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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 6 — Mar. 22, 2004
  • pp: 1136–1143

Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multi-wavelength interferometry

Catherine E. Towers, David P. Towers, and Julian D.C. Jones  »View Author Affiliations


Optics Express, Vol. 12, Issue 6, pp. 1136-1143 (2004)
http://dx.doi.org/10.1364/OPEX.12.001136


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Abstract

We present a computationally efficient method for solving the method of excess fractions used in multi-frequency interferometry for absolute phase measurement. The Chinese remainder theorem, an algorithm from number theory is used to provide a unique solution for absolute distance via a set of congruence’s based on modulo arithmetic. We describe a modified version of this theorem to overcome its sensitivity to phase measurement noise. A comparison with the method of excess fractions has been performed to assess the performance of the algorithm and processing speed achieved. Experimental data has been obtained via a full-field fringe projection system for three projected fringe frequencies and processed using the modified Chinese remainder theorem algorithm.

© 2004 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry

ToC Category:
Research Papers

History
Original Manuscript: February 19, 2004
Revised Manuscript: March 13, 2004
Published: March 22, 2004

Citation
Catherine Towers, David Towers, and Julian Jones, "Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multi-wavelength interferometry," Opt. Express 12, 1136-1143 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-6-1136


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References

  1. C. Fabry and A. Perot, �??Measures of absolute wavelengths in the solar spectrum and in the spectrum of iron,�?? Astrophysical J. 15, 73 (1902). [CrossRef]
  2. F. H. Rolt, �??The application of optics to engineering measurements,�?? Engineering 144, 162 (1937).
  3. M. Kujawinska, J. Wojciak, �??High Accuracy Fourier Transform Fringe Pattern Analysis,�?? Opt. Lasers Eng. 14, 325 (1991). [CrossRef]
  4. M. R. Benoit, �??Applications des phenomenes d�??interference a des determinations metrologiques,�?? J. Phys. 3, 57 (1898).
  5. M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Seventh Edition, 2002).
  6. C. R. Tilford, �??Analytical procedure for determining lengths from fractional fringes,�?? Appl. Opt. 16, 1857 (1977). [CrossRef] [PubMed]
  7. A. Pfoertner, J. Schwider, �??Red-green-blue interferometer for the metrology of discontinuous structures,�?? Appl. Opt. 42, 667 (2003). [CrossRef]
  8. Y. Cheng, J. Wyant, �??Multiple-wavelength phase-shifting interferometry,�?? Appl. Opt. 24, 804 (1985). [CrossRef] [PubMed]
  9. C. Creath, �??Temporal Phase Measurement,�?? in Interferogram Analysis editors D.W. Robinson G. T. Reid (Bristol, Institute of Physics Publishing 1993).
  10. P.J. de Groot, �??Extending the unambiguous range of two-color interferometers,�?? Appl. Opt. 33, 5948 (1994). [CrossRef] [PubMed]
  11. C. E. Towers, D. P. Towers, J. D. C. Jones, �??Optimum frequency selection in multi-frequency interferometry,�?? Opt. Lett. 28, 887 (2003). [CrossRef] [PubMed]
  12. M. Reeves, A.J. Moore, D.P. Hand, J.D.C. Jones, �??Dynamic shape measurement system for laser materials processing,�?? Opt. Eng. 42, 2923 (2003). [CrossRef]
  13. K. H. Rosen, Elementary number theory and its applications (Addison-Wesley publishing Co., 1988).
  14. I. Agurok, �??The rigorous decision of the excess fraction method in absolute distance interferometry,�?? SPIE 3134, 504 (1997). [CrossRef]
  15. M Takeda, Q. Gu, M. Kinoshita, H Takai, Y Takahash, �??Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,�?? Appl. Opt. 36, 5347 (1997). [CrossRef] [PubMed]
  16. J. Zhong, Y. Zhang, �??Absolute phase measurement technique based on number theory in multi-frequency grating projection profilometry,�?? Appl. Opt. 40, 492 (2001). [CrossRef]
  17. J. M. Huntley, �??Random phase measurement errors in digital speckle pattern interferometry,�?? Opt. Lasers Eng. 26, 131 (1997). [CrossRef]

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