn, S. H. Izen, “Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope,” J. Opt. Soc. of Am. A 17, 1202–1213 (2000).
    [CrossRef]
  14. C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
    [CrossRef]
  15. L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
  16. F. Slimani, G. Grehan, G. Goueshet, D. Allano, “Near-field Lorenz-Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
    [CrossRef] [PubMed]
  17. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, New York, 1990).

2002

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[CrossRef]

2001

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

2000

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

S. Murata, S. N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[CrossRef]

B. Ovryn, “Three-dimensional forward scattering particle image velocimetry applied to a microscopic field-of-view,” Exp. Fluids 29, S175–S184 (2000).
[CrossRef]

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. Fluids 29, 184–197 (2000).
[CrossRef]

Y. Pu, X. Song, H. Meng, “Off-axis holographic particle image velocimetry for diagnosing particulate flows,” Exp. Fluids 29, S117–S128 (2000).
[CrossRef]

B. Ovryn, S. H. Izen, “Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope,” J. Opt. Soc. of Am. A 17, 1202–1213 (2000).
[CrossRef]

1997

M. Virant, T. Dracos, “3D PTV and its application on Lagrangian motion,” Meas. Sci. Technol. 8, 1539–1552 (1997).
[CrossRef]

1992

L. Onural, M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. of Am. A 9, 252–260 (1992).
[CrossRef]

1991

H. Meng, F. Hussain, “Holographic particle velocimetry, a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

1984

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

F. Slimani, G. Grehan, G. Goueshet, D. Allano, “Near-field Lorenz-Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
[CrossRef] [PubMed]

Adams, M.

M. Adams, T. Kreis, W. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

Alexander, J.

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

Allano, D.

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, New York, 1990).

Billet, M. L.

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

Bodenschatz, E.

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

Crawford, A. M.

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

Dracos, T.

M. Virant, T. Dracos, “3D PTV and its application on Lagrangian motion,” Meas. Sci. Technol. 8, 1539–1552 (1997).
[CrossRef]

Gharib, M.

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[CrossRef]

Goueshet, G.

Grehan, G.

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, New York, 1990).

Hussain, F.

H. Meng, F. Hussain, “Holographic particle velocimetry, a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

Izen, S. H.

B. Ovryn, S. H. Izen, “Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope,” J. Opt. Soc. of Am. A 17, 1202–1213 (2000).
[CrossRef]

Jüptner, W.

M. Adams, T. Kreis, W. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

Kreis, T.

M. Adams, T. Kreis, W. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

Meng, H.

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. Fluids 29, 184–197 (2000).
[CrossRef]

Y. Pu, X. Song, H. Meng, “Off-axis holographic particle image velocimetry for diagnosing particulate flows,” Exp. Fluids 29, S117–S128 (2000).
[CrossRef]

H. Meng, F. Hussain, “Holographic particle velocimetry, a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

Merzlyakov, N. S.

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).

Murata, S.

S. Murata, S. N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[CrossRef]

Onural, L.

L. Onural, M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. of Am. A 9, 252–260 (1992).
[CrossRef]

Ovryn, B.

B. Ovryn, S. H. Izen, “Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope,” J. Opt. Soc. of Am. A 17, 1202–1213 (2000).
[CrossRef]

B. Ovryn, “Three-dimensional forward scattering particle image velocimetry applied to a microscopic field-of-view,” Exp. Fluids 29, S175–S184 (2000).
[CrossRef]

Owen, R. B.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Ozgen, M. T.

L. Onural, M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. of Am. A 9, 252–260 (1992).
[CrossRef]

Pereira, F.

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[CrossRef]

Porta, A. L.

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

Pu, Y.

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. Fluids 29, 184–197 (2000).
[CrossRef]

Y. Pu, X. Song, H. Meng, “Off-axis holographic particle image velocimetry for diagnosing particulate flows,” Exp. Fluids 29, S117–S128 (2000).
[CrossRef]

Slimani, F.

Song, X.

Y. Pu, X. Song, H. Meng, “Off-axis holographic particle image velocimetry for diagnosing particulate flows,” Exp. Fluids 29, S117–S128 (2000).
[CrossRef]

Vikram, C. S.

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

C. S. Vikram, Particle Field Holography (Cambridge Univ., Cambridge, UK, 1992).
[CrossRef]

Virant, M.

M. Virant, T. Dracos, “3D PTV and its application on Lagrangian motion,” Meas. Sci. Technol. 8, 1539–1552 (1997).
[CrossRef]

Voth, G. A.

