Abstract

A design method for the wedge projection display system based on the ray retracing method is proposed. To analyze the principle of image formation on the inclined surface of the wedge-shaped waveguide, the bundle of rays is retraced from an imaging point on the inclined surface to the aperture of the waveguide. In consequence of ray retracing, we obtain the incident conditions of the ray, such as the position and the angle at the aperture, which provide clues for image formation. To illuminate the image formation, the concept of the equivalent imaging point is proposed, which is the intersection where the incident rays are extended over the space regardless of the refraction and reflection in the waveguide. Since the initial value of the rays arriving at the equivalent imaging point corresponds to that of the rays converging into the imaging point on the inclined surface, the image formation can be visualized by calculating the equivalent imaging point over the entire inclined surface. Then, we can find image characteristics, such as their size and position, and their degree of blur—by analyzing the distribution of the equivalent imaging point—and design the optimized wedge projection system by attaching the prism structure at the aperture. The simulation results show the feasibility of the ray retracing analysis and characterize the numerical relation between the waveguide parameters and the aperture structure for on-axis configuration. The experimental results verify the designed system based on the proposed method.

© 2013 Optical Society of America

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References

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  1. E. Stupp and M. Brennesholtz, Projection Display (Wiley, 1999).
  2. Y. H. Ju, J.-H. Park, J. H. Lee, J.-Y. Lee, K.-B. Nahm, and J.-H. Ko, “Study on the simulation model for the optimization of optical structures of edge-lit backlight for LCD applications,” J. Opt. Soc. Korea 12, 25–30 (2008).
    [CrossRef]
  3. A. Travis, F. Payne, J. Zhong, and J. Moore, “Flat panel display using projection within a wedge-shaped waveguide,” in Proceedings of 20th International Disaster and Risk Conference, Palm Beach, Florida (2000), pp. 292–295.
  4. W. Smith, Modern Optical Engineering (McGraw-Hill, 1966).
  5. J. J. Zhong, A. Travis, and F. Payne, “The anti-reflection coating for a wedge flat panel projection display,” in Proceedings of the Society for Information Display, San Jose, California, (2001), pp. 914–917.
  6. J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
    [CrossRef]
  7. A. Travis and J. Zhong, “Linearity in flat panel wedge projection,” in Proceedings of the Society for Information Display, Baltimore, Maryland (2003), pp. 716–719.
  8. A. Travis, C. MØller, and C. M. G. Lee, “Flat projection for 3-D,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 539–549.
  9. M. Large, T. Large, and A. Travis, “Parallel optics in waveguide displays: a flat panel autostereoscopic display,” J. Disp. Technol. 6, 431–437 (2010).
    [CrossRef]
  10. A. Travis, T. Large, N. Emerton, and S. Bathiche, “Wedge optics in flat panel displays,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1–16.
  11. A. Travis, “The focal surface of a wedge projection display,” in Proceedings of the Society for Information Display (2005), Vol. 36, pp. 896–897.
  12. Y. K. Cheng, S. N. Chung, and J. L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357–2362 (2007).
    [CrossRef]
  13. K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).
  14. Y. K. Cheng, S. N. Chung, and J. L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge-plate displays,” J. Soc. Inf. Disp. 14, 813–818 (2006).
    [CrossRef]
  15. More information on MATLAB can be found at http://www.mathworks.com .

2010 (1)

M. Large, T. Large, and A. Travis, “Parallel optics in waveguide displays: a flat panel autostereoscopic display,” J. Disp. Technol. 6, 431–437 (2010).
[CrossRef]

2009 (1)

K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).

2008 (1)

2007 (1)

2006 (1)

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge-plate displays,” J. Soc. Inf. Disp. 14, 813–818 (2006).
[CrossRef]

2002 (1)

J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
[CrossRef]

Bathiche, S.

A. Travis, T. Large, N. Emerton, and S. Bathiche, “Wedge optics in flat panel displays,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1–16.

Brennesholtz, M.

E. Stupp and M. Brennesholtz, Projection Display (Wiley, 1999).

Chen, K. W.

K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).

Cheng, Y. K.

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357–2362 (2007).
[CrossRef]

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge-plate displays,” J. Soc. Inf. Disp. 14, 813–818 (2006).
[CrossRef]

Chern, J. L.

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357–2362 (2007).
[CrossRef]

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge-plate displays,” J. Soc. Inf. Disp. 14, 813–818 (2006).
[CrossRef]

Chung, S. N.

