Abstract

The amplitude of the moiré patterns is estimated in relation to the opening ratio in line gratings and square grids. The theory is developed; the experimental measurements are performed. The minimum and the maximum of the amplitude are found. There is a good agreement between the theoretical and experimental data. This is additionally confirmed by the visual observation. The results can be applied to the image quality improvement in autostereoscopic 3D displays, to the measurements, and to the moiré displays.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Integral imaging microscopy with enhanced depth-of-field using a spatial multiplexing

Ki-Chul Kwon, Munkh-Uchral Erdenebat, Md. Ashraful Alam, Young-Tae Lim, Kwang Gi Kim, and Nam Kim
Opt. Express 24(3) 2072-2083 (2016)

Quantitative measurement and control of optical Moiré pattern in an autostereoscopic liquid crystal display system

Yangui Zhou, Peter Krebs, Hang Fan, Haowen Liang, Jianbang Su, Jiahui Wang, and Jianying Zhou
Appl. Opt. 54(6) 1521-1527 (2015)

Theoretical estimation of moiré effect using spectral trajectories

Vladimir Saveljev and Sung-Kyu Kim
Opt. Express 21(2) 1693-1712 (2013)

References

  • View by:
  • |
  • |
  • |

  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]
  2. K. Patorsky, The Moiré Fringe Technique (Elsevier, 1993).
  3. D. Post, B. Han, and P. Ifju, High Sensitivity Moiré. Experimental Analysis for Mechanics and Materials (Springer, 1994).
  4. V. Saveljev and S.-K. Kim, “Three-dimensional Moiré display,” J. Soc. Inf. Disp. 22(9), 482–486 (2014).
    [Crossref]
  5. V. Saveljev, “Orientations and branches of moiré waves in three-dimensional displays,” J. Korean Phys. Soc. 57(6), 1392–1396 (2010).
    [Crossref]
  6. V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
    [Crossref] [PubMed]
  7. V. Saveljev and S.-K. Kim, “Estimation of contrast of moiré patterns in 3D displays,” in Proceedings of 14th International Meeting on Information Display (IMID), (2014), pp. 417.
  8. I. Amidror, The Theory of Moiré Phenomenon (Springer, 2009).
  9. R. D. Hersch and S. Chosson, “Band Moiré Images,” ACM Trans. Graphic 23(3), 239–248 (2004).
    [Crossref]
  10. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012).
    [Crossref] [PubMed]
  11. A. A. Michelson, Studies in Optics (Dover, 1995), Ch. 3.
  12. K. Patorski, S. Yokozeki, and T. Suzuki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15(3), 443–456 (1976).
    [Crossref]
  13. S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
    [Crossref]
  14. S. Yokozeki and K. Patorski, “Moiré fringe profile prediction method and its application to fringe sharpening,” Appl. Opt. 17(16), 2541–2547 (1978).
    [Crossref] [PubMed]
  15. Y. Yoshino and H. Takasaki, “Doubling and visibility enhancement of moire fringes of the summation type,” Appl. Opt. 15(5), 1124–1126 (1976).
    [Crossref] [PubMed]
  16. C. A. Sciammarella, “Basic optical law in the interpretation of moiré patterns applied to the analysis of strains,” Exp. Mech. 5(5), 154–160 (1965).
    [Crossref]
  17. V. Saveljev, S.-K. Kim, and B. Lee, “Experimental estimation of contrast of moiré patterns for 3D displays,” in Proceedings of Winter Conference of the Optical Society of Korea (2015), pp. 63–64.
  18. V. Saveljev and S.-K. Kim, “Theoretical estimation of moiré effect using spectral trajectories,” Opt. Express 21(2), 1693–1712 (2013).
    [Crossref] [PubMed]
  19. M. Abolhassani, “Formulation of moiré fringes based on spatial averaging,” Optik (Stuttg.) 122(6), 510–513 (2011).
    [Crossref]
  20. S. Yokozeki, Y. Kusaka, and K. Patorski, “Geometric parameters of moiré fringes,” Appl. Opt. 15(9), 2223–2227 (1976).
    [Crossref] [PubMed]

2014 (1)

V. Saveljev and S.-K. Kim, “Three-dimensional Moiré display,” J. Soc. Inf. Disp. 22(9), 482–486 (2014).
[Crossref]

2013 (2)

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

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

2012 (2)

2011 (1)

M. Abolhassani, “Formulation of moiré fringes based on spatial averaging,” Optik (Stuttg.) 122(6), 510–513 (2011).
[Crossref]

2010 (1)

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

2004 (1)

R. D. Hersch and S. Chosson, “Band Moiré Images,” ACM Trans. Graphic 23(3), 239–248 (2004).
[Crossref]

1978 (1)

1976 (3)

1965 (1)

C. A. Sciammarella, “Basic optical law in the interpretation of moiré patterns applied to the analysis of strains,” Exp. Mech. 5(5), 154–160 (1965).
[Crossref]

Abolhassani, M.

