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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Appl. Opt. (2)

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

S. Coëtmellec, D. Lebrun and C. �?zkul, "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. Tech. (1)

S. Coëtmellec, C. Buraga-Lefebvre, D. Lebrun and C. �?zkul, "Application of in-line digital holography to multiple plane velocimetry," Meas. Sci. Tech. 12, 1392-1397 (2001).
[CrossRef]

Opt. Eng. (2)

S. Belaïd, D. Lebrun and C. �?zkul, "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, W.P.O. Jüptner, "Suppression of the dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun and C. �?zkul, "Application of wavelet transform to hologram analysis : three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Opt. Lett. (2)

Yamaguchi and T. Zhang, �??Phase-shifting digital holography,�?? Opt. Lett. 22, 1268-1270, (1997)
[CrossRef] [PubMed]

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

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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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