Abstract

Digital in-line holography is widely used in flow studies where the 3D position, size and velocity of particles or fibers has to be known at a given time. When holograms are recorded by using a sub-picosecond laser, the enlargement of the spectral distribution acts as a spatial low-pass filter over the intensity distribution of the diffraction pattern. This is not a disadvantage as regards to the spatial sampling. Indeed, the Moiré effect, due to the sub-sampling of the fringe pattern is naturally reduced. Experimental results are provided.

© 2007 Optical Society of America

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References

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  1. L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18,846–848 (1993).
    [CrossRef] [PubMed]
  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]
  3. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” App. Opt. 33,179–181 (1994).
    [CrossRef]
  4. 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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. L. Onural, “Sampling of the diffraction field,” App. Opt. 39,5929–5935 (2000).
    [CrossRef]
  9. M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” App. Opt. 14,1093–1099 (1975).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun, 268,27–33 (2006).
[CrossRef]

2004 (1)

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]

2003 (1)

2002 (1)

2000 (2)

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation : application in digital holographic microscopy,” Opt. Commun. 182,59–69 (2000).
[CrossRef]

L. Onural, “Sampling of the diffraction field,” App. Opt. 39,5929–5935 (2000).
[CrossRef]

1999 (1)

F. Dubois, L. Joannes, and J.C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” App. Opt. 34,7085–7094 (1999)
[CrossRef]

1997 (1)

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)

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” App. Opt. 33,179–181 (1994).
[CrossRef]

1993 (1)

1991 (1)

D Lebrun, C Ozkul, D Allano, and A Leduc,“Use of the moiré effect to improve diameter measurements with charge coupled imagers,” J. Opt. 22175–184 (1991).
[CrossRef]

1975 (1)

M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” App. Opt. 14,1093–1099 (1975).
[CrossRef]

Allano, D

D Lebrun, C Ozkul, D Allano, and A Leduc,“Use of the moiré effect to improve diameter measurements with charge coupled imagers,” J. Opt. 22175–184 (1991).
[CrossRef]

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]

Brunel, M.

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun, 268,27–33 (2006).
[CrossRef]

Coëtmellec, S.

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun, 268,27–33 (2006).
[CrossRef]

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

Cuche, E.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation : application in digital holographic microscopy,” Opt. Commun. 182,59–69 (2000).
[CrossRef]

Depeursinge, C.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation : application in digital holographic microscopy,” Opt. Commun. 182,59–69 (2000).
[CrossRef]

Dubois, F.

F. Dubois, L. Joannes, and J.C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” App. Opt. 34,7085–7094 (1999)
[CrossRef]

Ducottet, C.

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]

Fournel, T.

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]

Fournier, C.

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]

Jericho, M. H.

Joannes, L.

F. Dubois, L. Joannes, and J.C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” App. Opt. 34,7085–7094 (1999)
[CrossRef]

Jüptner, W.

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” App. Opt. 33,179–181 (1994).
[CrossRef]

Kato, M.

M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” App. Opt. 14,1093–1099 (1975).
[CrossRef]

Kreuzer, H. J.

Lebrun, D

D Lebrun, C Ozkul, D Allano, and A Leduc,“Use of the moiré effect to improve diameter measurements with charge coupled imagers,” J. Opt. 22175–184 (1991).
[CrossRef]

Lebrun, D.

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun, 268,27–33 (2006).
[CrossRef]

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

Leduc, A

D Lebrun, C Ozkul, D Allano, and A Leduc,“Use of the moiré effect to improve diameter measurements with charge coupled imagers,” J. Opt. 22175–184 (1991).
[CrossRef]

Legros, J.C.

F. Dubois, L. Joannes, and J.C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” App. Opt. 34,7085–7094 (1999)
[CrossRef]

Marquet, P.

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation : application in digital holographic microscopy,” Opt. Commun. 182,59–69 (2000).
[CrossRef]

Nakayama, Y.

M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” App. Opt. 14,1093–1099 (1975).
[CrossRef]

Nicolas, F.

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun, 268,27–33 (2006).
[CrossRef]

Onural, L.

L. Onural, “Sampling of the diffraction field,” App. Opt. 39,5929–5935 (2000).
[CrossRef]

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

Ozkul, C

D Lebrun, C Ozkul, D Allano, and A Leduc,“Use of the moiré effect to improve diameter measurements with charge coupled imagers,” J. Opt. 22175–184 (1991).
[CrossRef]

Özkul, C.

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

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” App. Opt. 33,179–181 (1994).
[CrossRef]

Suzuki, T.

M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” App. Opt. 14,1093–1099 (1975).
[CrossRef]

Xu, W.

App. Opt. (4)

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” App. Opt. 33,179–181 (1994).
[CrossRef]

L. Onural, “Sampling of the diffraction field,” App. Opt. 39,5929–5935 (2000).
[CrossRef]

M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” App. Opt. 14,1093–1099 (1975).
[CrossRef]

F. Dubois, L. Joannes, and J.C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” App. Opt. 34,7085–7094 (1999)
[CrossRef]

J. Opt. (1)

D Lebrun, C Ozkul, D Allano, and A Leduc,“Use of the moiré effect to improve diameter measurements with charge coupled imagers,” J. Opt. 22175–184 (1991).
[CrossRef]

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

Meas. Sci. Technol (1)

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]

Opt. Commun (1)

F. Nicolas, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography with a sub-picosecond laser beam,” Opt. Commun, 268,27–33 (2006).
[CrossRef]

Opt. Commun. (1)

E. Cuche, P. Marquet, and C. Depeursinge, “Aperture apodization using cubic spline interpolation : application in digital holographic microscopy,” Opt. Commun. 182,59–69 (2000).
[CrossRef]

Opt. Eng. (1)

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]

Opt. Lett. (2)

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Figures (5)

Fig. 1.
Fig. 1.

Fiber hologram recorded in the Gabor configuration

Fig. 2.
Fig. 2.

Intensity distribution of the diffraction pattern sampled by the imaging system (p=11 μm, d = 40 μm, ze = 30 mm and λ=0,6328 μm).

Fig. 3.
Fig. 3.

Intensity distribution of the diffraction pattern : low-pass filtering effect produced by a short laser pulse (T=85 fs). p=11 μm, d = 40 μm, ze = 30 mm and λ0=800 μm.

Fig. 4.
Fig. 4.

Experimental intensity distribution in the diffraction pattern of a fiber. p=11 μm, d = 40 μm, ze = 30 mm. (a) with an He-Ne laser, λ0=632.8 nm, (b) with a femtosecond Ti:Sa laser, T=85 fs and λ0=800 nm.

Fig. 5.
Fig. 5.

Digital reconstruction of the holograms of Fig. 4. (a). with an He-Ne laser, λ0=632.8 nm, (b). with a femtosecond Ti:Sa laser, T=85 fs and λ0=800 nm.

Equations (25)

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I z e x λ = 1 [ h z e x λ + h z e ˉ x λ ] F x λ + 1 λ z e F 2 x λ
rect ( x d ) = { 1 for d 2 x d 2 0 elsewhere
h z e x λ = 1 λ z e exp j ( π x 2 λ z e π 4 )
F x λ = d sin ( πdx λ z e ) ( πdx λ z e ) = d sin c ( dx λ z e )
x = x M = ± λ z e p .
u ( t ) = exp [ j ω 0 t t 2 T 2 ]
U ( ω ) = T π exp [ T 2 4 ( ω ω 0 ) 2 ]
I z e x ω = 1 [ h z e x ω + h z e ˉ x ω ] F x ω + ω 2 πc z e F 2 x ω
h z e x ω = ω 2 πc z e exp j ( ω x 2 2 c z e π 4 ) and F x ω = d sin c ( ωdx 2 πc z e )
I z e ( x ) = C + I z e x ω U ( ω ) 2
I z e ( x ) = I 1 I 2 I 3 + I 4
I 1 = + exp [ T 2 2 ( ω ω 0 ) 2 ] ,
I 2 = + h z e ( x , ω ) F ( x , ω ) exp [ T 2 2 ( ω ω 0 ) 2 ] ,
I 3 = + h z e ˉ x ω F x ω exp [ T 2 2 ( ω ω 0 ) 2 ]
I 4 = + ω 2 πc z e F 2 x ω exp [ T 2 2 ( ω ω 0 ) 2 ] .
I z e ( x ) = 1 [ h z e x ω 0 + h z e ˉ x ω 0 ] W x T F x ω 0 + ω 0 2 πc z e F 2 x ω 0
W x T = exp [ x 4 8 c 2 z e 2 T 2 ]
T < λ 0 2 z e 4 c p 2
+ exp ( p 2 u 2 ± qu ) du = π p exp ( q 2 4 p 2 )
I 1 = 2 π T
χ = ω ω 0 , β = T 2 ω 0 2 2 , γ = ω 0 x 2 2 c z e and δ = ω 0 dx 2 πc z e
I 2 = ω 0 d exp ( j π 4 ) + exp [ β ( χ 1 ) 2 ] ω 0 χ 2 πc z e exp ( jγχ ) sin c ( δ χ ) d χ
I 2 ω 0 d exp ( j π 4 ) sin c ( δ ) ω 0 2 πc z e + exp [ β ( χ 1 ) 2 ] exp ( jγχ )
I 2 ω 0 π β ω 0 2 πc z e d sin c ( δ ) exp [ j ( γ π 4 ) ] exp [ γ 2 4 β ]
I z e ( x ) = 1 [ h z e x ω 0 + h z e ˉ x ω 0 ] W x T F x ω 0 + ω 0 2 πc z e F 2 x ω 0

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