OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 24 — Aug. 20, 2010
  • pp: 4647–4654

Method to calculate the far field of three-dimensional objects for computer-generated holography

Muharrem Bayraktar and Meriç Özcan  »View Author Affiliations


Applied Optics, Vol. 49, Issue 24, pp. 4647-4654 (2010)
http://dx.doi.org/10.1364/AO.49.004647


View Full Text Article

Enhanced HTML    Acrobat PDF (524 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Here, a new method for calculating the computer-generated holograms of three-dimensional (3D) objects is presented along with a review of current techniques. The method, the planar layers method (PLM), is established on the idea of representing 3D objects in discrete planar layers perpendicular to the observation plane, then calculating the total far field pattern by summing up the far field patterns of each layer. Simulation results, computational complexity, and error comparisons reveal that this new method can be used to calculate far field patterns—hence, the holograms—of computer-synthesized objects very efficiently.

© 2010 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(100.3010) Image processing : Image reconstruction techniques
(350.5500) Other areas of optics : Propagation
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: April 9, 2010
Revised Manuscript: July 27, 2010
Manuscript Accepted: July 29, 2010
Published: August 19, 2010

Citation
Muharrem Bayraktar and Meriç Özcan, "Method to calculate the far field of three-dimensional objects for computer-generated holography," Appl. Opt. 49, 4647-4654 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-24-4647


