Abstract

We developed a 3D simulation model describing the optical phenomena on a slanted lenticular surface with aspherical lenses for autostereoscopic displays and analyzed the optical behavior of the multiview autostereoscopic display under actual design conditions by using a 3D simulation model. Optical characteristics, such as 3D crosstalk and 3D luminance differences, are obtained from the simulation of the light distribution for the multiview autostereoscopic displays with slated angles of 0.0°, 9.46°, 12.59°, and 14.04°. By investigating the effect of the conic constant of an aspherical lens surface on the 3D crosstalk and the 3D luminance differences for given several design conditions, we find the optimal values of the conic constant for slanted angles of 0.0° and 9.46° in order to minimize the 3D crosstalk and the 3D luminance difference. From these results, we think that our simulation model is very useful for designing the lens array to optimize the optical characteristics of autostereoscopic displays.

© 2014 Optical Society of America

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References

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  1. M. Fihn, “Predicting the future,” Inf. Disp. 27, 20–24 (2011).
  2. H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).
  3. H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).
  4. M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16, 1033–1040 (2008).
    [CrossRef]
  5. M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proc. of International Display Workshops (2011), pp. 1849–1851.
  6. S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
    [CrossRef]
  7. S.-M. Jung, S.-C. Lee, and K.-M. Lim, “Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays,” Curr. Appl. Phys. 13, 1339–1343 (2013).
    [CrossRef]
  8. S.-M. Jung and I.-B. Kang, “Three-dimensional modeling of light rays on the surface of a slanted lenticular array for autostereoscopic displays,” Appl. Opt. 52, 5591–5599 (2013).
    [CrossRef]
  9. P. D. Lin and C. Y. Tsai, “Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays,” J. Opt. Soc. Am. A 29, 174–178 (2012).
    [CrossRef]
  10. A. Miks and A. Novak, “Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays: comment,” J. Opt. Soc. Am. A 29, 1356–1357 (2012).
    [CrossRef]
  11. P. D. Lin and C.-Y. Tsai, “Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays: reply,” J. Opt. Soc. Am. A 29, 1358 (2012).
    [CrossRef]
  12. W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, 1992).
  13. E. Hecht, Optics (Addison-Wesley, 1987).
  14. E. Kreiszig, Advanced Engineering Mathematics (Wiley, 1999).

2013 (3)

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

S.-M. Jung, S.-C. Lee, and K.-M. Lim, “Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays,” Curr. Appl. Phys. 13, 1339–1343 (2013).
[CrossRef]

S.-M. Jung and I.-B. Kang, “Three-dimensional modeling of light rays on the surface of a slanted lenticular array for autostereoscopic displays,” Appl. Opt. 52, 5591–5599 (2013).
[CrossRef]

2012 (3)

2011 (1)

M. Fihn, “Predicting the future,” Inf. Disp. 27, 20–24 (2011).

2008 (3)

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16, 1033–1040 (2008).
[CrossRef]

Fihn, M.

M. Fihn, “Predicting the future,” Inf. Disp. 27, 20–24 (2011).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1987).

Hong, H.-K.

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

Im, H.-J.

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

Jang, J.-H.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

Järvenpää, T.

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16, 1033–1040 (2008).
[CrossRef]

Jung, S.-M.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

S.-M. Jung and I.-B. Kang, “Three-dimensional modeling of light rays on the surface of a slanted lenticular array for autostereoscopic displays,” Appl. Opt. 52, 5591–5599 (2013).
[CrossRef]

S.-M. Jung, S.-C. Lee, and K.-M. Lim, “Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays,” Curr. Appl. Phys. 13, 1339–1343 (2013).
[CrossRef]

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

Kang, H.-Y.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

Kang, I.-B.

Kang, J.-N.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

Kreiszig, E.

E. Kreiszig, Advanced Engineering Mathematics (Wiley, 1999).

Lee, B.-J.

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

Lee, H.-D.

M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proc. of International Display Workshops (2011), pp. 1849–1851.

Lee, K.-J.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

Lee, S.-C.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

S.-M. Jung, S.-C. Lee, and K.-M. Lim, “Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays,” Curr. Appl. Phys. 13, 1339–1343 (2013).
[CrossRef]

Lim, K.-M.

S.-M. Jung, S.-C. Lee, and K.-M. Lim, “Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays,” Curr. Appl. Phys. 13, 1339–1343 (2013).
[CrossRef]

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

Lin, P. D.

Miks, A.

Novak, A.

Park, M.-C.

M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proc. of International Display Workshops (2011), pp. 1849–1851.

Press, W. H.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, 1992).

Salmimaa, M.

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16, 1033–1040 (2008).
[CrossRef]

Shin, H.-H.

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

Son, J.-Y.

M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proc. of International Display Workshops (2011), pp. 1849–1851.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, 1992).

Tsai, C. Y.

Tsai, C.-Y.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, 1992).

Yeo, S.-D.

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

Appl. Opt. (1)

Curr. Appl. Phys. (1)

S.-M. Jung, S.-C. Lee, and K.-M. Lim, “Two-dimensional modeling of optical transmission on the surface of a lenticular array for autostereoscopic displays,” Curr. Appl. Phys. 13, 1339–1343 (2013).
[CrossRef]

Inf. Disp. (1)

M. Fihn, “Predicting the future,” Inf. Disp. 27, 20–24 (2011).

J. Opt. Soc. Am. A (3)

J. Soc. Inf. Disp. (1)

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16, 1033–1040 (2008).
[CrossRef]

Proc. SPIE (1)

S.-M. Jung, J.-H. Jang, H.-Y. Kang, K.-J. Lee, J.-N. Kang, S.-C. Lee, K.-M. Lim, and S.-D. Yeo, “Optical modeling of a lenticular array for autostereoscopic displays,” Proc. SPIE 8648, 864805 (2013).
[CrossRef]

SID Symp. Digest Tech. Papers (2)

H.-K. Hong, S.-M. Jung, B.-J. Lee, H.-J. Im, and H.-H. Shin, “Autostereoscopic 2D/3D switching display using electric-field-driven LC; lens (ELC Lens),” SID Symp. Digest Tech. Papers 39, 348–351 (2008).

H.-J. Im, S.-M. Jung, B.-J. Lee, H.-K. Hong, and H.-H. Shin, “Mobile 3D displays based on a LTPS 2.4” VGA LCD panel attached with lenticular lens sheets,” SID Symp. Digest Tech. Papers 39, 256–259 (2008).

Other (4)

M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proc. of International Display Workshops (2011), pp. 1849–1851.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, 1992).

E. Hecht, Optics (Addison-Wesley, 1987).

E. Kreiszig, Advanced Engineering Mathematics (Wiley, 1999).

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Figures (9)

Fig. 1.
Fig. 1.

General configuration of the optical calculation model. Coordinate system, interface and plane of incidence, wave vectors of the incident and transmitted light, the surface normal vector and their angles are also described.

Fig. 2.
Fig. 2.

Optical configuration of the slanted lenticular array. Lenticular surfaces are considered to be an aspherical surface for the mathematical formulation. The lenticular array and pixel array are located at z=0 and z=g, respectively, and the space between the lenticular surface and the subpixel array is filled with the medium of refractive index, ni. The structural parameters used for the simulation are illustrated.

Fig. 3.
Fig. 3.

Basic construction of the simulation structure given our design conditions for autostereoscopic displays. We used the (a) 4-, (b) 8-, (c) 12-, and (d) 16-view design conditions with a subpixel group comprised of 4 horizontal subpixels and one, two, three, and four vertical lines for a 4-, 8-, 12-, and 16-view display. The subpixel structure of TFT–LCDs for the base panel of the autostereoscopic displays is also illustrated in the figure.

Fig. 4.
Fig. 4.

Luminance distributions of light for each view collected within Δy/2yΔy/2 at the given observer position, x, on the detector plane under our design conditions of (a) 4-view, (b) 8-view, (c) 12-view, and (d) 16-view autostereoscopic displays for the conic constant of aspherical lenticular surface, k=0.

