OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 4 — Feb. 1, 2013
  • pp: B46–B51

Influence of tilt on collinear calibration of a laser interferometer

Shanzhi Tang, Zhao Wang, Jianmin Gao, and Lihong Zhong  »View Author Affiliations

Applied Optics, Vol. 52, Issue 4, pp. B46-B51 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (638 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Collinear calibration is a typical and common method for a laser (heterodyne) interferometer, but it usually suffers from the influence of the tilt of the target retroreflectors and the dissymmetry of the optical paths during the calibration. This paper mainly analyzes and models the calibration error caused by the tilt error of the target retroreflectors and reveals the error source that is the disturbance from the rotary error of the guideway slider pair. Experimental results prove the validity of the analysis and model of the calibration error. The calibration error is up to 0.5 μm when the tilt error is 0.36°, which is large enough to equal the maximum tolerance of laser interferometer (0.5 μm) in use.

© 2013 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.4640) Instrumentation, measurement, and metrology : Optical instruments

Original Manuscript: August 23, 2012
Revised Manuscript: November 26, 2012
Manuscript Accepted: December 17, 2012
Published: January 16, 2013

Shanzhi Tang, Zhao Wang, Jianmin Gao, and Lihong Zhong, "Influence of tilt on collinear calibration of a laser interferometer," Appl. Opt. 52, B46-B51 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. Wang and B. Griffin, “A noncontact laser technique for circular contouring accuracy measurement,” Rev. Sci. Instrum. 72, 1594–1596 (2001). [CrossRef]
  2. K. Iwasawa, A. Iwama, and K. Mistsui, “Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder,” Precis. Eng. 28, 399–408 (2004). [CrossRef]
  3. XL-80 laser interferometer product manual of Renishaw Corporation (Renishaw, 2007).
  4. K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008). [CrossRef]
  5. S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.
  6. M. M. Colavita, M. Shao, and M. D. Rayman, “Orbiting stellar interferometer for astrometry and imaging,” Appl. Opt. 32, 1789–1797 (1993). [CrossRef]
  7. P. G. Halverson and R. E. Spero, “Signal processing and testing of displacement metrology gauges with picometre-scale cyclic nonlinearity,” J. Opt. A 4, S304–S310 (2002). [CrossRef]
  8. I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010). [CrossRef]
  9. F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001). [CrossRef]
  10. H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16, 2155–2166 (2005). [CrossRef]
  11. P. F. Luo, S. P. Pan, and C. L. Lee, “Application of computer vision and laser interferometer to two-dimensional inspection,” Opt. Eng. 47, 123601 (2008). [CrossRef]
  12. W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006). [CrossRef]
  13. H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. 57, 660–675 (2008). [CrossRef]
  14. J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol. 15, 1879–1884 (2009). [CrossRef]
  15. F. G. P. Peeters, “Interferometer with added flexibility in its use,” Opt. Eng. 35, 1953–1956 (1996). [CrossRef]
  16. D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl. Opt. 36, 4034–4042 (1997). [CrossRef]
  17. H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003). [CrossRef]
  18. M. Pisani and M. Astrua, “Angle amplification for nanoradian measurements,” Appl. Opt. 45, 1725–1729 (2006). [CrossRef]
  19. H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol. 17, 746–752 (2006). [CrossRef]
  20. Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006). [CrossRef]
  21. Z. Zhang, and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum. 78, 1–8 (2007). [CrossRef]
  22. M. Pisani, “Multiple reflection Michelson interferometer with picometer resolution,” Opt. Express 16, 21558–21563 (2008). [CrossRef]
  23. S. Sandwith, “Thermal stability of laser tracking interferometer calibration,” Proc. SPIE 3835, 93–103 (1999). [CrossRef]
  24. D. A. Swyt, S. D. Philips, and J. Palmateer, “Developments at NIST on Traceability in dimensional measurements,” Proc. SPIE 4401, 245–252 (2001). [CrossRef]
  25. A. Takahashi, Y. Takigawa, and N. Miwa, “Error contributor of defocus and quadratic caustic in line scale measurement,” Meas. Sci. Technol. 22, 015302 (2011).
  26. M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998). [CrossRef]
  27. J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).
  28. H. Hussein, M. A. Sobee, and M. Amer, “Calibration of a Michelson-type laser wavemeter and evaluation of its accuracy,” Opt. Laser Eng. 48, 393–397 (2007). [CrossRef]
  29. L. Cai, J. Lu, and Y. Wei, “Calibration method for wavelength of laser interferometer,” Proceedings of 1st National Measurement Conference of China (1998), pp. 463–468.
  30. S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012). [CrossRef]
  31. ISO 10012-1, “Quality assurance requirements for measuring equipment-Part 1: metrological confirmation system for measuring equipment first edition,” Corrected and reprinted (1993).

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