Abstract

We present optical characteristics of view image provided by a high-density multi-view autostereoscopic 3D display (HD-MVA3D) with a parallax barrier (PB). Diffraction effects that become of great importance in such a display system that uses a PB, are considered in an one-dimensional model of the 3D display, in which the numerical simulation of light from display panel pixels through PB slits to viewing zone is performed. The simulation results are then compared to the corresponding experimental measurements with discussion. We demonstrate that, as a main parameter for view image quality evaluation, the Fresnel number can be used to determine the PB slit aperture for the best performance of the display system. It is revealed that a set of the display parameters, which gives the Fresnel number of ∼ 0.7 offers maximized brightness of the view images while that corresponding to the Fresnel number of 0.4 ∼ 0.5 offers minimized image crosstalk. The compromise between the brightness and crosstalk enables optimization of the relative magnitude of the brightness to the crosstalk and lead to the choice of display parameter set for the HD-MVA3D with a PB, which satisfies the condition where the Fresnel number lies between 0.4 and 0.7.

© 2016 Optical Society of America

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References

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  1. N.A. Dodgson, “Autostereoscopic 3D Displays,” IEEE Computer 38(8), 31–36 (2005).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  9. J. Nakamura, K. Tanaka, and Y. Takaki, “Increase in depth of field of eyes using reduced-view super multi-view displays,” Appl. Phys. Express 6, 022501 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  19. K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
    [Crossref]
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2015 (1)

S.-K Kim, K.-H Yoon, S. Yoon, and H. Ju, “Defragmented image based autostereoscopic 3D displays with dynamic eye tracking,” Opt. Commun. 357, 185–192 (2015).
[Crossref]

2014 (1)

2013 (4)

J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photon. 5, 456–535 (2013).
[Crossref]

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

J. Nakamura, K. Tanaka, and Y. Takaki, “Increase in depth of field of eyes using reduced-view super multi-view displays,” Appl. Phys. Express 6, 022501 (2013).
[Crossref]

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

2011 (3)

2010 (1)

2008 (2)

S.-K. Kim, D.W. Kim, Y.M. Kwon, and J.Y. Son, “Evaluation of the monocular depth cue in 3D displays,” Opt. Express 16(26), 21415–21422 (2008).
[Crossref] [PubMed]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref] [PubMed]

2007 (1)

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Display 8(4), 23–26 (2007).
[Crossref]

2006 (1)

J.-Y Son, B. Javidi, and K.-D Kwack, “Methods for displaying three-dimensional images,” Proc. of the IEEE 94(3), 502–523 (2006).
[Crossref]

2005 (3)

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

H. Nakanuma, H. Kamei, and Y. Takaki, “Natural 3D display with 128 directional images used for human-engineering evaluation,” Proc. SPIE 5664, 28–35 (2005).
[Crossref]

N.A. Dodgson, “Autostereoscopic 3D Displays,” IEEE Computer 38(8), 31–36 (2005).
[Crossref]

2002 (1)

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays 23, 191–201 (2002).
[Crossref]

1997 (1)

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE 3012, 154–166 (1997).
[Crossref]

Akeley, K.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref] [PubMed]

Banks, M. S.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref] [PubMed]

Chen, F. H

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Chen, N.

Chen, Y. H.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Choi, H.-J.

Chou, Y. H.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Dodgson, N.A.

N.A. Dodgson, “Autostereoscopic 3D Displays,” IEEE Computer 38(8), 31–36 (2005).
[Crossref]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics, 2nd edition (Holt, Rinehart and Winston, Inc., 1975).

Geng, J.

Girshick, A. R.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company, 2005).

Hahn, J.

Hoffman, D. M.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref] [PubMed]

Honda, T.

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE 3012, 154–166 (1997).
[Crossref]

Hong, H.-K.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Display 8(4), 23–26 (2007).
[Crossref]

Hong, J.

Hsu, W. H.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Huang, K. C.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Ide, S.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays 23, 191–201 (2002).
[Crossref]

Im, H.-J.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Display 8(4), 23–26 (2007).
[Crossref]

Javidi, B.

J.-Y Son, B. Javidi, and K.-D Kwack, “Methods for displaying three-dimensional images,” Proc. of the IEEE 94(3), 502–523 (2006).
[Crossref]

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

Ju, H.

