Abstract

In this paper, we developed an optical model describing the behavior of light at the surface of a slanted lenticular array for autostereoscopic displays in three dimensions and simulated the optical characteristics of autostereoscopic displays using the Monte Carlo method under actual design conditions. The behavior of light is analyzed by light rays for selected inclination and azimuthal angles; numerical aberrations and conditions of total internal reflection for the lenticular array were found. The intensity and the three-dimensional crosstalk distributions calculated from our model coincide very well with those from conventional design software, and our model shows highly enhanced calculation speed that is 67 times faster than that of the conventional software. From the results, we think that the optical model is very useful for predicting the optical characteristics of autostereoscopic displays with enhanced calculation speed.

© 2013 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).
    [CrossRef]
  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).
    [CrossRef]
  4. S. E. Brigham and J. Schultz, “Directional backlight timing requirements for full resolution autostereoscopic displays,” SID Symp. Digest Tech. Papers 41, 226–229 (2010).
    [CrossRef]
  5. V. M. Bove and D. Smalley, “Holographic television at the MIT media lab,” Inf. Disp. 28, 18–21 (2012).
  6. M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proceedings of International Display Workshops (2011), pp. 1849–1851.
  7. 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]
  8. 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. App. Phys. (to be published), http://dx.doi.org/10.1016/j.cap.2013.04.009 .
  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 291356–1357 (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. S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).
  15. S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).
  16. 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]

2013

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]

2012

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

V. M. Bove and D. Smalley, “Holographic television at the MIT media lab,” Inf. Disp. 28, 18–21 (2012).

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]

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 291356–1357 (2012).
[CrossRef]

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]

2011

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

2010

S. E. Brigham and J. Schultz, “Directional backlight timing requirements for full resolution autostereoscopic displays,” SID Symp. Digest Tech. Papers 41, 226–229 (2010).
[CrossRef]

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).
[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).
[CrossRef]

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]

Bove, V. M.

V. M. Bove and D. Smalley, “Holographic television at the MIT media lab,” Inf. Disp. 28, 18–21 (2012).

Brigham, S. E.

S. E. Brigham and J. Schultz, “Directional backlight timing requirements for full resolution autostereoscopic displays,” SID Symp. Digest Tech. Papers 41, 226–229 (2010).
[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).
[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).
[CrossRef]

Hwang, Y.-K.

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

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).
[CrossRef]

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).
[CrossRef]

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]

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

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, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

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).
[CrossRef]

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).
[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. App. Phys. (to be published), http://dx.doi.org/10.1016/j.cap.2013.04.009 .

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, 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]

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

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).
[CrossRef]

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).
[CrossRef]

Lee, H.-D.

M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proceedings 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]

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

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, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

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. App. Phys. (to be published), http://dx.doi.org/10.1016/j.cap.2013.04.009 .

Lee, Y.-K.

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

Lim, K.-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, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

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. App. Phys. (to be published), http://dx.doi.org/10.1016/j.cap.2013.04.009 .

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 Proceedings 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]

Schultz, J.

S. E. Brigham and J. Schultz, “Directional backlight timing requirements for full resolution autostereoscopic displays,” SID Symp. Digest Tech. Papers 41, 226–229 (2010).
[CrossRef]

Shin, H.-H.

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).
[CrossRef]

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).
[CrossRef]

Smalley, D.

V. M. Bove and D. Smalley, “Holographic television at the MIT media lab,” Inf. Disp. 28, 18–21 (2012).

Son, J.-Y.

M.-C. Park, H.-D. Lee, and J.-Y. Son, “Interactive 3D simulator for autostereoscopic display systems,” in Proceedings 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]

Inf. Disp.

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

V. M. Bove and D. Smalley, “Holographic television at the MIT media lab,” Inf. Disp. 28, 18–21 (2012).

J. Opt. Soc. Am. A

J. Soc. Inf. Disp.

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

S.-M. Jung, K.-J. Lee, J.-N. Kang, S.-C. Lee, and K.-M. Lim, “New approach on calculating multi-view 3D crosstalk for autostereoscopic displays,” Proc. SPIE 8288, 828818 (2012).

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

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).
[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).
[CrossRef]

S. E. Brigham and J. Schultz, “Directional backlight timing requirements for full resolution autostereoscopic displays,” SID Symp. Digest Tech. Papers 41, 226–229 (2010).
[CrossRef]

S.-M. Jung, K.-J. Lee, J.-H. Jang, J.-N. Kang, Y.-K. Lee, S.-C. Lee, K.-M. Lim, and Y.-K. Hwang, “New characterization of 3D performance for multi-view autostereoscopic displays,” SID Symp. Digest Tech. Papers 43, 1155–1158 (2012).

Other

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

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. App. Phys. (to be published), http://dx.doi.org/10.1016/j.cap.2013.04.009 .

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

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

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Figures (7)

Fig. 1.
Fig. 1.