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357–2362 (2007).
[CrossRef]

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge-plate displays,” J. Soc. Inf. Disp. 14, 813–818 (2006).
[CrossRef]

Emerton, N.

A. Travis, T. Large, N. Emerton, and S. Bathiche, “Wedge optics in flat panel displays,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1–16.

Ju, Y. H.

Ko, J.-H.

Large, M.

M. Large, T. Large, and A. Travis, “Parallel optics in waveguide displays: a flat panel autostereoscopic display,” J. Disp. Technol. 6, 431–437 (2010).
[CrossRef]

Large, T.

M. Large, T. Large, and A. Travis, “Parallel optics in waveguide displays: a flat panel autostereoscopic display,” J. Disp. Technol. 6, 431–437 (2010).
[CrossRef]

A. Travis, T. Large, N. Emerton, and S. Bathiche, “Wedge optics in flat panel displays,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1–16.

Lee, C. M. G.

A. Travis, C. MØller, and C. M. G. Lee, “Flat projection for 3-D,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 539–549.

Lee, J. H.

Lee, J.-Y.

MØller, C.

A. Travis, C. MØller, and C. M. G. Lee, “Flat projection for 3-D,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 539–549.

Moore, J.

A. Travis, F. Payne, J. Zhong, and J. Moore, “Flat panel display using projection within a wedge-shaped waveguide,” in Proceedings of 20th International Disaster and Risk Conference, Palm Beach, Florida (2000), pp. 292–295.

Moore, J. R.

J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
[CrossRef]

Nahm, K.-B.

Park, J.-H.

Payne, F.

J. J. Zhong, A. Travis, and F. Payne, “The anti-reflection coating for a wedge flat panel projection display,” in Proceedings of the Society for Information Display, San Jose, California, (2001), pp. 914–917.

A. Travis, F. Payne, J. Zhong, and J. Moore, “Flat panel display using projection within a wedge-shaped waveguide,” in Proceedings of 20th International Disaster and Risk Conference, Palm Beach, Florida (2000), pp. 292–295.

Payneb, F.

J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
[CrossRef]

Smith, W.

W. Smith, Modern Optical Engineering (McGraw-Hill, 1966).

Stupp, E.

E. Stupp and M. Brennesholtz, Projection Display (Wiley, 1999).

Tan, S. Y.

K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).

Travis, A.

M. Large, T. Large, and A. Travis, “Parallel optics in waveguide displays: a flat panel autostereoscopic display,” J. Disp. Technol. 6, 431–437 (2010).
[CrossRef]

K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).

J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
[CrossRef]

J. J. Zhong, A. Travis, and F. Payne, “The anti-reflection coating for a wedge flat panel projection display,” in Proceedings of the Society for Information Display, San Jose, California, (2001), pp. 914–917.

A. Travis, “The focal surface of a wedge projection display,” in Proceedings of the Society for Information Display (2005), Vol. 36, pp. 896–897.

A. Travis, C. MØller, and C. M. G. Lee, “Flat projection for 3-D,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 539–549.

A. Travis, T. Large, N. Emerton, and S. Bathiche, “Wedge optics in flat panel displays,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1–16.

A. Travis, F. Payne, J. Zhong, and J. Moore, “Flat panel display using projection within a wedge-shaped waveguide,” in Proceedings of 20th International Disaster and Risk Conference, Palm Beach, Florida (2000), pp. 292–295.

A. Travis and J. Zhong, “Linearity in flat panel wedge projection,” in Proceedings of the Society for Information Display, Baltimore, Maryland (2003), pp. 716–719.

Wilkinson, T.

K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).

Zhong, J.

A. Travis and J. Zhong, “Linearity in flat panel wedge projection,” in Proceedings of the Society for Information Display, Baltimore, Maryland (2003), pp. 716–719.

A. Travis, F. Payne, J. Zhong, and J. Moore, “Flat panel display using projection within a wedge-shaped waveguide,” in Proceedings of 20th International Disaster and Risk Conference, Palm Beach, Florida (2000), pp. 292–295.

Zhong, J. J.

J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
[CrossRef]

J. J. Zhong, A. Travis, and F. Payne, “The anti-reflection coating for a wedge flat panel projection display,” in Proceedings of the Society for Information Display, San Jose, California, (2001), pp. 914–917.

