OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23054–23066

Optimal conditions for using the binary approximation of continuously self-imaging gratings

Martin Piponnier, Guillaume Druart, Nicolas Guérineau, Jean-Louis de Bougrenet, and Jérôme Primot  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 23054-23066 (2011)
http://dx.doi.org/10.1364/OE.19.023054


View Full Text Article

Enhanced HTML    Acrobat PDF (1575 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Diffractive Optical Elements (DOE), that generate a propagation-invariant transverse intensity pattern, can be used for metrology and imaging application because they provide a very wide depth of focus. However, exact implementation of such DOE is not easy, so we generally code the transmittance by a binary approximation. In this paper, we will study the influence of the binary approximation of Continuously Self-Imaging Gratings (CSIG) on the propagated intensity pattern, for amplitude or phase coding. We will thus demonstrate that under specific conditions, parasitic effects due to the binarization disappear and we retrieve the theoretical non-diffracting property of CSIG’s.

© 2011 OSA

OCIS Codes
(050.1380) Diffraction and gratings : Binary optics
(050.1950) Diffraction and gratings : Diffraction gratings
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(070.3185) Fourier optics and signal processing : Invariant optical fields

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 28, 2011
Revised Manuscript: August 19, 2011
Manuscript Accepted: September 2, 2011
Published: October 28, 2011

Citation
Martin Piponnier, Guillaume Druart, Nicolas Guérineau, Jean-Louis de Bougrenet, and Jérôme Primot, "Optimal conditions for using the binary approximation of continuously self-imaging gratings," Opt. Express 19, 23054-23066 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23054


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. A57(6), 772–778 (1967). [CrossRef]
  2. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987). [CrossRef]
  3. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett.29(1), 44–46 (2004). [CrossRef] [PubMed]
  4. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am.44(8), 592–597 (1954). [CrossRef]
  5. A. T. Friberg, “Stationary-phase analysis of generalized axicons,” J. Opt. Soc. Am. A13(4), 743–750 (1996). [CrossRef]
  6. Z. Jaroszewicz and J. Morales, “Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens,” J. Opt. Soc. Am. A15(9), 2383–2390 (1998). [CrossRef]
  7. V. Kettunen and J. Turunen, “Propagation-invariant spot arrays,” Opt. Lett.23(16), 1247–1249 (1998). [CrossRef] [PubMed]
  8. N. Guérineau and J. Primot, “Nondiffracting array generation using an N-wave interferometer,” J. Opt. Soc. Am. A16(2), 293–298 (1999). [CrossRef]
  9. N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, “Generation of achromatic and propagation-invariant spot arrays by use of continuously self-imaging gratings,” Opt. Lett.26(7), 411–413 (2001). [CrossRef] [PubMed]
  10. J. Primot and N. Guérineau, “Extended hartmann test based on the pseudoguiding property of a hartmann mask completed by a phase chessboard,” Appl. Opt.39(31), 5715–5720 (2000). [CrossRef] [PubMed]
  11. N. Guérineau, S. Rommeluere, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C. R. Phys.4(10), 1175–1185 (2003).
  12. G. Druart, N. Guérineau, R. Haïdar, J. Primot, A. Kattnig, and J. Taboury, “Image formation by use of continuously self-imaging gratings and diffractive axicons,” Proc. SPIE6712, 1–11 (2007).
  13. G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett.33(4), 366–368 (2008). [CrossRef] [PubMed]
  14. G. Druart, N. Guérineau, R. Haïdar, J. Primot, P. Chavel, and J. Taboury, “Non-paraxial analysis of continuous self-imaging gratings in oblique illumination,” J. Opt. Soc. Am. A24(10), 3379–3387 (2007). [CrossRef]
  15. S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Nondiffracting light on-demand,” Opt. Photonics News21(12), 43 (2010). [CrossRef]
  16. W. J. Dallas, “Phase quantization–a compact derivation,” Appl. Opt.10(3), 673–674 (1971). [CrossRef] [PubMed]
  17. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7(6), 961–969 (1990). [CrossRef]
  18. J. A. Davis, E. Carcole, and D. M. Cottrell, “Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator,” Appl. Opt.35(4), 593–598 (1996). [CrossRef] [PubMed]
  19. L. Niggl, T. Lanzl, and M. Maier, “Properties of Bessel beams generated by periodic gratings of circular symmetry,” J. Opt. Soc. Am. A14(1), 27–33 (1997). [CrossRef]
  20. J. W. Goodman, “Foundations of Scalar Diffraction Theory,” in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 31 - 62.

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