Abstract

In the past few years there has been much interest in use of tunable diode lasers for absolute interferometry. Here we report on use of an external cavity diode laser operating in the visible (λ ∼ 670 nm) for absolute distance measurements. Under laboratory conditions we achieve better than 1-µm standard uncertainty in distance measurements over a range of 5 m, but significantly larger uncertainties will probably be more typical of shop-floor measurements where conditions are far from ideal. We analyze the primary sources of uncertainty limiting the performance of wavelength-sweeping methods for absolute interferometry, and we discuss how errors can be minimized. Many errors are greatly magnified when the wavelength sweeping technique is used; sources of error that are normally relevant only at the nanometer level when standard interferometric techniques are used may be significant here for measurements at the micrometer level.

© 1999 Optical Society of America

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References

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  1. R. J. Tansey, “An absolute distance interferometer using a dye laser heterodyne interferometer and spatial separation of beams,” in Precision Surface Metrology, J. C. Wyant, ed., Proc. SPIE429, 43–54 (1983), and references therein.
  2. J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.
  3. J. A. Stone, A. Stejskal, L. Howard, “Wavelength shift interferometry: using a dither to improve accuracy,” in Proceedings of the Eleventh Annual Meeting of the American Society for Precision Engineering (American Society for Precision Engineering, Raleigh, N.C., 1996), pp. 357–362.
  4. J. Thiel, T. Pfeifer, C. Haas, “Absolute interferometric distance measurement with tunable laser diodes,” in Third International IMEKO Symposium on Laser Metrology for Precision Measurement and Inspection in Industry, VDI Berichte 1118, T. Pfeifer, ed. (VDI-Verlag, Duesseldorf, 1994), pp. 79–84.
  5. J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
    [CrossRef]
  6. D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
    [CrossRef]
  7. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by wavelength shift of laser diode light,” Appl. Opt. 25, 976–980 (1986).
    [CrossRef]
  8. H. Kikuta, R. Nagata, “Absolute distance measurement by wavelength shift interferometry with a laser diode: some systematic error sources,” Appl. Opt. 26, 1654–1660 (1987).
    [CrossRef] [PubMed]
  9. G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
    [CrossRef]
  10. K.-H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
    [CrossRef]
  11. R. R. Baldwin, G. B. Gordon, A. F. Rudé, “Remote laser interferometry,” Hewlett-Packard J. 23, 14–19 (1971).
  12. K. Liu, M. G. Littman, “Novel geometry for single-mode scanning of tunable lasers,” Opt. Lett. 6, 117–118 (1981).
    [CrossRef] [PubMed]
  13. The laser is New Focus Model 6308. See Ref. 14.
  14. Certain trade names and company products are mentioned in the text or identified in illustrations for adequate specification of the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by NIST nor does it imply that the products are necessarily the best available for the purpose.
  15. C.-M. Wu, C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996), and references therein.
    [CrossRef]
  16. J. Stone, L. Howard, “A simple technique for observing fringe interpolation errors in Michelson interferometers,” Precis. Eng. 22, 220–232 (1998).
    [CrossRef]
  17. J. Stone, S. D. Phillips, G. A. Mandolfo, “Corrections for wavelength variations in precision interferometric displacement measurements,” J. Res. Natl. Inst. Stand. Technol. 101, 671–674 (1996).
    [CrossRef]
  18. J. Stone, M. Schroeck, M. Stocker, “Testing displacement measuring interferometer systems,” presented at the 1998 Measurement Science Conference, Pasadena, Calif., 4–6 February 1998.
  19. International Organization for Standardization, “Guide to the expression of uncertainty in measurement” (ISO, Geneva, Switzerland, 1995).
  20. K. P. Birch, M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
    [CrossRef]
  21. The group refractive index ng is related to the phase refractive index np by ng ≈ np – (dnp/dλ0)λ0, where λ0 is the vacuum wavelength. See, for example, J. M. Rüeger, Electronic Distance Measurement (Springer-Verlag, Berlin, 1990), pp. 51–52.
  22. Y. Gürsel, “Metrology for spatial interferometry,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 27–34 (1994).
    [CrossRef]
  23. Association of German Engineers, VDI/VDE Society for Measurement and Control Technology, “Laser interferometry in length measurement,” (VDI-Verlag, Duesseldorf, 1985).

