Abstract

A major problem with integral photography using a lens array is overlapping recordings (cross talk) between elemental images. Another problem is the decrease in the number of pixels in the elemental images. We describe two methods (including analyses) of manipulating the aperture of a telecentric optical system to improve these problems. The first method locates the aperture on the focal plane of a field lens. The advantage of this method is that cross talk can be reduced without changing the size of the whole optical system. The second method establishes a telecentric optical system between objects and the lens array. The advantage of this method, even though the whole optical system becomes bigger, is that cross talk can be completely eliminated. In addition, the number of pixels in the elemental images can be increased by varying the aperture position sequentially with respect to time. We also describe how cross talk is reduced in both methods by taking diffraction into consideration. Experimental results are presented to verify this reduction.

© 2009 Optical Society of America

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References

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  1. M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. 7, 821-825 (1908). English translation available at http://www.tgeorgiev.net/Lippman/index.html.
  2. T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
    [CrossRef]
  3. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]
  4. M. Kawakita, K. Iizuka, T. Aida, H. Kikuchi, H. Fujikake, J. Yonai, and K. Takizawa, “Axi-vision camera (real-time distance-mapping camera),” Appl. Opt. 39, 3931-3939 (2000).
    [CrossRef]
  5. J. Arai, M. Okui, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional image,” Appl. Opt. 37, 2031-2045 (1998).
    [CrossRef]
  6. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598-1603 (1997).
    [CrossRef] [PubMed]
  7. J. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27, 324-326 (2002).
    [CrossRef]
  8. T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).
  9. R. Martinez-Cuenca, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted integral image display,” Opt. Express 14, 9657-9663 (2006).
    [CrossRef] [PubMed]
  10. J. Arai, H. Hoshino, M. Okui, and F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996-1004 (2003).
    [CrossRef]
  11. E. Hecht, Optics, 4th ed. (Addison Wesley, 2002), pp. 485-509.

2008 (1)

T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).

2006 (1)

2003 (1)

2002 (1)

2000 (1)

1998 (1)

J. Arai, M. Okui, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional image,” Appl. Opt. 37, 2031-2045 (1998).
[CrossRef]

1997 (2)

1908 (1)

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. 7, 821-825 (1908). English translation available at http://www.tgeorgiev.net/Lippman/index.html.

Aida, T.

Arai, J.

Fujii, T.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

Fujikake, H.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002), pp. 485-509.

Hoshino, H.

Iizuka, K.

Jang, J.

Javidi, B.

Kawakita, M.

Kikuchi, H.

Lippmann, M. G.

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. 7, 821-825 (1908). English translation available at http://www.tgeorgiev.net/Lippman/index.html.

Martinez-Corral, M.

Martinez-Cuenca, R.

Mase, K.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

Mishina, T.

T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).

Mori, K.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

Oi, R.

T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).

Okano, F.

Okui, M.

T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).

J. Arai, H. Hoshino, M. Okui, and F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996-1004 (2003).
[CrossRef]

J. Arai, M. Okui, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional image,” Appl. Opt. 37, 2031-2045 (1998).
[CrossRef]

Pons, A.

Saavedra, G.

Suenaga, Y.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

Takeda, K.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

Takizawa, K.

Tanimoto, M.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

Yamaguchi, I.

Yamamoto, K.

T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).

Yonai, J.

Yuyama, I.

J. Arai, M. Okui, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional image,” Appl. Opt. 37, 2031-2045 (1998).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598-1603 (1997).
[CrossRef] [PubMed]

Zhang, T.

Appl. Opt. (3)

J. Inst. Image Inf. Telev. Eng. (1)

T. Mishina, K. Yamamoto, R. Oi, and M. Okui, “Reducing of interference between elemental images during integral photography pickup suitable for producing holograms,”J. Inst. Image Inf. Telev. Eng. 62, 1132-1137 (2008) (in Japanese).

J. Opt. Soc. Am. A (1)

J. Phys. (1)

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. 7, 821-825 (1908). English translation available at http://www.tgeorgiev.net/Lippman/index.html.

Opt. Express (1)

Opt. Lett. (2)

Other (2)

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002), pp. 485-509.

T. Fujii, K. Mori, K. Takeda, K. Mase, M. Tanimoto, and Y. Suenaga, “Multipoint measuring system for video and sound--100-camera and microphone system,” in 2006 IEEE International Conference on Multimedia and Expo (IEEE, 2006), pp. 437-440.
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Cross talk.

Fig. 2
Fig. 2

Optical system of technique 1.

Fig. 3
Fig. 3

Trajectories of light rays in technique 1.

Fig. 4
Fig. 4

Transit area of the ray in the focal plane of the field lens.

Fig. 5
Fig. 5

Optical system of technique 2.

Fig. 6
Fig. 6

Trajectories of light rays in technique 2.

Fig. 7
Fig. 7

Notations for Subsection 4B.

Fig. 8
Fig. 8

Aperture location.

Fig. 9
Fig. 9

Experimental setup in Section 6.

Fig. 10
Fig. 10

Experimental results for reducing cross talk.

Fig. 11
Fig. 11

Experimental setup in Section 7.

Fig. 12
Fig. 12

Experimental results for high resolution image.

