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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 18 — Jun. 20, 2007
  • pp: 3668–3673

Talbot effect with rough reflection gratings

Francisco Jose Torcal-Milla, Luis Miguel Sanchez-Brea, and Eusebio Bernabeu  »View Author Affiliations

Applied Optics, Vol. 46, Issue 18, pp. 3668-3673 (2007)

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The Talbot effect is analyzed when steel tape gratings are used. These gratings are made on a steel substrate, and, because of the manufacture process, both levels of the grating are rough with different roughness parameters. A theoretical analysis based on Fresnel regime, which considers the statistical properties of roughness, is developed. Analytical formulas that show a decreasing exponential dependence on the intensity in terms of the distance between the grating and the observation plane are obtained, and an experimental verification is also performed.

© 2007 Optical Society of America

OCIS Codes
(030.5770) Coherence and statistical optics : Roughness
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.2770) Diffraction and gratings : Gratings
(290.5880) Scattering : Scattering, rough surfaces

ToC Category:
Diffraction and Gratings

Original Manuscript: October 30, 2006
Revised Manuscript: February 12, 2007
Manuscript Accepted: February 12, 2007
Published: May 31, 2007

Francisco Jose Torcal-Milla, Luis Miguel Sanchez-Brea, and Eusebio Bernabeu, "Talbot effect with rough reflection gratings," Appl. Opt. 46, 3668-3673 (2007)

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  1. W. H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401-407 (1836).
  2. K. Patorski, "The self-imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989). [CrossRef]
  3. E. Keren and O. Kafri, "Diffraction effects in moiré deflectometry," J. Opt. Soc. Am. A 2, 111-120 (1985) [CrossRef]
  4. A. W. Lohmann and D. E. Silva, "An interferometer based on the Talbot effect," Opt. Commun. 2, 413-415 (1971). [CrossRef]
  5. G. Schirripa Spagnolo, D. Ambrosini, and D. Paoletti, "Displacement measurement using the Talbot effect with a Ronchi grating," J. Opt. A , Pure Appl. Opt. 4, S376-S380 (2002). [CrossRef]
  6. B. F. Oreb and R. G. Dorsch, "Profilometry by phase-shifted Talbot images," Appl. Opt. 33, 7955-7962 (1994). [CrossRef] [PubMed]
  7. S. Wei, S. Wu, I. Kao, and F. P. Chiang, "Measurement of wafer surface using shadow moiré technique with Talbot effect," Trans. ASME J. Electron. Packag. 120, 166-170 (1998). [CrossRef]
  8. M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996). [CrossRef]
  9. N. Guérineau, B. Harchaoui, and J. Primot, "Talbot experiment re-examined: demonstration of an achromatic and continuous self-imaging regime," Opt. Commun. 180, 199-203 (2000). [CrossRef]
  10. S. Teng, L. Liu, J. Zu, Z. Luan, and De'an, "Uniform theory of the Talbot effect with partially coherent light illumination," J. Opt. Soc. Am. A 20, 1747-1754 (2003). [CrossRef]
  11. Y. Lu, C. Zhou, and H. Luo, "Talbot effect of a grating with different kinds of flaws," J. Opt. Soc. Am. A 22, 2662-2667 (2005). [CrossRef]
  12. Y. Lu, C. Zhou, S. Wang, and B. Wang, "Polarization-dependent Talbot effect," J. Opt. Soc. Am. A 23, 2154-2160 (2006). [CrossRef]
  13. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, 1987).
  14. J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).
  15. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institute of Physics, 1991).
  16. F. Perez-Quintián, A. Lutenberg, and M. A. Rebollo, "Linear displacement measurement with a grating and speckle pattern illumination," Appl. Opt. 45, 4821-4825 (2006). [CrossRef] [PubMed]

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