OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 28 — Oct. 1, 2003
  • pp: 5670–5678

Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry—application to absolute long gauge block measurement

Jennifer E. Decker, John R. Miles, Alan A. Madej, Ralph F. Siemsen, Klaus J. Siemsen, Sebastian de Bonth, Krijn Bustraan, Sara Temple, and James R. Pekelsky  »View Author Affiliations

Applied Optics, Vol. 42, Issue 28, pp. 5670-5678 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (318 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An instrument for step-height measurement by multiple-wavelength interferometry is described. The addition of a 1152-nm wavelength to a multiple-wavelength scheme applying wavelengths of 633, 612, and 543 nm relaxes the tolerance range of the required preliminary measurement to ±140 μm, if the total uncertainty in the fringe fraction measurement can be kept below 2%. For larger fringe fraction measurement uncertainty, numerical simulations show that the integer number of interference orders can still be determined unambiguously if the range in the preliminary knowledge of the length has been correspondingly reduced. The interferometer instrument is described, and experimental data are presented in the context of long gauge block calibration at the National Research Council of Canada.

© 2003 Optical Society of America

OCIS Codes
(000.2170) General : Equipment and techniques
(120.2830) Instrumentation, measurement, and metrology : Height measurements
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: December 13, 2002
Revised Manuscript: April 30, 2003
Published: October 1, 2003

Jennifer E. Decker, John R. Miles, Alan A. Madej, Ralph F. Siemsen, Klaus J. Siemsen, Sebastian de Bonth, Krijn Bustraan, Sara Temple, and James R. Pekelsky, "Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry—application to absolute long gauge block measurement," Appl. Opt. 42, 5670-5678 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. J. Quinn, “Practical realisation of the definition of the metre (2001),” Metrologia 40, 103–133 (2003), www.bipm.fr . [CrossRef]
  2. A. A. Michelson, J. R. Benoit, “Valeur du mètre en longueurs d’ondes,” Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).
  3. J. R. Benoit, “Application des phénomènes d’interférence à des déterminations métrologiques,” J. Phys. (Paris) VII 3, 57–68 (1898).
  4. D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 7.
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 286–306.
  6. K. Creath, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds, (Institute of Physics, London), (1993), pp. 136–138.
  7. C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977). [CrossRef] [PubMed]
  8. K. Creath, “Step-height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987). [CrossRef] [PubMed]
  9. Y. Cheng, J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,”Appl. Opt. 24, 804–807 (1985). [CrossRef] [PubMed]
  10. Bureau International des Poids et Mesures, Comité Consultatif pour la Définition du Mètre, 3rd session 18–19 (1962).
  11. Bureau International des Poids et Mesures, Procès-Verbaux52nd session 26–27 (1963).
  12. A. Lewis, “Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple-wavelength phase-stepping interferometry,” Meas. Sci. Technol. 5, 694–703 (1994). [CrossRef]
  13. P. Hariharan, Basics of Interferometry (Academic, New York, 1992), Chap. 8.
  14. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement [International Organization for Standardization (ISO) Central Secretariat, Geneva, Switzerland 1993], iso@iso.ch).
  15. K. J. Siemsen, R. F. Siemsen, J. E. Decker, L. Marmet, J. R. Pekelsky, “A multiple frequency heterodyne technique for the measurement of long gauges,” Metrologia 33, 555–563 (1996).
  16. International Organization for Standardization, International Vocabulary of Basic and General Terms in Metrology, 2nd ed. International Organization for Standardization (Central Secretariat, Geneva Switzerland, 1993).
  17. J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34(6), 479–493 (1997). [CrossRef]
  18. R. Schödel, A. Nicolaus, G. Bönsch, “Phase-stepping interferometry: methods for reducing errors caused by camera nonlinearities,” Appl. Opt. 41, 55–63 (2002). [CrossRef] [PubMed]
  19. I. Powell, E. Goulet, “Absolute figure measurements with a liquid-flat reference,” Appl. Opt. 37, 2579–2588 (1998). [CrossRef]
  20. J. E. Decker, K. Bustraan, S. de Bonth, J. R. Pekelsky, “Updates to the NRC gauge block interferometer,” National Research Council Document. 42753National Research Council, Ottawa, Canada, (2000).
  21. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996). [CrossRef] [PubMed]
  22. K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994). [CrossRef]
  23. G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998). [CrossRef]
  24. The gallium melting point is one of the fixed points identified in the International Temperature Scale of 1990 (ITS-90) to define the SI temperature scale. The thermistor probes are placed in a specially designed cell (Thermometry Group, NRC) that allows the probes to be placed in close thermal contact with high-purity gallium during the phase transition. The temperature is measured over the melting-point plateau, verifying that the temperature measurement of the GBIF system agrees with the 29.765 °C fixed point of the cell.
  25. D. C. Williams, “The parallelism of a length bar with an end load,” J. Sci. Instrum. 39, 608–610 (1962). [CrossRef]
  26. G. Bönsch, “Interferometric calibration of an integrating sphere for determination of the roughness correction of gauge blocks,” in Recent Developments in Optical Gauge Block Metrology, J. E. Decker, N. Brown, eds., Proc. SPIE3477, 152–160 (1998). [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