J. Disp. Technol. (1)

M. Large, T. Large, and A. Travis, “Parallel optics in waveguide displays: a flat panel autostereoscopic display,” J. Disp. Technol. 6, 431–437 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (1)

J. Soc. Inf. Disp. (1)

Y. K. Cheng, S. N. Chung, and J. L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge-plate displays,” J. Soc. Inf. Disp. 14, 813–818 (2006).
[CrossRef]

Proc. SPIE (2)

K. W. Chen, A. Travis, S. Y. Tan, and T. Wilkinson, “Parabolic transition region curve for a wedge projection display,” Proc. SPIE 7232, 1–11 (2009).

J. J. Zhong, A. Travis, F. Payneb, and J. R. Moore, “Flat projection display panel and its near critical angle AR coating,” Proc. SPIE 4657, 67–76 (2002).
[CrossRef]

Other (9)

A. Travis and J. Zhong, “Linearity in flat panel wedge projection,” in Proceedings of the Society for Information Display, Baltimore, Maryland (2003), pp. 716–719.

A. Travis, C. MØller, and C. M. G. Lee, “Flat projection for 3-D,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 539–549.

A. Travis, F. Payne, J. Zhong, and J. Moore, “Flat panel display using projection within a wedge-shaped waveguide,” in Proceedings of 20th International Disaster and Risk Conference, Palm Beach, Florida (2000), pp. 292–295.

W. Smith, Modern Optical Engineering (McGraw-Hill, 1966).

J. J. Zhong, A. Travis, and F. Payne, “The anti-reflection coating for a wedge flat panel projection display,” in Proceedings of the Society for Information Display, San Jose, California, (2001), pp. 914–917.

A. Travis, T. Large, N. Emerton, and S. Bathiche, “Wedge optics in flat panel displays,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1–16.

A. Travis, “The focal surface of a wedge projection display,” in Proceedings of the Society for Information Display (2005), Vol. 36, pp. 896–897.

E. Stupp and M. Brennesholtz, Projection Display (Wiley, 1999).

More information on MATLAB can be found at http://www.mathworks.com .

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Figures (15)

Fig. 1.
Fig. 1.

Angle variation in wedge-shaped waveguide.

Fig. 2.
Fig. 2.

Difference in initial information of bundle of ray from an imaging point.

Fig. 3.
Fig. 3.

Ray retracing scheme: (a) reflection at interface and (b) arrival at aperture.

Fig. 4.
Fig. 4.

Concept of equivalent imaging point (a) without refraction and (b) with refraction at aperture.

Fig. 5.
Fig. 5.

Ray retracing simulation algorithms: (a) ray retracing and (b) equivalent imaging point.

Fig. 6.
Fig. 6.

Distribution of equivalent imaging point (a) without refraction and (b) with refraction.

Fig. 7.
Fig. 7.

Discontinuity inspection result.

Fig. 8.
Fig. 8.

Discontinuity inspection simulation: (a) trajectory for two cases, (b) without refraction, and (c) with refraction.

Fig. 9.
Fig. 9.

Concept of prism structure at aperture.

Fig. 10.
Fig. 10.

On-axis simulation with prism aperture structure: (a) 40°, (b) 50°, and (c) 60°.

Fig. 11.
Fig. 11.

Relation between taper angle and parallel prism angle: (a) when reflection number varies, (b) scheme of relation of both angles, and (c) when refractive index varies.

Fig. 12.
Fig. 12.

Scheme of designed wedge projection display system.

Fig. 13.
Fig. 13.

Experimental setup with light source, SLM, lens, and wedge-shaped waveguide.

Fig. 14.
Fig. 14.

Experimental result with calculated equivalent imaging plane: (a) reflection condition and (b) blurred image at the curved equivalent imaging plane.

Fig. 15.
Fig. 15.

Experimental result from optimized wedge projection display system: (a) position of image on inclined surface, (b) image with dark zone, and (c) image free of dark zone.

Tables (2)

Tables Icon

Table 1. Specifications of Wedge-Shaped Waveguide and Condition of Ray Retracing Simulation

Tables Icon

Table 2. Specifications of Wedge-Shaped Waveguide Used in Experiment

Equations (8)

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θc<θiπ/2ϕ,
P0=(hyi)cotθi,
y0=yiP0tanϕ.
When n is odd{Pn=(hyn1)/{tan(θi(n1)ϕ)tanϕ}yn=yn1Pntanϕ,
when n is even{Pn=(hyn1)cot(θinϕ)yn=yn1Pntanϕ.
When n is odd{θe_odd=(θi(n1)ϕ)Podd=|yodd|cotϕye_odd=Poddtan|θe_odd|,
when n is even{θe_even=θinϕPeven=|yeven|cotϕye_even=h(|yeven|+Peventanθeeven),
θp=(1+N)θt+Yn,

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