Abstract

Computation of diffraction patterns, and thus holograms, of scenes with photorealistic properties is a highly complicated and demanding process. An algorithm, based primarily on computer graphics methods, for computing full-parallax diffraction patterns of complicated surfaces with realistic texture and reflectivity properties is proposed and tested. The algorithm is implemented on single-CPU, multiple-CPU and GPU platforms. An alternative algorithm, which implements reduced occlusion diffraction patterns for much faster but somewhat lower quality results, is also developed and tested. The algorithms allow GPU-aided calculations and easy parallelization. Both numerical and optical reconstructions are conducted. The results indicate that the presented algorithms compute diffraction patterns that provide successful photorealistic reconstructions; the computation times are acceptable especially on the GPU implementations.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
    [CrossRef] [PubMed]
  2. D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
    [CrossRef]
  3. L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
    [CrossRef]
  4. L. Yaroslavskii and N. Merzlyakov, Methods of Digital Holography, (Consultants Bureau, 1980).
  5. G. Tricoles, “Computer generated holograms: an historical review,” Appl. Opt. 26, 4351-4360 (1987).
    [CrossRef] [PubMed]
  6. J. Rosen, “Computer-generated holograms of images reconstructed on curved surfaces,” Appl. Opt. 38, 6136-6140 (1999).
    [CrossRef]
  7. D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, “Encoding technique for design of zero-order (on-axis) fraunhofer computer-generated holograms,” Appl. Opt. 36, 8427-8434 (1997).
    [CrossRef]
  8. A. G. Kirk and T. J. Hall, “Design of computer generated holograms by simulated annealing: observation of meta-stable states,” J. Mod. Opt. 39, 2531-2539 (1992).
    [CrossRef]
  9. V. Arrizón, G. Méndez, and D. Sánchez-de La-Llave, “Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators,” Opt. Express 13, 7913-7927 (2005).
    [CrossRef] [PubMed]
  10. Y. Sando, M. Itoh, and T. Yatagai, “Full-color computer-generated holograms using 3-D Fourier spectra,” Opt. Express 12, 6246-6251 (2004).
    [CrossRef] [PubMed]
  11. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587-6594 (2000).
    [CrossRef]
  12. M. Cywiak, M. Servin, and F. M. Santoyo, “Wave-front propagation by gaussian superposition,” Opt. Commun. 195, 351-359 (2001).
    [CrossRef]
  13. 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]
  14. A. Ritter, J. Böttger, O. Deussen, M. König, and T. Strothotte, “Hardware-based rendering of full-parallax synthetic holograms,” Appl. Opt. 38, 1364-1369 (1999).
    [CrossRef]
  15. J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).
  16. G. D. Sherman, “Application of the convolution theorem to Rayleigh's integral formulas,” J. Opt. Soc. Am. 57, 546-547 (1967).
    [CrossRef] [PubMed]
  17. N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” J. Opt. Soc. Am. A 15, 857-867 (1998).
    [CrossRef]
  18. G. Esmer and L. Onural, “Computation of holographic patterns between tilted planes,” Proc. SPIE 6252, 62521K (2006).
    [CrossRef]
  19. L. Onural and H. M. Ozaktas, “Signal processing issues in diffraction and holographic 3DTV,” Signal Process. Image Commun. 22, ss169-177 (2007).
    [CrossRef]
  20. L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929-5935 (2000).
    [CrossRef]
  21. A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23, 1227-1235 (2006).
    [CrossRef]
  22. L. Onural, “Exact analysis of the effects of sampling of the scalar diffraction field,” J. Opt. Soc. Am. A 24, 359-367 (2007).
    [CrossRef]
  23. J. T. Kajiya, “The rendering equation,” ACM SIGGRAPH Comput. Graph. 20, 143-150 (1986).
    [CrossRef]
  24. A. S. Glassner, Principles of Digital Image Synthesis, (Morgan Kaufmann, 1995), 1st ed..
  25. A. Watt, 3D Computer Graphics, 3rd ed. (Addison-Wesley, 2000).
  26. M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).
    [CrossRef]
  27. M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of SIGGRAPH '95 (ACM, 1995), pp. 387-394.
    [CrossRef]
  28. J. L. Juárez-Pérez, A. Olivares-Pérez, and L. R. Berriel-Valdos, “Nonredundant calculation for creating digital Fresnel holograms,” Appl. Opt. 36, 7437-7443 (1997).
    [CrossRef]
  29. G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.
  30. M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.
  31. S. D. Roth, “Ray Casting for Modeling Solids,” J. Comput. Graph. Image Process. 18, 109-144 (1982).
    [CrossRef]
  32. D. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching2nd ed. (Addison-Wesley, 1998).
  33. M. Janda, I. Hanák, and V. Skala, “Digital HPO hologram rendering pipeline,” in Proceedings of EG2006 Short Papers, (Eurographics Association, 2006), pp. 81-84.
  34. M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. thesis (MIT, 1994).
  35. G. Amdahl, “Validity of the single-processor approach to achieving large scale computing capabilities,” in AFIPS Conference Proceedings, Vol. 30 (American Federation of Information Processing Societies Press, 1967), pp. 483-485.
  36. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).
  37. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 603-608 (2006).
    [CrossRef] [PubMed]
  38. C. Petz and M. Magnor, “Fast hologram synthesis for 3d geometry models using graphics hardware,” Proc. SPIE 5005, 266-275 (2003).
    [CrossRef]
  39. B. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
    [CrossRef]

