Abstract

A mathematical formula of calculating the fringe periods of the color moirés appearing at the contact-type 3-D displays is derived. It is typical that the color moirés are chirped and the period of the line pattern in viewing zone forming optics is more than two times of that of the pixel pattern in the display panel. These make impossible to calculate the fringe periods of the color moirés with the conventional beat frequency formula. The derived formula work very well for any combination of two line patterns having either a same line period or different line periods. This is experimentally proved. Furthermore, it is also shown that the fringe period can be expressed in terms of the viewing distance and focal length of the viewing zone forming optics.

© 2016 Optical Society of America

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References

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  1. J.-Y. Son and B. Javidi, “3-dimensional imaging systems based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005).
    [Crossref]
  2. B.-R. Lee, J.-Y. Son, O. O. Chernyshov, H. Lee, and I. K. Jeong, “Color moiré simulations in contact-type 3-D displays,” Opt. Express 23(11), 14114–14125 (2015).
    [Crossref] [PubMed]
  3. J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
    [Crossref]
  4. S. Uehara, T. Hiroya, K. Shigemura, and H. Asada, “Reduction and measurement of 3D Moiré caused by lenticular sheet and backlight,” SID Symposium Digest of Technical Papers, 432–435 (2009).
  5. V. V. Saveljev, J.-Y. Son, and K.-H. Cha, “About a moire-less condition in Non-Square Grids,” J. Disp. Technol. 4(3), 332–339 (2008).
    [Crossref]
  6. K. Nagasaki, “A 3D display with variable depth moire pattern,” in Proceeding of SICE Annual Conference (IEEE, 2008), pp. 1936–1941.
    [Crossref]
  7. 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]
  8. F. P. Chiang and B. Ranganayakamma, “Deflection measurements using moirè gap effect,” Exp. Mech. 11(4), 296–302 (1971).
    [Crossref]
  9. I. Amidror, The Theory of the Moiré Phenomenon (Kluwer Academic Publishers, 2000).
  10. G. Oster and Y. Nishijima, “Moire patterns,” Sci. Am. 5(208), 54–63 (1963).
    [Crossref]
  11. A. W. Rihaczek, Principle of High Resolution Radar (McGraw Hill, 1969).
  12. J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
    [Crossref]
  13. W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
    [Crossref]
  14. www.ucamco.com
  15. http://imaging.nikon.com/lineup

2015 (2)

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

B.-R. Lee, J.-Y. Son, O. O. Chernyshov, H. Lee, and I. K. Jeong, “Color moiré simulations in contact-type 3-D displays,” Opt. Express 23(11), 14114–14125 (2015).
[Crossref] [PubMed]

2013 (1)

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

2009 (1)

2008 (1)

V. V. Saveljev, J.-Y. Son, and K.-H. Cha, “About a moire-less condition in Non-Square Grids,” J. Disp. Technol. 4(3), 332–339 (2008).
[Crossref]

2005 (1)

J.-Y. Son and B. Javidi, “3-dimensional imaging systems based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005).
[Crossref]

2003 (1)

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

1971 (1)

F. P. Chiang and B. Ranganayakamma, “Deflection measurements using moirè gap effect,” Exp. Mech. 11(4), 296–302 (1971).
[Crossref]

1963 (1)

G. Oster and Y. Nishijima, “Moire patterns,” Sci. Am. 5(208), 54–63 (1963).
[Crossref]

Asada, H.

S. Uehara, T. Hiroya, K. Shigemura, and H. Asada, “Reduction and measurement of 3D Moiré caused by lenticular sheet and backlight,” SID Symposium Digest of Technical Papers, 432–435 (2009).

Bahn, J.-E.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

Cha, K.-H.

V. V. Saveljev, J.-Y. Son, and K.-H. Cha, “About a moire-less condition in Non-Square Grids,” J. Disp. Technol. 4(3), 332–339 (2008).
[Crossref]

Chernyshov, O. O.

Chiang, F. P.

F. P. Chiang and B. Ranganayakamma, “Deflection measurements using moirè gap effect,” Exp. Mech. 11(4), 296–302 (1971).
[Crossref]

Choi, H.-H.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

Choi, Y.-J.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

Hiroya, T.

S. Uehara, T. Hiroya, K. Shigemura, and H. Asada, “Reduction and measurement of 3D Moiré caused by lenticular sheet and backlight,” SID Symposium Digest of Technical Papers, 432–435 (2009).

Javidi, B.

J.-Y. Son and B. Javidi, “3-dimensional imaging systems based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005).
[Crossref]

Jeong, I. K.

Jung, J.-H.

Kim, J.

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

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]

Kim, Y.

Lee, B.

Lee, B.-R.

B.-R. Lee, J.-Y. Son, O. O. Chernyshov, H. Lee, and I. K. Jeong, “Color moiré simulations in contact-type 3-D displays,” Opt. Express 23(11), 14114–14125 (2015).
[Crossref] [PubMed]

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

Lee, H.

B.-R. Lee, J.-Y. Son, O. O. Chernyshov, H. Lee, and I. K. Jeong, “Color moiré simulations in contact-type 3-D displays,” Opt. Express 23(11), 14114–14125 (2015).
[Crossref] [PubMed]

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

Lee, K.-H.

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

Nagasaki, K.

K. Nagasaki, “A 3D display with variable depth moire pattern,” in Proceeding of SICE Annual Conference (IEEE, 2008), pp. 1936–1941.
[Crossref]

Nishijima, Y.

G. Oster and Y. Nishijima, “Moire patterns,” Sci. Am. 5(208), 54–63 (1963).
[Crossref]

Oster, G.