General configuration of the optical calculation model. The coordinate system, interface and plane of incidence, wave vectors of the incident and transmitted light, 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 a cylindrical surface for mathematical formulation. The structural parameters used for the simulation are illustrated.

Fig. 3.
Fig. 3.

Simulation procedure to obtain the light distribution of autostereoscopic displays. After configuring the number of views and the number of light rays and randomizing the starting positions and angles of the incident rays, the inclination and azimuthal angles of the transmitted light ray are obtained by the iterative bisection method to solve the set of nonlinear equations for the light rays.

Fig. 4.
Fig. 4.

Design condition of the nine-view autostereoscopic displays used in our simulation. The lenticular pitch, P , the horizontal and vertical subpixel pitches, P s x and P s y , and the slanted angle of lenticular array ϕ s are expressed in the figure. We used just nine subpixels for each view, and the subpixel corresponding to view 5 is located at the origin of the coordinate system for the light heading to the normal direction of the display panel.

Fig. 5.
Fig. 5.

Lines of spots on the detector plane at z = D with selected initial light rays of the condition (a) under varying ϕ 0 values, ranging from 0° to 360°, for given θ 0 = 5 ° , 10°, 15°, 20°, 30°, and 40° of the initial light ray and (b) under varying θ 0 values from 0° to 90° for given ϕ 0 values from 0° to 315° in 45° steps.

Fig. 6.
Fig. 6.

Positional distributions of the intensity for views 2, 4, 6, and 8 of the nine-view autostereoscopic display configuration under our design condition. The patterns have an angle similar to the slanted angle of the lenticular array with respect to the y axis and shifted from left to right with equal spacing of 65 mm as the view number increases by a factor of 2.

Fig. 7.
Fig. 7.

(a) Positional intensity profiles and (b) 3D crosstalk distribution profiles of light rays for each view at the optimal viewing distance for the autostereoscopic display under our design condition in the horizontal direction at the y = 0 plane. The results from our model and the conventional design software are plotted simultaneously as straight and dashed lines. The light profile of each single view has a FWHM of around 65 mm, and the peak-to-peak interval of a single view is around 295 mm, which is the same as our design condition.

Tables (1)

Tables Icon

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

Equations (23)

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

k i = 2 π λ n i ( sin θ i cos ϕ i · x + sin θ i sin ϕ i · y + cos θ i · z ) ,
k t = 2 π λ n t ( sin θ t cos ϕ t · x + sin θ t sin ϕ t · y + cos θ t · z ) ,
n = sin θ n cos ϕ n · x + sin θ n sin ϕ n · y + cos θ n · z .
k i × n = k t × n .
n i ( sin θ i sin ϕ i cos θ n sin θ n sin ϕ n cos θ i ) = n t ( sin θ t sin ϕ t cos θ n sin θ n sin ϕ n cos θ t ) ,
n i ( sin θ i cos ϕ i cos θ n sin θ n cos ϕ n cos θ i ) = n t ( sin θ t cos ϕ t cos θ n sin θ n cos ϕ n cos θ t ) ,
n i sin θ i sin ( ϕ i ϕ n ) = n t sin θ t sin ( ϕ t ϕ n ) .
n = f ( x , y , z ) | f ( x , y , z ) | .
f ( x , y , z ) = ( x cos ϕ s + y sin ϕ s P · l ) 2 + ( z + S ) 2 R 2 = 0 .
n = x cos ϕ s + y sin ϕ s P · l R cos ϕ s · x + x cos ϕ s + y sin ϕ s P · l R sin ϕ s · y + z + S R · z
θ n = tan 1 ( | x cos ϕ s + y sin ϕ s P · l z + S | ) .
x x s sin θ i cos ϕ i = y y s sin θ i sin ϕ i = z z s cos θ i = t .
x c = t c · sin θ i cos ϕ i + x s ,
y c = t c · sin θ i sin ϕ i + y s ,
z c = t c · cos θ i + z s ,
t c = A α B β + [ α 2 + β 2 ] R 2 ( A β B α ) 2 [ α 2 + β 2 ] .
z d = D ,
x d = ( z d z c ) · tan θ t cos ϕ t + x c ,
y d = ( z d z c ) · tan θ t sin ϕ t + y c .
T = n t cos θ tn n i cos θ in [ 2 n i cos θ in n i cos θ in + n t cos θ tn ] 2 ,
T = n t cos θ tn n i cos θ in [ 2 n i cos θ in n i cos θ tn + n t cos θ in ] 2 .
I t ( θ t , ϕ t ) = 1 2 ( T + T ) · I i ( θ i , ϕ i ) .
I i ( θ i , ϕ i ) = n i cos θ i n 0 cos θ 0 [ ( 2 n 0 cos θ 0 n 0 cos θ 0 + n i cos θ i ) 2 + ( 2 n 0 cos θ 0 n 0 cos θ i + n i cos θ 0 ) 2 ] I 0 ( θ 0 , ϕ 0 ) .

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