Abstract

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

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  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]

2003 (1)

T. J. Quinn, “Practical realisation of the definition of the metre (2001),” Metrologia 40, 103–133 (2003), www.bipm.fr .
[CrossRef]

2002 (1)

1998 (2)

I. Powell, E. Goulet, “Absolute figure measurements with a liquid-flat reference,” Appl. Opt. 37, 2579–2588 (1998).
[CrossRef]

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

1997 (1)

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34(6), 479–493 (1997).
[CrossRef]

1996 (2)

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
[CrossRef] [PubMed]

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).

1994 (2)

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

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]

1987 (1)

1985 (1)

1977 (1)

1962 (1)

D. C. Williams, “The parallelism of a length bar with an end load,” J. Sci. Instrum. 39, 608–610 (1962).
[CrossRef]

1898 (1)

J. R. Benoit, “Application des phénomènes d’interférence à des déterminations métrologiques,” J. Phys. (Paris) VII 3, 57–68 (1898).

1895 (1)

A. A. Michelson, J. R. Benoit, “Valeur du mètre en longueurs d’ondes,” Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Benoit, J. R.

J. R. Benoit, “Application des phénomènes d’interférence à des déterminations métrologiques,” J. Phys. (Paris) VII 3, 57–68 (1898).

A. A. Michelson, J. R. Benoit, “Valeur du mètre en longueurs d’ondes,” Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Birch, K. P.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Bönsch, G.

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]

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

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]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 286–306.

Bustraan, K.

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).

Cheng, Y.

Ciddor, P. E.

Creath, K.

K. Creath, “Step-height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

K. Creath, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds, (Institute of Physics, London), (1993), pp. 136–138.

de Bonth, S.

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).

Decker, J. E.

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34(6), 479–493 (1997).
[CrossRef]

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).

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).

Downs, M. J.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Goulet, E.

Hariharan, P.

P. Hariharan, Basics of Interferometry (Academic, New York, 1992), Chap. 8.

Lewis, A.

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]

Malacara, D.

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 7.

Malacara, Z.

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 7.

Marmet, L.

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).

Michelson, A. A.

A. A. Michelson, J. R. Benoit, “Valeur du mètre en longueurs d’ondes,” Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Nicolaus, A.

Pekelsky, J. R.

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34(6), 479–493 (1997).
[CrossRef]

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).

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).

Potulski, E.

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

Powell, I.

Quinn, T. J.

T. J. Quinn, “Practical realisation of the definition of the metre (2001),” Metrologia 40, 103–133 (2003), www.bipm.fr .
[CrossRef]

Schödel, R.

Servin, M.

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 7.

Siemsen, K. J.

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).

Siemsen, R. F.

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).

Tilford, C. R.

Williams, D. C.

D. C. Williams, “The parallelism of a length bar with an end load,” J. Sci. Instrum. 39, 608–610 (1962).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 286–306.

Wyant, J. C.

Appl. Opt. (6)

J. Phys. (Paris) VII (1)

J. R. Benoit, “Application des phénomènes d’interférence à des déterminations métrologiques,” J. Phys. (Paris) VII 3, 57–68 (1898).

J. Sci. Instrum. (1)

D. C. Williams, “The parallelism of a length bar with an end load,” J. Sci. Instrum. 39, 608–610 (1962).
[CrossRef]

Meas. Sci. Technol. (1)

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]

Metrologia (5)

T. J. Quinn, “Practical realisation of the definition of the metre (2001),” Metrologia 40, 103–133 (2003), www.bipm.fr .
[CrossRef]

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

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).

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34(6), 479–493 (1997).
[CrossRef]

Trav. Mem. Bur. Int. Poids Mes. (1)

A. A. Michelson, J. R. Benoit, “Valeur du mètre en longueurs d’ondes,” Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Other (11)

P. Hariharan, Basics of Interferometry (Academic, New York, 1992), Chap. 8.

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).

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 7.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 286–306.

K. Creath, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds, (Institute of Physics, London), (1993), pp. 136–138.

Bureau International des Poids et Mesures, Comité Consultatif pour la Définition du Mètre, 3rd session 18–19 (1962).

Bureau International des Poids et Mesures, Procès-Verbaux52nd session 26–27 (1963).

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).

International Organization for Standardization, International Vocabulary of Basic and General Terms in Metrology, 2nd ed. International Organization for Standardization (Central Secretariat, Geneva Switzerland, 1993).

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.

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]

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Figures (6)

Fig. 1
Fig. 1

Gauge block central length measurement is the geometrically simplest form of a step-height measurement.

Fig. 2
Fig. 2

Plot of R, the rms of the residuals, versus the test length for a 100-mm gauge block with theoretical fractions: (a) the two-wavelength scheme of 543 and 633 nm; (b) the three-wavelength scheme of 543, 612, and 633 nm; (c) the four-wavelength scheme of 543, 612, 633, and 1152 nm. The minima are labeled with their distance from the 100-mm minimum in micrometers. Wavelengths used in the calculations are 632.9911815, 611.9703403, 543.5153670, and 1152.59116 nm.

Fig. 3
Fig. 3

Blunder solutions for increasing total fringe fraction measurement uncertainty plotted for the three (open circles) and four-wavelength (filled triangles) schemes presented in the text. This figure demonstrates that the first blunder would be possible with a fringe fraction measurement uncertainty of 1% in the three-wavelength scheme and 2% for the four-wavelength scheme. This figure also shows the improved discrimination of the four-wavelength technique.

Fig. 4
Fig. 4

Schematic diagram of the NRC GBIF instrument. Laser beams are directed by high-reflecting mirrors (HR) and interference filters (IF) through a microscope objective (OBJ) into a multimode fiber. The fiber end (FE) serves as the point light source for the entrance collimator. At the beam splitter (BS) one beam is directed along the test arm toward the gauge block (GB), or step height, and the other beam is directed to the reference mirror (RM). The exit collimator is fitted with a pupil and Dove prism (DP) or autocollimation alignment optics (AA). The image is viewed on a video monitor, and data are collected and analyzed by computer. The interferometer system is covered with a hermetic enclosure (HE) and supported on air pucks for stability of the image. Air temperature (T), pressure (P), and relative humidity (RH) are measured by sensors as described in the text.

Fig. 5
Fig. 5

Length evaluation results from experimental data for a 100-mm gauge block by the three-wavelength scheme. Note the number of possible solutions and the small differences in R values between them. The minima are labeled with their distance from the 100-mm minimum in micrometers.

Fig. 6
Fig. 6

The four-wavelength case, with the same three-wavelength experimental data used in Fig. 5, and the addition of the infrared wavelength and associated measurements. The correct solution is clearly identified, within a range of ±138 μm. The minima are labeled with their distance from the 100-mm minimum in micrometers.

Equations (3)

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l=m1+f1λ12=m2+f2λ22=  =mi+fiλi2,
R=inlt-mi+fiλi221/2
λs=λ1λ2|λ1-λ2|.

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