Abstract

Digital in-line holography (DIH) with a divergent beam is used to measure size and concentration of cavitation bubbles (6100μm) in hydrodynamic facilities. A sampling probe is directly inserted in the cavitation tunnel, and the holograms of the bubbles are recorded through a transparent test section specially designed for DIH measurements. The recording beam coming from a fiber-coupled laser diode illuminates the sample volume, and holograms are recorded by a CMOS camera. From each hologram, the sampling volume can be reconstructed slice by slice by applying a wavelet-based reconstruction method. Because of the geometry of the recording beam, a magnification ratio must be introduced for recovering the 3D location and size of each bubble. The method used for processing holograms recorded in such a configuration is presented. Then, statistical results obtained from 5000 holograms recorded under different pressures in the cavitation tunnel are compared and discussed.

© 2011 Optical Society of America

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References

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  1. M. Malek, D. Lebrun, and D. Allano, “Digital in-line holography system for 3D-3C particle tracking velocimetry,” in A.Schröder and C.E.Willert, eds., Particle Image Velocimetry: New Developments and Recent Applications (Springer-Verlag, 2008), pp. 155–170.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008 (3)

2007 (1)

2006 (4)

2005 (1)

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 (1)

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 (1)

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

2000 (1)

C. Buraga, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

1993 (1)

1988 (1)

C. S. Vikram and M. L. Billet, “Some salient features of in-line Fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

1976 (2)

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis: a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

R. Bexon, J. Gibbs, and G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[CrossRef]

Allano, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[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]

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

M. Malek, D. Lebrun, and D. Allano, “Digital in-line holography system for 3D-3C particle tracking velocimetry,” in A.Schröder and C.E.Willert, eds., Particle Image Velocimetry: New Developments and Recent Applications (Springer-Verlag, 2008), pp. 155–170.

Bexon, R.

R. Bexon, J. Gibbs, and G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[CrossRef]

Billet, M. L.

C. S. Vikram and M. L. Billet, “Some salient features of in-line Fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

Bishop, G. D.

R. Bexon, J. Gibbs, and G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[CrossRef]

Boucheron, R.

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

Brunel, M.

Buraga, C.

C. Buraga, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Callens, N.

Cen, K. F.

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]

Coetmellec, S.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Coëtmellec, S.

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef] [PubMed]

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Suppression of the moiré effect in sub-picosecond digital in-line holography,” Opt. Express 15, 887–895 (2007).
[CrossRef] [PubMed]

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

C. Buraga, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Dubois, F.

Fréchou, D.

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

Garcia-Sucerquia, J.

Gibbs, J.

R. Bexon, J. Gibbs, and G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[CrossRef]

Godard, G.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Jericho, M. H.

Katz, J.

Kompenhans, J.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801(2006).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005).

Kreuzer, H. J.

Lebrun, D.

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef] [PubMed]

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Suppression of the moiré effect in sub-picosecond digital in-line holography,” Opt. Express 15, 887–895 (2007).
[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]

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

C. Buraga, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

M. Malek, D. Lebrun, and D. Allano, “Digital in-line holography system for 3D-3C particle tracking velocimetry,” in A.Schröder and C.E.Willert, eds., Particle Image Velocimetry: New Developments and Recent Applications (Springer-Verlag, 2008), pp. 155–170.

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

Lecoffre, Y.

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

Leval, J.

Malek, M.

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]

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

M. Malek, D. Lebrun, and D. Allano, “Digital in-line holography system for 3D-3C particle tracking velocimetry,” in A.Schröder and C.E.Willert, eds., Particle Image Velocimetry: New Developments and Recent Applications (Springer-Verlag, 2008), pp. 155–170.

Malkiel, E.

Méès, L.

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

Meng, H.

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]

Nicolas, F.

Onural, L.

Özkul, C.

C. Buraga, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Pan, G.

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]

Paranthoën, P.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Patte-Rouland, B.

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]

Picart, P.

Pu, S. L.

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]

Pu, Y.

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]

Salah, N.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Schockaert, C.

Schröder, A.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801(2006).
[CrossRef]

Shen, G.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801(2006).
[CrossRef]

Sheng, J.

Thompson, B. J.

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis: a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Tyler, G. A.

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis: a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Verrier, N.

Vikram, C. S.

C. S. Vikram and M. L. Billet, “Some salient features of in-line Fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

Walle, F.

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

Woodward, S. H.

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]

Xu, W.

Yourassowsky, C.