S.-K Kim, K.-H Yoon, S. Yoon, and H. Ju, “Defragmented image based autostereoscopic 3D displays with dynamic eye tracking,” Opt. Commun. 357, 185–192 (2015).
[Crossref]

K.-H. Yoon, H. Ju, I. Park, and S.-K. Kim, “Determination of the optimum viewing distance for a multi-view auto-stereoscopic 3D display,” Opt. Express 22(19), 22616–22631 (2014).
[Crossref] [PubMed]

Kajiki, Y.

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE 3012, 154–166 (1997).
[Crossref]

Kamei, H.

H. Nakanuma, H. Kamei, and Y. Takaki, “Natural 3D display with 128 directional images used for human-engineering evaluation,” Proc. SPIE 5664, 28–35 (2005).
[Crossref]

Kim, D.W.

Kim, D.-W.

S.-K Kim, E.-H Kim, and D.-W. Kim, “Full parallax multifocus three-dimensional display using a slanted light source array,” Opt. Eng. 50(11), 114001 (2011).
[Crossref]

Kim, E.-H

S.-K Kim, E.-H Kim, and D.-W. Kim, “Full parallax multifocus three-dimensional display using a slanted light source array,” Opt. Eng. 50(11), 114001 (2011).
[Crossref]

Kim, H.

Kim, S.-K

S.-K Kim, K.-H Yoon, S. Yoon, and H. Ju, “Defragmented image based autostereoscopic 3D displays with dynamic eye tracking,” Opt. Commun. 357, 185–192 (2015).
[Crossref]

S.-K Kim, E.-H Kim, and D.-W. Kim, “Full parallax multifocus three-dimensional display using a slanted light source array,” Opt. Eng. 50(11), 114001 (2011).
[Crossref]

Kim, S.-K.

Kim, Y.

Kwack, K.-D

J.-Y Son, B. Javidi, and K.-D Kwack, “Methods for displaying three-dimensional images,” Proc. of the IEEE 94(3), 502–523 (2006).
[Crossref]

Kwon, Y.M.

Lee, B.

Lee, B.-J.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Display 8(4), 23–26 (2007).
[Crossref]

Lee, K.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Liao, C. C.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Lin, H. Y.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Lin, L.

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

Min, S.-W.

Mitsuhashi, T.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays 23, 191–201 (2002).
[Crossref]

Nago, N.

Nakamura, J.

J. Nakamura, K. Tanaka, and Y. Takaki, “Increase in depth of field of eyes using reduced-view super multi-view displays,” Appl. Phys. Express 6, 022501 (2013).
[Crossref]

Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express 19(5), 4129–4139 (2011).
[Crossref] [PubMed]

Nakanuma, H.

H. Nakanuma, H. Kamei, and Y. Takaki, “Natural 3D display with 128 directional images used for human-engineering evaluation,” Proc. SPIE 5664, 28–35 (2005).
[Crossref]

Park, I.

Park, J.-H.

Shin, H.-H.

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Display 8(4), 23–26 (2007).
[Crossref]

Son, J.-Y

J.-Y Son, B. Javidi, and K.-D Kwack, “Methods for displaying three-dimensional images,” Proc. of the IEEE 94(3), 502–523 (2006).
[Crossref]

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

Son, J.Y.

Takaki, Y.

J. Nakamura, K. Tanaka, and Y. Takaki, “Increase in depth of field of eyes using reduced-view super multi-view displays,” Appl. Phys. Express 6, 022501 (2013).
[Crossref]

Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express 19(5), 4129–4139 (2011).
[Crossref] [PubMed]

Y. Takaki and N. Nago, “Multi-projection of lenticular displays to construct a 256-view super multi-view display,” Opt. Express 18(9), 8824–8835 (2010).
[Crossref] [PubMed]

H. Nakanuma, H. Kamei, and Y. Takaki, “Natural 3D display with 128 directional images used for human-engineering evaluation,” Proc. SPIE 5664, 28–35 (2005).
[Crossref]

Tanaka, K.