1998 (4)

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

K.-H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

J. Stone, L. Howard, “A simple technique for observing fringe interpolation errors in Michelson interferometers,” Precis. Eng. 22, 220–232 (1998).
[CrossRef]

1996 (2)

J. Stone, S. D. Phillips, G. A. Mandolfo, “Corrections for wavelength variations in precision interferometric displacement measurements,” J. Res. Natl. Inst. Stand. Technol. 101, 671–674 (1996).
[CrossRef]

C.-M. Wu, C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996), and references therein.
[CrossRef]

1995 (1)

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

1994 (1)

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

1987 (1)

1986 (1)

1981 (1)

1971 (1)

R. R. Baldwin, G. B. Gordon, A. F. Rudé, “Remote laser interferometry,” Hewlett-Packard J. 23, 14–19 (1971).

Baldwin, R. R.

R. R. Baldwin, G. B. Gordon, A. F. Rudé, “Remote laser interferometry,” Hewlett-Packard J. 23, 14–19 (1971).

Barwood, G. P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Bechstein, K.-H.

K.-H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Birch, K. P.

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

Downs, M. J.

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

Fuchs, W.

K.-H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Gill, P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Gordon, G. B.

R. R. Baldwin, G. B. Gordon, A. F. Rudé, “Remote laser interferometry,” Hewlett-Packard J. 23, 14–19 (1971).

Gürsel, Y.

Y. Gürsel, “Metrology for spatial interferometry,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 27–34 (1994).
[CrossRef]

Haas, C.

J. Thiel, T. Pfeifer, C. Haas, “Absolute interferometric distance measurement with tunable laser diodes,” in Third International IMEKO Symposium on Laser Metrology for Precision Measurement and Inspection in Industry, VDI Berichte 1118, T. Pfeifer, ed. (VDI-Verlag, Duesseldorf, 1994), pp. 79–84.

Haetmann, M.

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Hollberg, L.

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

Howard, L.

J. Stone, L. Howard, “A simple technique for observing fringe interpolation errors in Michelson interferometers,” Precis. Eng. 22, 220–232 (1998).
[CrossRef]

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

J. A. Stone, A. Stejskal, L. Howard, “Wavelength shift interferometry: using a dither to improve accuracy,” in Proceedings of the Eleventh Annual Meeting of the American Society for Precision Engineering (American Society for Precision Engineering, Raleigh, N.C., 1996), pp. 357–362.

Iwata, K.

Katuo, S.

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Kikuta, H.

Littman, M. G.

Liu, K.

Mandolfo, G. A.

J. Stone, S. D. Phillips, G. A. Mandolfo, “Corrections for wavelength variations in precision interferometric displacement measurements,” J. Res. Natl. Inst. Stand. Technol. 101, 671–674 (1996).
[CrossRef]

Nagata, R.

Oates, C.

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

Pfeifer, T.

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

J. Thiel, T. Pfeifer, C. Haas, “Absolute interferometric distance measurement with tunable laser diodes,” in Third International IMEKO Symposium on Laser Metrology for Precision Measurement and Inspection in Industry, VDI Berichte 1118, T. Pfeifer, ed. (VDI-Verlag, Duesseldorf, 1994), pp. 79–84.

Phillips, S. D.

J. Stone, S. D. Phillips, G. A. Mandolfo, “Corrections for wavelength variations in precision interferometric displacement measurements,” J. Res. Natl. Inst. Stand. Technol. 101, 671–674 (1996).
[CrossRef]

Rowley, W. R. C.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Rudé, A. F.

R. R. Baldwin, G. B. Gordon, A. F. Rudé, “Remote laser interferometry,” Hewlett-Packard J. 23, 14–19 (1971).

Rüeger, J. M.