2007 (3)

L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
[CrossRef]

L. Onural and H. M. Ozaktas, “Signal processing issues in diffraction and holographic 3DTV,” Signal Process. Image Commun. 22, ss169-177 (2007).
[CrossRef]

L. Onural, “Exact analysis of the effects of sampling of the scalar diffraction field,” J. Opt. Soc. Am. A 24, 359-367 (2007).
[CrossRef]

2006 (4)

2005 (1)

2004 (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]

2001 (1)

M. Cywiak, M. Servin, and F. M. Santoyo, “Wave-front propagation by gaussian superposition,” Opt. Commun. 195, 351-359 (2001).
[CrossRef]

2000 (2)

1999 (2)

1998 (1)

1997 (2)

1992 (2)

M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).
[CrossRef]

A. G. Kirk and T. J. Hall, “Design of computer generated holograms by simulated annealing: observation of meta-stable states,” J. Mod. Opt. 39, 2531-2539 (1992).
[CrossRef]

1987 (1)

1986 (1)

J. T. Kajiya, “The rendering equation,” ACM SIGGRAPH Comput. Graph. 20, 143-150 (1986).
[CrossRef]

1982 (1)

S. D. Roth, “Ray Casting for Modeling Solids,” J. Comput. Graph. Image Process. 18, 109-144 (1982).
[CrossRef]

1975 (1)

B. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

1967 (1)

1949 (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
[CrossRef]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Ahrenberg, L.

Amdahl, G.

G. Amdahl, “Validity of the single-processor approach to achieving large scale computing capabilities,” in AFIPS Conference Proceedings, Vol. 30 (American Federation of Information Processing Societies Press, 1967), pp. 483-485.

Arrizón, V.

Benzie, P.

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]

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

Berriel-Valdos, L. R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

Böttger, J.

Cywiak, M.

M. Cywiak, M. Servin, and F. M. Santoyo, “Wave-front propagation by gaussian superposition,” Opt. Commun. 195, 351-359 (2001).
[CrossRef]

Delen, N.

Deussen, O.

Esmer, G.

G. Esmer and L. Onural, “Computation of holographic patterns between tilted planes,” Proc. SPIE 6252, 62521K (2006).
[CrossRef]

Esmer, G. B.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
[CrossRef]

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Galyean, T. A.

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of SIGGRAPH '95 (ACM, 1995), pp. 387-394.
[CrossRef]

Glassner, A. S.

A. S. Glassner, Principles of Digital Image Synthesis, (Morgan Kaufmann, 1995), 1st ed..

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

Gotchev, A.

L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
[CrossRef]

G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.

Hall, T. J.

A. G. Kirk and T. J. Hall, “Design of computer generated holograms by simulated annealing: observation of meta-stable states,” J. Mod. Opt. 39, 2531-2539 (1992).
[CrossRef]

Hanák, I.

M. Janda, I. Hanák, and V. Skala, “Digital HPO hologram rendering pipeline,” in Proceedings of EG2006 Short Papers, (Eurographics Association, 2006), pp. 81-84.

Hooker, B.

Ilieva, R.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

Ito, T.

Itoh, M.

Janda, M.

M. Janda, I. Hanák, and V. Skala, “Digital HPO hologram rendering pipeline,” in Proceedings of EG2006 Short Papers, (Eurographics Association, 2006), pp. 81-84.

Javidi, B.

Juárez-Pérez, J. L.

