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

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.

Appl. Opt.

• 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]
• W. J. Dallas, “Phase quantization–a compact derivation,” Appl. Opt.10(3), 673–674 (1971). [CrossRef] [PubMed]
• 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]

C. R. Phys.

• N. Guérineau, S. Rommeluere, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C. R. Phys.4(10), 1175–1185 (2003).

J. Opt. Soc. Am.

• J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am.44(8), 592–597 (1954). [CrossRef]

J. Opt. Soc. Am. A

• A. T. Friberg, “Stationary-phase analysis of generalized axicons,” J. Opt. Soc. Am. A13(4), 743–750 (1996). [CrossRef]
• 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]
• W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. A57(6), 772–778 (1967). [CrossRef]
• J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987). [CrossRef]
• N. Guérineau and J. Primot, “Nondiffracting array generation using an N-wave interferometer,” J. Opt. Soc. Am. A16(2), 293–298 (1999). [CrossRef]
• 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]
• 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]
• F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7(6), 961–969 (1990). [CrossRef]

Opt. Lett.

• 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]
• 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]
• V. Kettunen and J. Turunen, “Propagation-invariant spot arrays,” Opt. Lett.23(16), 1247–1249 (1998). [CrossRef] [PubMed]
• 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]

Opt. Photonics News

• S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Nondiffracting light on-demand,” Opt. Photonics News21(12), 43 (2010). [CrossRef]

Proc. SPIE

• 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).

Other

• J. W. Goodman, “Foundations of Scalar Diffraction Theory,” in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 31 - 62.

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