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Synthetic aperture single-exposure on-axis digital holography

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Abstract

We present a system for reconstructing single-exposure on-line (SEOL) digital holograms with improved resolution using a synthetic aperture. Several recordings are made in order to compose the synthetic aperture, shifting the camera within the hologram plane. After processing the synthetic hologram, an inverse Fresnel transformation provides an enhanced resolution reconstruction. We show that recognition capacity for high frequency details is increased. Experimental results with a test target and with a microscopic biological sample are presented. Both visualization and correlation results are reported.

©2008 Optical Society of America

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Figures (6)

Fig. 1.
Fig. 1. Experimental set-up. SF, spatial filter; L1, collimating lens; BS1, BS2, beam splitters; L2, L3, lenses in object and reference beams; M1, M2, mirrors; OBJ, sample object.
Fig. 2.
Fig. 2. Reconstruction of a USAF resolution test target using a low resolution (a), a synthetic aperture (b), and a high resolution digital hologram (c).
Fig. 3.
Fig. 3. Correlation between high frequency groups in the resolution test target reconstructions. Correlation peaks, comparing with the high resolution hologram, for the low resolution (a) and the synthetic aperture hologram (b), and autocorrelation for the high resolution hologram (c). Images of the high frequency regions used for these calculations, with groups 6 and 7 in the resolution chart, are also shown: low resolution (d), synthetic aperture (e), and high resolution digital holograms (f).
Fig. 4.
Fig. 4. Reconstruction of a sphacelaria alga sample using a low resolution (a), a synthetic aperture (b), and a high resolution digital hologram (c).
Fig. 5.
Fig. 5. Reconstruction of a USAF resolution test target, with a diffuser next to it, using a low resolution (a), a synthetic aperture (b), and a high resolution digital hologram (c).
Fig. 6.
Fig. 6. Reconstruction detail of the resolution test target, with a diffuser, showing the speckle size for a low resolution (a), a synthetic aperture (b), and a high resolution digital hologram (c).

Equations (5)

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H ( x , y ) = O ( x , y ) + R ( x , y ) 2 O ( x , y ) 2 R ( x , y ) 2
= R ( x , y ) O * ( x , y ) + R * ( x , y ) O ( x , y ) ,
O ( m , n ) = exp [ i π λ d ( m 2 Δ x 2 + n 2 Δ y 2 ) ] m = 1 M n = 1 N R ( m , n ) H ( m , n )
× exp [ i π λ d ( m 2 Δ x 2 + n 2 Δ y 2 ) ] exp [ i 2 π λ d ( m Δ x m Δ x + n Δ y n Δ y ) ] .
Δ x = λ d M Δ x , Δ y = λ d N Δ y .
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