Abstract

Computer generated holography is an extremely demanding and complex task when it comes to providing realistic reconstructions with full parallax, occlusion, and shadowing. We present an algorithm designed for data-parallel computing on modern graphics processing units to alleviate the computational burden. We apply Gaussian interpolation to create a continuous surface representation from discrete input object points. The algorithm maintains a potential occluder list for each individual hologram plane sample to keep the number of visibility tests to a minimum. We experimented with two approximations that simplify and accelerate occlusion computation. It is observed that letting several neighboring hologram plane samples share visibility information on object points leads to significantly faster computation without causing noticeable artifacts in the reconstructed images. Computing a reduced sample set via nonuniform sampling is also found to be an effective acceleration technique.

© 2009 Optical Society of America

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References

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  1. C. Petz and M. Magnor, “Fast hologram synthesis for 3D geometry models using graphics hardware,” Proc. SPIE 5005, 266-275 (2003).
    [CrossRef]
  2. T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
    [CrossRef]
  3. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14, 603-608 (2006).
    [CrossRef] [PubMed]
  4. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 7636-7641 (2006).
    [CrossRef] [PubMed]
  5. R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48, 4246-4255 (2009).
    [CrossRef] [PubMed]
  6. H. Kang, T. Yamaguchi, H. Yoshikawa, S.-C. Kim, and E.-S. Kim, “Acceleration method of computing a compensated phase-added stereogram on a graphic processing unit,” Appl. Opt. 47, 5784-5789 (2008).
    [CrossRef]
  7. Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
    [CrossRef]
  8. M. Janda, I. Hanak, and L. Onural, “Hologram synthesis for photorealistic reconstruction,” J. Opt. Soc. Am. A 25, 3083-3096 (2008).
    [CrossRef]
  9. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
    [CrossRef] [PubMed]
  10. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer-generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47, 1567-1574 (2008).
    [CrossRef] [PubMed]
  11. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47, D117-D127(2008).
    [CrossRef] [PubMed]
  12. R. Ziegler, S. Croci, and M. Gross, “Lighting and occlusion in a wave-based framework,” Comput. Graph. Forum 27, 211-220 (2008).
    [CrossRef]
  13. A. Ritter, O. Deussen, H. Wagener, and T. Strothotte, “Holographic imaging of lines: a texture based approach,” in International Conference on Information Visualization, P. Storms, ed. (IEEE Computer Society, 1997), pp. 272-278.
  14. W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 2005), pp. 55-58.
  16. F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767-773 (1965).
    [CrossRef]
  17. M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graph. Qrtrly. 43, (2009), retrieved 28/09/2009 from http://www.siggraph.org/publications/newsletter/volume-43-number-2/a-survey-of-brdf-models-for-computer-graphics
  18. K. Schwenk, “A survey of shading models for real-time rendering,” retrieved 28/09/2009 from http://www.devmaster.net/articles/survey-of-shading-models/a_survey_of_shading_models.pdf
  19. A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
    [CrossRef]
  20. L. B. Lesen, P. Hirsch, and J. A. Jordan, Jr., “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  21. M. Harris, “Introduction to NVIDIA CUDA and Tesla,” presented at the Workshop on High Performance Computing with NVIDIA CUDA, Sydney, Australia, 17 April 2009, http://www.cse.unsw.edu.au/~pls/cuda-workshop09/slides/01_TeslaCUDAIntro.pdf.
  22. M. Lucente, “Interactive computation of holograms using a lookup table,” J. Electron. Imaging 2, 28-34 (1993).
    [CrossRef]
  23. S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986-5995 (2008).
    [CrossRef] [PubMed]
  24. I. Bilinskis and G. Cain, “Fully digital alias-free processing of sensor signals in a substantially enlarged frequency range,” Sensor Rev. 17, 54-63 (1997).
    [CrossRef]
  25. “CUDPP: CUDA data-parallel primitives library,” http://www.gpgpu.org/developer/cudpp/.
  26. N. Satish, M. Harris, and M. Garland, “Designing efficient sorting algorithms for manycore GPUs,” in Proceedings of 23rd IEEE International Parallel and Distributed Processing Symposium (IEEE, 2009).
    [CrossRef]
  27. “CUDA CUFFT library,” http://developer.download.nvidia.com/compute/cuda/2_1/toolkit/docs/CUFFT_Library_2.1.pdf
  28. R. H.-Y. Chen and T. D. Wilkinson, “Field of view expansion for 3-D holographic display using a single spatial light modulator with scanning reconstruction light,” in Proceedings of IEEE 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, 2009 (IEEE, 2009), pp. 1-4.
    [CrossRef] [PubMed]
  29. P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, “The Princeton shape benchmark,” http://shape.cs.princeton.edu/benchmark/index.cgi

