Abstract

A three-dimensional simulation model calculating the optical intensity distribution for the entire screen of an autostereoscopic display at a given eye position was developed in this study. A parallax barrier array was used for the optical model and reverse ray tracing of light from the observer’s eye to the subpixels through the slits of the barrier was performed based on reverse geometrical optics. By investigating the optical behavior of the displayed image for the nine-view design condition for various viewing distances, we found the inhomogeneous crosstalk from the unwanted views and predicted segmented images which were comprised of multiple images from different views on the entire display screen. From the results, our simulation model shows good potentiality for predicting the displayed image on the entire display screen of autostereoscopic displays for various positions of the observer’s eye with sufficient calculation speed.

© 2015 Optical Society of America

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References

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  1. 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]
  2. 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).
  3. 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(10), 1033–1040 (2008).
    [Crossref]
  4. 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.
  5. 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]
  6. 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(7), 1339–1343 (2013).
    [Crossref]
  7. 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(23), 5591–5599 (2013).
    [Crossref] [PubMed]
  8. S.-M. Jung and I.-B. Kang, “Numerical simulation of the optical characteristics of autostereoscopic displays that have an aspherical lens array with a slanted angle,” Appl. Opt. 53(5), 868–877 (2014).
    [Crossref] [PubMed]
  9. C. Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999).
    [Crossref]
  10. G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
    [Crossref]
  11. E. Hecht, Optics (Addison-Wesley Publishing Co., 1987).
  12. A. Boev, A. Gotchev, and K. Egiazarian, “Crosstalk measurement methodology for auto-stereoscopic screen,” in Proceedings of IEEE 3D TV Conference (IEEE, 2007), pp. 1−4.

2014 (1)

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(7), 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(23), 5591–5599 (2013).
[Crossref] [PubMed]

2008 (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(10), 1033–1040 (2008).
[Crossref]

2000 (1)

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[Crossref]

1999 (1)

C. Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999).
[Crossref]

Berkel, C.

C. Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999).
[Crossref]

Boev, A.

A. Boev, A. Gotchev, and K. Egiazarian, “Crosstalk measurement methodology for auto-stereoscopic screen,” in Proceedings of IEEE 3D TV Conference (IEEE, 2007), pp. 1−4.

Egiazarian, K.

A. Boev, A. Gotchev, and K. Egiazarian, “Crosstalk measurement methodology for auto-stereoscopic screen,” in Proceedings of IEEE 3D TV Conference (IEEE, 2007), pp. 1−4.

Ezra, D.

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[Crossref]

Gotchev, A.

A. Boev, A. Gotchev, and K. Egiazarian, “Crosstalk measurement methodology for auto-stereoscopic screen,” in Proceedings of IEEE 3D TV Conference (IEEE, 2007), pp. 1−4.

Harrold, J.

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[Crossref]

Jacobs, A. M. S.

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[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]

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(10), 1033–1040 (2008).
[Crossref]

Jung, S.-M.

S.-M. Jung and I.-B. Kang, “Numerical simulation of the optical characteristics of autostereoscopic displays that have an aspherical lens array with a slanted angle,” Appl. Opt. 53(5), 868–877 (2014).
[Crossref] [PubMed]

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(23), 5591–5599 (2013).
[Crossref] [PubMed]

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(7), 1339–1343 (2013).
[Crossref]

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]

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(7), 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(7), 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]

Moseley, R. R.

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[Crossref]

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(10), 1033–1040 (2008).
[Crossref]

Woodgate, G. J.

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[Crossref]

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. (2)

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(7), 1339–1343 (2013).
[Crossref]

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(10), 1033–1040 (2008).
[Crossref]

Proc. SPIE (3)

C. Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999).
[Crossref]

G. J. Woodgate, J. Harrold, A. M. S. Jacobs, R. R. Moseley, and D. Ezra, “Flat panel autostereoscopic displays-characterisation and enhancement,” Proc. SPIE 3957, 153–164 (2000).
[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]

Other (5)

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

A. Boev, A. Gotchev, and K. Egiazarian, “Crosstalk measurement methodology for auto-stereoscopic screen,” in Proceedings of IEEE 3D TV Conference (IEEE, 2007), pp. 1−4.

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.

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).