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778(1948). [CrossRef] [PubMed]
  2. J. Goodman, “An introduction to the principles and applications of holography,” Proc. IEEE 59, 1292–1304 (1971). [CrossRef]
  3. Y. Frauel, T. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006). [CrossRef]
  4. Y. Takaki and H. Ohzu, “Hybrid holographic microscopy: visualization of three-dimensional object information by use of viewing angles,” Appl. Opt. 39, 5302–5308 (2000). [CrossRef]
  5. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001). [CrossRef]
  6. Y. Frauel, E. Tajahuerce, M.-A. Castro, and B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001). [CrossRef]
  7. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132 (2002). [CrossRef] [PubMed]
  8. A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering,” Opt. Commun. 259, 499–506(2006). [CrossRef]
  9. L. Onural, A. Gotchev, H. M. Özaktaş, and E. Stoykova, “A survey of signal processing problems and tools in holographic three-dimensional television,” IEEE Trans. Circuits Syst. Video Technol. 17, 1631–1646 (2007). [CrossRef]
  10. C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: Three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000). [CrossRef]
  11. Y. Aoki, “Watermarking technique using computer-generated holograms,” Electron. Commun. Jpn. 84, 21–31 (2001). [CrossRef]
  12. R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970). [CrossRef]
  13. T. Huang, “Digital holography,” Proc. IEEE 59, 1335–1346(1971). [CrossRef]
  14. M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).
  15. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994). [CrossRef] [PubMed]
  16. U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer-Verlag, 2005).
  17. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 02, 28–34(1993). [CrossRef]
  18. S.-C. Kim and E.-S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008). [CrossRef] [PubMed]
  19. 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]
  20. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T.-C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009). [CrossRef]
  21. J. L. Juárez-Pérez, A. Olivares-Pérez, and L. R. Berriel-Valdos, “Nonredundant calculations for creating digital Fresnel holograms,” Appl. Opt. 36, 7437–7443 (1997). [CrossRef]
  22. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000). [CrossRef]
  23. H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000). [CrossRef]
  24. 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]
  25. 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]
  26. Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “Horn-6 special-purpose clustered computing system for electroholography,” Opt. Express 17, 13895–13903 (2009). [CrossRef] [PubMed]
  27. S. Ganci, “Fourier diffraction through a tilted slit,” Eur. J. Phys. 2, 158–160 (1981). [CrossRef]
  28. K. Patorski, “Fraunhofer diffraction patterns of titled planar objects,” Opt. Acta 30, 673–679 (1983). [CrossRef]
  29. H. J. Rabal, N. Bolognini, and E. E. Sicre, “Diffraction by a tilted aperture,” Opt. Acta 32, 1309–1311 (1985). [CrossRef]
  30. D. Leseberg and C. Frere, “Computer-generated holograms of 3D objects composed of tilted planar segments,” Appl. Opt. 27, 3020–3024 (1988). [CrossRef] [PubMed]
  31. T. Tommasi and B. Bianco, “Frequency analysis of light diffraction between rotated planes,” Opt. Lett. 17, 556–558(1992). [CrossRef] [PubMed]
  32. 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]
  33. K. Matsushima and A. Kondoh, “Wave optical algorithm for creating digitally snythetic holograms of three-dimensional surface objects,” Proc. SPIE 5005, 190–197 (2003). [CrossRef]
  34. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005). [CrossRef] [PubMed]
  35. R. Ziegler, P. Kaufmann, and M. Gross, “A framework for holographic scene representation and image synthesis,” IEEE Trans. Vis. Comput. Graph. 13, 403–415 (2007). [CrossRef] [PubMed]
  36. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48, H54–H63 (2009). [CrossRef] [PubMed]
  37. J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997). [CrossRef]
  38. K. Matsushima and A. Kondoh, “A wave-optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004). [CrossRef]
  39. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005) . [CrossRef]
  40. T. Yatagai, “Stereoscopic approach to 3D display using computer-generated holograms,” Appl. Opt. 15, 2722–2729 (1976). [CrossRef] [PubMed]
  41. M. W. Halle, S. A. Benton, M. A. Klug, and J. S. Underkoffler, “Ultragram: a generalized holographic stereogram,” Proc. SPIE 1461, 142–155 (1991). [CrossRef]
  42. N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48, H120–H136 (2009). [CrossRef] [PubMed]
  43. M. Bayraktar and M. Özcan, “A new method for computer-generated holography of 3D objects,” in 24th International Symposium on Computer and Information Sciences (ISCIS) (IEEE, 2009), pp. 66–69. [CrossRef]
  44. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  45. U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms in hologram interferometry and shearography,” Appl. Opt. 33, 4373–4377 (1994). [CrossRef] [PubMed]
  46. F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh–Sommerfeld diffraction formula,” Appl. Opt. 45, 1102–1110 (2006). [CrossRef] [PubMed]
  47. 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]
  48. 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]
  49. Y. Li, D. Abookasis, and J. Rosen, “Computer-generated holograms of three-dimensional realistic objects recorded without wave interference,” Appl. Opt. 40, 2864–2870 (2001). [CrossRef]
  50. D. Abookasis and J. Rosen, “Computer-generated holograms of three-dimensional objects synthesized from their multiple angular viewpoints,” J. Opt. Soc. Am. A 20, 1537–1545 (2003). [CrossRef]
  51. Y. Sando, M. Itoh, and T. Yatagai, “Holographic three-dimensional display synthesized from three-dimensional Fourier spectra of real existing objects,” Opt. Lett. 28, 2518–2520 (2003). [CrossRef] [PubMed]
  52. D. Abookasis and J. Rosen, “Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene,” Appl. Opt. 45, 6533–6538 (2006). [CrossRef] [PubMed]
  53. N. T. Shaked and J. Rosen, “Modified Fresnel computer-generated hologram directly recorded by multiple-viewpoint projections,” Appl. Opt. 47, D21–D27 (2008). [CrossRef] [PubMed]
  54. Y. Sando, M. Itoh, and T. Yatagai, “Color computer-generated holograms from projection images,” Opt. Express 12, 2487–2493 (2004). [CrossRef] [PubMed]
  55. Y. Sando, M. Itoh, and T. Yatagai, “Full-color computer-generated holograms using 3D Fourier spectra,” Opt. Express 12, 6246–6251 (2004). [CrossRef] [PubMed]
  56. B. Katz, N. T. Shaked, and J. Rosen, “Synthesizing computer-generated holograms with reduced number of perspective projections,” Opt. Express 15, 13250–13255(2007). [CrossRef] [PubMed]
  57. “User’s Manual,” http://download.autodesk.com/us/maya/2009help/index.html, Autodesk, San Rafael, California, USA.
  58. M. Özcan and M. Bayraktar, “Digital holography image reconstruction methods,” Proc. SPIE 7233, 72330B (2009). [CrossRef]
  59. Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited