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3-D computational synthetic aperture integral imaging (COMPSAII)

Adrian Stern and Bahram Javidi

Open Access Open Access

Abstract

We propose a computational synthetic aperture integral imaging technique that increases the field of view (FOV) and viewing angle of integral imagines systems. The synthetic aperture is obtained by relative movement of the imaging system and the object in a plane perpendicular to the optical axis. Integral images (IIs) captured during the scanning process are combined together to create a synthetic aperture integral image (SAII) that has an enlarged effective FOV. Three-dimensional (3D) images are computed digitally from the constructed SAII in similar ways that are computed from single digital II. Since the synthetic aperture is obtained by a scanning process, the proposed method is suitable when the integral imaging system is located on moving platforms such as aircrafts or when the object is in motion such as objects on assembly lines. CompSAII allows reconstruction of the images at different distances from the lenslets using light backward or forward propagation to position the viewing plane at any arbitrary position. To the best of our knowledge this is the first time a computational synthetic aperture technique is applied to integral imaging.

©2003 Optical Society of America

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Supplementary Material (1)

Media 1: AVI (21 KB)     

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Figures (7)
Fig.1.
Fig.1. A typical digital integral imaging recording setup

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Fig. 2.
Fig. 2. The FOV for is primarily limited by the maximum lenslet exit angle θl

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Fig. 3.
Fig. 3. A finite pickup lens induces further limitation on the viewing angles and viewing area.

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Fig. 4
Fig. 4 Minimal (solid line) and maximal (dashed) viewing angles of an object placed at optimum location for widest viewing angle range.

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Fig. 5.
Fig. 5. Synthetic aperture II principle. The object is scanned in the vertical direction. A displacement of Δx between two consecutive exposures increases the effective system aperture byΔx.

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Fig. 6
Fig. 6 (a) and (b)- two displaced lls. (c) Sll computed from (a) and (b).

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Fig. 7.
Fig. 7. (Movie 21 KB) Computer perspective reconstruction from the II of Fig. 6(a) (upper row) and from the SAII shown in Fig. 6(c) (lower row). θ and ϕ are the horizontal and vertical components of the viewing angle respectively. It can be seen that images wider viewing area can be reconstructed from the SAII.

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Equations (8)

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− θ l ≤ θ ≤ θ l
θ l = ∣ t g − 1 p l ( z 1 − f l ) 2 z 1 f ∣
L 0 max = 2 z 1 tg ( θ l ) .
− ( L A 2 + z 1 θ l ) ≤ x ≤ ( L A 2 + z 1 θ l )
− min ( θ m , θ l ) ≤ θ ≤ min ( θ m , θ l )
θ m = t g − 1 ( ( L A + D ) 2 − L o z 2 ) .
− ( L A 2 + z 1 t g θ m ) ≤ x ≤ L A 2 + z 1 t g θ m .
− min { tg [ D − L 0 2 ( z 1 + z 2 ) ] , tg ( L A − L 0 2 z 1 ) , θ l } ≤ α ≤ min { tg [ D − L 0 2 ( z 1 + z 2 ) ] , tg ( L A − L 0 2 z 1 ) , θ l } .
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