Torcal Milla, Francisco JoséSánchez Brea, Luis MiguelBernabeu Martínez, Eusebio2023-06-202023-06-202007-06-201. 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). 3. E. Keren and O. Kafri, “Diffraction effects in moiré deflectometry,” J. Opt. Soc. Am. A 2, 111–120 (1985) 4. A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413–415 (1971). 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). 6. B. F. Oreb and R. G. Dorsch, “Profilometry by phase-shifted Talbot images,” Appl. Opt. 33, 7955–7962 (1994). 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). 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). 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). 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). 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). 12. Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarizationdependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154–2160 (2006). 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. Pérez-Quintián, A. Lutenberg, and M. A. Rebollo, “Linear displacement measurement with a grating and speckle pattern illumination,” Appl. Opt. 45, 4821–4825 (2006).1559-128X10.1364/AO.46.003668https://hdl.handle.net/20.500.14352/51189© 2007 Optical Society of America. This work has been supported by the DPI2005- 02860 project of the Ministerio de Educación y Ciencia of Spain and the “Tecnologías en ecología, alta precisión y productividad, multifuncionalidad, y tecnologías de la información y comunicaciones en Máquina Herramienta” CENIT project of the Ministerio de Industria, turismo y comercio. Sanchez-Brea is currently contracted by the Universidad Complutense de Madrid under the “Ramón y Cajal” research program of the Ministerio de Educación y Ciencia of Spain.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.engjournal articlehttp://dx.doi.org/10.1364/AO.46.003668http://www.opticsinfobase.orgopen access535OpticsÓptica (Física)2209.19 Óptica Física