Micro displacement measured by the grating interferometer with rings pattern
A. Olivares-Perez
National Institute of Astrophysics, Optics and Electronics, Street Luis Enrique Erro No. 1, Santa Maria Tonantzintla, Z.P. 72840, Puebla, México, Tel: 52 22 26 63100. e-mail: olivares@inaoep.mx
Received 21 April 2014. ]]> Accepted 19 September 2014.
Abstract
Micro displacements are measured with holographic gratings by using a grating interferometer of one order that detects the phase changes in the diffracted orders caused by movement of the grooves in the diffraction gratings. The period can be on the order of fractions of a micron, with high reproducibility and an error of a half period. The basic operating principle involves the superposition of order +1, with order 0. The interferometer system produces standing waves; it works by measuring the intensity variations at the center of a ring-shaped interference pattern, which indicate the phase shift introduced by displacement of the grating grooves. When these rings move to the center of the pattern or to the border, the direction of the grating displacement can be detected; the interferometer system has no moving parts, except for the diffraction grating, and is very stable and robust. This system has the ability to measure micro displacements even with damaged gratings, as long as the gratings diffract evenly.
Keywords: Diffraction gratings; grating interferometer; micrometer; displacement measurement.
PACS: 42.40.-I; 42.40.Eq; 42.40.Kw; 42.40.My
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1. D. G. Heflinger and L. O. Heflinger, US Patent 6243168 B1, 5 June (2001). [ Links ]
2. T. J. Rolbiecki and D. L. Sanders, US Patent 5414646 A, 9 May (1995). [ Links ]
3. B. Richter and B. Brand , US Patent 4492473, 1 August (1985). [ Links ]
4. S. H Jones, C. DeMain, R. A Ross, D. Abdallah, and T. Digges, US Patent 5754294, 19 May (1998). [ Links ]
5. K. Ishizuka and T. Nishimura, US Patent 5436724 A, 25 July (1995). [ Links ]
6. E. Leitz, UK Patent GB1439645(A), 16 June (1976). [ Links ]
7. C. Kabushiki-Kaisha (Tokyo, JA), US Patent 3836257, 17 September (1974). [ Links ]
8. A. Kuroda (Tokyo, JP), US Patent 20120257214, 10 November (2012). [ Links ]
9. M. R. Gomez-Colin, A. Olivares-Pérez, and V. Sánchez-Villicaña, in Proceedings Practical Holography XV and Holographic Materials VII, 2001, edited by Stephen A. Benton, Sylvia H. Stevenson, T. John Trout, (SPIE-The International Society for Optical Engineering, San Jose California USA, 2001)4296, p. 108. [ Links ]
10. F. Kuang-Chao, L. Yu-Sheng, C.Ye-Jin, and C. Fang, in Proceedings Third International Sym. on Precision Mechanical Measurements, edited by Fan Kuang-Chao, Wei Gao, Xiaofen Yu, Wenhao Huang, Penghao Hu, (SPIE-The International Society for Optical Engineering, Urumqi, China, 2006), 6280, p. 628008-1. [ Links ]
11. G. Rodriguez-Zurita, C. Meneses-Fabian, Noel-Ivan Toto-Arellano, J. F. Vázquez-Castillo, and C. Robledo-Sánchez, Opt. Exp. 16 (2008) 7806. [ Links ]
12. J. Howard, Appl. Opt. 31 (1992) 1419. [ Links ]
13. Y. Zahid, W. Jigang, C. Xiquan, H. Xin, and Y. Changhuei, Opt. Exp. 14 (2006) 8127. [ Links ]
14. J. Minlan, L. Fupeng, W. Xiaodong, App. Mech. and Mat. 103 (2012) 35. [ Links ]
15. A. Olivares-Pérez, M. Alejandra Lara-Peña, J. A. García-Monge, P. A. Valencia-Acuña, J. M. Villa-Hernández, and I. Fuentes-Tapia, in Proceedings Practical Holography XXVII: Materials and Applications, 2013, edited by Hans I. Bjelkhagen, V. Michael Bove, Jr., (SPIE-The International Society for Optical Engineering, San Francisco USA, 2013) 8644, p. 864415-1. [ Links ]
16. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic Press, New York, USA, 1971) p. 266. [ Links ]
17. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52 (1962) 987. [ Links ]
18. M. Hazewinkel, Periodic function, Encyclopedia of Mathematics (Springer, ISBN 978-1-55608-010-4, 2001). [ Links ]
19. K. Knopp, Periodic Functions (Dover, 1996). pp. 58-92. [ Links ]
20. J. Spanier and K. B. Oldham, Periodic Functions (Hemisphere, 1987). pp. 343-349. [ Links ]
21. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, ISBN 0-691-08078-X, 1971). [ Links ]
22. K. B. Howell, Principles of Analysis (CRC Press. ISBN 978-08493-8275-8, 2001). [ Links ]
23. M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications Inc., New York USA, 1972) pp. 360-361. [ Links ]
24. D. Malacara, Óptica Básica (Fondo de Cultura Económica, USA, ISBN-13: 9789681673130 2004). [ Links ]
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