M. Abolhassani, “Formulation of moiré fringes based on spatial averaging,” Optik (Stuttg.) 122(6), 510–513 (2011).
[Crossref]

Chosson, S.

R. D. Hersch and S. Chosson, “Band Moiré Images,” ACM Trans. Graphic 23(3), 239–248 (2004).
[Crossref]

Hersch, R. D.

R. D. Hersch and S. Chosson, “Band Moiré Images,” ACM Trans. Graphic 23(3), 239–248 (2004).
[Crossref]

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]

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, S.-K.

V. Saveljev and S.-K. Kim, “Three-dimensional Moiré display,” J. Soc. Inf. Disp. 22(9), 482–486 (2014).
[Crossref]

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, S.-K. Kim, and B. Lee, “Experimental estimation of contrast of moiré patterns for 3D displays,” in Proceedings of Winter Conference of the Optical Society of Korea (2015), pp. 63–64.

V. Saveljev and S.-K. Kim, “Estimation of contrast of moiré patterns in 3D displays,” in Proceedings of 14th International Meeting on Information Display (IMID), (2014), pp. 417.

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]

Kusaka, Y.

Lee, B.

V. Saveljev, S.-K. Kim, and B. Lee, “Experimental estimation of contrast of moiré patterns for 3D displays,” in Proceedings of Winter Conference of the Optical Society of Korea (2015), pp. 63–64.

Liu, S.

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

Luo, X.

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

Patorski, K.

Pokorski, K.

Saveljev, V.

V. Saveljev and S.-K. Kim, “Three-dimensional Moiré display,” J. Soc. Inf. Disp. 22(9), 482–486 (2014).
[Crossref]

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, “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, 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, “Estimation of contrast of moiré patterns in 3D displays,” in Proceedings of 14th International Meeting on Information Display (IMID), (2014), pp. 417.

V. Saveljev, S.-K. Kim, and B. Lee, “Experimental estimation of contrast of moiré patterns for 3D displays,” in Proceedings of Winter Conference of the Optical Society of Korea (2015), pp. 63–64.

Sciammarella, C. A.

C. A. Sciammarella, “Basic optical law in the interpretation of moiré patterns applied to the analysis of strains,” Exp. Mech. 5(5), 154–160 (1965).
[Crossref]

Son, J.-Y.

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]

Suzuki, T.

K. Patorski, S. Yokozeki, and T. Suzuki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15(3), 443–456 (1976).
[Crossref]

Takasaki, H.

Wang, C.

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

Yang, X.

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

Yokozeki, S.

Yoshino, Y.

Zhang, S.

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

ACM Trans. Graphic (1)

R. D. Hersch and S. Chosson, “Band Moiré Images,” ACM Trans. Graphic 23(3), 239–248 (2004).
[Crossref]

Appl. Opt. (4)

Exp. Mech. (1)

C. A. Sciammarella, “Basic optical law in the interpretation of moiré patterns applied to the analysis of strains,” Exp. Mech. 5(5), 154–160 (1965).
[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. Nanophotonics (1)

S. Zhang, S. Liu, X. Yang, C. Wang, and X. Luo, “Near-field Moiré effect with dielectric–metal–dielectric sandwich structure,” J. Nanophotonics 7(1), 073080 (2013).
[Crossref]

J. Soc. Inf. Disp. (1)

V. Saveljev and S.-K. Kim, “Three-dimensional Moiré display,” J. Soc. Inf. Disp. 22(9), 482–486 (2014).
[Crossref]

Jpn. J. Appl. Phys. (1)

K. Patorski, S. Yokozeki, and T. Suzuki, “Moiré profile prediction by using Fourier series formalism,” Jpn. J. Appl. Phys. 15(3), 443–456 (1976).
[Crossref]

Opt. Express (2)

Optik (Stuttg.) (1)

M. Abolhassani, “Formulation of moiré fringes based on spatial averaging,” Optik (Stuttg.) 122(6), 510–513 (2011).
[Crossref]

Other (6)

V. Saveljev, S.-K. Kim, and B. Lee, “Experimental estimation of contrast of moiré patterns for 3D displays,” in Proceedings of Winter Conference of the Optical Society of Korea (2015), pp. 63–64.

V. Saveljev and S.-K. Kim, “Estimation of contrast of moiré patterns in 3D displays,” in Proceedings of 14th International Meeting on Information Display (IMID), (2014), pp. 417.

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

K. Patorsky, The Moiré Fringe Technique (Elsevier, 1993).

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré. Experimental Analysis for Mechanics and Materials (Springer, 1994).

