Abstract

We propose a color moiré pattern simulation and analysis method in integral imaging for finding the moiré-reducing tilted angle of a lens array. According to the tilted angle, the color moiré patterns are simulated on the assumption of ray optics. The spatial frequencies of the color moiré patterns are numerically analyzed using a spatial Fourier transform for finding the optimal angle where the moiré is reduced. With the proposed technique the visualization of the color moiré pattern and its analysis are enabled. The moiré-reduced three-dimensional images can be displayed. The principle of the proposed method, simulation results, and their analysis are provided. Experimental results verify the validity of the proposed method.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. M.-S. Kim, G. Baasantseren, N. Kim, and J.-H. Park, “Hologram generation of 3D objects using multiple orthographic view images,” J. Opt. Soc. Korea 12, 269-274(2008).
    [CrossRef]
  15. R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57-64 (1999).
    [CrossRef]
  16. L. Lipton and M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” Proc. SPIE 4660, 229-235(2002).
    [CrossRef]
  17. M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. 44, 4475-4483 (2005).
    [CrossRef] [PubMed]
  18. V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Display Technol. 1, 347-353 (2005).
    [CrossRef]
  19. J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.
  20. V. V. Saveljev, J.-Y. Son, J.-H Chun, K.-D. Kwack, and K.-Y. Cha, “About a moiré-less condition for non-square grids,” J. Display Technol. 4, 332-339 (2008).
    [CrossRef]
  21. M. Okui, M. Kobayashi, J. Arai, T. Mishina, and F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15 April 2004).
  22. T. Koike, M. Oikawa, and K. Utsugi, “Moire reduction for integral photography,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2007), pp. 1917-1918.
  23. Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

2008 (4)

2007 (2)

2005 (2)

2004 (2)

2003 (1)

2002 (2)

2001 (1)

1999 (1)

R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57-64 (1999).
[CrossRef]

1997 (1)

1988 (1)

1908 (1)

G. Lippmann, “Épreuves réversibles photograhies integrales,” C. R. Acad. Sci. 146, 446-451 (1908).

Arai, J.

Baasantseren, G.

Börner, R.

R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57-64 (1999).
[CrossRef]

Cha, K.-Y.

Cho, S.-W.

Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

Choi, H.

Choi, Y.

Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

Choi, Y.-J.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.

Chun, J.-H

Davies, N.

Dohi, T.

Feldman, M.

L. Lipton and M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” Proc. SPIE 4660, 229-235(2002).
[CrossRef]

Forman, M. C.

Hoshino, H.

Iwahara, M.

Jang, J.-S.

Javidi, B.

Jeong, M.-O.

Jung, J.-H.

Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

Y. Kim, J. Kim, J.-M. Kang, J.-H. Jung, H. Choi, and B. Lee, “Point light source integral imaging with improved resolution and viewing angle by the use of electrically movable pinhole array,” Opt. Express 15, 18253-18267 (2007).
[CrossRef] [PubMed]

Jung, S.

Kang, J.-M.

Kim, D.-S.

Kim, J.

Kim, M.-S.

Kim, N.

Kim, S.-K.

Kim, S.-S.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.

Kim, Y.

Kobayashi, M.

M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. 44, 4475-4483 (2005).
[CrossRef] [PubMed]

M. Okui, M. Kobayashi, J. Arai, T. Mishina, and F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15 April 2004).

Koike, T.

T. Koike, M. Oikawa, and K. Utsugi, “Moire reduction for integral photography,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2007), pp. 1917-1918.

Kwack, K.-D.

Lee, B.

Lee, M.-G.

Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

Liao, H.

Lippmann, G.

G. Lippmann, “Épreuves réversibles photograhies integrales,” C. R. Acad. Sci. 146, 446-451 (1908).

Lipton, L.

L. Lipton and M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” Proc. SPIE 4660, 229-235(2002).
[CrossRef]

McCormick, M.

Min, S.-W.

Mishina, T.

M. Okui, M. Kobayashi, J. Arai, T. Mishina, and F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15 April 2004).

Oikawa, M.

T. Koike, M. Oikawa, and K. Utsugi, “Moire reduction for integral photography,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2007), pp. 1917-1918.

Okano, F.

Okoshi, T.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, 1976).

Okui, M.

M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. 44, 4475-4483 (2005).
[CrossRef] [PubMed]

M. Okui, M. Kobayashi, J. Arai, T. Mishina, and F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15 April 2004).

Park, G.

Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

Park, J.-H.

Saveljev, V.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.

Saveljev, V. V.

Shin, S.-H.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.

Son, J.-Y.

V. V. Saveljev, J.-Y. Son, J.-H Chun, K.-D. Kwack, and K.-Y. Cha, “About a moiré-less condition for non-square grids,” J. Display Technol. 4, 332-339 (2008).
[CrossRef]

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Display Technol. 1, 347-353 (2005).
[CrossRef]

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.

