Abstract

Digital holography is applied to the reconstruction of small particles in a plane whose orientation is arbitrary as specified by the user. The diffraction pattern produced by the particles is directly recorded by a conventional CCD camera. The digital recorded image enables the recovery of particle-images in several parallel planes of the probe volume. Afterwards, an interrogation slice corresponding to a thin layer around a theoretical arbitrary tilted plane is fixed. The pixels whose 3D coordinates belong to this slice are selected and juxtaposed to rebuild the particle images. The feasibility is demonstrated on a fiber tilted with respect to the camera plane. A second example is given on an experimental particle field. These results let us predict future applications such as the characterization of particle fields in planes other than those parallel with the camera plane.

© 2003 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. M.K. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express 7, 305–310, (2000) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-9-305
    [Crossref] [PubMed]
  3. O. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994)
    [Crossref] [PubMed]
  4. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270, (1997)
    [Crossref] [PubMed]
  5. S. Belaïd, D. Lebrun, and C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997)
    [Crossref]
  6. C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
    [Crossref]
  7. L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848, (1993)
    [Crossref] [PubMed]
  8. S. Coëtmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform,” App. Optics,  41, 312–319, (2002)
    [Crossref]
  9. S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
    [Crossref]
  10. S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of two-dimensional fractional-order Fourier transformation to particle field digital holography,” J. Opt. Soc. Am. A.,  19, 1537–1546, (2002)
    [Crossref]
  11. L. Yu, Y. An, and L. Cai, “Numerical reconstruction of digital holograms with variable viewing angles,” Opt. Express 10, 1250–1257, (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1250
    [Crossref] [PubMed]

2002 (3)

S. Coëtmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform,” App. Optics,  41, 312–319, (2002)
[Crossref]

S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of two-dimensional fractional-order Fourier transformation to particle field digital holography,” J. Opt. Soc. Am. A.,  19, 1537–1546, (2002)
[Crossref]

L. Yu, Y. An, and L. Cai, “Numerical reconstruction of digital holograms with variable viewing angles,” Opt. Express 10, 1250–1257, (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1250
[Crossref] [PubMed]

2001 (1)

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
[Crossref]

2000 (2)

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
[Crossref]

M.K. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express 7, 305–310, (2000) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-9-305
[Crossref] [PubMed]

1997 (3)

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

Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270, (1997)
[Crossref] [PubMed]

S. Belaïd, D. Lebrun, and C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997)
[Crossref]

1994 (1)

1993 (1)

An, Y.

Belaïd, S.

S. Belaïd, D. Lebrun, and C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997)
[Crossref]

Buraga-Lefebvre, C.

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
[Crossref]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
[Crossref]

Cai, L.

Coëtmellec, S.

S. Coëtmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform,” App. Optics,  41, 312–319, (2002)
[Crossref]

S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of two-dimensional fractional-order Fourier transformation to particle field digital holography,” J. Opt. Soc. Am. A.,  19, 1537–1546, (2002)
[Crossref]

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
[Crossref]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
[Crossref]

Juptner, W.

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]

Kim, M.K.

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]

Lebrun, D.

S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of two-dimensional fractional-order Fourier transformation to particle field digital holography,” J. Opt. Soc. Am. A.,  19, 1537–1546, (2002)
[Crossref]

S. Coëtmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform,” App. Optics,  41, 312–319, (2002)
[Crossref]

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
[Crossref]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
[Crossref]

S. Belaïd, D. Lebrun, and C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997)
[Crossref]

Onural, L.

Özkul, C.

S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of two-dimensional fractional-order Fourier transformation to particle field digital holography,” J. Opt. Soc. Am. A.,  19, 1537–1546, (2002)
[Crossref]

S. Coëtmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform,” App. Optics,  41, 312–319, (2002)
[Crossref]

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
[Crossref]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
[Crossref]

S. Belaïd, D. Lebrun, and C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997)
[Crossref]

Schnars, O.

Yamaguchi,

Yu, L.

Zhang, T.

App. Optics (1)

S. Coëtmellec, D. Lebrun, and C. Özkul, “Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier Transform,” App. Optics,  41, 312–319, (2002)
[Crossref]

Appl. Opt. (1)

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

S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of two-dimensional fractional-order Fourier transformation to particle field digital holography,” J. Opt. Soc. Am. A.,  19, 1537–1546, (2002)
[Crossref]

Meas. Sci and Tech. (1)

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Özkul, “Application of in-line digital holography to multiple plane velocimetry,” Meas. Sci and Tech. 12, 1392–1397 (2001)
[Crossref]

Opt. Eng. (2)

S. Belaïd, D. Lebrun, and C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997)
[Crossref]

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 (2)

Opt. Lett. (2)

Optics and Lasers in Eng. (1)

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Optics and Lasers in Eng. 33, 09–421 (2000)
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1.

Hologram recording in the Gabor configuration

Fig. 2.
Fig. 2.

Geometrical configuration for a tilted fiber

Fig. 3.
Fig. 3.

Reconstruction in a tilted plane. (a) Intensity distribution in the diffraction pattern for a tilted fiber (d=60 µm, D0=73 mm and θ0=84.2°), (b) image reconstructed at zr=D0 and (c) image reconstructed in the fiber plane by selecting the pixels owing to this plane

Fig. 4.
Fig. 4.

Reconstruction in a tilted plane, experimental results. (a) Intensity distribution in the diffraction pattern for a tilted fiber (d=30 µm, D0=40 mm and θ0=67°), (b) image reconstructed at zr=50 mm, (c) image reconstructed in the fiber plane by selecting the pixels owing to this plane

Fig. 5.
Fig. 5.

Experimental recording setup

Fig. 6.
Fig. 6.

Experimental results on a particle field produced by a spray: (a) diffraction pattern recorded by the CCD camera, (b) image reconstruction at zr=120 mm, (c) image reconstruction on a tilted plane (Dr=100 mm, θr=76°)

Equations (5)

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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 ( x , y ) = 1 a 2 sin ( x 2 + y 2 a 2 )
a 0 = λ z 0 π
W T I z 0 ( a 0 , x , y ) = 1 O ( x , y ) 1 2 λ z 0 O ( x , y ) * * sin [ π ( x 2 + y 2 ) 2 λ z 0 ]

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