Abstract

We present a method of rapidly producing computer-generated holograms that exhibit geometric occlusion in the reconstructed image. Conceptually, a bundle of rays is shot from every hologram sample into the object volume. We use z buffering to find the nearest intersecting object point for every ray and add its complex field contribution to the corresponding hologram sample. Each hologram sample belongs to an independent operation, allowing us to exploit the parallel computing capability of modern programmable graphics processing units (GPUs). Unlike algorithms that use points or planar segments as the basis for constructing the hologram, our algorithm’s complexity is dependent on fixed system parameters, such as the number of ray-casting operations, and can therefore handle complicated models more efficiently. The finite number of hologram pixels is, in effect, a windowing function, and from analyzing the Wigner distribution function of windowed free-space transfer function we find an upper limit on the cone angle of the ray bundle. Experimentally, we found that an angular sampling distance of 0.01° for a 2.66° cone angle produces acceptable reconstruction quality.

© 2009 Optical Society of America

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References

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  1. M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (MIT, 1994).
  2. 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]
  3. W. Plesniak, “Incremental update of computer-generated holograms,” Opt. Eng. 42, 1560-1571 (2003).
    [CrossRef]
  4. B. Munjuluri, M. L. Huebschman, and H. R. Garner, “Rapid hologram updates for real-time volumetric information displays,” Appl. Opt. 44, 5076-5085 (2005).
    [CrossRef]
  5. M. Pharr and R. Fernando, GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation (Addison-Wesley Professional, 2005).
  6. 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]
  7. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 7636-7641(2006).
    [CrossRef]
  8. M. Janda, I. Hanak, and V. Skala, “HPO hologram synthesis for full-parallax reconstruction setup,” in proceedings of IEEE 3DTV Conference, 2007 (IEEE, 2007), pp. 1-4.
  9. D. Leseberg, “Computer-generated three-dimensional image holograms,” Appl. Opt. 31, 223-229 (1992).
    [CrossRef]
  10. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
    [CrossRef]
  11. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
    [CrossRef]
  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. 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]
  14. 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]
  15. M. Janda, I. Hanak, and L. Onural, “Hologram synthesis for photorealistic reconstruction,” J. Opt. Soc. Am. A 25, 3083-3096 (2008).
    [CrossRef]
  16. 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]
  17. 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]
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    [CrossRef]
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    [CrossRef]
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  22. J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 53-60 (1997).
    [CrossRef]
  23. M. J. Bastiaans, “Application of the Wigner distribution function in optics,” in The Wigner Distribution--Theory and Applications in Signal Processing, W. Mecklenbräuker and F. Hlawatsch, eds. (Elsevier, 1997) pp. 375-426.
  24. A. Torre, Linear Ray and Wave Optics in Phase Space (Elsevier, 2005).
  25. S. Curtis, A. Oppenheim, and J. Lim, “Signal reconstruction from Fourier transform sign information,” IEEE Trans. Acoust. Speech Signal Process. 33, 643-657 (1985).
    [CrossRef]
  26. T. T. Huang and J. C. Sanz, “Image representation by one-bit Fourier phase: theory, sampling, and coherent image model,” IEEE Trans. Acoust. Speech Signal Process. 36, 1292-1304(1988).
    [CrossRef]
  27. T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41, 1489-1499 (2002).
    [CrossRef]
  28. C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
    [CrossRef]
  29. A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
    [CrossRef]
  30. Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. 47, D6-D11 (2008).
    [CrossRef]
  31. 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.

2009

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]

2008

2006

2005

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
[CrossRef]

B. Munjuluri, M. L. Huebschman, and H. R. Garner, “Rapid hologram updates for real-time volumetric information displays,” Appl. Opt. 44, 5076-5085 (2005).
[CrossRef]

A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
[CrossRef]

2004

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

2003

W. Plesniak, “Incremental update of computer-generated holograms,” Opt. Eng. 42, 1560-1571 (2003).
[CrossRef]

2002

1998

1997

J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 53-60 (1997).
[CrossRef]

1992

1988

T. T. Huang and J. C. Sanz, “Image representation by one-bit Fourier phase: theory, sampling, and coherent image model,” IEEE Trans. Acoust. Speech Signal Process. 36, 1292-1304(1988).
[CrossRef]

1985

S. Curtis, A. Oppenheim, and J. Lim, “Signal reconstruction from Fourier transform sign information,” IEEE Trans. Acoust. Speech Signal Process. 33, 643-657 (1985).
[CrossRef]

1964

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]

Bastiaans, M. J.

M. J. Bastiaans, “Application of the Wigner distribution function in optics,” in The Wigner Distribution--Theory and Applications in Signal Processing, W. Mecklenbräuker and F. Hlawatsch, eds. (Elsevier, 1997) pp. 375-426.

Benzie, P.

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]

Cameron, C. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Chen, R. H.-Y.

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.

Coomber, S. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

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]

Curtis, S.

S. Curtis, A. Oppenheim, and J. Lim, “Signal reconstruction from Fourier transform sign information,” IEEE Trans. Acoust. Speech Signal Process. 33, 643-657 (1985).
[CrossRef]

Delen, N.

