Publication: Diffraction by random Ronchi gratings
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Publication Date
2016-08-01
Authors
Torcal Milla, Francisco José
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Optical Society Of America
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Abstract
In this work, we obtain analytical expressions for the near-and far-field diffraction of random Ronchi diffraction gratings where the slits of the grating are randomly displaced around their periodical positions. We theoretically show that the effect of randomness in the position of the slits of the grating produces a decrease of the contrast and even disappearance of the self-images for high randomness level at the near field. On the other hand, it cancels high-order harmonics in far field, resulting in only a few central diffraction orders. Numerical simulations by means of the Rayleigh–Sommerfeld diffraction formula are performed in order to corroborate the analytical results. These results are of interest for industrial and technological applications where manufacture errors need to be considered.
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© 2016 Optical Society of America.
Funding:
Universidad Complutense de Madrid (UCM), project art. 83 num. 52-2016 with Fagor Automation S. Coop.
Acknowledgment:
In memoriam of J. M. Rico-Garcia. The authors thank A. Luis for his inspirational and encouraging comments.
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1. C. Palmer and E. Loewen Diffraction grating handbook 2005 (New York: Richardson Grating Loboratory)
2. A. W. Lohmann and D. E. Silva , “An interferometer based on the Talbot effect”, Opt. Commun. 2, 413–415 (1971).
3. G. Schirripa-Spagnolo, G. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating”, J. Opt. A: Pure Appl. Opt. 4, S376–S380 (2002).
4. B. F. Oreb and R. G. Dorsch, “Profilometry by phase-shifted Talbot images”, Appl. Opt. 33, 7955–7962 (1994).
5. S. Wei, S. Wu, I. Kao, and F. P. Chiang, “Measurement of wafer surface using shadow moire technique with Talbot effect”, Trans. ASME J. Electron. Packag. 120, 166–170 (1998).
6. L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Far field of gratings with rough strips”, J Opt. Soc. Am. A 25, 828-833 (2008).
7. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Self-imaging of gratings with rough strips”, J Opt. Soc. Am. A 25, 2390-2394 (2008).
8. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating”, Opt. Commun. 281, 5647-5652 (2008).
9. F. J. Salgado-Remacha, F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Use of steel substrates in diffractive optics: Near field of high surface quality steel tape gratings”, Opt. Laser Eng. 49, 356-360 (2011).
10. M. J. Madou “Manufacturing techniques for microfabrication and nanotechnology 2011 (Boca Raton: CRC Press,)
11. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu “Diffraction of gratings with rough edges”, Opt. Express 16, 19757-19769 (2008).
12. J. M. Rico-Garcia and L. M. Sanchez-Brea “Binary gratings with random heights”, Appl. Opt. 48, 3062-3069 (2009).
13. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu “Talbot effect with rough reflection gratings”, Appl. Opt. 46, 3668-3673 (2007).
14. L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu “Talbot effect in metallic gratings under Gaussian illumination”, Opt. Commun. 278, 23-27 (2007).
15. L. M. Sanchez-Brea and F. J. Torcal-Milla “Near-field diffraction of gratings with surface defects”, App. Opt. 49, 2190-2197 (2010).
16. Y. Lu, C. Zhou, and H. Luo “Talbot effect of a grating with different kind of flaws”, J Opt. Soc. Am. A 22, 2662-2667 (2005).
17. A. Lin and J. Phillips “Optimization of random diffraction gratings in thin-film-solar cell using genetic algorithms”, Sol. Energy Mat. Sol. C 92, 1689-1696 (2008).
18. W. H. F. Talbot “Facts relating to optical science”, Philos. Mag. 9, 401–407 (1836).
19. K. Patorski “The self-imaging phenomenon and its applications”, Prog. Opt. 27, 1–108 (1989).
20. E. Keren and O. Kafri “Diffraction effects in moire deflectometry”, J. Opt. Soc. Am. A 2, 111-120 (1985).
21. Goodman J W 2000 Statistical Optics (New York: John Wiley and Sons Inc.)
22. F. J. Torcal-Milla, L. M. Sanchez-Brea, and J. Vargas “Effect of aberrations on the self-imaging phenomenon”, J. Lightwave Technol. 29, 1051-1057 (2011).
23. F. Shen and A. Wang “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula”, Appl. Opt. 45, 1102-1110 (2006).