OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25553–25564

Displacement measurement using a wavelength-phase-shifting grating interferometer

Ju-Yi Lee and Geng-An Jiang  »View Author Affiliations

Optics Express, Vol. 21, Issue 21, pp. 25553-25564 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1939 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A grating interferometer based on the wavelength-modulated phase-shifting method for displacement measurements is proposed. A laser beam with sequential phase shifting can be accomplished using a wavelength-modulated light passing through an unequal-path-length optical configuration. The optical phase of the moving grating is measured by the wavelength-modulated phase-shifting technique and the proposed time-domain quadrature detection method. The displacement of the grating is determined by the grating interferometry theorem with the measured phase variation. Experimental results reveal that the proposed method can detect a displacement up to a large distance of 1 mm and displacement variation down to the nanometer range.

© 2013 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: August 9, 2013
Revised Manuscript: September 27, 2013
Manuscript Accepted: October 9, 2013
Published: October 18, 2013

Ju-Yi Lee and Geng-An Jiang, "Displacement measurement using a wavelength-phase-shifting grating interferometer," Opt. Express 21, 25553-25564 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. M. Wu, “Heterodyne interferometric system with sub-nanometer accuracy for measurement of straightness,” Appl. Opt.43(19), 3812–3816 (2004). [CrossRef] [PubMed]
  2. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol.9(7), 1024–1030 (1998). [CrossRef]
  3. W. T. Estler, “High-accuracy displacement interferometry in air,” Appl. Opt.24(6), 808–815 (1985). [CrossRef] [PubMed]
  4. M. Nevièvre, E. Popov, B. Bojhkov, L. Tsonev, and S. Tonchev, “High-accuracy translation-rotation encoder with two gratings in a Littrow mount,” Appl. Opt.38(1), 67–76 (1999). [CrossRef] [PubMed]
  5. J. Y. Lin, K. H. Chen, and J. H. Chen, “Measurement of small displacement based on surface plasmon resonance heterodyne interferometry,” Opt. Lasers Eng.49(7), 811–815 (2011). [CrossRef]
  6. M. H. Chiu, B. Y. Shih, C. W. Lai, L. H. Shyu, and T. H. Wu, “Small absolute distance measurement with nanometer resolution using geometrical optics principles and a SPR angular sensor,” Sens. Actuators A Phys.141(1), 217–223 (2008). [CrossRef]
  7. S. F. Wang, M. H. Chiu, W. W. Chen, F. H. Kao, and R. S. Chang, “Small-displacement sensing system based on multiple total internal reflections in heterodyne interferometry,” Appl. Opt.48(13), 2566–2573 (2009). [CrossRef] [PubMed]
  8. K. H. Chen, J. H. Chen, C. H. Cheng, and T. H. Yang, “Measurement of small displacements with polarization properties of internal reflection and heterodyne interferometry,” Opt. Eng.48(4), 043606 (2009). [CrossRef]
  9. K. H. Chen, H. S. Chiu, J. H. Chen, and Y. C. Chen, “An alternative method for measuring small displacements with differential phase difference of dual-prism and heterodyne interferometry,” Meas.45(6), 1510–1514 (2012). [CrossRef]
  10. K. Chen, J. H. Chen, S. H. Lu, W. Y. Chang, and C. C. Wu, “Absolute distance measurement by using modified dual-wavelength heterodyne Michelson interferometer,” Opt. Commun.282(9), 1837–1840 (2009). [CrossRef]
  11. A. Teimel, “Technology and applications of grating interferometers in high-precision measurement,” Precis. Eng.14(3), 147–154 (1992). [CrossRef]
  12. S. Fourment, P. Arguel, J. L. Noullet, F. Lozes, S. Bonnefont, G. Sarrabayrouse, Y. Jourlin, J. Jay, and O. Parriaux, “A silicon integrated opto–electro–mechanical displacement sensor,” Sens. Actuators A Phys.110(1-3), 294–300 (2004). [CrossRef]
  13. C. F. Kao, C. C. Chang, and M. H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44, 023063 (2005).
  14. J. Y. Lee and M. P. Lu, “Optical heterodyne grating shearing interferometry for long-range positioning applications,” Opt. Commun.284(3), 857–862 (2011). [CrossRef]
  15. C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys.47, 1833–1837 (2008).
  16. C. C. Wu, C. C. Hsu, J. Y. Lee, Y. Z. Chen, and J. S. Yang, “Littrow-type self-aligned laser encoder with high tolerance using double diffractions,” Opt. Commun.297, 89–97 (2013). [CrossRef]
  17. A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21, 054005 (2010).
  18. A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012). [CrossRef]
  19. X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013). [CrossRef]
  20. C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun.281(9), 2582–2589 (2008). [CrossRef]
  21. J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys.137(1), 185–191 (2007). [CrossRef]
  22. R. Onodera and Y. Ishii, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt.33(22), 5052–5061 (1994). [CrossRef] [PubMed]
  23. R. Onodera and Y. Ishii, “Two-wavelength laser-diode heterodyne interferometry with one phasemeter,” Opt. Lett.20(24), 2502–2504 (1995). [CrossRef] [PubMed]
  24. J. Y. Lee, M. P. Lu, K. Y. Lin, and S. H. Huang, “Measurement of in-plane displacement by wavelength-modulated heterodyne speckle interferometry,” Appl. Opt.51(8), 1095–1100 (2012). [CrossRef] [PubMed]
  25. R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid Sci.1(1), 3–17 (1988). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited