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Particle field digital holographic reconstruction in arbitrary tilted planes

D. Lebrun, A.M. Benkouider, S. Coëtmellec, and M. Malek

Open Access Open Access

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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Figures (6)
Fig. 1.
Fig. 1. Hologram recording in the Gabor configuration

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Fig. 2.
Fig. 2. Geometrical configuration for a tilted fiber

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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

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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

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Fig. 5.
Fig. 5. Experimental recording setup

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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°)

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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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