Abstract

The Cambridge autostereoscopic three-dimensional display is a time-multiplexed device that gives both stereo and movement parallax to the viewer without the need for any special glasses. This analysis derives the size and position of the fully illuminated, and hence useful, viewing zone for a Cambridge display. The viewing zone of such a display is shown to be completely determined by four parameters: the width of the screen, the optimal distance of the viewer from the screen, the width over which an image can be seen across the whole screen at this optimal distance, and the number of views. A display's viewing zone can thus be completely described without reference to the internal implementation of the device. An equation that describes what the eye sees from any position in front of the display is derived. The equations derived can be used in both the analysis and design of this type of time-multiplexed autostereoscopic display.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Okosi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).
  2. H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
    [CrossRef]
  3. J. Hamasaki, M. Okada, S. Utsunomiya, “Autostereo-scopic 3D TV on a CRT,” SID Dig. 22, 844–847 (1991).
  4. P. St-Hilaire, S. A. Benton, M. Lucente, P. M. Hubel, “Color images with the MIT holographic video display,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE1667, 73–84 (1992).
    [CrossRef]
  5. M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” Comput. Graph. Ann. Conf. Ser.387–394 (1995).
  6. G. R. Little, S. C. Gustafson, V. E. Nikolaou, “Multiperspective autostereoscopic display,” in Cockpit Displays, D. G. Hopper, ed., Proc. SPIE2219, 388–394 (1994).
    [CrossRef]
  7. A. R. L. Travis, “Autostereoscopic 3-D display,” Appl. Opt. 29, 4341–4342 (1990).
    [CrossRef] [PubMed]
  8. A. R. L. Travis, S. R. Lang, “The design and evaluation of a CRT-based autostereoscopic 3-D display,” Proc. Soc. Inf. Disp. 32, 279–283 (1991).
  9. S. R. Lang, A. R. L. Travis, O. M. Castle, J. R. Moore, “A 2nd generation autostereoscopic 3-D display,” in Seventh Eurographics Workshop on Graphics Hardware, P. F. Lister, ed., Tech. Rep. EG92 HW (Eurographics, Oxford, U.K., 1992), pp. 53–63.
  10. J. R. Moore, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institution of Electrical Engineers, London, 1992), pp. 4/1–4/16.
  11. A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).
  12. L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, New York, 1982).

1995 (2)

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” Comput. Graph. Ann. Conf. Ser.387–394 (1995).

A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).

1991 (2)

A. R. L. Travis, S. R. Lang, “The design and evaluation of a CRT-based autostereoscopic 3-D display,” Proc. Soc. Inf. Disp. 32, 279–283 (1991).

J. Hamasaki, M. Okada, S. Utsunomiya, “Autostereo-scopic 3D TV on a CRT,” SID Dig. 22, 844–847 (1991).

1990 (1)

Benton, S. A.

P. St-Hilaire, S. A. Benton, M. Lucente, P. M. Hubel, “Color images with the MIT holographic video display,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE1667, 73–84 (1992).
[CrossRef]

Castle, O. M.

J. R. Moore, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institution of Electrical Engineers, London, 1992), pp. 4/1–4/16.

S. R. Lang, A. R. L. Travis, O. M. Castle, J. R. Moore, “A 2nd generation autostereoscopic 3-D display,” in Seventh Eurographics Workshop on Graphics Hardware, P. F. Lister, ed., Tech. Rep. EG92 HW (Eurographics, Oxford, U.K., 1992), pp. 53–63.

Chiba, K.

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Dodgson, N. A.

A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).

Galyean, T. A.

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” Comput. Graph. Ann. Conf. Ser.387–394 (1995).

Gustafson, S. C.

G. R. Little, S. C. Gustafson, V. E. Nikolaou, “Multiperspective autostereoscopic display,” in Cockpit Displays, D. G. Hopper, ed., Proc. SPIE2219, 388–394 (1994).
[CrossRef]

Hamasaki, J.

J. Hamasaki, M. Okada, S. Utsunomiya, “Autostereo-scopic 3D TV on a CRT,” SID Dig. 22, 844–847 (1991).

Hubel, P. M.

P. St-Hilaire, S. A. Benton, M. Lucente, P. M. Hubel, “Color images with the MIT holographic video display,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE1667, 73–84 (1992).
[CrossRef]

Isono, H.

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Kanayama, H.

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Lang, S. R.

A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).

A. R. L. Travis, S. R. Lang, “The design and evaluation of a CRT-based autostereoscopic 3-D display,” Proc. Soc. Inf. Disp. 32, 279–283 (1991).

