Abstract

The inability to distinguish between particle images and noise in holographic reconstruction of dense particle fields hampers the advancement of holographic particle diagnostic techniques including holographic particle image velocimetry. We developed a method to separate particles from the noise by unlocking a unique particle signature in the complex reconstructed field. This complex-wave signature is present in digital particle holograms recorded at any scattering angle. Simulations of single and multiple particle holograms, as well as preliminary laboratory particle-field experiments, not only demonstrated the existence of the particle signature but also evaluated its ability to remove noise. Regardless of particle seeding density, scattering angle of hologram recording and particle size range, the particle identification∕validation routine consistently provides >50% removal of “bad” particles and <8% of good particles.

© 2007 Optical Society of America

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References

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    [CrossRef]
  33. M. Malek, D. Allano, S. Coetmellec, C. Ozkul, and D. Lebrun, "Digital in-line holography for three-dimensional-two-components particle tracking velocimetry," Meas. Sci. Technol. 15, 699-705 (2004).
    [CrossRef]

2007 (1)

2006 (2)

A. Asundi and V. R. Singh, "Sectioning of amplitude images in digital holography," Meas. Sci. Technol. 17, 75-78 (2006).
[CrossRef]

W. Yang, A. B. Kostinski, and R. A. Shaw, "Phase signature for particle detection with digital inline holography," Opt. Lett. 31, 1399-1401 (2006).
[CrossRef] [PubMed]

2005 (3)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrum, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

W. D. Koek, N. Bhattacharya, J. J. Braat, T. A. Ooms, and J. Westerweel, "Influence of virtual images on the signal-to-noise ratio in digital in-line particle holography," Opt. Express 13, 2578-2589 (2005).
[CrossRef] [PubMed]

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

2004 (4)

Y. Pu and H. Meng, "Intrinsic speckle noise in off-axis particle holography," J. Opt. Soc. Am. A 21, 1221-1230 (2004).
[CrossRef]

M. Malek, D. Allano, S. Coetmellec, C. Ozkul, and D. Lebrun, "Digital in-line holography for three-dimensional-two-components particle tracking velocimetry," Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, "Holographic particle image velocimetry: from film to digital recording," Meas. Sci. Technol. 15, 673-685 (2004).
[CrossRef]

2003 (3)

2002 (3)

K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

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

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kruzer, "Digital in-line holography of microspheres," Appl. Opt. 41, 5367-5375 (2002).
[CrossRef] [PubMed]

2000 (2)

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

M. Stellmacher and K. Obermayer, "A new particle tracking algorithm based on deterministic annealing and alternative distance measures," Exp. Fluids 28, 506-518 (2000).
[CrossRef]

1997 (2)

J. Sheng and H. Meng, "A generic algorithm approach for 3D velocity field extraction in holographic particle image velocimetry," Exp. Fluids 29, 461-475 (1997).

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

1995 (1)

1994 (2)

1993 (1)

1977 (1)

H. Royer, "Holographic velocimetry of submicron particles," Opt. Commun. 20, 73-75 (1977).
[CrossRef]

1975 (1)

J. D. Trolinger, "Particle field holography," Opt. Eng. 14, 383-392 (1975).

1971 (1)

B. J. Matthews, "Measurement of fine particulate in pollution control," Proc. SPIE 25, 157-168 (1971).

Appl. Opt. (4)

Exp. Fluids (6)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrum, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

J. Sheng and H. Meng, "A generic algorithm approach for 3D velocity field extraction in holographic particle image velocimetry," Exp. Fluids 29, 461-475 (1997).

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

M. Stellmacher and K. Obermayer, "A new particle tracking algorithm based on deterministic annealing and alternative distance measures," Exp. Fluids 28, 506-518 (2000).
[CrossRef]

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

J. Fluid Mech. (1)

J. P. L. C. Salazar, J. de Jong, L. Cao, S. Woodward, H. Meng, and L. R. Collins, "Experimental and numerical investigation of inertial particle clustering in isotropic turbulence," J. Fluid Mech. (to be published).

J. Opt. Soc. Am. A (4)

Meas. Sci. Technol. (6)

M. Malek, D. Allano, S. Coetmellec, C. Ozkul, and D. Lebrun, "Digital in-line holography for three-dimensional-two-components particle tracking velocimetry," Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, "Holographic particle image velocimetry: from film to digital recording," Meas. Sci. Technol. 15, 673-685 (2004).
[CrossRef]

A. Asundi and V. R. Singh, "Sectioning of amplitude images in digital holography," Meas. Sci. Technol. 17, 75-78 (2006).
[CrossRef]

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

K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

Opt. Commun. (1)

H. Royer, "Holographic velocimetry of submicron particles," Opt. Commun. 20, 73-75 (1977).
[CrossRef]

Opt. Eng. (1)

J. D. Trolinger, "Particle field holography," Opt. Eng. 14, 383-392 (1975).

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (1)

B. J. Matthews, "Measurement of fine particulate in pollution control," Proc. SPIE 25, 157-168 (1971).

Other (5)

M. Pluta, Holographic Microscopy, Advances in Optical and Electron Microscopy, Vol. 10, R. Barer and V. E. Cosslett, eds. (Academic, 1977).

