Abstract

The probability of the moiré effect in LCD displays is estimated as a function of angle based on the experimental data; a theoretical function (node spacing) is proposed basing on the distance between nodes. Both functions are close to each other. The connection between the probability of the moiré effect and the Thomae’s function is also found. The function proposed in this paper can be used in the minimization of the moiré effect in visual displays, especially in autostereoscopic 3D displays.

© 2015 Optical Society of America

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References

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  1. I. Amidror, The Theory of the Moiré Phenomenon, Vol. 1 (Springer, 2009).
  2. 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 [Invited],” Appl. Opt. 50(34), H87–H115 (2011).
    [Crossref] [PubMed]
  3. V. Saveljev, “Orientations and branches of moiré waves in three-dimensional displays,” J. Korean Phys. Soc. 57(6), 1392–1396 (2010).
    [Crossref]
  4. V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
    [Crossref]
  5. V. Saveljev and S.-K. Kim, “Moiré period as function of angle for moiré minimization in autostereoscopic 3D displays,” Optical Society of Korea Summer Meeting, paper W1G–VII4, Gyeongju, Korea (13–15 July, 2015).
  6. V. Saveljev and S.-K. Kim, “Experimental observation of moiré angles in parallax barrier 3D displays,” Opt. Express 22(14), 17147–17157 (2014).
    [Crossref] [PubMed]
  7. R. P. Williams, D. H. Davies, and G. Harburn, “On randomization techniques for the suppression of unwanted moiré patterns in images generated by a scanning system with a periodic amplitude defect,” Opt. Acta (Lond.) 33(10), 1311–1319 (1986).
    [Crossref]
  8. P. Hopstone, A. Katz, and J. Politch, “Infrastructure of time-averaged projection moire fringes in vibration analysis,” Appl. Opt. 28(24), 5305–5311 (1989).
    [Crossref] [PubMed]
  9. L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
    [Crossref] [PubMed]
  10. V. Saveljev and S.-K. Kim, “Theoretical estimation of moiré effect using spectral trajectories,” Opt. Express 21(2), 1693–1712 (2013).
    [Crossref] [PubMed]
  11. B. Grünbaum and G. C. Shephard, Tilings and Patterns (Freeman and Co., 1987).
  12. D. Chavey, “Tilings by regular polygons—IIs,” Comput. Math. Appl. 17(1-3I-3), 147–165 (1989).
    [Crossref]
  13. I. Amidror, The Theory of the Moiré Phenomenon, Vol. 2 (Springer, 2007).
  14. C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
    [Crossref] [PubMed]
  15. V. Saveljev and S.-K. Kim, “Estimation of Probability of the Moiré Effect,” in Proceedings of Collaborative Conference on 3D and Materials Research (CC3DMR), pp. 397–398, Busan, Korea (2015).
  16. V. Saveljev and S.-K. Kim, “Experimental probability of moiré effect in autostereoscopic displays with lenticular plate,” in Proceedings of 22th Conference on Optoelectronics and Optical Communications (COOC), pp. 263–264, Busan, Korea (2015).
  17. D. Zwillinger, CRC Standard Mathematical Tables and Formulae (CRC, 2002), Chap. 4.4.
  18. S. Abbott, Understanding Analysis (Springer, 2001), Chap. 4.1.
  19. V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
    [Crossref]

2014 (2)

C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
[Crossref] [PubMed]

V. Saveljev and S.-K. Kim, “Experimental observation of moiré angles in parallax barrier 3D displays,” Opt. Express 22(14), 17147–17157 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

V. Saveljev, “Orientations and branches of moiré waves in three-dimensional displays,” J. Korean Phys. Soc. 57(6), 1392–1396 (2010).
[Crossref]

2009 (1)

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

2005 (1)

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

1989 (2)

1986 (1)

R. P. Williams, D. H. Davies, and G. Harburn, “On randomization techniques for the suppression of unwanted moiré patterns in images generated by a scanning system with a periodic amplitude defect,” Opt. Acta (Lond.) 33(10), 1311–1319 (1986).
[Crossref]

Chavey, D.