J. R. Moore, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institution of Electrical Engineers, London, 1992), pp. 4/1–4/16.

S. R. Lang, A. R. L. Travis, O. M. Castle, J. R. Moore, “A 2nd generation autostereoscopic 3-D display,” in Seventh Eurographics Workshop on Graphics Hardware, P. F. Lister, ed., Tech. Rep. EG92 HW (Eurographics, Oxford, U.K., 1992), pp. 53–63.

Lipton, L.

L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, New York, 1982).

Little, G. R.

G. R. Little, S. C. Gustafson, V. E. Nikolaou, “Multiperspective autostereoscopic display,” in Cockpit Displays, D. G. Hopper, ed., Proc. SPIE2219, 388–394 (1994).
[CrossRef]

Lucente, M.

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” Comput. Graph. Ann. Conf. Ser.387–394 (1995).

P. St-Hilaire, S. A. Benton, M. Lucente, P. M. Hubel, “Color images with the MIT holographic video display,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE1667, 73–84 (1992).
[CrossRef]

Moore, J. R.

A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).

J. R. Moore, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institution of Electrical Engineers, London, 1992), pp. 4/1–4/16.

S. R. Lang, A. R. L. Travis, O. M. Castle, J. R. Moore, “A 2nd generation autostereoscopic 3-D display,” in Seventh Eurographics Workshop on Graphics Hardware, P. F. Lister, ed., Tech. Rep. EG92 HW (Eurographics, Oxford, U.K., 1992), pp. 53–63.

Nikolaou, V. E.

G. R. Little, S. C. Gustafson, V. E. Nikolaou, “Multiperspective autostereoscopic display,” in Cockpit Displays, D. G. Hopper, ed., Proc. SPIE2219, 388–394 (1994).
[CrossRef]

Okada, M.

J. Hamasaki, M. Okada, S. Utsunomiya, “Autostereo-scopic 3D TV on a CRT,” SID Dig. 22, 844–847 (1991).

Okosi, T.

T. Okosi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

St-Hilaire, P.

P. St-Hilaire, S. A. Benton, M. Lucente, P. M. Hubel, “Color images with the MIT holographic video display,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE1667, 73–84 (1992).
[CrossRef]

Takemori, D.

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Travis, A. R. L.

A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).

A. R. L. Travis, S. R. Lang, “The design and evaluation of a CRT-based autostereoscopic 3-D display,” Proc. Soc. Inf. Disp. 32, 279–283 (1991).

A. R. L. Travis, “Autostereoscopic 3-D display,” Appl. Opt. 29, 4341–4342 (1990).
[CrossRef] [PubMed]

J. R. Moore, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institution of Electrical Engineers, London, 1992), pp. 4/1–4/16.

S. R. Lang, A. R. L. Travis, O. M. Castle, J. R. Moore, “A 2nd generation autostereoscopic 3-D display,” in Seventh Eurographics Workshop on Graphics Hardware, P. F. Lister, ed., Tech. Rep. EG92 HW (Eurographics, Oxford, U.K., 1992), pp. 53–63.

Utsunomiya, S.

J. Hamasaki, M. Okada, S. Utsunomiya, “Autostereo-scopic 3D TV on a CRT,” SID Dig. 22, 844–847 (1991).

Yamada, C.

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Yasuda, M.

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Appl. Opt. (1)

Comput. Graph. Ann. Conf. Ser. (1)

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” Comput. Graph. Ann. Conf. Ser.387–394 (1995).

Proc. Soc. Inf. Disp. (1)

A. R. L. Travis, S. R. Lang, “The design and evaluation of a CRT-based autostereoscopic 3-D display,” Proc. Soc. Inf. Disp. 32, 279–283 (1991).

SID Dig. (1)

J. Hamasaki, M. Okada, S. Utsunomiya, “Autostereo-scopic 3D TV on a CRT,” SID Dig. 22, 844–847 (1991).

Soc. Inf. Disp. Dig. (1)

A. R. L. Travis, S. R. Lang, J. R. Moore, N. A. Dodgson, “Time-manipulated three-dimensional video,” Soc. Inf. Disp. Dig. 26, 851–854 (1995).

Other (7)

L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, New York, 1982).

