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Digital in-line holography: influence of the shadow density on particle field extraction

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun

Open Access Open Access

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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Figures (10)
Fig. 1.
Fig. 1. Hologram recording in the Gabor configuration.

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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.

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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.

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Fig. 4.
Fig. 4. General process for determining the 3D particle locations.

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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.

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Fig. 6.
Fig. 6. Histogram of depth-error δz on a reconstructed hologram. ns = 15 mm-3,d = 30μm and L = 3mm.

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Fig. 7.
Fig. 7. Variation of the extracted particle (Ep) number versus shadow density (sd ).

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Fig. 8.
Fig. 8. Variation of the signal to noise ratio versus shadow density (sd ).

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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.

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Fig. 10.
Fig. 10. Histogram of the deviation between the measured z-position and the fitted z-position obtained by a 2D polynomial regression.

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Equations (9)

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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 = 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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