Double grating systems with one steel tape grating

dc.contributor.authorTorcal Milla, Francisco José
dc.contributor.authorSánchez Brea, Luis Miguel
dc.contributor.authorBernabeu Martínez, Eusebio
dc.description© 2008 Elsevier B.V. The authors thank Agustin Gonzalez-Cano for his invaluable help. This work was supported by the DPI2005-02860 project of the Ministerio de Educación y Ciencia of Spain and the “Tecnologías avanzadas para los equipos y procesos de fabricación de 2015: e-eficiente, e-cológica, e-máquina” CENIT project of the Ministerio de Industria, Turismo y Comercio. During the realization of this work Sanchez-Brea was contracted by the Universidad Complutense de Madrid under the “Ramón y Cajal” research program of the Ministerio de Educación y Ciencia of Spain.
dc.description.abstractSteel tape gratings are used in different metrology applications. As the period of these gratings was large (around 100μm,), its analytical study has been performed, up to date, using a geometrical approach. Nowadays, steel tape gratings can be manufactured with lower periods, around 20–40 μm, and diffractive effects must be taken into account. Also, due to the roughness of the surface, statistical techniques need to be considered to analyze their behavior. In this work, an analysis of the pseudo-imaging formation in a double grating system including one steel tape grating is performed. In particular Moiré and Lau configurations are analyzed. We have found that roughness significantly affects to Moiré configuration. However, its effect is negligible in Lau configuration. Generalized grating imaging configuration is also studied in depth. It is shown that roughness does not affect to the contrast of pseudoimages, but it modifies their depth of focus.
dc.description.departmentDepto. de Óptica
dc.description.facultyFac. de Ciencias Físicas
dc.description.sponsorshipMinisterio de Educación y Ciencia (MEC), España
dc.description.sponsorshipMinisterio de Industria, Turismo y Comercio, España
dc.description.sponsorshipUniversidad Complutense de Madrid (UCM)
dc.identifier.citation[1] G.W.R. Leibbrandt, G. Harbers, P.J. Kunst, App. Opt. 35 (1996) 6151. [2] Y. Xu, O. Sasaki, T. Suzuki, Opt. Lett. 28 (2003) 1751. [3] Y. Xu, O. Sasaki, T. Suzuki, App. Opt. 43 (2004). [4] I.B. Gornushkin, N. Omenetto, B.W. Smith, J.D. Winefordner, App. Spectrosc. 58 (2004). [5] S. Grabarnik, R. Wolffenbuttel, A. Emadi, M. Loktev, E. Sokolova, G. Vdovin, Opt. Express 15 (2007) 3581. [6] K. Patorski, The self-imaging phenomenon and its applications, in: E. Wolf (Ed.), Progress in Optics 27, North Holland, Amsterdam, 1989. [7] A.W. Lohmann, D.E. Silva, Opt. Commun. 2 (1971) 413. [8] K. Patorski, Moirè Metrology, Pergamon, New York, 1998. [9] E. Lau, Ann. Phys. 6 (1948) 417. [10] D. Crespo, J. Alonso, T. Morlanes, E. Bernabéu, Opt. Eng. 39 (2000) 817. [11] J. Jahns, W. Lohmann, Opt. Commun. 28 (1979) 263. [12] G.J. Swanson, E.N. Leith, J. Opt. Soc. Am. A 2 (1985) 789. [13] S.C. Som, A. Satpathi, J. Mod. Opt. 37 (1990) 1215. [14] D. Crespo, J. Alonso, E. Bernabéu, J. Opt. Soc. Am. A 17 (2000) 1231. [15] D. Crespo, J. Alonso, E. Bernabéu, Appl. Opt. 41 (7) (2002) 1223. [16] Fagor Automation S. Coop. (, Heidenhain Coorporation (, Renishaw Group ( [17] F.J. Torcal-Milla, L.M. Sánchez-Brea, E. Bernabéu, Appl. Opt. 46 (2007) 3668. [18] L.M. Sánchez-Brea, F.J. Torcal-Milla, E. Bernabéu, J. Opt. Soc. Am. A 25 (2008) 828. [19] P. Beckmann, The Scattering of Electromagnetic Waves from Rough Surfaces, Artech House INC, 1987. [20] J.A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces, IOP, Bristol, 1991. [21] F. Pérez-Quintián, A. Lutenberg, M.A. Rebollo, Appl. Opt. 45 (2006) 4821. [22] G.J. Swanson, E.N. Leith, J. Opt. Soc. Am. A 72 (1972) 552. [23] L. García-Rodríguez, J. Alonso, E. Bernabéu, Opt. Express 12 (2004) 2529.
dc.journal.titleOptics Communications
dc.publisherElsevier Science BV
dc.relation.projectID‘‘Ramón y Cajal” research program
dc.relation.projectIDCENIT project ‘‘Tecnologías avanzadas para los equipos y procesos de fabricación de 2015: e-eficiente, e-cológica, e-máquina”
dc.rights.accessRightsopen access
dc.subject.ucmÓptica (Física)
dc.subject.unesco2209.19 Óptica Física
dc.titleDouble grating systems with one steel tape grating
dc.typejournal article
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
305.55 KB
Adobe Portable Document Format