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An automatic method for assembling a large synthetic aperture digital hologram

A. Pelagotti, M. Paturzo, M. Locatelli, A. Geltrude, R. Meucci, A. Finizio, and P. Ferraro

Open Access Open Access

Abstract

A major issue so far for digital holography is the low spatial resolution generally achieved. The numerical aperture is limited by the area of currently available detectors, such as CCD sensors, which is significantly lower than that of a holographic plate. This is an even more severe constraint when IR sensors such as microbolometers are taken into account. In order to increase the numerical aperture of such systems, we developed an automatic technique which is capable of recording several holograms and of stitching them together, obtaining a digital hologram with a synthetic but larger numerical aperture. In this way we show that more detail can be resolved and a wider parallax angle can be achieved. The method is demonstrated for visible as well IR digital holography, recording and displaying large size objects.

©2012 Optical Society of America

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Supplementary Material (2)

Media 1: MOV (504 KB)     
Media 2: AVI (3909 KB)     

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Figures (9)
Fig. 1
Fig. 1 Sketch of the experimental setup used to acquire the statuettes’ holograms: BS (beamsplitter), L1and L2 (lenses), M1 and M2 (mirrors).

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Fig. 2
Fig. 2 Numerical reconstructions of a single (a) and a stitched hologram obtained joining 4 × 3 single holograms by the proposed algorithm (b).

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Fig. 3
Fig. 3 Scattered plot of MI (a) CC (b) values obtained by the registration algorithm when changing the tx and ty parameters.

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Fig. 4
Fig. 4 Numerical reconstructions of a stitched hologram obtained sewing up four IR hologram of a “Perseus” statuette, by means of the proposed algorithm (a) and by manual joining (b).

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Fig. 5
Fig. 5 (a) One of the acquired hologram, (b) Synthetic hologram obtained by means of the stitching algorithm, (c) picture of the object.

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Fig. 6
Fig. 6 Numerical reconstruction: Amplitude reconstruction obtained by the single hologram (a) and by the joint hologram (b).

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Fig. 7
Fig. 7 (a) synthetic hologram obtained stitching together 3 × 7 single holograms and its numerical reconstructions at two different distances, 515 mm (b) and 505 mm (c). The increasing of the numerical aperture implies a decreasing of the depth of focus.

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Fig. 8
Fig. 8 Single IR hologram (a) and its numerical reconstructions at two different distances, 515 mm (b) and 505 mm (c). Because of the low numerical aperture no differences in the two images is visible.

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Fig. 9
Fig. 9 (a, Media 1) Frame of the movie showing the numerical reconstruction of the left and right part of the stitched hologram, (b, Media 2) frame of the movie displaying sequentially seven 1920 × 1080 holograms extracted from the stitched hologram.

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

I(X,Y)= ∑ x,y p XY (x,y)× log 2 p XY (x,y) p X (x)⋅ p Y (y)
α*=arg max α I(X,Y)
p XY,α (x,y)= h α (x,y) ∑ x,y h α (x,y) p X,α (x)= ∑ y p XY,α (x,y) p Y,α (y)= ∑ x p XY,α (x,y)
x → '=L x → + t →
t → =[ t x , t y ]
R=[ cosθ senθ −senθ cosθ ]
x → '=sR x → + t →
∑ i w i ( T α (p))=1 Y( T α (p))= ∑ i w i ⋅Y( n i ) h α (X(p),Y( T α (p)))=+1
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