G. Oster and Y. Nishijima, “Moire patterns,” Sci. Am. 5(208), 54–63 (1963).
[Crossref]

Park, G.

Park, M.-C.

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

Ranganayakamma, B.

F. P. Chiang and B. Ranganayakamma, “Deflection measurements using moirè gap effect,” Exp. Mech. 11(4), 296–302 (1971).
[Crossref]

Saveljev, V. V.

V. V. Saveljev, J.-Y. Son, and K.-H. Cha, “About a moire-less condition in Non-Square Grids,” J. Disp. Technol. 4(3), 332–339 (2008).
[Crossref]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

Shigemura, K.

S. Uehara, T. Hiroya, K. Shigemura, and H. Asada, “Reduction and measurement of 3D Moiré caused by lenticular sheet and backlight,” SID Symposium Digest of Technical Papers, 432–435 (2009).

Son, J.-Y.

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

B.-R. Lee, J.-Y. Son, O. O. Chernyshov, H. Lee, and I. K. Jeong, “Color moiré simulations in contact-type 3-D displays,” Opt. Express 23(11), 14114–14125 (2015).
[Crossref] [PubMed]

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

V. V. Saveljev, J.-Y. Son, and K.-H. Cha, “About a moire-less condition in Non-Square Grids,” J. Disp. Technol. 4(3), 332–339 (2008).
[Crossref]

J.-Y. Son and B. Javidi, “3-dimensional imaging systems based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005).
[Crossref]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

Son, W.-H.

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

Uehara, S.

S. Uehara, T. Hiroya, K. Shigemura, and H. Asada, “Reduction and measurement of 3D Moiré caused by lenticular sheet and backlight,” SID Symposium Digest of Technical Papers, 432–435 (2009).

Appl. Opt. (1)

Exp. Mech. (1)

F. P. Chiang and B. Ranganayakamma, “Deflection measurements using moirè gap effect,” Exp. Mech. 11(4), 296–302 (1971).
[Crossref]

J. Disp. Technol. (2)

J.-Y. Son and B. Javidi, “3-dimensional imaging systems based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005).
[Crossref]

V. V. Saveljev, J.-Y. Son, and K.-H. Cha, “About a moire-less condition in Non-Square Grids,” J. Disp. Technol. 4(3), 332–339 (2008).
[Crossref]

J. Opt. (1)

J. Kim, J.-Y. Son, K.-H. Lee, H. Lee, and M.-C. Park, “Behaviors of moiré fringes induced by plate thickness,” J. Opt. 17(3), 035801 (2015).
[Crossref]

Opt. Eng. (2)

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, and H.-H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates,” Opt. Eng. 42(11), 3326–3333 (2003).
[Crossref]

W.-H. Son, J. Kim, M.-C. Park, B.-R. Lee, and J.-Y. Son, “The basic image cell in contact-type multiview 3-D Imaging systems,” Opt. Eng. 52(10), 103107 (2013).
[Crossref]

Opt. Express (1)

Sci. Am. (1)

G. Oster and Y. Nishijima, “Moire patterns,” Sci. Am. 5(208), 54–63 (1963).
[Crossref]

Other (6)

A. W. Rihaczek, Principle of High Resolution Radar (McGraw Hill, 1969).

I. Amidror, The Theory of the Moiré Phenomenon (Kluwer Academic Publishers, 2000).

www.ucamco.com

http://imaging.nikon.com/lineup

S. Uehara, T. Hiroya, K. Shigemura, and H. Asada, “Reduction and measurement of 3D Moiré caused by lenticular sheet and backlight,” SID Symposium Digest of Technical Papers, 432–435 (2009).

K. Nagasaki, “A 3D display with variable depth moire pattern,” in Proceeding of SICE Annual Conference (IEEE, 2008), pp. 1936–1941.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 A geometry of formingmoiré fringes
Fig. 2
Fig. 2 Moiré fringes for VZFO line period of 3.4 mm: (a) Viewed at 500 mm and (b) Viewed at 1,000 mm.
Fig. 3
Fig. 3 Moiré fringe periods for VZFO line period of 3.4 mm.
Fig. 4
Fig. 4 Moiré fringes for the case when the VZFO line period is integer multiples of a sub-pixel pitch
Fig. 5
Fig. 5 Moiré fringes for VZFO line period of 1.4509 mm.
Fig. 6
Fig. 6 Moiré fringes for VZFO line period of 1.608 mm.
Fig. 7
Fig. 7 Moiré fringe periods for VZFO line period of 1.608 mm.

Tables (2)

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Table 1 Fringe Periods calculated by equation and symbol definition.

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Table 2 Symbol definition

Equations (9)

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P M =3| O P S P O P A S P |=3| 1/3( 1 3 S P 1 3 O P /A ) |=| 1/( 1 P P A 3 O P ) |
A=k when 0R S P /2 A=k+1 when S P /2R< S P
P M (x)= [cos{π( P Px (x) P P Ax 3 O P )}] 2
P M (l)= 3 O P A P P { P Px ( x 2l+1.5 ) P Px ( x 2l+0.5 )} 3 O P A ,
d d+f = O P n S P = [ O P / S P ] S P +R n S P
d d+f = k S P +R n S P ˙ 1 f d
(nj) S P +R n S P =1 j S P R n S P ˙ 1 f d
P M (l)= n(1f/d) A { P Px ( x 2l+1.5 ) P Px ( x 2l+0.5 ) P P }
P M (l)=(1f/d){ P Px ( x 2l+1.5 ) P Px ( x 2l+0.5 ) P P }

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