Fernando, R.

M. Pharr and R. Fernando, GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation (Addison-Wesley Professional, 2005).

Fujii, K.

A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
[CrossRef]

Garner, H. R.

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.

Hanak, I.

M. Janda, I. Hanak, and L. Onural, “Hologram synthesis for photorealistic reconstruction,” J. Opt. Soc. Am. A 25, 3083-3096 (2008).
[CrossRef]

M. Janda, I. Hanak, and V. Skala, “HPO hologram synthesis for full-parallax reconstruction setup,” in proceedings of IEEE 3DTV Conference, 2007 (IEEE, 2007), pp. 1-4.

Hayashi, Y.

Hooker, B.

Huang, T. T.

T. T. Huang and J. C. Sanz, “Image representation by one-bit Fourier phase: theory, sampling, and coherent image model,” IEEE Trans. Acoust. Speech Signal Process. 36, 1292-1304(1988).
[CrossRef]

Huebschman, M. L.

Ito, T.

Janda, M.

M. Janda, I. Hanak, and L. Onural, “Hologram synthesis for photorealistic reconstruction,” J. Opt. Soc. Am. A 25, 3083-3096 (2008).
[CrossRef]

M. Janda, I. Hanak, and V. Skala, “HPO hologram synthesis for full-parallax reconstruction setup,” in proceedings of IEEE 3DTV Conference, 2007 (IEEE, 2007), pp. 1-4.

Kang, H.

Kim, E.-S.

Kim, H.

Kim, S.-C.

Lee, B.

Leith, E. N.

Leseberg, D.

Lim, J.

S. Curtis, A. Oppenheim, and J. Lim, “Signal reconstruction from Fourier transform sign information,” IEEE Trans. Acoust. Speech Signal Process. 33, 643-657 (1985).
[CrossRef]

Lucente, M.

M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (MIT, 1994).

Magnor, M.

Masuda, N.

Matsushima, K.

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
[CrossRef]

Miller, R. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Mishina, T.

Morimoto, M.

A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
[CrossRef]

Munjuluri, B.

Okano, F.

Okui, M.

Onural, L.

Oppenheim, A.

S. Curtis, A. Oppenheim, and J. Lim, “Signal reconstruction from Fourier transform sign information,” IEEE Trans. Acoust. Speech Signal Process. 33, 643-657 (1985).
[CrossRef]

Payne, D. A.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Pharr, M.

M. Pharr and R. Fernando, GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation (Addison-Wesley Professional, 2005).

Plesniak, W.

W. Plesniak, “Incremental update of computer-generated holograms,” Opt. Eng. 42, 1560-1571 (2003).
[CrossRef]

Saleh, B.

B. Saleh and M. Teich, Fundamentals of Photonics (Wiley, 1991), p. 117.

Sanz, J. C.

T. T. Huang and J. C. Sanz, “Image representation by one-bit Fourier phase: theory, sampling, and coherent image model,” IEEE Trans. Acoust. Speech Signal Process. 36, 1292-1304(1988).
[CrossRef]

Sato, K.

A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
[CrossRef]

Shiraki, A.

Skala, V.

M. Janda, I. Hanak, and V. Skala, “HPO hologram synthesis for full-parallax reconstruction setup,” in proceedings of IEEE 3DTV Conference, 2007 (IEEE, 2007), pp. 1-4.

Slinger, C. W.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

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]

Smith, A. P.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Smith, M. G.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Smithwick, Q. Y.

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]

Stanley, M.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Sugie, T.

Sugita, A.

A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
[CrossRef]

Takaki, Y.

Tanaka, T.

Teich, M.

B. Saleh and M. Teich, Fundamentals of Photonics (Wiley, 1991), p. 117.

Torre, A.

A. Torre, Linear Ray and Wave Optics in Phase Space (Elsevier, 2005).

Underkoffler, J. S.

J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 53-60 (1997).
[CrossRef]

Upatnieks, J.

Watson, J.

Watson, P. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

Wilkinson, T. D.

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.

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.

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]

B. Munjuluri, M. L. Huebschman, and H. R. Garner, “Rapid hologram updates for real-time volumetric information displays,” Appl. Opt. 44, 5076-5085 (2005).
[CrossRef]

D. Leseberg, “Computer-generated three-dimensional image holograms,” Appl. Opt. 31, 223-229 (1992).
[CrossRef]

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
[CrossRef]

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]

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]

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]

T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41, 1489-1499 (2002).
[CrossRef]

Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. 47, D6-D11 (2008).
[CrossRef]

Comput. Graph. Forum

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

IEEE Trans. Acoust. Speech Signal Process.

