OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 5 — Mar. 10, 2014
  • pp: 5060–5066

Fast conversion of digital Fresnel hologram to phase-only hologram based on localized error diffusion and redistribution

P. W. M. Tsang, A. S. M. Jiao, and T.-C. Poon  »View Author Affiliations

Optics Express, Vol. 22, Issue 5, pp. 5060-5066 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (381 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Past research has demonstrated that a digital, complex Fresnel hologram can be converted into a phase-only hologram with the use of the bi-direction error diffusion (BERD) algorithm. However, the recursive nature error diffusion process is lengthy and increases monotonically with hologram size. In this paper, we propose a method to overcome this problem. Briefly, each row of a hologram is partitioned into short non-overlapping segments, and a localized error diffusion algorithm is applied to convert the pixels in each segment into phase only values. Subsequently, the error signal is redistributed with low-pass filtering. As the operation on each segment is independent of others, the conversion process can be conducted at high speed with the graphic processing unit. The hologram obtained with the proposed method, known as the Localized Error Diffusion and Redistribution (LERDR) hologram, is over two orders of magnitude faster than that obtained by BERD for a 2048 × 2048 hologram, exceeding the capability of generating quality phase-only holograms in video rate.

© 2014 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(090.1760) Holography : Computer holography
(090.1995) Holography : Digital holography

ToC Category:

Original Manuscript: January 2, 2014
Revised Manuscript: January 30, 2014
Manuscript Accepted: January 30, 2014
Published: February 25, 2014

P. W. M. Tsang, A. S. M. Jiao, and T.-C. Poon, "Fast conversion of digital Fresnel hologram to phase-only hologram based on localized error diffusion and redistribution," Opt. Express 22, 5060-5066 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008 (2011).
  2. M.-L. Hsieh, M.-L. Chen, C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng. 46(7), 070501 (2007). [CrossRef]
  3. R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A5, S189–S194 (2003).
  4. C. K. Hsueh, A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Opt. 17(24), 3874–3883 (1978). [CrossRef] [PubMed]
  5. X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator” in Dig. Holo. and 3D Img., OSA Technical Digest, OSA, paper DTh2A.3 (2013).
  6. S. Reichelt, R. Häussler, G. Fütterer, N. Leister, H. Kato, N. Usukura, Y. Kanbayashi, “Full-range, complex spatial light modulator for real-time holography,” Opt. Lett. 37(11), 1955–1957 (2012). [CrossRef] [PubMed]
  7. H. Song, G. Sung, S. Choi, K. Won, H. S. Lee, H. Kim, “Optimal synthesis of double-phase computer generated holograms using a phase-only spatial light modulator with grating filter,” Opt. Express 20(28), 29844–29853 (2012). [CrossRef] [PubMed]
  8. J.-P. Liu, W. Y. Hsieh, T.-C. Poon, P. W. M. Tsang, “Complex Fresnel hologram display using a single SLM,” Appl. Opt. 50(34), H128–H135 (2011). [CrossRef] [PubMed]
  9. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
  10. J. Yeom, J. Hong, J.-H. Jung, K. Hong, J.-H. Park, B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett. 9(12), 120009 (2011).
  11. E. Buckley, “Holographic laser projection technology” Proc. SID Symp., 1074–1078 (2008). [CrossRef]
  12. A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004). [CrossRef]
  13. E. Buckley, “Real-time error diffusion for signal-to-noise ratio improvement in a holographic projection system,” J. Disp. Tech. 7(2), 70–76 (2011). [CrossRef]
  14. R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp. 17, 75–77 (1976).
  15. P. W. Tsang, T.-C. Poon, “Novel method for converting digital Fresnel hologram to phase-only hologram based on bidirectional error diffusion,” Opt. Express 21(20), 23680–23686 (2013). [CrossRef] [PubMed]

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.


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

Supplementary Material

» Media 1: JPG (795 KB)     
» Media 2: JPG (6110 KB)     
» Media 3: JPG (2496 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited