Abstract

A proposed amplified optical window can form an observable three-dimensional image of an object in darkness. The window comprises two gradient-index (GRIN) lens arrays with an image intensifier between them. The length of the individual GRIN lenses that constitute the arrays is three fourths of the cycle of the meandering optical path on the input side and one fourth of the cycle on the output side. A primitive experimental result proved that the method produces three-dimensional images to be observed. This device would be used as a viewer for observing three-dimensional objects in a dark space without a camera and display equipment.

© 2006 Optical Society of America

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References

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  1. D. Marcuse and S. E. Miller, Bell Syst. Tech. J. 43, 1759 (1964).
  2. G. Lippmann, C. R. Hebd. Seances Acad. Sci. 146, 446 (1908).
  3. H. E. Ives, J. Opt. Soc. Am. 21, 171 (1931).
    [CrossRef]
  4. M. McCormick, in Proceedings of the Second International Display Workshop, T.Hatada, ed. (ITE, Hamamatsu, 1995), paper 3-D-9, p. 77.
  5. F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
    [CrossRef]
  6. B.Javidi and F.Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer Verlag, 2002).
  7. J. Y. Son, V. Saveljev, B. Javidi, and K. Kwack, Opt. Eng. 44, 024003-1 (2005).
    [CrossRef]
  8. M. Martines-Corral, B. Javidi, R. Martinez-Cuenca, and G. Saavedra, J. Opt. Soc. Am. A 22, 597 (2005).
    [CrossRef]
  9. S. Yeom, B. Javidi, and E. Watson, Opt. Express 13, 9310 (2005).
    [CrossRef] [PubMed]
  10. F. Okano and J. Arai, Appl. Opt. 40, 4140 (2002).
    [CrossRef]
  11. F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).
  12. F. Okano, J. Arai, and M. Okui, in Proc. SPIE 5599, 89 (2004).
    [CrossRef]
  13. F. Okano, J. Arai, and M. Okui, in Proc. SPIE 6016, 601601 (2005).
    [CrossRef]

2005 (4)

J. Y. Son, V. Saveljev, B. Javidi, and K. Kwack, Opt. Eng. 44, 024003-1 (2005).
[CrossRef]

M. Martines-Corral, B. Javidi, R. Martinez-Cuenca, and G. Saavedra, J. Opt. Soc. Am. A 22, 597 (2005).
[CrossRef]

S. Yeom, B. Javidi, and E. Watson, Opt. Express 13, 9310 (2005).
[CrossRef] [PubMed]

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 6016, 601601 (2005).
[CrossRef]

2004 (1)

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 5599, 89 (2004).
[CrossRef]

2002 (2)

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

F. Okano and J. Arai, Appl. Opt. 40, 4140 (2002).
[CrossRef]

2000 (1)

F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).

1999 (1)

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

1995 (1)

M. McCormick, in Proceedings of the Second International Display Workshop, T.Hatada, ed. (ITE, Hamamatsu, 1995), paper 3-D-9, p. 77.

1964 (1)

D. Marcuse and S. E. Miller, Bell Syst. Tech. J. 43, 1759 (1964).

1931 (1)

1908 (1)

G. Lippmann, C. R. Hebd. Seances Acad. Sci. 146, 446 (1908).

Arai, J.

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 6016, 601601 (2005).
[CrossRef]

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 5599, 89 (2004).
[CrossRef]

F. Okano and J. Arai, Appl. Opt. 40, 4140 (2002).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).

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

Hoshino, H.

F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).

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

Ives, H. E.

Javidi, B.

Kwack, K.

J. Y. Son, V. Saveljev, B. Javidi, and K. Kwack, Opt. Eng. 44, 024003-1 (2005).
[CrossRef]

Lippmann, G.

G. Lippmann, C. R. Hebd. Seances Acad. Sci. 146, 446 (1908).

Marcuse, D.

D. Marcuse and S. E. Miller, Bell Syst. Tech. J. 43, 1759 (1964).

Martines-Corral, M.

Martinez-Cuenca, R.

McCormick, M.

M. McCormick, in Proceedings of the Second International Display Workshop, T.Hatada, ed. (ITE, Hamamatsu, 1995), paper 3-D-9, p. 77.

Miller, S. E.

D. Marcuse and S. E. Miller, Bell Syst. Tech. J. 43, 1759 (1964).

Mishina, T.

