Abstract

We propose a parameter design of the parallax barrier (PB) based on the color moiré patterns in autostereoscopic displays. First, the display device and the PB are approximated as two corresponding binary gratings. In order to obtain different corresponding predominant Fourier low-frequency terms, the superposition of the equivalent grating for the display device and the special radial grating is analyzed, referring to the indicial equation method and Fourier theory. Moreover, the two transition regions are considered as the regions where moiré patterns vary gently. Finally, the appropriate parameter of the PB can be obtained. The validity of the proposed design is verified in the experiment.

© 2011 Optical Society of America

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  1. K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993), pp. 186–216.
  2. O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, 1989), pp. 19–38, 75–87.
  3. A. T. Shepherd, “25 years of moiré fringe measurement,” Precis. Eng. 1, 61–69 (1979).
    [CrossRef]
  4. H. Takasaki, “Moiré topography,” Appl. Opt. 9, 1467–1472(1970).
    [CrossRef]
  5. A. J. Durelli and V. J. Parks, Moiré Analysis of Strain(Prentice-Hall,1970), pp. 64–78.
  6. J. C. Wyant, Moiré and Fringe Projection Techniques (Wiley, 1992), pp. 653–681.
  7. I. Amidror, The Theory of the Moiré Phenomenon (Springer, 2009), pp. 1, 9–21, 23–30, and 62.
  8. J. P. Allebach, “Random nucleated halftone screen,” Photogr. Sci. Eng. 22, 89–91 (1978).
  9. D. Blattner, C. Chaves, G. Fleishman, and S. Roth, Real World Scanning and Halftones, 3rd ed. (Peachpit, 2004), pp. 291–297.
  10. K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.
  11. K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
    [CrossRef]
  12. T. Koike, M. Oikawa, and K. Utsugi, “Moiré reduction for integral photography,” in International Display Workshops (Society for Information Display, 2007), pp. 1917–1918.
  13. M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moiré fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. 44, 4475–4483 (2005).
    [CrossRef]
  14. L. Lipton and M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” Proc. SPIE 4660, 229–235(2002).
    [CrossRef]
  15. Y. Kim, G. Park, J.-H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. 48, 2178–2187 (2009).
    [CrossRef]
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    [CrossRef]
  17. V. V. Saveljev, J.-Y. Son, J.-H. Chun, and K.-D. Kwack, “About a Moiré-less condition for non-square grids,” J. Disp. Technol. 4, 332–339 (2008).
    [CrossRef]
  18. G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).
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    [CrossRef]
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    [CrossRef]
  21. P. S. Theocaris, “Radial gratings as moiré gauges,” J. Phys. E 1, 613–618 (1968).
    [CrossRef]
  22. M. Abolhassani and M. Mirzaei, “Unification of formulation of moiré fringe spacing in parametric equation and Fourier analysis methods,” Appl. Opt. 46, 7924–7926 (2007).
    [CrossRef]
  23. K. Patorski and S. Yokozeki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15, 443–456(1976).
    [CrossRef]
  24. S. Yokozeki and K. Patorski, “Moiré fringe profile prediction method and its application to fringe sharpening,” Appl. Opt. 17, 2541–2547 (1978).
  25. R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

2009 (1)

2008 (2)

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

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

2007 (1)

2005 (3)

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

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[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. Disp. Technol. 1, 347–353 (2005).
[CrossRef]

2002 (1)

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

1998 (1)

1997 (1)

1979 (1)

A. T. Shepherd, “25 years of moiré fringe measurement,” Precis. Eng. 1, 61–69 (1979).
[CrossRef]

1978 (2)

1976 (1)

K. Patorski and S. Yokozeki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15, 443–456(1976).
[CrossRef]

1970 (1)

1968 (1)

P. S. Theocaris, “Radial gratings as moiré gauges,” J. Phys. E 1, 613–618 (1968).
[CrossRef]

1908 (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Abolhassani, M.

Allebach, J. P.

J. P. Allebach, “Random nucleated halftone screen,” Photogr. Sci. Eng. 22, 89–91 (1978).

Amidror, I.

I. Amidror, The Theory of the Moiré Phenomenon (Springer, 2009), pp. 1, 9–21, 23–30, and 62.

Arai, J.

Blattner, D.

D. Blattner, C. Chaves, G. Fleishman, and S. Roth, Real World Scanning and Halftones, 3rd ed. (Peachpit, 2004), pp. 291–297.

Chaves, C.

D. Blattner, C. Chaves, G. Fleishman, and S. Roth, Real World Scanning and Halftones, 3rd ed. (Peachpit, 2004), pp. 291–297.

Chun, J.-H.

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

Durelli, A. J.

A. J. Durelli and V. J. Parks, Moiré Analysis of Strain(Prentice-Hall,1970), pp. 64–78.

Feldman, M.

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

Fleishman, G.

D. Blattner, C. Chaves, G. Fleishman, and S. Roth, Real World Scanning and Halftones, 3rd ed. (Peachpit, 2004), pp. 291–297.

Fukushima, R.

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[CrossRef]

Glatt, I.

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, 1989), pp. 19–38, 75–87.

Hamagishi, G.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

Hirayama, Y.

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[CrossRef]

Hoshino, H.

Inoue, M.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

Isono, H.

Javidi, B.

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

Jung, J.-H.

Kafri, O.

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, 1989), pp. 19–38, 75–87.

Kim, D.-S.

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

Kim, J.

Kim, S.-K.

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

Kim, Y.

Kobayashi, H.