D. Chavey, “Tilings by regular polygons—IIs,” Comput. Math. Appl. 17(1-3I-3), 147–165 (1989).
[Crossref]

Chen, N.

Choi, H. J.

Davies, D. H.

R. P. Williams, D. H. Davies, and G. Harburn, “On randomization techniques for the suppression of unwanted moiré patterns in images generated by a scanning system with a periodic amplitude defect,” Opt. Acta (Lond.) 33(10), 1311–1319 (1986).
[Crossref]

Du, S.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Gao, H.-J.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Hahn, J.

Harburn, G.

R. P. Williams, D. H. Davies, and G. Harburn, “On randomization techniques for the suppression of unwanted moiré patterns in images generated by a scanning system with a periodic amplitude defect,” Opt. Acta (Lond.) 33(10), 1311–1319 (1986).
[Crossref]

Hong, J.

Hopstone, P.

Javidi, B.

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

Katz, A.

Kim, D.-S.

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

Kim, H.

Kim, S.-K.

V. Saveljev and S.-K. Kim, “Experimental observation of moiré angles in parallax barrier 3D displays,” Opt. Express 22(14), 17147–17157 (2014).
[Crossref] [PubMed]

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, “Experimental probability of moiré effect in autostereoscopic displays with lenticular plate,” in Proceedings of 22th Conference on Optoelectronics and Optical Communications (COOC), pp. 263–264, Busan, Korea (2015).

Kim, S.-S.

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

Kim, Y.

Kwack, K.-D.

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

Lee, B.

Lee, D.-S.

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

Li, C.

C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
[Crossref] [PubMed]

Li, L.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Liu, Z.

C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
[Crossref] [PubMed]

Meng, L.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Min, S. W.

Park, J. H.

Park, M.-C.

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

Politch, J.

Saveljev, V.

V. Saveljev and S.-K. Kim, “Experimental observation of moiré angles in parallax barrier 3D displays,” Opt. Express 22(14), 17147–17157 (2014).
[Crossref] [PubMed]

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, “Orientations and branches of moiré waves in three-dimensional displays,” J. Korean Phys. Soc. 57(6), 1392–1396 (2010).
[Crossref]

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

V. Saveljev and S.-K. Kim, “Experimental probability of moiré effect in autostereoscopic displays with lenticular plate,” in Proceedings of 22th Conference on Optoelectronics and Optical Communications (COOC), pp. 263–264, Busan, Korea (2015).

Son, J.-Y.

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

Wang, Y.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Williams, R. P.

R. P. Williams, D. H. Davies, and G. Harburn, “On randomization techniques for the suppression of unwanted moiré patterns in images generated by a scanning system with a periodic amplitude defect,” Opt. Acta (Lond.) 33(10), 1311–1319 (1986).
[Crossref]

Woo, S.-B.

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

Wu, D.

C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
[Crossref] [PubMed]

Wu, R.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Xie, H.

C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
[Crossref] [PubMed]

Zhang, L.

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Appl. Opt. (2)

Comput. Math. Appl. (1)

D. Chavey, “Tilings by regular polygons—IIs,” Comput. Math. Appl. 17(1-3I-3), 147–165 (1989).
[Crossref]

J. Disp. Technol. (1)

V. Saveljev, J.-Y. Son, B. Javidi, S.-S. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005).
[Crossref]

J. Korean Phys. Soc. (1)

V. Saveljev, “Orientations and branches of moiré waves in three-dimensional displays,” J. Korean Phys. Soc. 57(6), 1392–1396 (2010).
[Crossref]

J. Phys. Condens. Matter (1)

L. Meng, R. Wu, L. Zhang, L. Li, S. Du, Y. Wang, and H.-J. Gao, “Multi-oriented moiré superstructures of graphene on Ir(111): experimental observations and theoretical models,” J. Phys. Condens. Matter 24(31), 314214 (2012).
[Crossref] [PubMed]

Nanoscale (1)

C. Li, Z. Liu, H. Xie, and D. Wu, “Statistics-based electron Moiré technique: a novel method applied to the characterization of mesoporous structures,” Nanoscale 6(22), 13409–13415 (2014).
[Crossref] [PubMed]