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

Yaroslavsky, L. P.

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).

Yasuda, S. N.

S. Murata, S. N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[CrossRef]

Zozulya, A. A.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Appl. Opt.

Appl. Phys. B

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

Exp. Fluids

B. Ovryn, “Three-dimensional forward scattering particle image velocimetry applied to a microscopic field-of-view,” Exp. Fluids 29, S175–S184 (2000).
[CrossRef]

Y. Pu, H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. Fluids 29, 184–197 (2000).
[CrossRef]

Y. Pu, X. Song, H. Meng, “Off-axis holographic particle image velocimetry for diagnosing particulate flows,” Exp. Fluids 29, S117–S128 (2000).
[CrossRef]

Fluid Dyn. Res.

H. Meng, F. Hussain, “Holographic particle velocimetry, a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

J. Opt. Soc. of Am. A

L. Onural, M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. of Am. A 9, 252–260 (1992).
[CrossRef]

B. Ovryn, S. H. Izen, “Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope,” J. Opt. Soc. of Am. A 17, 1202–1213 (2000).
[CrossRef]

Meas. Sci. Technol.

M. Virant, T. Dracos, “3D PTV and its application on Lagrangian motion,” Meas. Sci. Technol. 8, 1539–1552 (1997).
[CrossRef]

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[CrossRef]

Nature

A. L. Porta, G. A. Voth, A. M. Crawford, J. Alexander, E. Bodenschatz, “Fluid particle accelerations in fully developed turbulence,” Nature 409, 1017–1019 (2001).
[CrossRef] [PubMed]

Opt. Eng.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Opt. Laser Technol.

S. Murata, S. N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[CrossRef]

Other

C. S. Vikram, Particle Field Holography (Cambridge Univ., Cambridge, UK, 1992).
[CrossRef]

M. Adams, T. Kreis, W. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, New York, 1990).

L. P. Yaroslavsky, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).

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Figures (8)

Fig. 1
Fig. 1

Typical setup of digital holographic recording of a particle field based on in-line holography.

Fig. 2
Fig. 2

Intensity variation near the in-focus position of small particles reconstructed from a digital hologram with N.A. = 0.076. The depth of focus is approximately 40 times the particle diameter based on 80% threshold.

Fig. 3
Fig. 3

(a) Schematic showing the object wave scattered off the particle and the propagate of the real image wave r to the reconstruction planes, (b) variance of Im(r) for a single particle computed in the planes near the particle in-focus plane z = z p . The curve displays the dipping shape with its minimum at the particle depth position.

Fig. 4
Fig. 4

Comparison of the variation of σ r 2 and σΩ 2 along the axial direction. (a) dσ r 2/dz versus the axial distance from the particle in-focus plane. (b) The cumulative distribution function of |dσ Ω 2/dz| obtained in the reconstruction of the hologram of a densely populated particle field. Obviously, the axial derivative of σΩ 2 is much smaller than that of σ r 2 in the neighborhood of the particle.

Fig. 5
Fig. 5

Experimental demonstration of a digital hologram of 10 μm particles on the surface of a glass plate for the purpose of calibration. (a) Hologram fringes recorded on a 12-bit digital camera with pixel size 6.7 μm. (b) Numerical reconstructed image at z = 33.2 mm (at different planes we obtain different images because the image is three-dimensional).

Fig. 6
Fig. 6

Experimental calibration of the PECA method. Particles originally placed on a glass plate are extracted from the digital hologram shown in Fig. 5(a) with the PECA method. The average deviation of the measured distances results (triangles) from the expected locations (solid line) is 22.3 μm.

Fig. 7
Fig. 7

Synthesized hologram of 10 μm particles in a 3.5 × 3.5 × 10 mm3 volume with number density of 18 particle/mm3.

Fig. 8
Fig. 8

Cumulative distribution function of the depth error δ z obtained by the PECA method at particle concentrations n p = 18 particle/mm3. The result of the intensity method is also shown for comparison.

Tables (1)

Tables Icon

Table 1 Error in Depth Positions of 10 μm Particles Extracted from Digital Holograms

Equations (6)

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

oj=Ajx, yhzjξ, η,
hzξ, η=expikziλzexpik2zξ2+η2.
rjx, y, z=oj*hz =Aj*hzj*hz.
U=rj+Ωj,
Ωj=i=1N vi+i=1,ijN ri.
σU2=σrj2+σΩj2,

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