C. S. Vikram, Particle Field Holography (Cambridge U. Press, 1992).
[CrossRef]

L. Cao, G. Pan, S. Woodward, and H. Meng, "Hybrid digital holographic imaging system for 3D dense particle field measurement," presented at the 7th International Symposium on Particle Image Velocimetry, Rome, Italy, 11-14 September 2007.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

G. Pan, "Digital holographic imaging for 3D particle and flow measurements," Ph.D. dissertation (State University of New York at Buffalo, 2003).

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Figures (8)

Fig. 1
Fig. 1

Symmetry breakdown in non-forward-scattering holography. Two particles are located at a distance z 2 from the CCD sensor. (a) Forwarding-scattering recording. Both particles have the same total distance from the collimator to the CCD plane z 1 + z 2 , hence there is no phase difference between them at the recording plane. (b) 90° scattering recording. One particle produces a scattering path length that is δ longer than the other. This results in a phase difference between the two particles at the recording plane. Therefore, in case (b), particles reconstructed the same distance z 2 from the hologram do not carry the same phase information.

Fig. 2
Fig. 2

(Color online) Signatures of particles on Y ( 0 , 0 , z ) , a complex function evaluated along the centerline of the reconstructed particle image varying with the z axis. Y is the product of A z ( 0 , 0 ) and ( d A z ( 0 , 0 ) / d z ) * . Variation of the phase-lag angle ϕ produces a shift in both A z and d A z / d z , but the shifted curves collapse into a single curve Y. When z crosses the particle location z 0 , Y experiences a unique sinusoidal zero crossing in its real part.

Fig. 3
Fig. 3

Effect of Mie scattering on the spatial variance of the real part of the particle signature function Y , σ Y 2 .

Fig. 4
Fig. 4

(Color online) Effect of Mie scattering on the axial deviation of min ( σ Y 2 ) from the true in-focus plane. Plots correspond to variations of both the scattering angle (angular direction) and distance of the particle from the hologram (radial direction) for two different particle diameters, (a) 5 μ m and (b) 10 μm. Plots show that axial depth errors that result from Mie scattering are approximately equal functions of all three parameters. More importantly, the particle signature is still present within ± 50 μ m from the true particle location for all combinations of the parameters in this study.

Fig. 5
Fig. 5

Probability density function of the axial depth errors from the true in-focus plane that result from Mie scattering. Result of 4914 single particle simulations. (a) From particle signature function, standard deviation, σ = 7.0 μ m , (b) from intensity centroid of particle image, σ = 13.5 μ m .

Fig. 6
Fig. 6

Performance of the particle validation filter, which filters extracted particles based on the existing particle signature function. (a) Performance versus seeding density for a particle with diameter d = 10 μ m and a scattering angle θ = 90 ° . (b) Performance versus scattering angle with d = 10 μ m and a seeding density n s = 4 particles / mm 3 . (c) Performance versus full width of a top-hat particle size distribution centered at d = 10 μ m with n s = 4 particles / mm 3 and θ = 90 ° . A width of 0 μ m corresponds to a monodisperse distribution.

Fig. 7
Fig. 7

Sketch of the digital hybrid holographic setup and experimental flow facility utilized to validate the existence of the particle signature function in a non-forward-scattering optical configuration.

Fig. 8
Fig. 8

Experimental validation of the spatial variance of the particle signature function. The minimum of σ Y 2 is compared to the intensity-based centroid of the particle image in the axial direction. The experiment was performed using 90° light-scattering off 10 μ m diameter glass spheres. Pu and Meng [27] have shown that for 90° scattering the axial deviation of the intensity-based centroid is negligible.

Equations (11)

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I 0 I N = π tan 2 Ω λ 2 n s L ,
Ω = tan 1 ( λ 2 Δ ) ,
I H = | R | 2 + | O | 2 + 2 | R | · | O | · cos ( π r 2 λ z 0 + ϕ ) ,
A z = I H h z ,
h z = e j k z j λ z e j k r 2 2 z ,
A z ( 0 , 0 ) = z 0   exp [ j ( k z ϕ ) ] [ sin 2 ( π λ 8 Δ 2 ( z 0 z ) ( z z 0 ) ) ( z z 0 ) j sin ( π λ 4 Δ 2 ( z 0 z ) ( z z 0 ) ) ( z z 0 ) ] = z 0   exp [ j ( k z ϕ ) ] [ f ( z ) j g ( z ) ] .
f ( z ) | z = z 0 = 0 ,
d g ( z ) d z | z = z 0 = 0.
Y ( 0 , 0 , z ) = A z ( 0 , 0 ) · ( d A z ( 0 , 0 ) d z ) * .
Y = f ( z ) d f ( z ) d z + g ( z ) d g ( z ) d z + j [ f ( z ) d g ( z ) d z g ( z ) d f ( z ) d z + k ( f 2 ( z ) + g 2 ( z ) ) ] .
Y | z = z 0 = j ( k g 2 ( z ) g ( z ) d f ( z ) d z ) .

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