OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 23 — Aug. 10, 2011
  • pp: 4587–4593

Double diffractive optical element system for near-field shaping

Jose Maria Herrera-Fernandez and Luis Miguel Sanchez-Brea  »View Author Affiliations

Applied Optics, Vol. 50, Issue 23, pp. 4587-4593 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (864 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Iterative algorithms based on Fourier transform are used for the design of diffractive optical elements (DOEs), which produce a given intensity distribution, usually at the far field. For the near field, these algorithms can also be used by changing the Fourier transform for the Fresnel transform. However, when the distance between the DOE and the observation plane is short, the results obtained with this modification are not always valid. In the present work, we develop a technique for obtaining the desired intensity distribution in the near field using two DOEs in tandem. We have designed an algorithm based on the standard Gerchberg–Saxton algorithm to determine the modulation of the two DOEs. The best results are obtained when the first DOE modulates the amplitude and the second DOE modulates the phase.

© 2011 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics
(230.3990) Optical devices : Micro-optical devices
(350.3950) Other areas of optics : Micro-optics

ToC Category:
Diffraction and Gratings

Original Manuscript: April 6, 2011
Revised Manuscript: June 17, 2011
Manuscript Accepted: June 17, 2011
Published: August 1, 2011

Jose Maria Herrera-Fernandez and Luis Miguel Sanchez-Brea, "Double diffractive optical element system for near-field shaping," Appl. Opt. 50, 4587-4593 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H.P.Herzig, Micro-Optics, Elements, Systems and Applications, 1st ed. (Taylor & Francis, 1997).
  2. F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988). [CrossRef]
  3. F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 28, 3864–3870 (1989). [CrossRef] [PubMed]
  4. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990). [CrossRef]
  5. J. Liu and M. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27, 1463–1465 (2002). [CrossRef]
  6. M. Thomson, J. Liu, and M. Taghizadeh, “Iterative algorithm for the design of free-space diffractive optical elements for fiber coupling,” Appl. Opt. 43, 1996–1999 (2004). [CrossRef] [PubMed]
  7. H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A 21, 2353–2365(2004). [CrossRef]
  8. W. Hsu and C. Lin, “Optimal quantization method for uneven-phase diffractive optical elements by use of a modified iterative Fourier-transform algorithm,” Appl. Opt. 44, 5802–5808 (2005). [CrossRef] [PubMed]
  9. J. S. Liu, M. J. Thomson, and M. R. Taghizadeh, “Automatic symmetrical iterative Fourier-transform algorithm for the design of diffractive optical elements for highly precise laser beam shaping,” J. Mod. Opt. 53, 461–471 (2006). [CrossRef]
  10. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–248 (1972).
  11. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holography,” Opt. Eng. 19, 297–305 (1980).
  12. http://sp.itme.edu.pl/PRdouble.htm.
  13. G. Vincent, R. Haidar, S. Collin, N. Guérineau, J. Primot, E. Cambril, and J.-L. Pelouard, “Realization of sinusoidal transmittance with subwavelength metallic structures,” J. Opt. Soc. Am. B 25834–840 (2008). [CrossRef]
  14. L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Continuous self-imaging regime with a double grating mask,” Appl. Opt. 48, 5722–5727 (2009). [CrossRef] [PubMed]
  15. J. Rodrigo, T. Alieva, and M. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007). [CrossRef]
  16. J. Rodrigo, T. Alieva, and M. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express 17, 4976–4983 (2009). [CrossRef] [PubMed]
  17. A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Near-perfect hologram reconstruction with a spatial light modulator,” Opt. Express 16, 2597–2603(2008). [CrossRef] [PubMed]
  18. D. X. Zheng, Y. Zhang, J. L. Shen, C. L. Zhang, and G. Pedrini, “Wave field reconstruction from a hologram sequence,” Opt. Commun. 249, 73–77 (2005). [CrossRef]
  19. 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]

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