Abstract

We have used a digital in-line holography system with numerical reconstruction for 3D particle field extraction. In this system the diffraction patterns (holograms) are directly recorded on a charge-coupled device (CCD) camera. The numerical reconstruction is based on the wavelet transformation method. A sample volume is reconstructed by computing the wavelet components for different scale parameters. These parameters are related to the axial distance between a particle and the CCD camera. The particle images are identified and localized by analyzing the maximum of the wavelet transform modulus and the equivalent diameter of the particle image. The general process for the 3D particle location and data processing method are presented. As in classical holography we found that the signal to noise ratio depends only on the shadow density. Nevertheless, we show that both the volume depth and the shadow density affect the percentage of extracted particles.

© 2004 Optical Society of America

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References

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  1. T.M. Kreis and W.P.O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
    [CrossRef]
  2. G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Opt. lett. 42, 827–833 (2003).
  3. L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993).
    [CrossRef] [PubMed]
  4. W.L. Anderson, “Two dimensional wavelet transform and application to holographic particle velocimetry,” Appl. Opt. 34249–255 (1995).
    [CrossRef] [PubMed]
  5. C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
    [CrossRef]
  6. D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
    [CrossRef] [PubMed]
  7. L. Onural and M.T. Özgen, “Extraction of the three dimensional object location information directly from the in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A. 9252–260 (1992).
    [CrossRef]
  8. S. Coätmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform,” Appl. Opt. 41312–319 (2002).
    [CrossRef]
  9. M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
    [CrossRef]
  10. K. D. Hinsch, “Holographic particle image velocimetry,” Meas. Sci. Technol. 13, R61–R72 (2002).
    [CrossRef]
  11. K. D. Hinsch,“Three-dimensional particle velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
    [CrossRef]
  12. D. H. Barnhart, N. A. Halliwell, and J. M. Coupland, “Holography particle image velocimetry: analysing using a conjugate reconstruction geometry,” Opt. Laser Technol. 32, 527–533 (2000).
    [CrossRef]
  13. Y. Pu and H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. in Fluid,  29184–197 (2000).
    [CrossRef]
  14. S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
    [CrossRef]
  15. Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
    [CrossRef] [PubMed]
  16. H. Meng, W. L. Anderson, Fazle Hussain, and David D. Liu, “Intrinsic speckle noise in in-line particle holography,” J. Opt. Soc. Am. A 10, 2046–2058 (1993).
    [CrossRef]
  17. H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
    [CrossRef]
  18. M. Malek, S. Coätmellec, D. Lebrun, and D. Allano, “Formulation of in-line holography process by a linear shift invariant system: Application to the measurement of fiber diameter,” Optics communications 223, 263–271 (2003).
    [CrossRef]
  19. Ronalds N. Bracewell, “The Fourier Transform and its applications,” second edition, p. 245 (1986).

2004 (1)

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

2003 (3)

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Opt. lett. 42, 827–833 (2003).

D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
[CrossRef] [PubMed]

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

2002 (2)

2001 (2)

S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
[CrossRef]

Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
[CrossRef] [PubMed]

2000 (3)

D. H. Barnhart, N. A. Halliwell, and J. M. Coupland, “Holography particle image velocimetry: analysing using a conjugate reconstruction geometry,” Opt. Laser Technol. 32, 527–533 (2000).
[CrossRef]

Y. Pu and H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. in Fluid,  29184–197 (2000).
[CrossRef]

C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
[CrossRef]

1997 (1)

T.M. Kreis and W.P.O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

1995 (2)

1993 (2)

1992 (1)

L. Onural and M.T. Özgen, “Extraction of the three dimensional object location information directly from the in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A. 9252–260 (1992).
[CrossRef]

1974 (1)

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Allano, D.

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

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

Anderson, W. L.

Anderson, W.L.

Barnhart, D. H.

D. H. Barnhart, N. A. Halliwell, and J. M. Coupland, “Holography particle image velocimetry: analysing using a conjugate reconstruction geometry,” Opt. Laser Technol. 32, 527–533 (2000).
[CrossRef]

Benkouider, A.M.

D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
[CrossRef] [PubMed]

Bracewell, Ronalds N.

Ronalds N. Bracewell, “The Fourier Transform and its applications,” second edition, p. 245 (1986).

Buraga-Lefebvre, C.

C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
[CrossRef]

Buraga-Lefevre, C.

S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
[CrossRef]

Coätmellec, S.

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
[CrossRef] [PubMed]

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

S. Coätmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform,” Appl. Opt. 41312–319 (2002).
[CrossRef]

S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
[CrossRef]

C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
[CrossRef]

Coupland, J. M.

D. H. Barnhart, N. A. Halliwell, and J. M. Coupland, “Holography particle image velocimetry: analysing using a conjugate reconstruction geometry,” Opt. Laser Technol. 32, 527–533 (2000).
[CrossRef]

Halliwell, N. A.

D. H. Barnhart, N. A. Halliwell, and J. M. Coupland, “Holography particle image velocimetry: analysing using a conjugate reconstruction geometry,” Opt. Laser Technol. 32, 527–533 (2000).
[CrossRef]

Hinsch, K. D.

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

K. D. Hinsch,“Three-dimensional particle velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

Hussain, Fazle

Jericho, M. H.

Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
[CrossRef] [PubMed]

Jüptner, W.P.O.

T.M. Kreis and W.P.O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kreis, T.M.

T.M. Kreis and W.P.O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kreuzer, H. J.

Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
[CrossRef] [PubMed]

Lebrun, D.

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
[CrossRef] [PubMed]

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

S. Coätmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform,” Appl. Opt. 41312–319 (2002).
[CrossRef]

S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
[CrossRef]

C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
[CrossRef]

Liu, David D.

Malek, M.

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
[CrossRef] [PubMed]

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

Meinertzhagen, I. A.

Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
[CrossRef] [PubMed]

Meng, H.

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Opt. lett. 42, 827–833 (2003).

Y. Pu and H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. in Fluid,  29184–197 (2000).
[CrossRef]

H. Meng, W. L. Anderson, Fazle Hussain, and David D. Liu, “Intrinsic speckle noise in in-line particle holography,” J. Opt. Soc. Am. A 10, 2046–2058 (1993).
[CrossRef]

Onural, L.

L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993).
[CrossRef] [PubMed]

L. Onural and M.T. Özgen, “Extraction of the three dimensional object location information directly from the in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A. 9252–260 (1992).
[CrossRef]

Özgen, M.T.

L. Onural and M.T. Özgen, “Extraction of the three dimensional object location information directly from the in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A. 9252–260 (1992).
[CrossRef]

Özkul, C.

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

S. Coätmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform,” Appl. Opt. 41312–319 (2002).
[CrossRef]

S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
[CrossRef]

C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
[CrossRef]

Pan, G.

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Opt. lett. 42, 827–833 (2003).

Pu, Y.

Y. Pu and H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. in Fluid,  29184–197 (2000).
[CrossRef]

Royer, H.

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Xu, Wenbo

Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
[CrossRef] [PubMed]

Appl. Opt. (2)

Exp. in Fluid (1)

Y. Pu and H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. in Fluid,  29184–197 (2000).
[CrossRef]

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

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

L. Onural and M.T. Özgen, “Extraction of the three dimensional object location information directly from the in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A. 9252–260 (1992).
[CrossRef]

Meas. Sci. Technol. (4)

M. Malek, D. Allano, S. Coätmellec, C. Özkul, and D. Lebrun, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol.,  15699–705 (2004).
[CrossRef]

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

K. D. Hinsch,“Three-dimensional particle velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

S. Coätmellec, C. Buraga-Lefevre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multipleplane velocimetry,” Meas. Sci. Technol. 121392–1397 (2001).
[CrossRef]

Nouv. Rev. Opt. (1)

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Opt. Eng. (1)

T.M. Kreis and W.P.O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Opt. Express. (1)

D. Lebrun, A.M. Benkouider, S. Coätmellec, and M. Malek, “Particle field digital holography reconstruction in arbitrary tilted planes,” Opt. Express. 11224–229 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-3-224.
[CrossRef] [PubMed]

Opt. Laser Technol. (1)

D. H. Barnhart, N. A. Halliwell, and J. M. Coupland, “Holography particle image velocimetry: analysing using a conjugate reconstruction geometry,” Opt. Laser Technol. 32, 527–533 (2000).
[CrossRef]

Opt. Lasers Eng. (1)

C. Buraga-Lefebvre, S. Coätmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33409–421 (2000).
[CrossRef]

Opt. lett. (1)

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Opt. lett. 42, 827–833 (2003).

L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993).
[CrossRef] [PubMed]

Optics communications (1)

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

PNAS (1)

Wenbo Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” PNAS 9811301–11305 (2001).
[CrossRef] [PubMed]

Other (1)

Ronalds N. Bracewell, “The Fourier Transform and its applications,” second edition, p. 245 (1986).

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Figures (10)

Fig. 1.
Fig. 1.

Hologram recording in the Gabor configuration.

Fig. 2.
Fig. 2.

Particle image reconstruction. (a) Simulated diffraction pattern of a particle, d = 30μm and z 0 = 50mm and (b) the reconstruction of particle image using WT method.

Fig. 3.
Fig. 3.

Principle of the particle extraction. (a) Variations of the WTMM and Deq versus zr and (b) the three-dimensional representation (isocontours) of the reconstructed particle image in the considered volume.

Fig. 4.
Fig. 4.

General process for determining the 3D particle locations.

Fig. 5.
Fig. 5.

(a) An in-line hologram of 30 μm particles in a 9.2 × 9.2 × 3mm3 volume (z ∈ [50,53mm]) with 3815 particles (15 mm-3) and (b) the numerical reconstruction of the particle field at zr = 51mm.

Fig. 6.
Fig. 6.

Histogram of depth-error δz on a reconstructed hologram. ns = 15 mm-3,d = 30μm and L = 3mm.

Fig. 7.
Fig. 7.

Variation of the extracted particle (Ep) number versus shadow density (sd ).

Fig. 8.
Fig. 8.

Variation of the signal to noise ratio versus shadow density (sd ).

Fig. 9.
Fig. 9.

Experimental diffraction pattern of particle field on the surface of a glass plate. (a) Hologram recorded by a CCD camera with pixel size 9 μm and (b) numerical reconstruction at z = 45 mm.

Fig. 10.
Fig. 10.

Histogram of the deviation between the measured z-position and the fitted z-position obtained by a 2D polynomial regression.

Equations (9)

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

I z 0 x y = 1 O x y * * 2 λ z 0 sin [ π ( x 2 + y 2 ) λ z 0 ] ,
I z 0 x y = 1 2 π W T O ( a 0 , x , y ) .
Ψ a = 1 a 2 sin ( x 2 + y 2 a 2 ) .
a 0 = λ z 0 π .
WT I z a x y = 1 O x y 1 2 λz O x y * * sin [ π ( x 2 + y 2 ) 2 λz ] .
Ψ Ga x y = 1 a 2 [ sin ( x 2 + y 2 a 2 ) M Ψ ( σ ) ] exp ( x 2 + y 2 σ 2 a 2 ) ,
D eq = 2 S eq π .
S eq = + + WT I z a x y dxdy WT I z a 0,0 ,
SNR = I sg σ bn .

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