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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References

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

2008

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]

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).

2007

2005

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]

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]

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] [PubMed]

2002

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

1998

1997

1979

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

1978

1976

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

1970

1968

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

1908

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.
[CrossRef]

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).
[PubMed]

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).
[PubMed]

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.

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.

C. R. Acad. Sci.

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

J. Disp. Technol.

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

J. Phys. E

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

Jpn. J. Appl. Phys.

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.

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

Precis. Eng.

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

Proc. SPIE

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

Other

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

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.

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.

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.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Layout of LCD color filter; (b) the equivalent binary grating of an LCD.

Fig. 2
Fig. 2

Special radial grating.

Fig. 3
Fig. 3

Superposition of the special grating and the equivalent grating of LCD.

Fig. 4
Fig. 4

(a) Indexed family of l m = n ; (b) the indexed family of l 2 m = n ; (c) the indexed family of l 3 m = n ; (d) the indexed family of l m = n and l 2 m = n ; (e) the indexed family of l 2 m = n and l 3 m = n ; (f) the indexed family of l m = n , l 2 m = n , and l 3 m = n .

Fig. 5
Fig. 5

Vectorial difference in the two transition regions.

Fig. 6
Fig. 6

Comparison of LCD image with and without the PB when the LCD image is white.

Fig. 7
Fig. 7

Autostereoscopic image comparison of an LCD with and without a PB.

Tables (3)

Tables Icon

Table 1 Unification of the Families of Curves and the Fourier Frequency Terms

Tables Icon

Table 2 Predominant Fourier Low-Frequency Terms in the Transition Regions

Tables Icon

Table 3 Parameters of the Autostereoscopic Display Based on a PB

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

T 1 ( x , y ) = r = r = a r cos ( 2 π r x / P 1 ) ,
T 2 ( x , y ) = s = s = b s cos ( 2 π s [ x cos θ + y sin θ ] P 2 ) ,
T ( x , y ) = T 1 ( x , y ) T 2 ( x , y ) = r = r = s = s = a r b s cos ( 2 π r x P 1 ) cos ( 2 π s [ x cos θ + y sin θ ] P 2 ) .
y = l p ,
x y = tan m α ,
| f 1 f 1.5 | = | f 1 2 f 1.5 | ,
| f 1.5 | = | f 1 * cos ( θ ) 1.5 | .
P 2 = 1.5 P 1 cos ( θ ) = 4.5 P cos ( θ ) .
P 2 = 2.5 P 1 cos ( θ ) = 7.5 P cos ( θ ) .

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