Kajiya, J. T.

J. T. Kajiya, “The rendering equation,” ACM SIGGRAPH Comput. Graph. 20, 143-150 (1986).
[CrossRef]

Kirk, A. G.

A. G. Kirk and T. J. Hall, “Design of computer generated holograms by simulated annealing: observation of meta-stable states,” J. Mod. Opt. 39, 2531-2539 (1992).
[CrossRef]

Knuth, D.

D. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching2nd ed. (Addison-Wesley, 1998).

König, M.

Kovachev, M.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

Levi, U.

Lucente, M.

M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).
[CrossRef]

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of SIGGRAPH '95 (ACM, 1995), pp. 387-394.
[CrossRef]

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

Magnor, M.

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]

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

Marom, E.

Masuda, N.

Matsushima, K.

Méndez, G.

Mendlovic, D.

Merzlyakov, N.

L. Yaroslavskii and N. Merzlyakov, Methods of Digital Holography, (Consultants Bureau, 1980).

Olivares-Pérez, A.

Onural, L.

L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
[CrossRef]

L. Onural and H. M. Ozaktas, “Signal processing issues in diffraction and holographic 3DTV,” Signal Process. Image Commun. 22, ss169-177 (2007).
[CrossRef]

L. Onural, “Exact analysis of the effects of sampling of the scalar diffraction field,” J. Opt. Soc. Am. A 24, 359-367 (2007).
[CrossRef]

G. Esmer and L. Onural, “Computation of holographic patterns between tilted planes,” Proc. SPIE 6252, 62521K (2006).
[CrossRef]

L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929-5935 (2000).
[CrossRef]

G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

Ozaktas, H. M.

L. Onural and H. M. Ozaktas, “Signal processing issues in diffraction and holographic 3DTV,” Signal Process. Image Commun. 22, ss169-177 (2007).
[CrossRef]

L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
[CrossRef]

G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.

Petz, C.

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

Phong, B.

B. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

Reyhan, T.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

Ritter, A.

Rosen, J.

Roth, S. D.

S. D. Roth, “Ray Casting for Modeling Solids,” J. Comput. Graph. Image Process. 18, 109-144 (1982).
[CrossRef]

Sánchez-de La-Llave, D.

Sando, Y.

Santoyo, F. M.

M. Cywiak, M. Servin, and F. M. Santoyo, “Wave-front propagation by gaussian superposition,” Opt. Commun. 195, 351-359 (2001).
[CrossRef]

Servin, M.

M. Cywiak, M. Servin, and F. M. Santoyo, “Wave-front propagation by gaussian superposition,” Opt. Commun. 195, 351-359 (2001).
[CrossRef]

Shabtay, G.

Sherman, G. D.

Shiraki, A.

Skala, V.

M. Janda, I. Hanák, and V. Skala, “Digital HPO hologram rendering pipeline,” in Proceedings of EG2006 Short Papers, (Eurographics Association, 2006), pp. 81-84.

Stern, A.

Stoykova, E.

L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
[CrossRef]

Strothotte, T.

Sugie, T.

Takai, M.

Tanaka, T.

Tricoles, G.

Uzunov, V.

G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.

Watson, J.

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]

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

Watt, A.

A. Watt, 3D Computer Graphics, 3rd ed. (Addison-Wesley, 2000).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

Yaroslavskii, L.

L. Yaroslavskii and N. Merzlyakov, Methods of Digital Holography, (Consultants Bureau, 1980).

Yatagai, T.

Zalevsky, Z.

ACM SIGGRAPH Comput. Graph. (1)

J. T. Kajiya, “The rendering equation,” ACM SIGGRAPH Comput. Graph. 20, 143-150 (1986).
[CrossRef]

Appl. Opt. (7)

Commun. ACM (1)

B. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol. (1)

L. Onural, A. Gotchev, H. M. Ozaktas, and E. Stoykova, “A survey of signal processing problems and tools in holographic 3DTV,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631-1646 (2007).
[CrossRef]

J. Comput. Graph. Image Process. (1)

S. D. Roth, “Ray Casting for Modeling Solids,” J. Comput. Graph. Image Process. 18, 109-144 (1982).
[CrossRef]

J. Mod. Opt. (1)

A. G. Kirk and T. J. Hall, “Design of computer generated holograms by simulated annealing: observation of meta-stable states,” J. Mod. Opt. 39, 2531-2539 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Cywiak, M. Servin, and F. M. Santoyo, “Wave-front propagation by gaussian superposition,” Opt. Commun. 195, 351-359 (2001).
[CrossRef]