J. Nakamura, K. Tanaka, and Y. Takaki, “Increase in depth of field of eyes using reduced-view super multi-view displays,” Appl. Phys. Express 6, 022501 (2013).
[Crossref]

Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express 19(5), 4129–4139 (2011).
[Crossref] [PubMed]

Thwaites, H.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays 23, 191–201 (2002).
[Crossref]

Yano, S.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays 23, 191–201 (2002).
[Crossref]

Yoon, K.-H

S.-K Kim, K.-H Yoon, S. Yoon, and H. Ju, “Defragmented image based autostereoscopic 3D displays with dynamic eye tracking,” Opt. Commun. 357, 185–192 (2015).
[Crossref]

Yoon, K.-H.

Yoon, S.

S.-K Kim, K.-H Yoon, S. Yoon, and H. Ju, “Defragmented image based autostereoscopic 3D displays with dynamic eye tracking,” Opt. Commun. 357, 185–192 (2015).
[Crossref]

Yoshikawa, H.

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE 3012, 154–166 (1997).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Express (1)

J. Nakamura, K. Tanaka, and Y. Takaki, “Increase in depth of field of eyes using reduced-view super multi-view displays,” Appl. Phys. Express 6, 022501 (2013).
[Crossref]

Displays (1)

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays 23, 191–201 (2002).
[Crossref]

IEEE Computer (1)

N.A. Dodgson, “Autostereoscopic 3D Displays,” IEEE Computer 38(8), 31–36 (2005).
[Crossref]

J. Disp. Technol. (1)

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

J. Inf. Display (1)

H.-J. Im, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Auto-stereoscopic 60 view 3D using slanted lenticular lens arrays,” J. Inf. Display 8(4), 23–26 (2007).
[Crossref]

J. Soc. Info. Disp. (1)

K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A study of optimal viewing distance in a parallax barrier 3D display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
[Crossref]

J. Vis. (1)

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref] [PubMed]

Opt. Commun. (1)

S.-K Kim, K.-H Yoon, S. Yoon, and H. Ju, “Defragmented image based autostereoscopic 3D displays with dynamic eye tracking,” Opt. Commun. 357, 185–192 (2015).
[Crossref]

Opt. Eng. (1)

S.-K Kim, E.-H Kim, and D.-W. Kim, “Full parallax multifocus three-dimensional display using a slanted light source array,” Opt. Eng. 50(11), 114001 (2011).
[Crossref]

Opt. Express (4)

Phys. Today (1)

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

Proc. of the IEEE (1)

J.-Y Son, B. Javidi, and K.-D Kwack, “Methods for displaying three-dimensional images,” Proc. of the IEEE 94(3), 502–523 (2006).
[Crossref]

Proc. SPIE (2)

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE 3012, 154–166 (1997).
[Crossref]

H. Nakanuma, H. Kamei, and Y. Takaki, “Natural 3D display with 128 directional images used for human-engineering evaluation,” Proc. SPIE 5664, 28–35 (2005).
[Crossref]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company, 2005).

G. R. Fowles, Introduction to Modern Optics, 2nd edition (Holt, Rinehart and Winston, Inc., 1975).

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Figures (17)