Tables (1)

Tables Icon

Table 1 Specifications of Experimental Setup in Section 6

Equations (38)

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θ ϕ .
ϕ = D 2 f ,
θ D 2 f .
L 1 i ( x 1 ) = C w x exp [ j k w x f 1 x 1 ] Π [ x 1 c D ] ,
L 1 o ( x 1 ) = L 1 i ( x 1 ) exp [ j k ( x 1 c ) 2 2 f 1 ] ,
Π [ x 1 c D ] = { 1 if c D 2 x 1 c + D 2 0 if x 1 < c D 2 , c + D 2 < x 1 } .
L 2 i ( x 2 ) = L 1 o ( x 1 ) exp [ j k ( x 1 x 2 ) 2 2 f 1 ] d x 1 ,
= exp [ j k x 1 2 x 2 2 2 f 1 ] S a [ π D x 2 c w x λ f 1 ] exp [ j k ( x 2 c w x f 1 ) c ] ,
L 2 o ( x 2 ) = L 2 i ( x 2 ) exp [ j k x 2 2 2 f 2 ] .
L 3 i ( x 3 ) = L 2 o ( x 2 ) exp [ j k ( x 2 x 3 ) 2 2 f 2 ] d x 2 ,
= Π [ x 2 f 2 f 1 D ] exp [ j k w x f 2 x 2 ] exp [ j k ( x 2 x 3 ) 2 2 ( f 2 2 f 1 ) ] d x 2 .
G 6 i ( x 6 ) = exp [ j k ( l 4 f 4 f 5 ) x 6 2 2 c ( l 4 f 4 ) x 6 2 f 5 2 ] Π ( x 6 c f 5 f 4 a ) F { G 1 o } ( k f 4 f 2 f 5 ) ( x 6 c ) .
F { f ( x ) } y = f ( x ) exp [ j x y ] d x .
a = f 4 f 5 D ,
L 3 o ( x 3 ) = Π [ x 3 b a ] L 3 i ( x 3 ) ,
G 6 i ( x 6 ) = exp [ j k ( l 4 f 4 f 5 ) x 6 2 2 c ( l 4 f 4 ) x 6 2 f 5 2 ] × Π ( x 6 c f 5 b f 4 f 5 f 4 a ) F { G 1 o } ( k f 4 f 2 f 5 ) ( x 6 c ) .
N = A I ,
M = B J .
N = A S I ,
M = B T J .
L 2 o ( x 2 ) = exp [ j k x 2 2 2 f 2 ] L 2 i ,
= exp [ j k x 2 2 2 f 2 ] G 1 o exp [ j k ( x 1 x 2 ) 2 2 f 2 ] d x 1 ,
= F { G 1 o exp [ j k x 1 2 2 f 2 ] } ( k f 2 ) x 2 .
L 3 o ( x 3 ) = Π ( x 3 a ) L 3 i ,
= Π ( x 3 a ) L 2 o exp [ j k ( x 2 x 3 ) 2 2 f 2 ] d x 2 ,
= Π ( x 3 a ) F { G 1 o exp [ j k x 1 2 2 f 2 ] } ( k f 2 ) x 2 exp [ j k ( x 2 x 3 ) 2 2 f 2 ] d x 2 ,
= Π ( x 3 a ) F { G 1 o } ( k f 2 ) x 3 .
L 4 o ( x 4 ) = exp [ j k x 4 2 2 f 4 ] L 4 i ,
= exp [ j k x 4 2 2 f 4 ] L 3 o exp [ j k ( x 3 x 4 ) 2 2 f 4 ] d x 3 ,
= exp [ j k x 4 2 2 f 4 ] Π ( x 3 a ) F { G 1 o } ( k f 2 ) x 3 exp [ j k ( x 3 x 4 ) 2 2 f 4 ] d x 3 ,
= F { Π ( x 3 a ) F { G 1 o } ( k f 2 ) x 3 exp [ j k x 3 2 2 f 4 ] } ( k f 4 ) x 4 .
G 6 i ( x 6 ) = L 5 o exp [ j k ( x 5 x 6 ) 2 2 f 5 ] d x 5 ,
= exp [ j k ( x 5 c ) 2 2 f 5 ] L 5 i exp [ j k ( x 5 x 6 ) 2 2 f 5 ] d x 5 ,
= exp [ j k x 6 2 2 f 5 ] F { L 5 i } ( k f 5 ) ( x 6 c ) ,
= exp [ j k x 6 2 2 f 5 ] F { L 4 o exp [ j k ( x 4 x 5 ) 2 2 l 4 ] d x 4 } ( k f 5 ) ( x 6 c ) ,
= exp [ j k ( l 4 f 5 ) x 6 2 2 c l 4 x 6 2 f 5 2 ] F { L 4 o } ( k f 5 ) ( x 6 c ) ,
= exp [ j k ( l 4 f 5 ) x 6 2 2 c l 4 x 6 2 f 5 2 ] F { F { Π ( x 3 a ) F { G 1 o } ( k f 2 ) x 3 exp [ j k x 3 2 2 f 4 ] } ( k f 4 ) x 4 } ( k f 5 ) ( x 6 c ) ,
= exp [ j k ( l 4 f 4 f 5 ) x 6 2 2 c ( l 4 f 4 ) x 6 2 f 5 2 ] Π ( x 6 c f 5 f 4 a ) F { G 1 o } ( k f 4 f 2 f 5 ) ( x 6 c ) .

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