Opt. Acta (Lond.) (1)

R. P. Williams, D. H. Davies, and G. Harburn, “On randomization techniques for the suppression of unwanted moiré patterns in images generated by a scanning system with a periodic amplitude defect,” Opt. Acta (Lond.) 33(10), 1311–1319 (1986).
[Crossref]

Opt. Express (2)

Proc. SPIE (1)

V. Saveljev, J.-Y. Son, S.-B. Woo, M.-C. Park, D.-S. Lee, and K.-D. Kwack, “Quality estimation for visual image in autostereoscopic 3D display,” Proc. SPIE 7329, 73290O (2009).
[Crossref]

Other (8)

B. Grünbaum and G. C. Shephard, Tilings and Patterns (Freeman and Co., 1987).

V. Saveljev and S.-K. Kim, “Moiré period as function of angle for moiré minimization in autostereoscopic 3D displays,” Optical Society of Korea Summer Meeting, paper W1G–VII4, Gyeongju, Korea (13–15 July, 2015).

I. Amidror, The Theory of the Moiré Phenomenon, Vol. 1 (Springer, 2009).

I. Amidror, The Theory of the Moiré Phenomenon, Vol. 2 (Springer, 2007).

V. Saveljev and S.-K. Kim, “Estimation of Probability of the Moiré Effect,” in Proceedings of Collaborative Conference on 3D and Materials Research (CC3DMR), pp. 397–398, Busan, Korea (2015).

V. Saveljev and S.-K. Kim, “Experimental probability of moiré effect in autostereoscopic displays with lenticular plate,” in Proceedings of 22th Conference on Optoelectronics and Optical Communications (COOC), pp. 263–264, Busan, Korea (2015).

D. Zwillinger, CRC Standard Mathematical Tables and Formulae (CRC, 2002), Chap. 4.4.

S. Abbott, Understanding Analysis (Springer, 2001), Chap. 4.1.

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Figures (11)

Fig. 1
Fig. 1 Example of experimental moiré period (mm) vs. the angle (degrees) in two display devices.
Fig. 2
Fig. 2 The maximal moiré period (spectral domain).
Fig. 3
Fig. 3 Examples of moiré patterns in printed samples. The aspect ratio is 0.33 in (a) and 0.58 in (b); the ratio of periods is 0.72 and 0.44, resp.
Fig. 4
Fig. 4 Experimental moiré probability function for autostereoscopic barrier displays.
Fig. 5
Fig. 5 Examples of moiré patterns in LCD displays with lenticular plates. The period of pixels is 0.204 mm in (a) and 0.266 mm in (b); the plates 50 lpi and 40 lpi were attached (periods 0.508 mm and 0.635 mm, resp.)
Fig. 6
Fig. 6 Experimental probability of the moiré effect in LCD displays with lenticular plate.
Fig. 7
Fig. 7 Composite experimental probability.
Fig. 8
Fig. 8 Slope of rays and the grid.
Fig. 9
Fig. 9 Spacing of nodes (theoretical function) for m, n ≤ 5.
Fig. 10
Fig. 10 Thomae's function for n ≤ 10.
Fig. 11
Fig. 11 The maxima of quality function for autostereoscopic displays.

Tables (2)

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Table 1 Lenticular Plates Used in Experiment [6] and Current Experiment

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Table 2 Display Devices Used in Experiment [6] and Current Experiment

Equations (6)

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

φ mn =arctan m n ,
D( x )={ 1 m 2 + n 2 ,for rational angles (x = m/n), 0,for non-rational angles.
Δ RMS ( F 1 , F 2 )= i ( F 1 ( x i ) F 2 ( x i ) ) 2 N ,
T( x )={ 1 n ,for rational angles (x = m/n), 0,for non-rational angles.
T( x ) D( x ) = 1+ ( m n ) 2 .
T( x ) D( x ) =1+ 1 2 ( m n ) 2 1 8 ( m n ) 2 + 1 16 ( m n ) 2 ...

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