F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).

Okano, F.

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 6016, 601601 (2005).
[CrossRef]

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 5599, 89 (2004).
[CrossRef]

F. Okano and J. Arai, Appl. Opt. 40, 4140 (2002).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).

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

Okui, M.

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 6016, 601601 (2005).
[CrossRef]

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 5599, 89 (2004).
[CrossRef]

Saavedra, G.

Saveljev, V.

J. Y. Son, V. Saveljev, B. Javidi, and K. Kwack, Opt. Eng. 44, 024003-1 (2005).
[CrossRef]

Son, J. Y.

J. Y. Son, V. Saveljev, B. Javidi, and K. Kwack, Opt. Eng. 44, 024003-1 (2005).
[CrossRef]

Watson, E.

Yeom, S.

Yuyama, I.

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

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Marcuse and S. E. Miller, Bell Syst. Tech. J. 43, 1759 (1964).

C. R. Hebd. Seances Acad. Sci. (1)

G. Lippmann, C. R. Hebd. Seances Acad. Sci. 146, 446 (1908).

J. Opt. Soc. Am. (1)

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

Opt. Eng. (2)

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

J. Y. Son, V. Saveljev, B. Javidi, and K. Kwack, Opt. Eng. 44, 024003-1 (2005).
[CrossRef]

Opt. Express (1)

Proc. SPIE (2)

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 5599, 89 (2004).
[CrossRef]

F. Okano, J. Arai, and M. Okui, in Proc. SPIE 6016, 601601 (2005).
[CrossRef]

Other (3)

F. Okano, H. Hoshino, J. Arai, and T. Mishina, U.S. Patent No. 6,137,937 (October 24, 2000).

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

M. McCormick, in Proceedings of the Second International Display Workshop, T.Hatada, ed. (ITE, Hamamatsu, 1995), paper 3-D-9, p. 77.

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Figures (4)

Fig. 1
Fig. 1

(a) Refractive index distribution of the radial GRIN lens. Fig. 1b Light beams through the GRIN lens. The rays enter the GRIN lens and meander through the lens in a cyclic pattern, focusing at 1 4 and 3 4 cycles. If the GRIN lens is as long as one optical path cycle, then the incident angle and output angle are the same.

Fig. 2
Fig. 2

Side view of the amplified optical window. Light rays are emitted from a point light source. The output rays from the window form an image on the object side of the output plane. ( x s , z s ) shows the object space. The object is assumed to be a delta function and is located at ( x δ , z δ ) . We use 2D coordinates ( x , y ) to simplify the description, although the space represented in the figure is in 3D coordinates ( x , y , z ) .

Fig. 3
Fig. 3

Experiment with the amplified optical window (side view). Objects I and O are letters, each with a 32 point font size. The I and O are set 30 and 50 mm , respectively, from array 1. The center of each letter is offset 6 mm horizontally. Each of their images is separated from the object’s position by T w ( 45.5 mm ) , the thickness of the amplified optical window.

Fig. 4
Fig. 4

Photographs of the images formed by the optical window. The four viewpoints are each off the center axis of the exit plane by about 9°. (a) Upper viewpoint: the O is situated below the I. (b) Lower viewpoint: O is slightly above I. (c) Left viewpoint: I and O partially overlap. (d) Right viewpoint: I and O are more separated.

Tables (2)

Tables Icon

Table 1 Specification of GRIN Lens Array

Tables Icon

Table 2 Specification of Image Intensifier

Equations (7)

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n ( r ) = n o ( 1 1 2 A G r 2 ) ,
( r 1 c r 1 c ) = [ 0 1 n 0 A G n 0 A G 0 ] ( r 1 s r 1 s ) .
( r d c r d c ) = [ 1 0 0 D ] ( r d s r d s ) .
( r 2 c r 2 c ) = [ 0 1 n 0 A G n 0 A G 0 ] ( r 2 s r 2 s ) .
( r 2 c r 2 c ) = [ 0 1 n 0 A G n 0 A G 0 ] [ 1 0 0 D ] × [ 0 1 n 0 A G n 0 A G 0 ] ( r 1 s r 1 s ) = [ D 0 0 1 ] ( r 1 s r 1 s ) .
m P a x δ L s = m P a x c z c z o = tan φ m .
( z c z o L s ) m P a x δ ( z c z o ) + L s x c = 0 .

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