Opt. Express (4)

Proc. R. Soc. London, Ser. A (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London, Ser. A 197, 454-487 (1949).
[CrossRef]

Proc. SPIE (3)

G. Esmer and L. Onural, “Computation of holographic patterns between tilted planes,” Proc. SPIE 6252, 62521K (2006).
[CrossRef]

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

M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).
[CrossRef]

Signal Process. Image Commun. (1)

L. Onural and H. M. Ozaktas, “Signal processing issues in diffraction and holographic 3DTV,” Signal Process. Image Commun. 22, ss169-177 (2007).
[CrossRef]

Other (12)

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

L. Yaroslavskii and N. Merzlyakov, Methods of Digital Holography, (Consultants Bureau, 1980).

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of SIGGRAPH '95 (ACM, 1995), pp. 387-394.
[CrossRef]

G. B. Esmer, L. Onural, H. M. Ozaktas, V. Uzunov, and A. Gotchev, “Performance assessment of a diffraction field computation method based on source model,” in Proceedings of the 3DTV-Conference 2008 (IEEE Xplore, 2008), pp. 257-260; http://ieeexplore.ieee.org.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, Three-Dimensional Television: Capture, Transmission, and Display, (Springer, 2007), chap. 15.

A. S. Glassner, Principles of Digital Image Synthesis, (Morgan Kaufmann, 1995), 1st ed..

A. Watt, 3D Computer Graphics, 3rd ed. (Addison-Wesley, 2000).

D. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching2nd ed. (Addison-Wesley, 1998).

M. Janda, I. Hanák, and V. Skala, “Digital HPO hologram rendering pipeline,” in Proceedings of EG2006 Short Papers, (Eurographics Association, 2006), pp. 81-84.

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

G. Amdahl, “Validity of the single-processor approach to achieving large scale computing capabilities,” in AFIPS Conference Proceedings, Vol. 30 (American Federation of Information Processing Societies Press, 1967), pp. 483-485.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

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 (13)

Fig. 1
Fig. 1

Relation between a differential solid angle d θ and a differential surface element d S . The line crossing the surface S delimits the surface S x visible from x and the rest of the surface S.

Fig. 2
Fig. 2

Parameterization of a ray direction r ̂ by two angles ξ and ψ.

Fig. 3
Fig. 3

The propagation angle restrictions associated with aliasing-free sampling of the optical field on H due to D x (lower cones) determine the propagation angle restrictions associated with the surface S (upper cones). The same restrictions are also in place for the y direction due to D y .

Fig. 4
Fig. 4

Range [ Ξ b , Ξ B ] inferred from the bounding box of the surface S. The situation for [ Ψ b , Ψ B ] is similar.

Fig. 5
Fig. 5

Cross section of a surface S and its decomposition into a stepwise surface S.

Fig. 6
Fig. 6

(a) A mesh G and (b) its modified version G M l transformed by Eq. (18). The dashed mesh G M l is the skewed mesh G without correction on the distance z v .

Fig. 7
Fig. 7

(a) Evaluation of the longest distance r κ and (b) decomposition of z v including distances proportional to phase shifts φ p q l m and Φ i l m . The longest distance is computed from D z and R p q l m , where l = max { L min , L max } and m = max { M min , M max } .

Fig. 8
Fig. 8

(a) Numerical reconstruction (intensity) from a GPU-computed optical field. The scene consists of a single textured plane (2D object) parallel to H. The distance between the object plane and the hologram plane is 0.42 m . The resulting image is clipped to 2048 × 1320 pixels . (b) An enlarged detail of the reconstruction is compared with (c) the original texture. (d) The magnitude of the entire computed optical field pattern which is then used to get the reconstruction. (The photo is courtesy of Libor Váša).

Fig. 9
Fig. 9

(a) Numerical reconstructions (intensity) from optical fields calculated by a GPU and (b) details of the reconstructions. Presented scenes are “Chess” and “Lancaster.” Both reconstructions are computed at a distance of 0.5 m .

Fig. 10
Fig. 10

Numerical reconstructions from a GPU-computed optical field focused at the (a) cone, (b) cylinder, (c) box, (d) sphere, (e) torus. (f) An out-of-focus reconstruction. The optical field is calculated by a GPU. All images are clipped to a resolution of 1100 × 1100 pixels .

