Abstract

In this paper, we present a method to scale (that is, to enlarge or reduce) three-dimensional integral images of objects. The scaling is achieved by controlling the spatial ray sampling rate of elemental images in the pickup procedure of the object. The sampling is obtained by using a moving array-lenslet technique (MALT) during the recording stage. In the display process, a stationary display lenslet array is used. The lateral and longitudinal magnifications obtained with the proposed method are the same, therefore three-dimensional image distortion can be avoided. To illustrate the feasibility of our method, experiments are performed to magnify a small object in three-dimensional space.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

C. R. Acad. Sci. (1)

G. Lippmann, �??La photographie integrale,�?? C. R. Acad. Sci. 146, 446-451 (1908).

J. Appl. Opt.-Info. Proc. (1)

S. W. Min, B. Javidi, and B. Lee, "Enhanced 3D Integral Imaging System by use of double display devices," J. Appl. Opt.-Info. Proc. 42, 4186-4195 (2003).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

LEOS 2003 (1)

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau and J.-P. Huignard, "Image reconstruction using electro-optic holography," in Proc. of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003, vol. 1 (IEEE, Piscataway, NJ, 2003) pp. 172-173.

Opt. Eng. (2)

N. Davies, M. McCormick and M. Brewin, "Design and analysis of an image transfer system using microlens array," Opt. Eng. 33, 3624-3633 (1994).
[CrossRef]

F. Okano, J. Arai, H. Hoshino and I. Yayuma, �??Three-dimensional video system based on integral photography,�?? Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Optics Express (1)

A. Stern, and B. Javidi,�??3D computational synthetic aperture integral imaging (COMPSAII),�?? Optics Express 11(19), 2446-2450 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-19-2446">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-19-2446</a>
[CrossRef]

Proc. IEEE (1)

T. Okoshi, �??Three-dimensional display,�?? Proc. IEEE 68, 548-564 (1980).
[CrossRef]

Other (2)

S. A. Benton, ed., Selected Papers on Three-Dimensional Displays (SPIE Optical Engineering Press, Bellingham. WA, 2001).

B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technology (Springer-Verlag, Berlin, 2002).

Supplementary Material (2)

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» Media 2: MOV (48 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Pickup and display in 3D II. (a) Pickup of elemental images using a lenslet array. (b) Conventional image display using a lenslet array and a display panel. (c) 3D projection II with a micro-convex-mirror array.

Fig. 2.
Fig. 2.

Ray integration to reconstruct 3D images in II. (a) 3D image formation in RPII. The display plane is placed at distance |g|>f from the array and the imaging plane is at distance Limg from the array. (b) 3D image formation in DPII. The display plane is placed at distance |g|=f from the array. The spot size is denoted by the gray ellipse and equals the lenslet diameter. (c) 3D image formation with changing the pitch of the lenslet array in RPII. (d) 3D image formation with changing the pitch of the lenslet array in DPII.

Fig. 3.
Fig. 3.

Controlling the spatial ray sampling rate by adjusting the lenslet pitch. The upper half of (a) and (b) indicates the pickup process. The lower half indicates the display process. (a) Increasing spatial ray sampling rate. The distance δ between the elemental images during the pickup is lower than the lenslet array pitch yielding a high sampling. The reconstructed 3D object is magnified. (b) Decreasing spatial ray sampling rate. The distance δ between the elemental images during the pickup is higher than the lenslet array pitch yielding a low sampling rate. The reconstructed 3D object is demagnified.

Fig. 4.
Fig. 4.

Controlling the 3D image size by controlling spatial ray sampling rate. The object consists of two points A and B. The lateral distance between the points is a and the longitudinal is b. (a) Pickup with sampling rate 1/δ. (b) Display with sampling rate 1/δ′.

Fig. 5.
Fig. 5.

An elemental image in the pickup process of conventional integral image.

Fig. 6.
Fig. 6.

Example of magnification. (a) Pickup process at y=0. (b) Pickup process at y=2/p. (c) The twice magnified 3D integral images.

Fig. 7.
Fig. 7.

(49 KB) Movie of magnifying object 2 times in pickup procedure.

Fig. 8.
Fig. 8.

Small 3D object and elemental images used in experiments. (a) Small 3D object used in the experiments. (b) Array of elemental images obtained from direct camera pickup without increasing spatial ray sampling rate. (c) New array of elemental image with increased spatial ray sampling rate of 5 times the rate in (b).

Fig. 9.
Fig. 9.

Experimental results for increasing spatial ray sampling rate. (a)~(e) Magnification 5 to 1 times on the left view. (f)~(j) Magnification 5 to 1 times on the center view.

Fig. 10.
Fig. 10.

(2.28 MB) Movie of 5 times magnified object.

Equations (10)

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w 1 = δ + ( δ f L ) ,
w 1 = δ + ( δ f L ) ,
w 1 δ = w 1 δ .
δ δ = L L .
δ δ = ( L + b ) ( L + b ) .
b / b = δ / δ = L / L .
a a = ( L + b ) ( L + b ) = δ δ .
Δ p = f δ 0 L ,
k = N D N P ,
2 h s k Δ p = f δ 0 L .

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