Utsugi, K.

T. Koike, M. Oikawa, and K. Utsugi, “Moire reduction for integral photography,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2007), pp. 1917-1918.

Yang, L.

Yuyama, I.

Appl. Opt. (3)

C. R. Acad. Sci. (1)

G. Lippmann, “Épreuves réversibles photograhies integrales,” C. R. Acad. Sci. 146, 446-451 (1908).

Displays (1)

R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57-64 (1999).
[CrossRef]

J. Display Technol. (2)

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

J. Opt. Soc. Korea (2)

Opt. Express (4)

Opt. Lett. (2)

Proc. SPIE (2)

L. Lipton and M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” Proc. SPIE 4660, 229-235(2002).
[CrossRef]

Y. Kim, G. Park, S.-W. Cho, J.-H. Jung, B. Lee, Y. Choi, and M.-G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE 6803, 68030L.1-68031L.8 (2008).

Other (5)

M. Okui, M. Kobayashi, J. Arai, T. Mishina, and F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15 April 2004).

T. Koike, M. Oikawa, and K. Utsugi, “Moire reduction for integral photography,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2007), pp. 1917-1918.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” International Display Workshops (Institute of Image Information and Television Engineers of Japan and Society of Information Display, 2003), pp. 1401-1404.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, 1976).

B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” in Digital Holography and Three-Dimensional Display, T. -C. Poon, ed. (Springer, 2006), Chap. 12, pp. 333-378.
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Regular arrangement of the (a) RGB subpixels in the display device and (b) lens array.

Fig. 2
Fig. 2

Simulation model: left, the display device and lens array slanted with angle θ; right, magnified side view of the model and the sampling based on ray optics.

Fig. 3
Fig. 3

Simulation results according to the rotated angle of the lens array on the display panel.

Fig. 4
Fig. 4

Simulation results when slant angle θ is (a)  10 ° and (b)  17 ° .

Fig. 5
Fig. 5

Sampled ratios of R, G, and B versus the slant angle.

Fig. 6
Fig. 6

Discrete Fourier transform of color moiré pattern according to the slant angle of (a)  0 ° , (b)  5 ° , (c)  10 ° , (d)  15 ° , (e)  20 ° , (f)  25 ° , (g)  30 ° , (h)  35 ° ,(i)  40 ° , (j)  45 ° .

Fig. 7
Fig. 7

Frequency of the dominant component according to the slant angle.

Fig. 8
Fig. 8

Color moiré patterns (simulation results) when the dominant spatial frequency is high. (a)  θ = 18 ° (b)  θ = 35 ° .

Fig. 9
Fig. 9

Low-frequency (LF) components when subtractive primaries CMY are observed: (a)  θ = 18 ° , (b)  θ = 35 ° . DHF, dominant high-frequency component.

Fig. 10
Fig. 10

Frequency versus the slant angle when the LF component is considered also. The figure also shows the DHF (the same as Fig. 7).

Fig. 11
Fig. 11

Color filter and the black matrix configuration of the HD LCD.

Fig. 12
Fig. 12

Spatial frequency components of the moiré pattern from the black matrix versus the slant angle.

Fig. 13
Fig. 13

Experimental setup.

Fig. 14
Fig. 14

Simulation results (left) and experimental results (right): (a)  0 ° , (b)  10 ° , (c)  11 ° , (d)  12 ° , (e)  16 ° , (f)  17 ° , (g)  18 ° , (h)  19 ° , (i)  25 ° , (j)  26 ° , (k)  27 ° , (l)  33 ° , (m)  34 ° , (n)  35 ° , (o)  36 ° , (p)  43 ° , (q)  44 ° .

Fig. 15
Fig. 15

Experimental results: integrated 3D images according to the slant angle of lens array.

Fig. 16
Fig. 16

Integrated 3D images observed from different directions using the conventional method observed from (a) left and (b) right, and using the proposed method observed from (c) left and (d) right.

Equations (5)

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L ( n , m ) = ( n φ p , m φ p ) ,
C ( n , m ) = { R 0 d ( n , m ) < 1 3 G 1 3 d ( n , m ) < 2 3 B 2 3 d ( n , m ) < 1 , where     d ( n , m ) = n φ p [ n φ p ] .
L θ ( n , m ) = ( cos θ sin θ sin θ cos θ ) ( n φ p m φ p ) .
C ( n , m ) = { R 0 d ( n , m ) < 1 3 G 1 3 d ( n , m ) < 2 3 B 2 3 d ( n , m ) < 1 , where     d ( n , m ) = L θ ( n , m ) x [ L θ ( n , m ) x ] .
F ( u , v ) = n = 0 N 1 m = 0 N 1 C θ [ x , y ] e j 2 π ( u x + v y ) / N R ,

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