Abstract

Angles of visible moiré patterns are observed experimentally. Experiments were made across the angular range 0 - 90° in a wide range of parameters. Two kinds of clusterization were observed, ray and discrete. In rational cells (LCD pixels), the moiré patterns appear at a few fixed discrete angles. The list of preferable moiré-less angles is presented basing on the experimental data; preferable areas in the parameter space are found. The problem of minimization of the moiré effect is formulated as the Diophantine inequality with complex coefficients. The classification of moiré angles basing on the probability of the moiré effect can be practically useful.

© 2014 Optical Society of America

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References

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  1. I. Amidror, The Theory of the Moiré Phenomenon, Volume I: Periodic Layers and Volume II: Aperiodic Layers (Springer, 2007–2009).
  2. K. Patorski and M. Kujawinska, Handbook of the moiré fringe technique (Elsiver Science Publisher, 1993).
  3. K. Creath and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd (John Wiley & Sons, 1995), Chap. 16.
  4. J. Hong, Y. Kim, H. J. Choi, J. Hahn, J. H. Park, H. Kim, S. W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50(34), H87–H115 (2011).
    [CrossRef] [PubMed]
  5. R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
    [CrossRef]
  6. L. Kong, G. Jin, and T. Wang, “Analysis of Moiré minimization in autostereoscopic parallax displays,” Opt. Express 21, 26068–26079 (2013).
  7. A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
    [CrossRef]
  8. V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
    [CrossRef]
  9. S. Rasouli and M. T. Tavassoly, “Analysis of the moiré pattern of moving periodic structures using reciprocal vector approach,” J. Phys. Conf. Ser. 350, 012032 (2012).
    [CrossRef]
  10. G. Strang, Computational Science and Engineering (Wellesley-Cambridge University, 2007), Chap. 4.1.
  11. V. Saveljev and S.-K. Kim, “Theoretical estimation of moiré effect using spectral trajectories,” Opt. Express 21(2), 1693–1712 (2013).
    [CrossRef] [PubMed]
  12. V. Saveljev and S.-K. Kim, “Estimation of moiré patterns using spectral trajectories in the complex plane,” Comput. Technol. Appl. 3, 353–360 (2012).
  13. P. Artal and R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11(1), 246–249 (1994).
    [CrossRef] [PubMed]
  14. R. C. Baker, Diophantine Inequalities (Oxford University Press, 1986).
  15. H. Davenport, Analytic Methods for Diophantine Equations and Diophantine Inequalities (Cambridge University, 2005), Chap. 20.
  16. V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
    [CrossRef] [PubMed]
  17. 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(11), 2178–2187 (2009).
    [CrossRef] [PubMed]
  18. S. S. Deshpande, “Screen angle combinations and effect on print quality parameters,” Int. J.Adv.Eng.Technol. II, 480–482 (2011).
  19. P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
    [CrossRef]

2013 (2)

2012 (4)

V. Saveljev and S.-K. Kim, “Estimation of moiré patterns using spectral trajectories in the complex plane,” Comput. Technol. Appl. 3, 353–360 (2012).

S. Rasouli and M. T. Tavassoly, “Analysis of the moiré pattern of moving periodic structures using reciprocal vector approach,” J. Phys. Conf. Ser. 350, 012032 (2012).
[CrossRef]

V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
[CrossRef] [PubMed]

P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
[CrossRef]

2011 (2)

2009 (2)

2008 (1)

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

2006 (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[CrossRef]

1994 (1)

Artal, P.

Bignon, T.

P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
[CrossRef]

Boher, P.

P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
[CrossRef]

Cha, K.-H.

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

Chen, N.

Choi, H. J.

Chun, J.-H.

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

Collomb-Patton, V.

P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
[CrossRef]

Deshpande, S. S.

S. S. Deshpande, “Screen angle combinations and effect on print quality parameters,” Int. J.Adv.Eng.Technol. II, 480–482 (2011).

Hahn, J.

Hong, J.

Javidi, B.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[CrossRef]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[CrossRef]

Jin, G.

Jung, J.-H.

Kim, H.

Kim, J.

Kim, S.-K.

Kim, Y.

Kong, L.

Kwack, K.-D.

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

Lee, B.

Leroux, T.

P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
[CrossRef]

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[CrossRef]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[CrossRef]

Min, S. W.

Navarro, R.

Park, G.

Park, J. H.

Rasouli, S.

S. Rasouli and M. T. Tavassoly, “Analysis of the moiré pattern of moving periodic structures using reciprocal vector approach,” J. Phys. Conf. Ser. 350, 012032 (2012).
[CrossRef]

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[CrossRef]

Saveljev, V.