P. St-Hilaire, S. A. Benton, M. Lucente, P. M. Hubel, “Color images with the MIT holographic video display,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE1667, 73–84 (1992).
[CrossRef]

T. Okosi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

H. Isono, M. Yasuda, D. Takemori, H. Kanayama, C. Yamada, K. Chiba, “50-inch autostereoscopic full-color 3-D TV display system,” in Stereoscopic Displays and Applications III, S. S. Fisher, J. O. Merritt, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

S. R. Lang, A. R. L. Travis, O. M. Castle, J. R. Moore, “A 2nd generation autostereoscopic 3-D display,” in Seventh Eurographics Workshop on Graphics Hardware, P. F. Lister, ed., Tech. Rep. EG92 HW (Eurographics, Oxford, U.K., 1992), pp. 53–63.

J. R. Moore, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institution of Electrical Engineers, London, 1992), pp. 4/1–4/16.

G. R. Little, S. C. Gustafson, V. E. Nikolaou, “Multiperspective autostereoscopic display,” in Cockpit Displays, D. G. Hopper, ed., Proc. SPIE2219, 388–394 (1994).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

(a) In viewing a real-world scene, there are an infinite number of possible images of the scene. (b) It is possible to divide this viewing space conceptually into a finite number of windows, in each of which only a single image is visible, while still retaining both stereo and movement parallax cues. (c) An autostereoscopic three-dimensional display uses this idea to provide a three-dimensional image, using a finite number of views taken from distinct view points.

Fig. 2.
Fig. 2.

(a) Conceptual design of a Cambridge autostereoscopic display. (b) Currently practicable design in operation at Cambridge. LCD, liquid-crystal display.

Fig. 3.
Fig. 3.

Basic parameters of a Cambridge autostereoscopic display.

Fig. 4.
Fig. 4.

Image of a pupil at (z, x) is (α(z), β(z, x)). At distance d b behind the lens, the point (z, x) images onto the area from k (z, x) to k +(z, x).

Fig. 5.
Fig. 5.

Three potential configurations of a Cambridge autostereoscopic display. In each the thick vertical bar at the left represents the display's screen, of width w l , and the thin vertical line is w o wide at a distance d o from the screen. (a) Screen wider than viewing zone, (b) screen and viewing zone the same width, (c) viewing zone wider than the screen. Each figure shows the umbra (u), penumbra (p), and fully illuminated zone (f).

Fig. 6.
Fig. 6.

Mosaic diagram for the current eight-view autostereo display (see Fig. 8 for the key). Parameters are w l = 200 mm, w o = 280 mm, d o = 1 m, and N = 8.

Fig. 7.
Fig. 7.

Mosaic diagram for a proposed 15-view autostereo display (see Fig. 8 for the key). Parameters are w l = 500 mm, w o = 315 mm, d o = 1.2 m, and N = 15.

Fig. 8.
Fig. 8.

Key for interpreting the mosaic diagrams in Figs. 6 and 7. Each mosaic diagram contains a grid of these elements. Note that the center of the display's screen is at (z, x) = (0, 0) and that the axes on the mosaic diagrams do not meet at this origin.

Fig. 9.
Fig. 9.

Photographs from the current display's screen. (a) Test pattern where each view is filled with digits showing the number of that view. This clearly shows the boundaries between views. Views 4, 3, and 2 illuminate different parts of the screen from this position. (b) Same location as (a), but with a computer-generated image of a room. The positions of the boundaries between the views are shown with arrows. The only noticeable artifacts of these boundaries are the slight discontinuities at the left edge of the table (above the left arrow) and at the back of the chair (above the right arrow). This demonstrates that, at least when the head is kept still, the discontinuities produce little degradation in the perceived image.

Equations (14)

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

1 f = 1 d o + 1 d b ,
w b d b = w o d o .
α ( z ) = 1 ( 1 / z ) ( 1 / f ) ,
β( z , x ) = x 1 ( z / f ) .
k + ( z , x ) = d b [ x z + w 1 2 ( 1 z 1 d o ) ] ,
k o ( z , x ) = d b ( x z ) ,
k ( z , x ) = d b [ x z w l 2 ( 1 z 1 d o ) ] ,
B ( p , z , x ) = [ b ( p , z , x ) ] ,
b ( p , z , x ) = N { 1 2 + d o w o [ x z + ( p 1 2 ) w l ( 1 z 1 d o ) ] } ,
x = ± [ ( 1 z d o ) w l 2 + ( z d o ) w o 2 ] ,
x = ± [ ( 1 z d o ) w l 2 ( z d o ) w o 2 ] .
z max = d o N s e w o .
z max = d o w l s e w l w o ,
z min = d o w l + s e w l + w o .

Metrics