Fig. 1
Fig. 1 Schematic of geometrical traces of light rays in a PB based multi-view autostereoscopic 3D display.
Fig. 2
Fig. 2 Optical characteristics of view images as a function of PB aperture ratio β in a PB based multi-view autostereoscopic 3D display (Wp = 30μm, Dvp= 5 mm, OVD = 600 mm) (a1) Normalized image brightness Inv and image crosstalk CTav in an one-dimensional PB based 3D display (a2) schematic of an one-dimensional PB used for the simulation results shown in (a1), (b1) Inv and CTav in a two-dimensional PB (b2) schematic of a two-dimensional PB used for the simulation results shown in (b1). The tilt angle with respect to the display panel is tan−1(1/3). (C) Relative ratio of image brightness to crosstalk.
Fig. 3
Fig. 3 Simulation results of image brightness distributions vs horizontal position at the OVD for the one-dimensional PB. Here Wp = 30 μm, Dvp = 5 mm, OVD= 600 mm. (a) β = 0.8, (b) β = 1, (c) β = 1.2.
Fig. 4
Fig. 4 Relative magnitude of full width at half maximum to the Dvp and crosstalk as a function of β in a PB based MVA3D display (Wp = 30 μm, Dvp = 5 mm, OVD= 600 mm) (a) the one-dimensional PB (b) the two-dimensional PB tilted by the angle of tan−1(1/3).
Fig. 5
Fig. 5 Schematic of diffraction of light through a PB aperture from a point on a subpixel surface for distribution of image brightness intensity in a PB-based MVA3D.
Fig. 6
Fig. 6 Schematic for introduction to the Fresnel number.
Fig. 7
Fig. 7 Optical characteristics for different Dvp as a function of β [(a)], and those as a function of nFR [(b)].
Fig. 8
Fig. 8 Optical characteristics for different Wp as a function of β [(a)], and those as a function of nFR [(b)].
Fig. 9
Fig. 9 Simulation results of the relative magnitude of view Image brightness to its crosstalk. Wp = 30 μm, and Dvp =5 mm. The blue and red solid lines represents results obtained with and without diffraction effects included in the simulation, respectively.
Fig. 10
Fig. 10 Simulated intensity distribution of a view image vs x for various nFR (Red: without diffraction, blue: with diffraction) in the one-dimensional PB based 3D display.
Fig. 11
Fig. 11 (a) Fresnel number (nFR) that optimizes Inv, γ, and CTav for various Dvp in the one-dimensional PB based 3D display (b) the optimized value of γ and CTav for various Dvp, in the one-dimensional PB based 3D display.
Fig. 12
Fig. 12 Comparison of optical characteristics between experiment and simulation (Wp = 30 μm, Dvp = 2.51 mm, PB Slanted angle= 0 deg) in the one-dimensional PB based 3D display.
Fig. 13
Fig. 13 The intensity distribution of a single view image vs x at the OVD (600 mm) for different nFR used in Fig. 12 (red curve: the theoretical simulation, blue curve: experiment) in the one-dimensional PB based 3D display.
Fig. 14
Fig. 14 The FWHM of the view intensity distribution vs nFR in the HD-MVA3D display with Dvp = 2.51 mm (a) the non-tilted one-dimensional PB (b) the two-dimensional PB tilted by tan−1(1/3) =18.435 deg).
Fig. 15
Fig. 15 Comparison of optical characteristics between experiment and simulation (Wp = 30 μm, Dvp = 5.06 mm, PB Slanted angle=0 deg).
Fig. 16
Fig. 16 Simulation results of optical characteristics for the three different wavelengths of light source.
Fig. 17
Fig. 17 Comparison of optical characteristics between the cases of using green and white light sources. (dotted line: simulation results, solid rectangles: experimental ones) (a) as a function of β (b) as a function of nFR.

Tables (1)

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Table 1 Display parameters of the HD-MVA3D for comparing experiment and simulation.

Equations (15)

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W PBS = D vp × W p D vp + W p ,
T PB = n × D vp × W p D vp + W p ,
d = L × W p D vp .
CT av [ % ] I av I view I view × 100 ,
γ I nv CT av / 100 .
U 2 ( x 2 , ξ s ) = L j λ U s ( ξ s ) exp ( j k R 1 ) exp ( j k R 2 ) R 1 R 2 2 d x 1 ,
I 2 ( x 2 , ξ s ) = | U 2 ( x 2 , ξ s ) | 2 .
I D ( x 2 ) = ξ s 1 ξ s 2 I 2 ( x 2 , ξ s ) d ξ s .
( R 1 + R 2 ) max = d 2 + ( W PB 2 ) 2 + L 2 + ( W PB 2 ) 2 .
( R 1 + R 2 ) max ( d + L ) + 1 2 ( W PB 2 ) 2 ( 1 d + 1 L ) .
( R 1 + R 2 ) max ( d + L ) = 1 2 ( W PB 2 ) 2 ( 1 d + 1 L ) = λ 2 n FR .
n FR = 1 λ ( W PB 2 ) 2 ( 1 d + 1 L ) = ( W PB 2 ) 2 ( d + L λ × d × L ) .
n FR = 1 λ × L ( W PB 2 ) 2 ( 1 + D vp W p ) 1 λ × L ( W PB 2 ) 2 D vp W p ,
β = W PB W PBS W PB W P .
n FR 1 4 1 λ × L β 2 ( W p × D vp ) .

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