2009 (3)

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48, 4246-4255 (2009).
[CrossRef] [PubMed]

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[CrossRef]

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graph. Qrtrly. 43, (2009), retrieved 28/09/2009 from http://www.siggraph.org/publications/newsletter/volume-43-number-2/a-survey-of-brdf-models-for-computer-graphics

2008 (6)

2006 (4)

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
[CrossRef]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14, 603-608 (2006).
[CrossRef] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 7636-7641 (2006).
[CrossRef] [PubMed]

2005 (1)

2003 (1)

C. Petz and M. Magnor, “Fast hologram synthesis for 3D geometry models using graphics hardware,” Proc. SPIE 5005, 266-275 (2003).
[CrossRef]

1997 (1)

I. Bilinskis and G. Cain, “Fully digital alias-free processing of sensor signals in a substantially enlarged frequency range,” Sensor Rev. 17, 54-63 (1997).
[CrossRef]

1993 (1)

M. Lucente, “Interactive computation of holograms using a lookup table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

1981 (1)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

1969 (1)

L. B. Lesen, P. Hirsch, and J. A. Jordan, Jr., “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

1965 (1)

Ahrenberg, L.

Barabas, J.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[CrossRef]

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

Benzie, P.

Bilinskis, I.

I. Bilinskis and G. Cain, “Fully digital alias-free processing of sensor signals in a substantially enlarged frequency range,” Sensor Rev. 17, 54-63 (1997).
[CrossRef]

Bove, V. M.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[CrossRef]

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

Cain, G.

I. Bilinskis and G. Cain, “Fully digital alias-free processing of sensor signals in a substantially enlarged frequency range,” Sensor Rev. 17, 54-63 (1997).
[CrossRef]

Chen, R. H.-Y.

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48, 4246-4255 (2009).
[CrossRef] [PubMed]

R. H.-Y. Chen and T. D. Wilkinson, “Field of view expansion for 3-D holographic display using a single spatial light modulator with scanning reconstruction light,” in Proceedings of IEEE 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, 2009 (IEEE, 2009), pp. 1-4.
[CrossRef] [PubMed]

Croci, S.

R. Ziegler, S. Croci, and M. Gross, “Lighting and occlusion in a wave-based framework,” Comput. Graph. Forum 27, 211-220 (2008).
[CrossRef]

Deussen, O.

A. Ritter, O. Deussen, H. Wagener, and T. Strothotte, “Holographic imaging of lines: a texture based approach,” in International Conference on Information Visualization, P. Storms, ed. (IEEE Computer Society, 1997), pp. 272-278.

Edwards, D.

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graph. Qrtrly. 43, (2009), retrieved 28/09/2009 from http://www.siggraph.org/publications/newsletter/volume-43-number-2/a-survey-of-brdf-models-for-computer-graphics

Funkhouser, T.

P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, “The Princeton shape benchmark,” http://shape.cs.princeton.edu/benchmark/index.cgi

Garland, M.

N. Satish, M. Harris, and M. Garland, “Designing efficient sorting algorithms for manycore GPUs,” in Proceedings of 23rd IEEE International Parallel and Distributed Processing Symposium (IEEE, 2009).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 2005), pp. 55-58.

Gross, M.

R. Ziegler, S. Croci, and M. Gross, “Lighting and occlusion in a wave-based framework,” Comput. Graph. Forum 27, 211-220 (2008).
[CrossRef]

Hahn, J.

Haist, T.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
[CrossRef]

Halle, M.

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

Hanak, I.

Harris, M.

N. Satish, M. Harris, and M. Garland, “Designing efficient sorting algorithms for manycore GPUs,” in Proceedings of 23rd IEEE International Parallel and Distributed Processing Symposium (IEEE, 2009).
[CrossRef]

M. Harris, “Introduction to NVIDIA CUDA and Tesla,” presented at the Workshop on High Performance Computing with NVIDIA CUDA, Sydney, Australia, 17 April 2009, http://www.cse.unsw.edu.au/~pls/cuda-workshop09/slides/01_TeslaCUDAIntro.pdf.

Hirsch, P.

L. B. Lesen, P. Hirsch, and J. A. Jordan, Jr., “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Ito, T.

Janda, M.

Jordan, J. A.

L. B. Lesen, P. Hirsch, and J. A. Jordan, Jr., “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Kang, H.

Kazhdan, M.

P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, “The Princeton shape benchmark,” http://shape.cs.princeton.edu/benchmark/index.cgi

Kim, E.-S.

Kim, H.

Kim, S.-C.

Kurt, M.

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graph. Qrtrly. 43, (2009), retrieved 28/09/2009 from http://www.siggraph.org/publications/newsletter/volume-43-number-2/a-survey-of-brdf-models-for-computer-graphics

Lee, B.

