Abstract

Both an analytical formula and an efficient numerical method for simulation of the accumulated intensity profile of light that is refracted through a lenticular lens array placed on top of a liquid-crystal display (LCD) are presented. The influence due to light refracted through adjacent lens is examined in the two-view and four-view systems. Our simulation results are in good agreement with those obtained by a piece of commercial software, ASAP, but our method is much more efficient. This proposed method allows one to adjust the design parameters and carry out simulation for the performance of a subpixel-matched auto-stereoscopic LCD more efficiently and easily.

© 2012 Optical Society of America

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Corrections

Yia-Chung Chang, Li-Chuan Tang, and Chun-Yi Yin, "Efficient simulation of intensity profile of light through subpixel-matched lenticular lens array for two- and four-view autostereoscopic liquid-crystal display: erratum," Appl. Opt. 53, 5640-5640 (2014)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-53-25-5640

References

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  1. L. Lipton and M. Feldman, “New autostereoscopic display technology: the synthaGram,” Proc. SPIE 4660, 229–235 (2002).
    [CrossRef]
  2. J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
    [CrossRef]
  3. K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
    [CrossRef]
  4. C. V. Berkel, A. R. Franklin, and J. R. Mansell, “Design and applications of multiview 3D-LCD,” Proc. SID Euro-Display 96, 109–112 (1996).
  5. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef]
  6. N. A. Dodgson, “Analysis of the viewing zone of multiview autostereoscopic displays,” Proc. SPIE 4660, 254–265 (2002).
    [CrossRef]
  7. J. Konrad and P. Agniel, “Artifact reduction in lenticular multiscopic 3D displays by means of anti-alias filtering,” Proc. SPIE 5006A, 336–347 (2003).
    [CrossRef]
  8. J. Konrad and P. Agniel, “Non-orthogonal subsampling and anti-alias filtering for multiscopic 3D displays,” Proc. SPIE 5291A, 105–116 (2004).
    [CrossRef]
  9. A. Schmidt and A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D-vision GmbH,” Proc. SPIE 4660, 212–221 (2002).
    [CrossRef]
  10. G. Breit and E. Wigner, “Capture of slow neutrons,” Phys. Rev. 49, 519–543 (1936).
    [CrossRef]

2004 (2)

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

J. Konrad and P. Agniel, “Non-orthogonal subsampling and anti-alias filtering for multiscopic 3D displays,” Proc. SPIE 5291A, 105–116 (2004).
[CrossRef]

2003 (2)

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

J. Konrad and P. Agniel, “Artifact reduction in lenticular multiscopic 3D displays by means of anti-alias filtering,” Proc. SPIE 5006A, 336–347 (2003).
[CrossRef]

2002 (3)

L. Lipton and M. Feldman, “New autostereoscopic display technology: the synthaGram,” Proc. SPIE 4660, 229–235 (2002).
[CrossRef]

A. Schmidt and A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D-vision GmbH,” Proc. SPIE 4660, 212–221 (2002).
[CrossRef]

N. A. Dodgson, “Analysis of the viewing zone of multiview autostereoscopic displays,” Proc. SPIE 4660, 254–265 (2002).
[CrossRef]

1997 (1)

1996 (1)

C. V. Berkel, A. R. Franklin, and J. R. Mansell, “Design and applications of multiview 3D-LCD,” Proc. SID Euro-Display 96, 109–112 (1996).

1936 (1)

G. Breit and E. Wigner, “Capture of slow neutrons,” Phys. Rev. 49, 519–543 (1936).
[CrossRef]

Agniel, P.

J. Konrad and P. Agniel, “Non-orthogonal subsampling and anti-alias filtering for multiscopic 3D displays,” Proc. SPIE 5291A, 105–116 (2004).
[CrossRef]

J. Konrad and P. Agniel, “Artifact reduction in lenticular multiscopic 3D displays by means of anti-alias filtering,” Proc. SPIE 5006A, 336–347 (2003).
[CrossRef]

Ando, T.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

Arai, J.

Balin, J.

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Berkel, C. V.

C. V. Berkel, A. R. Franklin, and J. R. Mansell, “Design and applications of multiview 3D-LCD,” Proc. SID Euro-Display 96, 109–112 (1996).

Breit, G.

G. Breit and E. Wigner, “Capture of slow neutrons,” Phys. Rev. 49, 519–543 (1936).
[CrossRef]

Choi, H.

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Choi, Y.

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Dodgson, N. A.

N. A. Dodgson, “Analysis of the viewing zone of multiview autostereoscopic displays,” Proc. SPIE 4660, 254–265 (2002).
[CrossRef]

Feldman, M.

L. Lipton and M. Feldman, “New autostereoscopic display technology: the synthaGram,” Proc. SPIE 4660, 229–235 (2002).
[CrossRef]

Franklin, A. R.

C. V. Berkel, A. R. Franklin, and J. R. Mansell, “Design and applications of multiview 3D-LCD,” Proc. SID Euro-Display 96, 109–112 (1996).