S. Curtis, A. Oppenheim, and J. Lim, “Signal reconstruction from Fourier transform sign information,” IEEE Trans. Acoust. Speech Signal Process. 33, 643-657 (1985).
[CrossRef]

T. T. Huang and J. C. Sanz, “Image representation by one-bit Fourier phase: theory, sampling, and coherent image model,” IEEE Trans. Acoust. Speech Signal Process. 36, 1292-1304(1988).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

W. Plesniak, “Incremental update of computer-generated holograms,” Opt. Eng. 42, 1560-1571 (2003).
[CrossRef]

Opt. Express

Proc. SPIE

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
[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]

J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 53-60 (1997).
[CrossRef]

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27-41 (2004).
[CrossRef]

A. Sugita, K. Sato, M. Morimoto, and K. Fujii, “Full-color holographic display with wide visual field and viewing zone,” Proc. SPIE 6016, 60160Y (2005).
[CrossRef]

Other

M. J. Bastiaans, “Application of the Wigner distribution function in optics,” in The Wigner Distribution--Theory and Applications in Signal Processing, W. Mecklenbräuker and F. Hlawatsch, eds. (Elsevier, 1997) pp. 375-426.

A. Torre, Linear Ray and Wave Optics in Phase Space (Elsevier, 2005).

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

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.

B. Saleh and M. Teich, Fundamentals of Photonics (Wiley, 1991), p. 117.

M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (MIT, 1994).

M. Janda, I. Hanak, and V. Skala, “HPO hologram synthesis for full-parallax reconstruction setup,” in proceedings of IEEE 3DTV Conference, 2007 (IEEE, 2007), pp. 1-4.

M. Pharr and R. Fernando, GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation (Addison-Wesley Professional, 2005).

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Figures (11)

Fig. 1
Fig. 1

In computational holography, each sample receives contributions from all visible objects. Note that only the bounding rays of each object are shown in the diagram.

Fig. 2
Fig. 2

Equally distributed sampling rays over a semicircle.

Fig. 3
Fig. 3

With naïve orthogonal projection, point A and B are projected onto different samples. As a result, point B will not be occluded by A under the z-buffer depth test.

Fig. 4
Fig. 4

Before and after applying a horizontal shear transformation.

Fig. 5
Fig. 5

Maximum ray angle φ.

Fig. 6
Fig. 6

Wigner distribution function of (a) a point source, (b) the same point source propagated over a distance z in free space. The dotted lines define the spatial-frequency limitation imposed by finite computation window.

Fig. 7
Fig. 7

Intensity profile of the light field in the hologram plane originated from a band-limited point source 5 cm away on the optical axis.

Fig. 8
Fig. 8

Angle made by the bounding rays of two arbitrary points P 1 and P 2 with spread-out angle 2 θ at sample S must also be 2 θ .

Fig. 9
Fig. 9

Optically reconstructed images of a bunny and teapot exhibiting geometric occlusion.

Fig. 10
Fig. 10

Optical reconstructions of CGHs generated with different sampling ray combinations.

Fig. 11
Fig. 11

Reconstructed images of a wireframe cube exhibiting horizontal parallax. The camera was shifted horizontally from (a) left to (b) right.

Tables (1)

Tables Icon

Table 1 Hologram Generation Time in Seconds

Equations (23)

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

u ( x ) = A δ ( x ) exp ( - j β ) ,
T = exp ( j 2 π λ z d 1 ( λ υ ) 2 ) ,
h ( x ) = F - 1 { F { u ( x ) } × T } = - A exp ( - j 2 π υ x ) exp ( - j β ) × exp ( j 2 π λ z d 1 ( λ υ ) 2 ) exp ( j 2 π υ x ) · d υ .
h ( x ) = - A exp ( - j k ( x - x ) sin θ ) exp ( - j β ) exp ( - j k z d co s θ ) cos θ λ d θ .
h [ x ] = F - 1 { F { u ( x ) } × T × comb ( υ - n W ) × rect ( υ W ) } ,
H [ υ ] = F { m M h m } ,
cone angle = 2 φ = tan 1 ( | x P 1 - x S | z P 1 ) .
PSF = exp ( j k r ) r z r ( 1 r - j k ) ,
PSF = exp ( j k r ) r z r ( 1 r - j k ) comb ( x - n W ) sinc ( x W ) ,
W ( x , υ ) = δ ( x - x 0 ) ,
W out ( x , υ ) = W in ( x - 2 π υ z k 2 - ( 2 π υ ) 2 , υ ) ,
| u ( x ) | 2 = x W ( x , υ ) d υ ,
W out ( x , υ ) = { W in ( x 2 π υ z k 2 - ( 2 π υ ) 2 , υ ) , υ ± υ max 0 , υ ± υ max .
x max = ± 2 π υ max z k 2 - ( 2 π υ max ) 2 ,
sin θ = λ υ .
θ = sin 1 ( 640 × 633 nm 1280 × 13.62 μm ) = 1.33 ° ,
h [ x ] = A e j β ( F 1 { ( F { δ ( x ) } × T ) × comb ( υ n W ) × rect ( υ W ) } ) .
H b i [ υ ] = { 1 , arg ( H [ υ ] ) > 0 0 , arg ( H [ υ ] ) 0 .
w = 2 λ f Δ ,
α 2 λ f M Δ .
[ 1 0 tan θ 0 1 0 0 0 1 ] .
index = ( int ) z tan θ ,
h [ m , n ] = base dist.LUT [ index ] × u [ m , n ] × exp ( random phase LUT [ index + m , n ] ) .

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