A. A. Michelson, Studies in Optics (Dover, 1995), Ch. 3.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1 Intensity profile of the moiré patterns in binary gratings. The letters A through D show the phases.
Fig. 2
Fig. 2 Moiré patterns in superposed 1D/2D gratings ε = 0.065; opening ratio is 0.5 in (a), and 0.625 in (b). Minimum and maximum are labeled as A and C.
Fig. 3
Fig. 3 Reflectance functions of gratings and moiré intensity in phases A (minimum) and C (maximum).
Fig. 4
Fig. 4 Sketches of theoretical surfaces of minimum, maximum and amplitude in 1D case drawn by Eqs. (13)-(15).
Fig. 5
Fig. 5 Sketches of theoretical surfaces of minimum, maximum and amplitude in 2D case drawn by Eqs. (18)-(20).
Fig. 6
Fig. 6 The cross-sections of 1D and 2D theoretical surfaces along diagonal; (a) minimum and maximum, (b) amplitude.
Fig. 7
Fig. 7 Central part of 1D and 2D matrices of samples (computer-generated image); r1 and r2 between 0.4 and 0.8.
Fig. 8
Fig. 8 Digital photographs of the 1D and 2D matrices. One region of measurement is indicated by dashed square in (a).
Fig. 9
Fig. 9 Example of the scan line.
Fig. 10
Fig. 10 Examples of experimental moiré amplitude maps of surfaces shown in Fig. 10 (1D and 2D cases).
Fig. 11
Fig. 11 1D and 2D experimental points and piece-wise theoretical curves along diagonal.
Fig. 12
Fig. 12 (a) 1D and (b) 2D samples for visual observation (opening ratio is 5/8).
Fig. 13
Fig. 13 Matrix for visual experiment (computer-generated image). The location of the origin is different from Figs. 7 and 8.
Fig. 14
Fig. 14 Estimated average visual amplitude of the moiré patterns for (a) 1D and (b) 2D cases.
Fig. 15
Fig. 15 Moiré patterns in superposed gratings: (a) parallel gratings of different periods, (b) non-parallel gratings of identical periods.

Equations (33)

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

A= I max I min
p 2 =( 1ε ) p 1 ,ε<<1
I min = I 0 min( w 1 + w 2 ,p )+ I 1 ( pmin( w 1 + w 2 ,p ) )
I max = I 0 max( w 1 , w 2 )+ I 1 ( pmax( w 1 , w 2 ) )
I 0 =0 I 1 =1
I min1D =pmin( w 1 + w 2 ,p )
I max1D =pmax( w 1 , w 2 )
I ' min1D ={ 0,if p 2 w 1 + w 2 r 1 + r 2 1+ε F 1 ( r 1 , r 2 ),if p 2 > w 1 + w 2
I ' max1D ={ r 2 +ε F 2 ( r 1 , r 2 ),if w 2 w 1 r 1 +ε F 3 ( r 1 , r 2 ),if w 1 > w 2
I ' min1D ={ 0,if r 1 + r 2 1+ε r 2 r 1 + r 2 1+ε F 1 ( r 1 , r 2 ),if r 1 + r 2 >1+ε r 2
I ' max1D ={ r 2 +ε F 2 ( r 1 , r 2 ),if r 2 r 1 ε+ε r 2 r 1 +ε F 3 ( r 1 , r 2 ),if r 2 > r 1 ε+ε r 2
A'={ min( r 1 , r 2 )+ε F 4 ( r 1 , r 2 ),if r 2 + r 1 1+ε r 2 min( r 1 , r 2 )( r 1 + r 2 1 )+ε F 5 ( r 1 , r 2 ),if r 2 + r 1 >1+ε r 2
I ' min1D ={ 0,if r 1 + r 2 1 r 1 + r 2 1if r 1 + r 2 >1
I ' max1D =min( r 1 , r 2 )
A ' 1D =min( r 1 , r 2 ,1 r 1 ,1 r 2 )
I ' min2D ={ 0, r 1 + r 2 1 ( r 1 + r 2 1ε r 2 ) 2 , r 1 + r 2 >1
I ' max2D = ( min( r 1 , r 2 )ε ) 2
I ' min2D ={ 0, r 1 + r 2 1 ( r 1 + r 2 1 ) 2 , r 1 + r 2 >1
I ' max2D = ( min( r 1 , r 2 ) ) 2
A ' 2D ={ ( min( r 1 , r 2 ) ) 2 , r 1 + r 2 1 ( max( r 1 , r 2 ) ) 2 2 r 1 r 2 +2( r 1 + r 2 )1, r 1 + r 2 >1
I min1Dd ={ 0,r1/2 2r1,r>1/2
I max1Dd =r
I min2Dd ={ 0,r1/2 ( 2r1 ) 2 ,r>1/2
I max2Dd = r 2
A 1Dd ={ r,r1/2 1r,r>1/2
A 2Dd ={ r 2 ,r1/2 3 r 2 +4r1,r>1/2
r max1D = 1 2
r max2D = 2 3
T= n=1 N p n k n e i α n
λ m = λ ρ 2 + s 2 2sρcosα
λ m = λ 1+ ρ 2 2ρcosα
λ m = λ ( 1ρ ) 2 +ρ α 2
( 1ρ ) 2 /ρ α 2

Metrics