V. Saveljev and S.-K. Kim, “Theoretical estimation of moiré effect using spectral trajectories,” Opt. Express 21(2), 1693–1712 (2013).
[CrossRef] [PubMed]

V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
[CrossRef] [PubMed]

V. Saveljev and S.-K. Kim, “Estimation of moiré patterns using spectral trajectories in the complex plane,” Comput. Technol. Appl. 3, 353–360 (2012).

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

Son, J.-Y.

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

Stern, A.

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[CrossRef]

Tavassoly, M. T.

S. Rasouli and M. T. Tavassoly, “Analysis of the moiré pattern of moving periodic structures using reciprocal vector approach,” J. Phys. Conf. Ser. 350, 012032 (2012).
[CrossRef]

Wang, T.

Appl. Opt. (2)

Comput. Technol. Appl. (1)

V. Saveljev and S.-K. Kim, “Estimation of moiré patterns using spectral trajectories in the complex plane,” Comput. Technol. Appl. 3, 353–360 (2012).

Int. J.Adv.Eng.Technol. (1)

S. S. Deshpande, “Screen angle combinations and effect on print quality parameters,” Int. J.Adv.Eng.Technol. II, 480–482 (2011).

J. Displ. Technol. (1)

V. Saveljev, J.-Y. Son, J.-H. Chun, K.-D. Kwack, and K.-H. Cha, “About a moiré-less condition for non-square grids,” J. Displ. Technol. 4(3), 332–339 (2008).
[CrossRef]

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

J. Phys. Conf. Ser. (1)

S. Rasouli and M. T. Tavassoly, “Analysis of the moiré pattern of moving periodic structures using reciprocal vector approach,” J. Phys. Conf. Ser. 350, 012032 (2012).
[CrossRef]

Opt. Express (3)

Proc. IEEE (2)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[CrossRef]

Proc. SPIE (1)

P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements,” Proc. SPIE 8288, 82880S (2012).
[CrossRef]

Other (6)

R. C. Baker, Diophantine Inequalities (Oxford University Press, 1986).

H. Davenport, Analytic Methods for Diophantine Equations and Diophantine Inequalities (Cambridge University, 2005), Chap. 20.

I. Amidror, The Theory of the Moiré Phenomenon, Volume I: Periodic Layers and Volume II: Aperiodic Layers (Springer, 2007–2009).

K. Patorski and M. Kujawinska, Handbook of the moiré fringe technique (Elsiver Science Publisher, 1993).

K. Creath and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd (John Wiley & Sons, 1995), Chap. 16.

G. Strang, Computational Science and Engineering (Wellesley-Cambridge University, 2007), Chap. 4.1.

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Figures (5)

Fig. 1
Fig. 1

The vector sums in the complex plane.

Fig. 2
Fig. 2

Illustration of variety of moiré fringes in Experiment 1. (Photographs ordered be tangents: 0, 1/3, 2/3, 1.) The full set of the experimental data is graphically shown in Fig. 3 below. (a) φ = 0°, σ = 1.5, ρ = 0.72; (b) φ = 18°, σ = 0.33, ρ = 0.55; (c) φ = 33°, σ = 0.67, ρ = 0.55; (d) φ = 45°, σ = 0.5, ρ = 0.72.

Fig. 3
Fig. 3

The full set of experimental data. The tangent of the moiré angle φ as a function of the aspect ratio σ for ρ = 0.55 and 0.72 (square and triangle markers). The clusterization of the experimental data along the rays. The constants of proportionality are indicated near some rays.

Fig. 4
Fig. 4

Discrete moiré angles φ (experimental). The clusterization of the experimental data with “small rational” aspect ratios.

Fig. 5
Fig. 5

Illustration of variety of moiré fringes in Experiment 2 (σ = 1, by angle). (a) φ = 0°, device D, ρ = 3.00; (b) φ = 18°, device C, ρ = 2.80; (c) φ = 33°, device B, ρ = 2.67; (d) φ = 45°, device C, ρ = 2.80. The corresponding set of the experimental data is given in Table 1.

Tables (2)

Tables Icon

Table 1 Observed Moiré Angles φ in LCD Panels Combined with Barrier Plates

Tables Icon

Table 2 Observed Moiré Angles φ in LCD Panels Combined with Lenticular Plates

Equations (7)

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M= j=1 N p j k j e i α j
M 4 =( p 1 σ 1 +i p 2 )+( p 3 σ 2 +i p 4 )ρ e iα
M< k 0
| p 1 k 1 e i α 1 +...+ p N k N e i α N |<1
{ Re( p 1 k 1 e i α 1 +...+ p N k N e i α N )<1 Im( p 1 k 1 e i α 1 +...+ p N k N e i α N )<1
σ kl = k l ( k, lintegers )
ϕ mn =arctan( m n ) ( m and n integers 4 )

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