The group refractive index ng is related to the phase refractive index np by ng ≈ np – (dnp/dλ0)λ0, where λ0 is the vacuum wavelength. See, for example, J. M. Rüeger, Electronic Distance Measurement (Springer-Verlag, Berlin, 1990), pp. 51–52.

Schroeck, M.

J. Stone, M. Schroeck, M. Stocker, “Testing displacement measuring interferometer systems,” presented at the 1998 Measurement Science Conference, Pasadena, Calif., 4–6 February 1998.

Stejskal, A.

J. A. Stone, A. Stejskal, L. Howard, “Wavelength shift interferometry: using a dither to improve accuracy,” in Proceedings of the Eleventh Annual Meeting of the American Society for Precision Engineering (American Society for Precision Engineering, Raleigh, N.C., 1996), pp. 357–362.

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

Stephens, M.

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

Stocker, M.

J. Stone, M. Schroeck, M. Stocker, “Testing displacement measuring interferometer systems,” presented at the 1998 Measurement Science Conference, Pasadena, Calif., 4–6 February 1998.

Stone, J.

J. Stone, L. Howard, “A simple technique for observing fringe interpolation errors in Michelson interferometers,” Precis. Eng. 22, 220–232 (1998).
[CrossRef]

J. Stone, S. D. Phillips, G. A. Mandolfo, “Corrections for wavelength variations in precision interferometric displacement measurements,” J. Res. Natl. Inst. Stand. Technol. 101, 671–674 (1996).
[CrossRef]

J. Stone, M. Schroeck, M. Stocker, “Testing displacement measuring interferometer systems,” presented at the 1998 Measurement Science Conference, Pasadena, Calif., 4–6 February 1998.

Stone, J. A.

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

J. A. Stone, A. Stejskal, L. Howard, “Wavelength shift interferometry: using a dither to improve accuracy,” in Proceedings of the Eleventh Annual Meeting of the American Society for Precision Engineering (American Society for Precision Engineering, Raleigh, N.C., 1996), pp. 357–362.

Su, C.-S.

C.-M. Wu, C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996), and references therein.
[CrossRef]

Tansey, R. J.

R. J. Tansey, “An absolute distance interferometer using a dye laser heterodyne interferometer and spatial separation of beams,” in Precision Surface Metrology, J. C. Wyant, ed., Proc. SPIE429, 43–54 (1983), and references therein.

Thiel, J.

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

J. Thiel, T. Pfeifer, C. Haas, “Absolute interferometric distance measurement with tunable laser diodes,” in Third International IMEKO Symposium on Laser Metrology for Precision Measurement and Inspection in Industry, VDI Berichte 1118, T. Pfeifer, ed. (VDI-Verlag, Duesseldorf, 1994), pp. 79–84.

Wu, C.-M.

C.-M. Wu, C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996), and references therein.
[CrossRef]

Xiaoli, D.

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Appl. Opt. (2)

Hewlett-Packard J. (1)

R. R. Baldwin, G. B. Gordon, A. F. Rudé, “Remote laser interferometry,” Hewlett-Packard J. 23, 14–19 (1971).

J. Opt. (1)

K.-H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol. (1)

J. Stone, S. D. Phillips, G. A. Mandolfo, “Corrections for wavelength variations in precision interferometric displacement measurements,” J. Res. Natl. Inst. Stand. Technol. 101, 671–674 (1996).
[CrossRef]

Meas. Sci. Technol. (3)

C.-M. Wu, C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996), and references therein.
[CrossRef]

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Measurement (1)

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Metrologia (1)

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

Opt. Lett. (1)

Precis. Eng. (1)

J. Stone, L. Howard, “A simple technique for observing fringe interpolation errors in Michelson interferometers,” Precis. Eng. 22, 220–232 (1998).
[CrossRef]

Other (11)

J. Stone, M. Schroeck, M. Stocker, “Testing displacement measuring interferometer systems,” presented at the 1998 Measurement Science Conference, Pasadena, Calif., 4–6 February 1998.

International Organization for Standardization, “Guide to the expression of uncertainty in measurement” (ISO, Geneva, Switzerland, 1995).

