OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 1 — Jan. 1, 2013
  • pp: A18–A25

Fast computation of Fresnel diffraction field of a three-dimensional object for a pixelated optical device

G. Bora Esmer  »View Author Affiliations

Applied Optics, Vol. 52, Issue 1, pp. A18-A25 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (699 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this paper, a fast algorithm is proposed for accurate calculation of the scalar optical diffraction on a pixelated optical device used in the reconstruction process from a three-dimensional object that is formed by scattered sample points over the space. In computer-generated holography, fast and accurate calculation of the diffraction field is an important and a challenging problem. Therefore, several fast algorithms can be found in the literature. The accuracy of the calculations can be determined by the signal processing techniques and the numerical methods used in the calculation of diffraction fields. Furthermore, the quality of reconstructed objects can be affected by the properties of optical devices employed in the reconstruction process. For instance, the pixelated structure of those devices has a significant effect on the reconstruction process. Therefore, the pixelated structure of the display device has to be taken into account. Furthermore, fast calculation of the diffraction pattern can be a bottleneck in dynamic holographic content generation. As a solution to the problems, we propose a fast and accurate algorithm based on a precomputed one-dimensional kernel and scaling of that kernel for the computation of the diffraction pattern for a pixelated display.

© 2013 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(070.6120) Fourier optics and signal processing : Spatial light modulators

Original Manuscript: May 31, 2012
Revised Manuscript: July 18, 2012
Manuscript Accepted: August 10, 2012
Published: October 10, 2012

G. Bora Esmer, "Fast computation of Fresnel diffraction field of a three-dimensional object for a pixelated optical device," Appl. Opt. 52, A18-A25 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Lucente, “Diffraction-specific fringe computation for electro-holography,” Ph.D. dissertation (Massachusetts Institute of Technology, 1994).
  2. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Real time generation of full color image hologram with compact distance lookup table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509 (2010). [CrossRef]
  3. T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776–11781 (2008). [CrossRef]
  4. 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]
  5. S.-C. Kim and E.-S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48, 1030–1041 (2009). [CrossRef]
  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. H. Kang, F. Yaras, and L. Onural, “Graphics processing unit accelerated computation of digital holograms,” Appl. Opt. 48, H137–H143 (2009). [CrossRef]
  8. D. Leseberg and C. Frére, “Computer generated holograms of 3D objects composed of tilted planar segments,” Appl. Opt. 27, 3020–3024 (1988). [CrossRef]
  9. C. Frére and D. Leseberg, “Large objects reconstructed from computer generated holograms,” Appl. Opt. 28, 2422–2425 (1989). [CrossRef]
  10. T. Tommasi and B. Bianco, “Frequency analysis of light diffraction between rotated planes,” Opt. Lett. 17, 556–558 (1992). [CrossRef]
  11. T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A 10, 299–305 (1993). [CrossRef]
  12. 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]
  13. G. B. Esmer, “Computation of holographic patterns between tilted planes,” M.S. thesis (Bilkent University, 2004).
  14. K. Matsushima, “Computer generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005). [CrossRef]
  15. K. Yamamoto, T. Senoh, R. Oi, and T. Kurita, “8K4K-size computer generated hologram for 3-D visual system using rendering technology,” in Proceedings of 4th International Universal Communication Symposium (IUCS) (IEEE, 2010), pp. 193–196.
  16. 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]
  17. 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]
  18. Y.-Z. Liu, J.-W. Dong, B.-C. Chen, H.-X. He, and H.-Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18, 3345–3351 (2010). [CrossRef]
  19. T. Haist, M. Schönleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308(1997). [CrossRef]
  20. L. Yu and L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A 18, 1033–1045 (2001). [CrossRef]
  21. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007). [CrossRef]
  22. R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express 15, 5631–5640 (2007). [CrossRef]
  23. 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]
  24. M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television: Capture, Transmission, Display (Springer-Verlag, 2008), pp. 529–556.
  25. V. Katkovnik, J. Astola, and K. Egiazarian, “Discrete diffraction transform for propagation, reconstruction, and design of wavefield distributions,” Appl. Opt. 47, 3481–3493 (2008). [CrossRef]
  26. V. Katkovnik, A. Migukin, and J. Astola, “Backward discrete wave field propagation modelling as an inverse problem: toward reconstruction of wave field distributions,” Appl. Opt. 48, 3407–3423 (2009). [CrossRef]
  27. HoloEye, “LC-R 720 Spatial Light Modulators”.
  28. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1980).
  29. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  30. F. N. Fritsch and R. E. Carlton, “Monotone piecewise cubic interpolation,” SIAM J. Numer. Anal. 17, 238–246 (1980). [CrossRef]
  31. D. Kahaner, C. Maler, and S. Nash, Numerical Methods and Software (Prentice-Hall, 1988).
  32. M. T. Heath, Scientific Computing: An Introductory Survey, 2nd ed. (McGraw-Hill, 2002).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited