Abstract

We present a foveated rendering method to accelerate the amplitude-only computer-generated hologram (AO-CGH) calculation in a holographic near-eye 3D display. For a given target image, we compute a high-resolution foveal region and a low-resolution peripheral region with dramatically reduced pixel numbers. Our technique significantly improves the computation speed of the AO-CGH while maintaining the perceived image quality in the fovea. Moreover, to accommodate the eye gaze angle change, we develop an algorithm to laterally shift the foveal image with negligible extra computational cost. Our technique holds great promise in advancing the holographic 3D display in real-time use.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

Corrections

16 January 2020: A typographical correction was made to Ref. 14.


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References

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2019 (6)

S. Kazempourradi, E. Ulusoy, and H. Urey, “Full-color computational holographic near-eye display,” J. Inf. Disp. 20(2), 45–59 (2019).
[Crossref]

W. Cui and L. Gao, “All-passive transformable optical mapping near-eye display,” Sci. Rep. 9(1), 6064 (2019).
[Crossref]

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

L. Wei and Y. Sakamoto, “Fast calculation method with foveated rendering for computer-generated holograms using an angle-changeable ray-tracing method,” Appl. Opt. 58(5), A258–A266 (2019).
[Crossref]

Y.-G. Ju and J.-H. Park, “Foveated computer-generated hologram and its progressive update using triangular mesh scene model for near-eye displays,” Opt. Express 27(17), 23725–23738 (2019).
[Crossref]

C. Chang, W. Cui, and L. Gao, “Holographic multiplane near-eye display based on amplitude-only wavefront modulation,” Opt. Express 27(21), 30960–30970 (2019).
[Crossref]

2018 (4)

2017 (4)

W. Cui and L. Gao, “Optical mapping near-eye three-dimensional display with correct focus cues,” Opt. Lett. 42(13), 2475–2478 (2017).
[Crossref]

J.-S. Chen, J. Jia, and D. Chu, “Minimizing the effects of unmodulated light and uneven intensity profile on the holographic images reconstructed by pixelated spatial light modulators,” Chin. Opt. Lett. 15(10), 100901 (2017).
[Crossref]

K. Akşit, W. Lopes, J. Kim, P. Shirley, and D. Luebke, “Near-eye varifocal augmented reality display using see-through screens,” ACM Trans. Graph. 36(6), 1–13 (2017).
[Crossref]

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 1–16 (2017).
[Crossref]

2016 (4)

T. Shimobaba, T. Kakue, and T. Ito, “Review of fast algorithms and hardware implementations on computer holography,” IEEE Trans. Ind. Inf. 12(4), 1611–1622 (2016).
[Crossref]

J. S. Hong, Y. M. Kim, S. H. Hong, C. S. Shin, and H. J. Kang, “Gaze contingent hologram synthesis for holographic head-mounted-display,” Proc. SPIE 9771, 97710K (2016).
[Crossref]

G. Li, D. Lee, Y. Jeong, J. Cho, and B. Lee, “Holographic display for see-through augmented reality using mirror-lens holographic optical element,” Opt. Lett. 41(11), 2486–2489 (2016).
[Crossref]

Q. Gao, J. Liu, J. Han, and X. Li, “Monocular 3D see-through head-mounted display via complex amplitude modulation,” Opt. Express 24(15), 17372–17383 (2016).
[Crossref]

2015 (3)

2014 (3)

2013 (2)

2012 (2)

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

B. Guenter, M. Finch, S. Drucker, D. Tan, and J. Snyder, “Foveated 3D graphics,” ACM Trans. Graph. 31(6), 1 (2012).
[Crossref]

2011 (1)

2009 (2)

2008 (1)

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence - accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref]

1999 (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Akeley, K.

S. Ravikumar, K. Akeley, and M. S. Banks, “Creating effective focus cues in multi-plane 3D displays,” Opt. Express 19(21), 20940–20952 (2011).
[Crossref]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence - accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref]

Aksit, K.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

K. Akşit, W. Lopes, J. Kim, P. Shirley, and D. Luebke, “Near-eye varifocal augmented reality display using see-through screens,” ACM Trans. Graph. 36(6), 1–13 (2017).
[Crossref]

Albert, R.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

Banks, M. S.

S. Ravikumar, K. Akeley, and M. S. Banks, “Creating effective focus cues in multi-plane 3D displays,” Opt. Express 19(21), 20940–20952 (2011).
[Crossref]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence - accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref]

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Boudaoud, B.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

Chang, C.

Chen, J. S.

Chen, J.-S.

Chen, K.

F. C. Huang, K. Chen, and G. Wetzstein, “The light field stereoscope: immersive computer graphics via factored near-eye light field displays with focus cues,” ACM Trans. Graph. 34(4), 1–12 (2015).
[Crossref]

Cho, J.

Chu, D.

Chu, D. P.

Cui, W.

Drucker, S.

B. Guenter, M. Finch, S. Drucker, D. Tan, and J. Snyder, “Foveated 3D graphics,” ACM Trans. Graph. 31(6), 1 (2012).
[Crossref]

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Finch, M.

B. Guenter, M. Finch, S. Drucker, D. Tan, and J. Snyder, “Foveated 3D graphics,” ACM Trans. Graph. 31(6), 1 (2012).
[Crossref]

Gao, L.

Gao, Q.

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Georgiou, A.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 1–16 (2017).
[Crossref]

Girshick, A. R.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence - accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

Greer, T.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

Guenter, B.

B. Guenter, M. Finch, S. Drucker, D. Tan, and J. Snyder, “Foveated 3D graphics,” ACM Trans. Graph. 31(6), 1 (2012).
[Crossref]

Hahn, J.

Han, J.

Hoffman, D. M.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence - accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 33 (2008).
[Crossref]

Hong, J. S.

J. S. Hong, Y. M. Kim, S. H. Hong, C. S. Shin, and H. J. Kang, “Gaze contingent hologram synthesis for holographic head-mounted-display,” Proc. SPIE 9771, 97710K (2016).
[Crossref]

Hong, S. H.

J. S. Hong, Y. M. Kim, S. H. Hong, C. S. Shin, and H. J. Kang, “Gaze contingent hologram synthesis for holographic head-mounted-display,” Proc. SPIE 9771, 97710K (2016).
[Crossref]

Hu, X.

Hua, H.

Huang, F. C.

F. C. Huang, K. Chen, and G. Wetzstein, “The light field stereoscope: immersive computer graphics via factored near-eye light field displays with focus cues,” ACM Trans. Graph. 34(4), 1–12 (2015).
[Crossref]

Huang, H.

Ichikawa, T.

Ito, T.

T. Shimobaba, T. Kakue, and T. Ito, “Review of fast algorithms and hardware implementations on computer holography,” IEEE Trans. Ind. Inf. 12(4), 1611–1622 (2016).
[Crossref]

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
[Crossref]

Javidi, B.

Jeong, Y.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

G. Li, D. Lee, Y. Jeong, J. Cho, and B. Lee, “Holographic display for see-through augmented reality using mirror-lens holographic optical element,” Opt. Lett. 41(11), 2486–2489 (2016).
[Crossref]

Ji, Y.-M.

Jia, J.

Ju, Y.-G.

Kakue, T.

T. Shimobaba, T. Kakue, and T. Ito, “Review of fast algorithms and hardware implementations on computer holography,” IEEE Trans. Ind. Inf. 12(4), 1611–1622 (2016).
[Crossref]

Kang, H. J.

J. S. Hong, Y. M. Kim, S. H. Hong, C. S. Shin, and H. J. Kang, “Gaze contingent hologram synthesis for holographic head-mounted-display,” Proc. SPIE 9771, 97710K (2016).
[Crossref]

Kazempourradi, S.

S. Kazempourradi, E. Ulusoy, and H. Urey, “Full-color computational holographic near-eye display,” J. Inf. Disp. 20(2), 45–59 (2019).
[Crossref]

Kim, H.

Kim, H.-J.

Kim, J.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

K. Akşit, W. Lopes, J. Kim, P. Shirley, and D. Luebke, “Near-eye varifocal augmented reality display using see-through screens,” ACM Trans. Graph. 36(6), 1–13 (2017).
[Crossref]

Kim, M.

Kim, S.-B.

Kim, S.-H.

Kim, Y. M.

J. S. Hong, Y. M. Kim, S. H. Hong, C. S. Shin, and H. J. Kang, “Gaze contingent hologram synthesis for holographic head-mounted-display,” Proc. SPIE 9771, 97710K (2016).
[Crossref]

Kollin, J. S.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 1–16 (2017).
[Crossref]

Lanman, D.

D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32(6), 1–10 (2013).
[Crossref]

Lee, B.

Lee, D.

Lee, Y.-H.

Li, B.

Li, G.

Li, X.

Li, Y.

Liu, J.

Liu, S.