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Figures (8)

Fig. 1
Fig. 1 Optical configuration of our 3D simulation model calculating the intensity distribution over the entire screen of the autostereoscopic display with the parallax barrier array. The coordinate systems, planes of interface, parallax barrier and the subpixel array are described. The wave vectors of the incident and the transmitted light rays are also depicted in the figure.
Fig. 2
Fig. 2 Illustrations of the calculation domains for (a) the parallax barrier array, (b) the subpixel array and (c) the display screen of the autostereoscopic display. The starting point (S) and crossing point (C) of each light ray are introduced. The slanted angle ϕs and horizontal barrier pitch Ph of the barrier array, and the subpixel sizes Px and Py in the x- and y-directions are defined. The rectangular grids on the display screen are also illustrated in the figure.
Fig. 3
Fig. 3 Simulation procedure for obtaining the intensity distribution over the entire display screen. After configuring all the numerical and physical parameters, reverse tracing for each light ray from the starting point to the observer’s eye is performed. All the intensities of the individual light rays are collected at each grid point corresponding to their position in relation to the crossing points on the display screen.
Fig. 4
Fig. 4 The design condition of nine-view autostereoscopic displays used in our simulation. The view map arrangement of subpixels assigned to all the view numbers is illustrated. We used the subpixel group of nine-view autostereoscopic displays having 4.5 subpixels and 2 lines in the horizontal and vertical directions. The intended view map angle of our configuration was designed to be φs = tan−1(1/6) = 9.462° in our configuration of the simulation.
Fig. 5
Fig. 5 Calculated intensity distribution on the display screen observed at the optimal viewing distance of ze = 2.5 m under various test images for which subpixels corresponding to a given view are white and the others are black. The observer’s eyes are located at the center front of the display, i. e., xe = 0 and ye = 0, where view 5 among the nine views can be observed over the entire display screen. Even though the observer’s eyes are located to see the full white image of view 5, the neighboring images for view numbers 4 and 6 are also observed for almost the whole display screen, and views for 3 and 7 are also found around the corners of the display screen.
Fig. 6
Fig. 6 Calculated intensity distribution over the display screen observed at various viewing distances from z = 0.5 m to 4.5 m with a step size of 0.5 m for a test image for which the subpixels correspond to view 5. The white regions in accordance with the viewing distance are found where the image for view 5 is displayed on the display screen.
Fig. 7
Fig. 7 Cross sectional intensity distribution on the display screen observed at various viewing distances from z = 2.1 m to 2.9 m with a step size of 0.1 m for various test images of the various views. The FWHM of each intensity distribution increases gradually for viewing distances between 2.1 m and 2.5 m and decreases again for viewing distances greater than 2.5 m.
Fig. 8
Fig. 8 Cross sectional 3D crosstalk distributions in the horizontal direction of the display screen under various viewing distances. The 3D crosstalk value around the center of the display screen is 100% for all the viewing distances and increases as the position on the display screen becomes far from the center of the display screen at viewing distances other than the optimal viewing distance.

Tables (1)

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Table 1 List of Parameters and Values Used in the Simulation

Equations (20)

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k i = 2π λ n i (sin θ i cos φ i x+sin θ i sin φ i y+cos θ i z),
k t = 2π λ n t (sin θ t cos φ t x+sin θ t sin φ t y+cos θ t z).
θ t = tan 1 [ ( x e x c ) 2 + ( y e y c ) 2 z e z c ],
φ t = tan 1 [ ( y e y c ) ( x e x c ) ].
θ i = sin 1 [( n t / n i ) sin θ t ],
φ i = φ t .
x s =tan θ i cos φ i ( z c z s )+ x c ,
y s =tan θ i sin φ i ( z c z s )+ y c ,
z s =g.
x=tan φ s y+ P h l+ x b .
x c =tan φ s y c + P h l+ x b ,
y c =Δym,
z c =0.
x s / P x + N x /21<i x s / P x + N x /2,
y s / P y + N y /21j< y s / P y + N y /2.
v ij = N t Mod[i+1(j+1)( P y / P x )tan ϕ s + x os , N h ]( N t N h ).
T = n t cos θ t n i cos θ i [ 2 n i cos θ i n i cos θ i + n t cos θ t ] 2 ,
T ll = n t cos θ t n i cos θ i [ 2 n i cos θ i n i cos θ t + n t cos θ i ] 2 .
I t ( θ t , φ t )= 1 2 ( T + T ll ) I i ( θ i , φ i ).
X i (x,y)= 1 L i (x,y) [ j=1 j= N t L j (x,y) L i (x,y) ]×100%

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