The laser is New Focus Model 6308. See Ref. 14.

Certain trade names and company products are mentioned in the text or identified in illustrations for adequate specification of the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by NIST nor does it imply that the products are necessarily the best available for the purpose.

R. J. Tansey, “An absolute distance interferometer using a dye laser heterodyne interferometer and spatial separation of beams,” in Precision Surface Metrology, J. C. Wyant, ed., Proc. SPIE429, 43–54 (1983), and references therein.

J. A. Stone, L. Howard, A. Stejskal, M. Stephens, C. Oates, L. Hollberg, “Novel methods for length measurement employing diode lasers,” in Proceedings of the 1996 NCSL Workshop and Symposium (National Conference of Standards Laboratories, Boulder Colo., 1996), pp. 667–676.

J. A. Stone, A. Stejskal, L. Howard, “Wavelength shift interferometry: using a dither to improve accuracy,” in Proceedings of the Eleventh Annual Meeting of the American Society for Precision Engineering (American Society for Precision Engineering, Raleigh, N.C., 1996), pp. 357–362.

J. Thiel, T. Pfeifer, C. Haas, “Absolute interferometric distance measurement with tunable laser diodes,” in Third International IMEKO Symposium on Laser Metrology for Precision Measurement and Inspection in Industry, VDI Berichte 1118, T. Pfeifer, ed. (VDI-Verlag, Duesseldorf, 1994), pp. 79–84.

The group refractive index ng is related to the phase refractive index np by ng ≈ np – (dnp/dλ0)λ0, where λ0 is the vacuum wavelength. See, for example, J. M. Rüeger, Electronic Distance Measurement (Springer-Verlag, Berlin, 1990), pp. 51–52.

Y. Gürsel, “Metrology for spatial interferometry,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 27–34 (1994).
[CrossRef]

Association of German Engineers, VDI/VDE Society for Measurement and Control Technology, “Laser interferometry in length measurement,” (VDI-Verlag, Duesseldorf, 1985).

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Figures (6)

Fig. 1
Fig. 1

Configuration of the ADI. AOM, acousto-optic modulator; Pr, wedge prisms; HWP, half-wave plate; BS, nonpolarizing beam splitter; PBS, polarizing beam splitter; Det, photodetector; Pol, 45° polarizer; R, cube-corner retroreflector. Some details are omitted for clarity. (The long arm of the reference interferometer is actually folded by use of two mirrors. Several other steering mirrors and the mode hop detector are not shown.)

Fig. 2
Fig. 2

Detailed view of interferometer geometry. We use solid beam-splitter cubes and solid cube-corner retroreflectors. The two incoming beams are offset from each other. One retroreflector is offset in an appropriate manner to ensure that the return beams overlap. The numbered points in the diagram show the location of some of the possible reflections at glass–air interfaces, as discussed in Subsection 5.E.

Fig. 3
Fig. 3

Errors in the absolute interferometer over a range 0.3–5 m, with a shielded beam path. The diagram shows 250 measurements of ADI errors determined by comparison of the ADI with an incremental interferometer.

Fig. 4
Fig. 4

Variations in rms in a 5-m path length under typical laboratory conditions.

Fig. 5
Fig. 5

Phasor diagram showing the change in phase of electric field E f resulting from the presence of a small spurious field component ε.

Fig. 6
Fig. 6

Alignment errors. The image of one retroreflector, indicated as a dashed-line triangle, is offset from the second retroreflector by a distance δ perpendicular to the beam direction.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

lmeas=lrefΔφmeas/Δφref,
lref=Δl/Δφmeas/Δφref1-Δφmeas/Δφref0,
1/λs=|1/λf-1/λi|Δλ/λ2,
δφmax±tan-1ε/E±ε/E.
δφmaxr1/2exp-2πwβ/λ2.
Δx=-d sin θΔθ-d cos θΔθ2/2=-δΔθ-d cos θΔθ2/2,
emax=±λs/4πtan-1Psecondary/Pprimary,

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