Lesen, L. B.

L. B. Lesen, P. Hirsch, and J. A. Jordan, Jr., “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Lim, J. S.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

Lucente, M.

M. Lucente, “Interactive computation of holograms using a lookup table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

Magnor, M.

Masuda, N.

Matsushima, K.

Min, P.

P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, “The Princeton shape benchmark,” http://shape.cs.princeton.edu/benchmark/index.cgi

Nicodemus, F. E.

Onural, L.

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

Pappu, R.

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

Petz, C.

C. Petz and M. Magnor, “Fast hologram synthesis for 3D geometry models using graphics hardware,” Proc. SPIE 5005, 266-275 (2003).
[CrossRef]

Plesniak, W. J.

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

Reicherter, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
[CrossRef]

Ritter, A.

A. Ritter, O. Deussen, H. Wagener, and T. Strothotte, “Holographic imaging of lines: a texture based approach,” in International Conference on Information Visualization, P. Storms, ed. (IEEE Computer Society, 1997), pp. 272-278.

Satish, N.

N. Satish, M. Harris, and M. Garland, “Designing efficient sorting algorithms for manycore GPUs,” in Proceedings of 23rd IEEE International Parallel and Distributed Processing Symposium (IEEE, 2009).
[CrossRef]

Schwenk, K.

K. Schwenk, “A survey of shading models for real-time rendering,” retrieved 28/09/2009 from http://www.devmaster.net/articles/survey-of-shading-models/a_survey_of_shading_models.pdf

Seifert, L.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
[CrossRef]

Shilane, P.

P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, “The Princeton shape benchmark,” http://shape.cs.princeton.edu/benchmark/index.cgi

Shiraki, A.

Smalley, D. E.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[CrossRef]

Smithwick, Q. Y. J.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[CrossRef]

Strothotte, T.

A. Ritter, O. Deussen, H. Wagener, and T. Strothotte, “Holographic imaging of lines: a texture based approach,” in International Conference on Information Visualization, P. Storms, ed. (IEEE Computer Society, 1997), pp. 272-278.

Sugie, T.

Tanaka, T.

Wagener, H.

A. Ritter, O. Deussen, H. Wagener, and T. Strothotte, “Holographic imaging of lines: a texture based approach,” in International Conference on Information Visualization, P. Storms, ed. (IEEE Computer Society, 1997), pp. 272-278.

Watson, J.

Wilkinson, T. D.

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48, 4246-4255 (2009).
[CrossRef] [PubMed]

R. H.-Y. Chen and T. D. Wilkinson, “Field of view expansion for 3-D holographic display using a single spatial light modulator with scanning reconstruction light,” in Proceedings of IEEE 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, 2009 (IEEE, 2009), pp. 1-4.
[CrossRef] [PubMed]

Wu, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
[CrossRef]

Yamaguchi, T.

Yoon, J.-H.

Yoshikawa, H.

Ziegler, R.

R. Ziegler, S. Croci, and M. Gross, “Lighting and occlusion in a wave-based framework,” Comput. Graph. Forum 27, 211-220 (2008).
[CrossRef]

Appl. Opt. (7)

Comput. Graph. Forum (1)

R. Ziegler, S. Croci, and M. Gross, “Lighting and occlusion in a wave-based framework,” Comput. Graph. Forum 27, 211-220 (2008).
[CrossRef]

Comput. Graph. Qrtrly. (1)

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graph. Qrtrly. 43, (2009), retrieved 28/09/2009 from http://www.siggraph.org/publications/newsletter/volume-43-number-2/a-survey-of-brdf-models-for-computer-graphics

Comput. Sci. Eng. (1)

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8-13 (2006).
[CrossRef]

IBM J. Res. Dev. (1)

L. B. Lesen, P. Hirsch, and J. A. Jordan, Jr., “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of holograms using a lookup table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

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

Opt. Eng. (1)

W. J. Plesniak, M. Halle, V. M. Bove, Jr., J. Barabas, and R. Pappu “Reconfigurable image projection holograms,” Opt. Eng. 45, 115801 (2006).
[CrossRef]

Opt. Express (2)

Proc. IEEE (1)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

Proc. SPIE (2)

C. Petz and M. Magnor, “Fast hologram synthesis for 3D geometry models using graphics hardware,” Proc. SPIE 5005, 266-275 (2003).
[CrossRef]

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove, Jr., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[CrossRef]

Sensor Rev. (1)

I. Bilinskis and G. Cain, “Fully digital alias-free processing of sensor signals in a substantially enlarged frequency range,” Sensor Rev. 17, 54-63 (1997).
[CrossRef]

Other (9)

“CUDPP: CUDA data-parallel primitives library,” http://www.gpgpu.org/developer/cudpp/.