Fig. 11
Fig. 11

(a) Full-color (online) numerical reconstruction. The color is composed of three components at wavelengths 650 mn (red), 510 nm (green), and 475 nm (blue). The three optical fields are simultaneously computed by a GPU. (b) A detail of the reconstruction. (c) The same detail reconstructed at a different depth.

Fig. 12
Fig. 12

Optical reconstruction from an off-axis hologram. The hologram is obtained from the optical field calculated by a GPU. The incidence angle of the reference beam is 0.758° diagonally to fit the SLM parameters. The reconstruction uses an amplitude-only SLM, and the reconstructed image is captured by a CCD camera without any lens.

Fig. 13
Fig. 13

Numerical reconstruction (a) from the CPU computed full-parallax optical field and (b) from the CPU-computed reduced-occlusion optical field. Focus of the numerical reconstruction is approximately at the black pawn in the middle of the picture.

Tables (6)

Tables Icon

Table 1 Algorithm 1. Skeleton of the algorithm for diffraction pattern computation. See the referred sections in the text for details.

Tables Icon

Table 2 Algorithm 2. A skeleton of an algorithm that evaluates the diffraction pattern on the GPU as described in Section 9. For details on computation, consult the referred portion of the text.

Tables Icon

Table 1 Properties of Scenes Used for the Tests

Tables Icon

Table 2 Difference Comparisons of the Scene “Photo”

Tables Icon

Table 3 Computation Times (hr)

Tables Icon

Table 4 Relative Speedup

Equations (32)

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

u ( x ) = c S x A ( s , r ̂ ) exp ( i k r ) r ( n ̂ H r ̂ ) d S ,
r = s x , r = r , r ̂ = r r ,
d S = r 2 d θ cos φ , cos φ = n ̂ s r ̂ ,
u ( x ) = Ω A ( s , r ̂ ) exp ( i k r ) r ( n ̂ H r ̂ ) r 2 cos φ d θ ,
A ( s , r ̂ ) = A ( s , r ̂ ) r 2 cos φ .
d θ = cos ξ d ξ d ψ ,
u ( x ) = π 2 π 2 π 2 π 2 A ( s , r ̂ ) exp ( i k r ) r ( n ̂ H r ̂ ) cos ξ d ξ d ψ ,
ψ l = l D ψ , ξ m = m D ξ ,
x p q = ( p D x , q D y , 0 ) H ,
u p q = l m A p q l m exp [ i k r p q l m ] r p q l m w p q l m cos ξ m ,
π D x < k x < π D x , π D y < k y < π D y ,
Ξ d = arcsin ( k x max k ) = arcsin ( λ 2 D x ) ,
Ψ d = arcsin ( k y max k ) = arcsin ( λ 2 D y ) ,
l [ L min , L max ] : ψ l [ Ψ d , Ψ d ] [ Ψ b , Ψ B ] ,
m [ M min , M max ] : ξ m [ Ξ d , Ξ d ] [ Ξ b , Ξ B ] .
R p q l m = { x : x = x p q + r r ̂ l m } .
ρ q l c : ( q D y y ) cos ψ l c + z sin ψ l c = 0 .
E A B = { x : x = v A + e ( v B v A ) , e [ 0 , 1 ] } ,
x p q + r r ̂ 0 m = v A + e ( v B v A ) .
α i p = arctan ( x p q x v i z v i ) ,
x v M l = x v ,
y v M l = y v z v tan ψ l ,
z v M l = z v 1 cos ψ l .
λ l m = λ n ̂ H r ̂ l m
exp ( i k r p q l m ) r p q l m 1 z p q l m exp ( i k z p q l m ) exp [ i k 2 z p q l m ( x p q l m 2 + y p q l m 2 ) ] ,
h z ( x , y ) = 1 z exp [ i k 2 z ( x 2 + y 2 ) ] ,
h z p q l m ( x , y ) = σ 2 h z ( σ x , σ y ) ,
P l m = [ 1 0 0 0 1 0 tan ξ ¯ m tan ψ ¯ l ζ l m ] .
tan ξ ¯ m = tan ξ m , tan ψ ¯ l = tan ψ l cos ξ m , ζ l m = 1 cos ξ m cos ψ l .
ϕ p q l m = ζ l m z v λ , Φ i l m = ζ l m i D z λ ,
Δ max = max p q { u p q 2 u p q 2 } max p q { u p q 2 }
MSE = 1 P Q p q ( u p q 2 u p q 2 ) 2 max p q { u p q 2 } ,

Metrics