Abstract

We present a method for controlling the depth of three-dimensional (3D) images reconstructed by integral photography. Incoherent light is reflected from 3D objects, propagates through a lens array, and is captured as the first elemental images by a capturing device. The second elemental images of the 3D images are generated by numerical processing from the first elemental images in accordance with the desired depth. The optical reconstruction of 3D images at the desired depth by the second elemental images is confirmed experimentally.

© 2008 Optical Society of America

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References

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  1. M. G. Lippmann, J. Phys. (France) 4, 821 (1908).
  2. H. E. Ives, J. Opt. Soc. Am. 21, 171 (1931).
    [CrossRef]
  3. N. Davies, M. McCormick, and M. Brewin, Opt. Eng. 33, 3624 (1994).
    [CrossRef]
  4. F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
    [CrossRef]

1999 (1)

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

1994 (1)

N. Davies, M. McCormick, and M. Brewin, Opt. Eng. 33, 3624 (1994).
[CrossRef]

1931 (1)

1908 (1)

M. G. Lippmann, J. Phys. (France) 4, 821 (1908).

J. Opt. Soc. Am. (1)

J. Phys. (France) (1)

M. G. Lippmann, J. Phys. (France) 4, 821 (1908).

Opt. Eng. (2)

N. Davies, M. McCormick, and M. Brewin, Opt. Eng. 33, 3624 (1994).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Procedure for the proposed method. (a) Step 1, first capturing. (b) Step 2, second capturing and calculation. (c) Step 3, reconstruction.

Fig. 2
Fig. 2

Calculation geometry of the proposed method.

Fig. 3
Fig. 3

(a) The object. (b) Captured elemental images. (c)–(e) Elemental images calculated by the proposed method, with (c) L = 1.83 mm ( z r = 100 mm ) , (d) L = 9.41 mm ( z r = 50 mm ) , and (e) L = 24.56 mm ( z r = 50 mm ) .

Fig. 4
Fig. 4

Views of the displayed 3D images from (a) the lower left-hand position, and (b) the upper right-hand position.

Fig. 5
Fig. 5

Images projected on the diffuser located 50 mm in front of the fourth lens array. Note that the right-hand image is depicted clearly, whereas the others are unclear.

Tables (1)

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Table 1 Lens Array Specifications

Equations (12)

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z r = d r d 2 ( L + z c d 1 d c ) .
U 2 ( x 2 , y 2 ) = h 1 = m m v 1 = n n { i λ U 1 ( x 1 , y 1 ) 1 r 1 exp [ i k r 1 ] d x 1 d y 1 } = h 1 = m m v 1 = n n { i λ A h 1 , v 1 δ ( x 1 h 1 p , y 1 v 1 p ) × 1 r 1 exp [ i k r 1 ] d x 1 d y 1 } = i λ h 1 = m m v 1 = n n A h 1 , v 1 1 r ̂ 1 exp [ i k r ̂ 1 ] ,
r 1 = [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 + d 1 2 ] 1 2 ,
r ̂ 1 = [ ( x 2 h 1 p 1 ) 2 + ( y 2 h 2 p 2 ) 2 + d 1 2 ] 1 2 .
U 2 ( x 2 , y 2 ) = U 2 ( x 2 , y 2 ) G ( x 2 , y 2 ) exp [ i k ( x 2 2 + y 2 2 ) 2 f 2 ] ,
G ( x 2 , y 2 ) = { 1 ( inside the lens aperture ) 0 ( otherwise ) } .
U 3 ( x 3 , y 3 ) = i λ U 2 ( x 2 , y 2 ) 1 r 2 exp [ i k r 2 ] d x 2 d y 2 ,
r 2 = [ ( x 3 x 2 ) 2 + ( y 3 y 2 ) 2 + L 2 ] 1 2 .
U 3 ( x 3 , y 3 ) = U 3 ( x 3 , y 3 ) G ( x 3 , y 3 ) exp [ i k ( x 3 2 + y 3 2 ) 2 f 3 ] ,
U 4 ( x 4 , y 4 ) = i λ U 3 ( x 3 , y 3 ) 1 r 3 exp [ i k r 3 ] d x 3 d y 3 ,
r 3 = [ ( x 4 x 3 ) 2 + ( y 4 y 3 ) 2 + d 2 2 ] 1 2 .
I ( x 4 , y 4 ) = U ( x 4 , y 4 ) 2 .

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