Grasnick, A.

A. Schmidt and A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D-vision GmbH,” Proc. SPIE 4660, 212–221 (2002).
[CrossRef]

Hamagishi, G.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

Higashino, M.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

Hoshino, H.

Kim, S. K.

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Konrad, J.

J. Konrad and P. Agniel, “Non-orthogonal subsampling and anti-alias filtering for multiscopic 3D displays,” Proc. SPIE 5291A, 105–116 (2004).
[CrossRef]

J. Konrad and P. Agniel, “Artifact reduction in lenticular multiscopic 3D displays by means of anti-alias filtering,” Proc. SPIE 5006A, 336–347 (2003).
[CrossRef]

Lipton, L.

L. Lipton and M. Feldman, “New autostereoscopic display technology: the synthaGram,” Proc. SPIE 4660, 229–235 (2002).
[CrossRef]

Mansell, J. R.

C. V. Berkel, A. R. Franklin, and J. R. Mansell, “Design and applications of multiview 3D-LCD,” Proc. SID Euro-Display 96, 109–112 (1996).

Mashitani, K.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

Okano, F.

Saveljev, V. V.

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Schmidt, A.

A. Schmidt and A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D-vision GmbH,” Proc. SPIE 4660, 212–221 (2002).
[CrossRef]

Son, J.

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Takemoto, S.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

Wigner, E.

G. Breit and E. Wigner, “Capture of slow neutrons,” Phys. Rev. 49, 519–543 (1936).
[CrossRef]

Yuyama, I.

Appl. Opt. (1)

Opt. Eng. (1)

J. Son, V. V. Saveljev, Y. Choi, J. Balin, S. K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallaxbarrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[CrossRef]

Phys. Rev. (1)

G. Breit and E. Wigner, “Capture of slow neutrons,” Phys. Rev. 49, 519–543 (1936).
[CrossRef]

Proc. SID Euro-Display (1)

C. V. Berkel, A. R. Franklin, and J. R. Mansell, “Design and applications of multiview 3D-LCD,” Proc. SID Euro-Display 96, 109–112 (1996).

Proc. SPIE (6)

L. Lipton and M. Feldman, “New autostereoscopic display technology: the synthaGram,” Proc. SPIE 4660, 229–235 (2002).
[CrossRef]

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, and S. Takemoto, “Step barrier system multiview glassless 3D display,” Proc. SPIE 5291, 265–272 (2004).
[CrossRef]

N. A. Dodgson, “Analysis of the viewing zone of multiview autostereoscopic displays,” Proc. SPIE 4660, 254–265 (2002).
[CrossRef]

J. Konrad and P. Agniel, “Artifact reduction in lenticular multiscopic 3D displays by means of anti-alias filtering,” Proc. SPIE 5006A, 336–347 (2003).
[CrossRef]

J. Konrad and P. Agniel, “Non-orthogonal subsampling and anti-alias filtering for multiscopic 3D displays,” Proc. SPIE 5291A, 105–116 (2004).
[CrossRef]

A. Schmidt and A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D-vision GmbH,” Proc. SPIE 4660, 212–221 (2002).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Illustration of ray tracing in an LLA display with (a) showing the auto-stereoscopic effect and (b) showing the definition of variables used in the simulation.

Fig. 2.
Fig. 2.

Simulated intensity profile on the viewing plane for an LLA covered display. (a) All curves are contributed by the three RGB subpixels in the right pixel of a two-view system. Black curves are due to light passing through the each lens directly above the each subpixel. The other color curves include the light refracted through the adjacent lens that makes the cross-talk effect. (b) Total intensity from three RGB subpixels in the right (in red) and left (in blue) pixels of a two-view system. The dashed line is the simulation result obtained by using the commercial ray-tracing software ASAP. (c) All curves are contributed by the three RGB subpixels in the right pixel of a four-view system. (d) Total intensity from three RGB subpixels in the right (in red and mauve) and left (in blue and cyan) pixels of a four-view system. The dashed line is the simulation result obtained by the ASAP software package.

Equations (7)

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

X=G(ϕ,x)=Rsin(θ+ϕ)(LdRcos(θ+ϕ))tanϕ,
Rsin(θ+ϕ)=x+(d+Rcos(θ+ϕ))tanϕ,
cos(θ+ϕ)=[1/(1+tan2ϕ)][tanϕ(x+dtanϕ)/R+1/(1+tan2ϕ[(x+dtanϕ)/R]2],
ϕ=sin1[ngsinθ](θ+ϕ).
Is(X)=xsxs+W/3dxϕ0ϕMdϕcosϕδ(XG(ϕ,x)),
Iσ(X)=σ2W/3+xsσ2W/3+W/3dxϕ0ϕMdϕcosϕδ(XG(ϕ,x)),
δ(XG(ϕ,x))(Γ/π)[(XG(ϕ,x))2+Γ2],

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