Lopes, W.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

K. Akşit, W. Lopes, J. Kim, P. Shirley, and D. Luebke, “Near-eye varifocal augmented reality display using see-through screens,” ACM Trans. Graph. 36(6), 1–13 (2017).
[Crossref]

Luebke, D.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

K. Akşit, W. Lopes, J. Kim, P. Shirley, and D. Luebke, “Near-eye varifocal augmented reality display using see-through screens,” ACM Trans. Graph. 36(6), 1–13 (2017).
[Crossref]

D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32(6), 1–10 (2013).
[Crossref]

Maimone, A.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 1–16 (2017).
[Crossref]

Majercik, Z.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Masuda, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
[Crossref]

Matsushima, K.

McGuire, M.

J. Kim, Y. Jeong, M. Stengel, K. Akşit, R. Albert, B. Boudaoud, T. Greer, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: Dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 1–15 (2019).
[Crossref]

Moon, E.

Nakahara, S.

Nishitsuji, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Okada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Park, J.-H.

Ravikumar, S.

Roh, J.

Sakamoto, Y.

Sakurai, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Shimobaba, T.

T. Shimobaba, T. Kakue, and T. Ito, “Review of fast algorithms and hardware implementations on computer holography,” IEEE Trans. Ind. Inf. 12(4), 1611–1622 (2016).
[Crossref]

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Figures (11)

Fig. 1.
Fig. 1. Principle of foveated rendering in a holographic multiplane display. (a) Computation model for CGH generation. (b) Rendering of foveal and peripheral sub-images. (c) Calculation of the foveal image. (d) Calculation of the peripheral image.
Fig. 2.
Fig. 2. Simulation reconstructions of the foveated display. The foveal images were rendered with Rh=0.5 in (a), (c) and Rh=0.25 in (b), (d).
Fig. 3.
Fig. 3. Shifted foveated rendering. (a) Shifting of the high-resolution foveal image to accommodate the eye gaze angle change. (b) Calculation of the shifted foveal image using a linear additive phase.
Fig. 4.
Fig. 4. Performance of CGH computation. (a) Convergence of the iteration algorithm for band-limited initial random phase optimization. (b) Comparison of computation time.
Fig. 5.
Fig. 5. Optical setup. BS, beam splitter.
Fig. 6.
Fig. 6. Experimental results of displaying 2D test images. (a) (b) Reconstructions of AO-CGHs without using foveated rendering. (c) (d) Reconstructions of AO-CGHs using foveated rendering with Rh=0.5. (e) (f) Reconstructions of AO-CGHs using foveated rendering with Rh=0.25.
Fig. 7.
Fig. 7. Experimental results of displaying a multiplane object. The images were captured at a nominal focus of 400mm, 700mm and 1000mm, respectively.
Fig. 8.
Fig. 8. Experimental results of displaying a continuous 3D scene. (a) 2D projection image. (b) Depth map. (c)-(e) Captured images at a nominal focus of 400 mm, 700 mm, and 1000 mm.
Fig. 9.
Fig. 9. Experimental results of 2D test images with a shifted foveal region. (a) Reconstructions with an eye-gazing coordinate (−200Δ, 200Δ). (b) Reconstructions with an eye-gazing coordinate (0, 0). (c) Reconstructions with an eye-gazing coordinate (200Δ, −200Δ).
Fig. 10.
Fig. 10. Experimental results of displaying a continuous 3D scene with a shifted foveal region. The eye gazes at (−150Δ, −150Δ), (0, 0) and (150Δ, 150Δ) for the results shown in the first, second, and third row, respectively. The camera focuses at 400 mm, 700 mm, and 1000 mm for the results shown in the first, second, and third column, respectively.
Fig. 11.
Fig. 11. Analysis of the grating diffraction effect in calculation and reconstruction. (a) Removal of high order diffraction aliasing by using an additional correction loop for updating the wavefront at the filtered plane. (b) Example of uneven intensity distribution due to the diffraction effect.

Equations (6)

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M h ( x h m , y h m ) = I h ( x , y ) exp [ i φ h i n i t ( x , y ) ] exp { i k 2 ( z + d ) [ ( x h m x ) 2 + ( y h m y ) 2 ] } d x d y ,
M L ( x L m , y L m ) = I L ( x , y ) exp [ i φ L i n i t ( x , y ) ] exp { i k 2 ( z + d ) [ ( x L m x ) 2 + ( y L m y ) 2 ] } d x d y ,
M ( x m , y m ) = M h ( x m , y m ) + α M L ( x m , y m ) ,
H ( x h , y h ) = M ( x m , y m ) exp { i k 2 d [ ( x h x m ) 2 + ( y h y m ) 2 ] } d x m d y m .
M h ( x m , y m ) = M h ( x m , y m ) exp [ i 2 π ( x m θ x + y m θ y ) λ ( z + d ) ] ,
θ x = arctan [ x s h i f t ( z + d ) ] , θ y = arctan [ y s h i f t ( z + d ) ] .