Fig. 5.
Fig. 5.

3D crosstalk distribution along the observer position at the optimal viewing position under our design conditions of (a) 4-view, (b) 8-view, (c) 12-view, and (d) 16-view autostereoscopic displays for the conic constant of the aspherical lenticular surface, k=0.

Fig. 6.
Fig. 6.

Cross sectional profile of lenticular surfaces for different conic constants of the aspherical lens for the slanted angle of 9.46° of the 8-views design condition, as an example. As shown in the figure, the lenticular surface is the same as the circular surface for k=0, and the surface profile has a rounded sawtooth shape having some linear range from the center to the edge for an individual lens as the conic constant decreases.

Fig. 7.
Fig. 7.

Variations of the luminance and 3D crosstalk distributions for the observer position on the detector plane at the optimal viewing distance of z=2.5m under the design condition for a 4-view autostereoscopic display in accordance with different conic constants of the aspherical lenticular surface. The conic constant, k, varies from 0 to 300, with a step size of 50 in our simulation.

Fig. 8.
Fig. 8.

Variation of the luminance and 3D crosstalk distributions on the detector plane, for the design condition of an 8-view autostereoscopic display, for different conic constants of the aspherical lenticular surface. The conic constant varies from 0 to 150, with a step size of 50 in this simulation.

Fig. 9.
Fig. 9.

3D crosstalk and 3D luminance difference as a function of the conic constant, for the (a) 4-view and (b) 8-view design conditions. The values are obtained from the simulation results in Figs. 7 and 8, which are the luminance and 3D crosstalk distributions for the 4- and 8-view design conditions for different conic constants of the lenticular surface.

Tables (1)

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Table 1. List of Parameters and Values Used in the Simulation

Equations (24)

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ki=2πλni(sinθicosϕi·x+sinθisinϕi·y+cosθi·z),
kt=2πλnt(sinθtcosϕt·x+sinθtsinϕt·y+cosθt·z),
n=sinθncosϕn·x+sinθnsinϕn·y+cosθn·z.
ki×n=kt×n.
ni(sinθisinϕicosθnsinθnsinϕncosθi)=nt(sinθtsinϕtcosθnsinθnsinϕncosθt),
ni(sinθicosϕicosθnsinθncosϕncosθi)=nt(sinθtcosϕtcosθnsinθncosϕncosθt),
nisinθisin(ϕiϕn)=ntsinθtsin(ϕtϕn).
n=f(x,y,z)|f(x,y,z)|.
f(x,y,z)=(xcosϕs+ysinϕsP·l)2+(1+k)(zd)2+2R(zd)=0.
n=xcosϕs+ysinϕsP·lk(zd)2+[k(zd)+R]2cosϕs·x+sinϕsxcosϕs+ysinϕsP·lk(zd)2+[k(zd)+R]2sinϕs·y+(1+k)(zd)+Rk(zd)2+[k(zd)+R]2·z,
θn=tan1(|xcosϕs+ysinϕsP·l(1+k)(zd)+R|).
xxssinθicosϕi=yyssinθisinϕi=zzscosθi=t.
xc=tc·sinθicosϕi+xs,
yc=tc·sinθisinϕi+ys,
zc=tc·cosθi+zs,
tc=[Aα+Bβ+kβ(BR)]+(α2+β2)R2(AβBα)2k[Aβ(BR)α]2α2+(1+k)β2.
zd=D,
xd=(zdzc)·tanθtcosϕt+xc,
yd=(zdzc)·tanθtsinϕt+yc.
T=ntcosθtnnicosθin[2nicosθinnicosθin+ntcosθtn]2,
T=ntcosθtnnicosθin[2nicosθinnicosθtn+ntcosθin]2.
It(θt,ϕt)=12(T+T)·Ii(θi,ϕi).
LD3D=LmaxLminLmax×100%.
X3D=1Li(x)[j=1j=NvLj(x)Li(x)]×100%.

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