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[CrossRef]

Kobayashi, M.

Koike, T.

T. Koike, M. Oikawa, and K. Utsugi, “Moiré reduction for integral photography,” in International Display Workshops (Society for Information Display, 2007), pp. 1917–1918.

Kwack, K.-D.

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

Lee, B.

Li, D. H.

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Lippmann, G.

G. Lippmann, “La photographie integrale,” 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]

Mashitani, K.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

Mirzaei, M.

Nakayama, E.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

Oikawa, M.

T. Koike, M. Oikawa, and K. Utsugi, “Moiré reduction for integral photography,” in International Display Workshops (Society for Information Display, 2007), pp. 1917–1918.

Okano, F.

Okui, M.

Park, G.

Parks, V. J.

A. J. Durelli and V. J. Parks, Moiré Analysis of Strain(Prentice-Hall,1970), pp. 64–78.

Patorski, K.

S. Yokozeki and K. Patorski, “Moiré fringe profile prediction method and its application to fringe sharpening,” Appl. Opt. 17, 2541–2547 (1978).

K. Patorski and S. Yokozeki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15, 443–456(1976).
[CrossRef]

K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993), pp. 186–216.

Roth, S.

D. Blattner, C. Chaves, G. Fleishman, and S. Roth, Real World Scanning and Halftones, 3rd ed. (Peachpit, 2004), pp. 291–297.

Saishu, T.

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[CrossRef]

Sakata, M.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

Saveljev, V. V.

V. V. Saveljev, J.-Y. Son, J.-H. Chun, and K.-D. Kwack, “About a Moiré-less condition for non-square grids,” J. Disp. 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. Disp. Technol. 1, 347–353 (2005).
[CrossRef]

Shepherd, A. T.

A. T. Shepherd, “25 years of moiré fringe measurement,” Precis. Eng. 1, 61–69 (1979).
[CrossRef]

Son, J.-Y.

V. V. Saveljev, J.-Y. Son, J.-H. Chun, and K.-D. Kwack, “About a Moiré-less condition for non-square grids,” J. Disp. 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. Disp. Technol. 1, 347–353 (2005).
[CrossRef]

Taira, K.

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[CrossRef]

Takasaki, H.

Theocaris, P. S.

P. S. Theocaris, “Radial gratings as moiré gauges,” J. Phys. E 1, 613–618 (1968).
[CrossRef]

Utsugi, K.

T. Koike, M. Oikawa, and K. Utsugi, “Moiré reduction for integral photography,” in International Display Workshops (Society for Information Display, 2007), pp. 1917–1918.

Wang, A. H.

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Wang, Q. H.

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Wyant, J. C.

J. C. Wyant, Moiré and Fringe Projection Techniques (Wiley, 1992), pp. 653–681.

Xin, Y. X.

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Yamashita, A.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

Yokozeki, S.

S. Yokozeki and K. Patorski, “Moiré fringe profile prediction method and its application to fringe sharpening,” Appl. Opt. 17, 2541–2547 (1978).

K. Patorski and S. Yokozeki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15, 443–456(1976).
[CrossRef]

Yuyama, I.

Zhao, R. L.

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Zhao, W. X.

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Acta Photon. Sin. (1)

R. L. Zhao, W. X. Zhao, Q. H. Wang, D. H. Li, A. H. Wang, and Y. X. Xin, “Research on stereo viewing zone in autostereoscopic display based on parallax barrier,” Acta Photon. Sin. 37, 960–963 (2008) (in Chinese).

Appl. Opt. (6)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

J. Disp. Technol. (2)

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

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

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

J. Phys. E (1)

P. S. Theocaris, “Radial gratings as moiré gauges,” J. Phys. E 1, 613–618 (1968).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Patorski and S. Yokozeki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15, 443–456(1976).
[CrossRef]

Photogr. Sci. Eng. (1)

J. P. Allebach, “Random nucleated halftone screen,” Photogr. Sci. Eng. 22, 89–91 (1978).

Precis. Eng. (1)

A. T. Shepherd, “25 years of moiré fringe measurement,” Precis. Eng. 1, 61–69 (1979).
[CrossRef]

Proc. SPIE (2)

K. Taira, R. Fukushima, T. Saishu, H. Kobayashi, and Y. Hirayama, “Autostereoscopic liquid crystal display using mosaic color pixel arrangement,” Proc. SPIE 5664, 349–359 (2005).
[CrossRef]

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

Other (8)

T. Koike, M. Oikawa, and K. Utsugi, “Moiré reduction for integral photography,” in International Display Workshops (Society for Information Display, 2007), pp. 1917–1918.

K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993), pp. 186–216.

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, 1989), pp. 19–38, 75–87.

D. Blattner, C. Chaves, G. Fleishman, and S. Roth, Real World Scanning and Halftones, 3rd ed. (Peachpit, 2004), pp. 291–297.

K. Mashitani, G. Hamagishi, M. Sakata, A. Yamashita, E. Nakayama, and M. Inoue, “New autostereoscopic (no-glasses) LCD image splitter displays,” in 3 Dimensional Image Conference ’96 (Operating Committee of 3 Dimensional Image Conference, 1996), pp. 90–95.

A. J. Durelli and V. J. Parks, Moiré Analysis of Strain(Prentice-Hall,1970), pp. 64–78.

J. C. Wyant, Moiré and Fringe Projection Techniques (Wiley, 1992), pp. 653–681.

I. Amidror, The Theory of the Moiré Phenomenon (Springer, 2009), pp. 1, 9–21, 23–30, and 62.

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