Zhang, Y.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801(2006).
[CrossRef]

Appl. Opt. (2)

Exp. Fluids (1)

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. Aerosol Sci. (1)

R. Bexon, J. Gibbs, and G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[CrossRef]

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

Meas. Sci. Technol. (2)

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]

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coetmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Opt. Acta (1)

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis: a reassessment,” Opt. Acta 23, 685–700 (1976).
[CrossRef]

Opt. Commun. (1)

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, “Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter,” Opt. Commun. 223, 263–271 (2003).
[CrossRef]

Opt. Eng. (1)

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801(2006).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

C. Buraga, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[CrossRef]

Opt. Lett. (2)

Optik (1)

C. S. Vikram and M. L. Billet, “Some salient features of in-line Fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

Other (3)

M. Malek, D. Lebrun, and D. Allano, “Digital in-line holography system for 3D-3C particle tracking velocimetry,” in A.Schröder and C.E.Willert, eds., Particle Image Velocimetry: New Developments and Recent Applications (Springer-Verlag, 2008), pp. 155–170.

T. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005).

L. Méès, D. Lebrun, D. Allano, F. Walle, Y. Lecoffre, R. Boucheron, and D. Fréchou, “Development of interferometric techniques for nuclei size measurement in cavitation tunnel,” presented at the 28th Symposium on Naval Hydrodynamics, Pasadena, Calif., 12–17 Sept. 2010.

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Figures (12)

Fig. 1
Fig. 1

Optical configuration of recording in-line holograms of bubbles with a divergent beam: S, laser source; ( ξ , η ) , object plane; ( x , y ) , 2D detector plane.

Fig. 2
Fig. 2

Optical configuration of recording in-line holograms with an imaging lens.

Fig. 3
Fig. 3

Hologram recording for size nuclei measurement: CCD, camera; LD, modulated laser diode; F, single-mode optical fiber; SV, sample volume.

Fig. 4
Fig. 4

Schematic views of the optical pipe used for digital holography.

Fig. 5
Fig. 5

Influence of the wavelet aperture θ on the diameter measurement of small particles in the equivalent space (plane wave configuration). (a) Simulated reconstructed image diameter versus equivalent object diameter, θ = 55 mrad . (b) Sensitivity of the diameter measurement for different working apertures.

Fig. 6
Fig. 6

Example of image bubble reconstructed in each range and at different depths. Estimated location and size: (a)  z e = 44 mm , d = 10 μm and (b)  z e = 50 mm , d = 85 μm .

Fig. 7
Fig. 7

Circular calibration target used for particle sizing in the range [ 2 1000 μm ].

Fig. 8
Fig. 8

Calibration curve obtained with opaque disks deposited by a microlithography technique on a quartz substrate.

Fig. 9
Fig. 9

Size distribution of nuclei measured by DIH in the range of 5 25 μm .

Fig. 10
Fig. 10

Images of bubbles reconstructed automatically from holograms in the range [ 12 140 μm ]: (a)  P = 567 mb , 1000 holograms (b), P = 927 mb , 2000 holograms, and (c)  P = 1287 mb , 2000 holograms.

Fig. 11
Fig. 11

Examples of nonspherical particles automatically extracted from the series.

Fig. 12
Fig. 12

Size nuclei distribution in the optical pipe for different flow pressures.

Tables (2)

Tables Icon

Table 1 Hologram Recording Conditions

Tables Icon

Table 2 Particle Detected in the Lower and Upper Range for Different Pressure Conditions in the Tunnel

Equations (18)

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

A 0 ( ξ , η ) = ( 1 O ) e i π ( ξ 2 + η 2 ) λ ( z s z e ) .
A z e ( x , y ) = e 2 i π λ z e i λ z e ( 1 O ) e i π ( ξ 2 + η 2 ) λ ( z s z e ) e i π ( x ξ ) 2 + ( y η ) 2 λ z e d ξ d η .
A z e ( r ) = 1 λ K z e e i π 2 e i π r 2 K λ z e F d λ z e ( r ) ,
F α ( r ) = π 2 α 2 J 1 ( α ) α ,
K = z s z s z e .
I z e ( r ) = 1 2 λ K z e sin ( π r 2 λ K z e ) F d λ z e ( r ) + ( λ K z e ) 2 F d λ z e 2 ( r ) .
I z e ( r ) = 1 2 λ z eq sin ( π r 2 λ z eq ) F d eq λ z eq ( r ) + ( λ z eq ) 2 F d eq λ z eq 2 ( r ) .
K = z s + z eq z s .
z e > N p 2 λ ( 1 + N p 2 λ z s ) 1 .
δ = p K 1 + ( K λ 2 p ) 2 .
z s = N p 2 ( K 1 ) λ .
γ = z s z e f .
K γ = z s f .
I z e ( x , y ) = 1 [ O * * ( h z e + h ¯ z e ) ] ( x , y ) ,
R ( x , y ) = [ I z e ** ( h z r + h ¯ z r ) ] ( x , y ) .
R ( x , y ) = 2 { 1 O ( x , y ) 1 2 [ O ( x , y ) * * ( h 2 z + h ¯ 2 z ) ] ( x , y ) } .
R ( x , y ) = [ I z e ** ψ θ , z ] ( x , y ) ,
ψ θ , z ( x , y ) = π λ z [ sin ( π x 2 + y 2 λ z M ψ ) ] × G θ ( x , y ) .

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