N. Satish, M. Harris, and M. Garland, “Designing efficient sorting algorithms for manycore GPUs,” in Proceedings of 23rd IEEE International Parallel and Distributed Processing Symposium (IEEE, 2009).
[CrossRef]

“CUDA CUFFT library,” http://developer.download.nvidia.com/compute/cuda/2_1/toolkit/docs/CUFFT_Library_2.1.pdf

R. H.-Y. Chen and T. D. Wilkinson, “Field of view expansion for 3-D holographic display using a single spatial light modulator with scanning reconstruction light,” in Proceedings of IEEE 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, 2009 (IEEE, 2009), pp. 1-4.
[CrossRef] [PubMed]

P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, “The Princeton shape benchmark,” http://shape.cs.princeton.edu/benchmark/index.cgi

M. Harris, “Introduction to NVIDIA CUDA and Tesla,” presented at the Workshop on High Performance Computing with NVIDIA CUDA, Sydney, Australia, 17 April 2009, http://www.cse.unsw.edu.au/~pls/cuda-workshop09/slides/01_TeslaCUDAIntro.pdf.

A. Ritter, O. Deussen, H. Wagener, and T. Strothotte, “Holographic imaging of lines: a texture based approach,” in International Conference on Information Visualization, P. Storms, ed. (IEEE Computer Society, 1997), pp. 272-278.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 2005), pp. 55-58.

K. Schwenk, “A survey of shading models for real-time rendering,” retrieved 28/09/2009 from http://www.devmaster.net/articles/survey-of-shading-models/a_survey_of_shading_models.pdf

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Figures (9)

Fig. 1
Fig. 1

Diagram showing incident and reflected light vectors as well as the normal vector at point p on surface Σ.

Fig. 2
Fig. 2

Line-of-sight visibility determination. θ 1 and θ 1 are the ray angles of points p 1 and p 2 , respectively.

Fig. 3
Fig. 3

Effect of Gaussian interpolation with varying σ: (a)  σ = 1 , (b)  σ = 5 , and (c)  σ = 10 .

Fig. 4
Fig. 4

Schematics illustrating (a) construction of LUT and (b) complex amplitude retrieval.

Fig. 5
Fig. 5

The illustration on the left shows the interpolation kernel centered on point p with radius R and four boundary points marked out. In the middle is an illustration of the occlusion culling strategy, from (a)–(c), showing conservative to aggressive culling. (d) Point p 2 is invisible from s if p 2 is within a radius R distance of p 1 .

Fig. 6
Fig. 6

Schematic of optical reconstruction setup.

Fig. 7
Fig. 7

Knight chess piece with varying σ value and Gaussian interpolation kernel radius: (a)  σ = 1 , kernal radius = 5 sample pitch; (b)  σ = 5 , kernal radius = 15 sample pitch; (c)  σ = 10 , kernal radius = 35 sample pitch. (d) Same kernel parameters as (c) but without lighting.

Fig. 8
Fig. 8

Bishop chess piece with a slanted opaque sheet cutting through it, showing clearly the effect of occlusion: (a) no approximation and (b) group visibility approximation.

Fig. 9
Fig. 9

Optical reconstruction of CGH generated with different sampling schemes: (a) no sampling, (b) nonuniform sampling, and (c) uniform sampling.

Tables (3)

Tables Icon

Table 1 Algorithm 1. Skeleton of CPU Code

Tables Icon

Table 2 Algorithm 2. Skeleton of the CUDA Kernel a

Tables Icon

Table 3 Hologram Generation Time in Seconds

Equations (8)

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

s ( x , y ) = F 1 { F { A exp ( j φ ) δ ( x x 0 , y y 0 ) } × exp ( j 2 π λ z d 1 ( λ μ ) 2 ( λ υ ) 2 ) } ,
s ( x , y ) = A exp ( j φ ) F 1 { exp ( j 2 π λ z d 1 ( λ μ ) 2 ( λ υ ) 2 ) } δ ( x x o , y y o ) .
I r I i = max { L ^ i n ^ , 0 } ,
g ( x , y ) = exp ( x 2 + y 2 2 σ 2 ) ,
g ( x , y ) = exp [ ( x 2 + y 2 2 σ 2 ) ρ ( x , y ) ] .
s ( x , y ) = A exp ( j φ ) b ( x , y ) δ ( x x o , y y o ) ,
b ( x , y ) = F 1 { F { g ( x , y ) } × exp ( j 2 π λ z d 1 ( λ μ ) 2 ( λ υ ) 2 ) } .
x 2 = z 1 ( x 2 x s ) z 2 + x s , y 2 = z 1 ( y 2 y s ) z 2 + y s ,

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