Abstract

We present a point-diffraction interferometer that has been specially devised to perform absolute distance measurements in three dimensions. It is composed of two main parts: One is a target that moves in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The target is made of point-diffraction sources that emit two spherical wave fronts, whose interference is monitored by the photodetectors. Application of a phase-shifting technique allows the phase values of the photodetectors to be precisely measured, which are then fitted to a geometric model of multilateration so as to determine the xyz location of the target by minimization of least-squares errors. Experimental results show that the proposed diffraction interferometer is capable of measuring the xyz coordinates of the target with a volumetric uncertainty of less than 1.0 µm over a working volume of a 100-mm side.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).
  2. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 7.
  3. J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).
  4. K. Freischlad, C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7, 542–551 (1990).
    [CrossRef]
  5. P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
    [CrossRef]
  6. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993), and references therein.
    [CrossRef]
  7. P. de Groot, “Grating interferometer for flatness testing,” Opt. Lett. 21, 228–230 (1996).
    [CrossRef] [PubMed]
  8. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [CrossRef]
  9. Z. Sodnik, E. Fischer, T. Ittner, H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
    [CrossRef] [PubMed]
  10. T. Li, A. Wang, K. Murphy, R. Claus, “White-light scanning fiber Michelson interferometer for absolute position-distance measurement,” Opt. Lett. 20, 785–787 (1995).
    [CrossRef] [PubMed]
  11. U. Schnell, R. Dandliker, “Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target,” Opt. Lett. 21, 528–530 (1996).
    [CrossRef] [PubMed]
  12. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
    [CrossRef] [PubMed]
  13. H. Kikuta, K. Iwata, R. Nagata, “Absolute distance measurement by wavelength shift interferometry with a laser diode light: some systematic error sources,” Appl. Opt. 26, 1654–1660 (1987).
    [CrossRef] [PubMed]
  14. A. J. den Boef, “Interferometric laser rangefinder using a frequency modulated diode laser,” Appl. Opt. 26, 4545–4550 (1987).
    [CrossRef]
  15. E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 34, 5589–5594 (1995).
    [CrossRef] [PubMed]
  16. J. A. Stone, A. Stejskal, L. Howard, “Absolute interferometry with a 670-nm external cavity diode laser,” Appl. Opt. 38, 5981–5994 (1999).
    [CrossRef]
  17. S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” Ann. CIRP 51, 357–360 (2001).
    [CrossRef]
  18. O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
    [CrossRef]
  19. E. B. Hughes, A. Wilson, G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Ann. CIRP 49, 391–394 (2000).
    [CrossRef]
  20. A. D. Belegundu, T. R. Chandrupatla, Optimization Concepts and Applications in Engineering (Prentice-Hall, Upper Saddle River, N.J., 1999), pp. 74–79.
  21. J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983), pp. 116–133.
  22. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 156–161.
  23. S. Kimura, T. Wilson, “Confocal scanning optical microscope using single-mode fiber for signal detection,” Appl. Opt. 30, 2143–2150 (1991).
    [CrossRef] [PubMed]
  24. I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).
    [CrossRef]
  25. K. A. Goldberg, J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
    [CrossRef]
  26. J. B. Bryan, “The Abbe principle revisited: an updated interpretation, Precis. Eng. 1, 129–132 (1979).
  27. International Organization for Standardization, “Guide to the expression of uncertainty in measurement,” in International Vocabulary of Basic and General Terms in Metrology, 2nd ed. (International Organization for Standardization, Geneva, Switzerland, 1993).

2001 (2)

S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” Ann. CIRP 51, 357–360 (2001).
[CrossRef]

K. A. Goldberg, J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
[CrossRef]

2000 (1)

E. B. Hughes, A. Wilson, G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Ann. CIRP 49, 391–394 (2000).
[CrossRef]

1999 (1)

1996 (2)

1995 (4)

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993), and references therein.
[CrossRef]

1991 (3)

1990 (1)

1987 (2)

1986 (2)

H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
[CrossRef] [PubMed]

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

1982 (1)

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).

1979 (1)

J. B. Bryan, “The Abbe principle revisited: an updated interpretation, Precis. Eng. 1, 129–132 (1979).

Belegundu, A. D.

A. D. Belegundu, T. R. Chandrupatla, Optimization Concepts and Applications in Engineering (Prentice-Hall, Upper Saddle River, N.J., 1999), pp. 74–79.

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993), and references therein.
[CrossRef]

Bokor, J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 7.

Bryan, J. B.

J. B. Bryan, “The Abbe principle revisited: an updated interpretation, Precis. Eng. 1, 129–132 (1979).

Chandrupatla, T. R.

A. D. Belegundu, T. R. Chandrupatla, Optimization Concepts and Applications in Engineering (Prentice-Hall, Upper Saddle River, N.J., 1999), pp. 74–79.

Claus, R.

Dalhoff, E.

Dandliker, R.

de Groot, P.

den Boef, A. J.

Dennis, J. E.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983), pp. 116–133.

Fischer, E.

Freischlad, K.

Goldberg, K. A.

Goto, M.

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
[CrossRef]

Heim, S.

Hofbauer, U.

Howard, L.

Hughes, E. B.

E. B. Hughes, A. Wilson, G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Ann. CIRP 49, 391–394 (2000).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 156–161.

Ittner, T.

Iwata, K.

Kikuta, H.

Kim, S. W.

S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” Ann. CIRP 51, 357–360 (2001).
[CrossRef]

Kim, S.-W.

I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).
[CrossRef]

Kimura, S.

Koliopoulos, C. L.

Kong, I.-B.

I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).
[CrossRef]

Kurosawa, T.

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
[CrossRef]

Li, T.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

Murphy, K.

Nagata, R.

Nakamura, O.

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
[CrossRef]

Peggs, G. N.

E. B. Hughes, A. Wilson, G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Ann. CIRP 49, 391–394 (2000).
[CrossRef]

Schnabel, R. B.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983), pp. 116–133.

Schnell, U.

Sodnik, Z.

Stejskal, A.

Stone, J. A.

Tanimura, Y.

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
[CrossRef]

Tiziani, H. J.

Toyoda, K.

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
[CrossRef]

Wang, A.

Wickramasinghe, H. K.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Williams, C. C.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Wilson, A.

E. B. Hughes, A. Wilson, G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Ann. CIRP 49, 391–394 (2000).
[CrossRef]

Wilson, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 7.

Wyant, J. C.

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).

Ann. CIRP (3)

S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” Ann. CIRP 51, 357–360 (2001).
[CrossRef]

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Ann. CIRP 40, 523–526 (1991).
[CrossRef]

E. B. Hughes, A. Wilson, G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Ann. CIRP 49, 391–394 (2000).
[CrossRef]

Appl. Opt. (9)

H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
[CrossRef] [PubMed]

H. Kikuta, K. Iwata, R. Nagata, “Absolute distance measurement by wavelength shift interferometry with a laser diode light: some systematic error sources,” Appl. Opt. 26, 1654–1660 (1987).
[CrossRef] [PubMed]

A. J. den Boef, “Interferometric laser rangefinder using a frequency modulated diode laser,” Appl. Opt. 26, 4545–4550 (1987).
[CrossRef]

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 34, 5589–5594 (1995).
[CrossRef] [PubMed]

J. A. Stone, A. Stejskal, L. Howard, “Absolute interferometry with a 670-nm external cavity diode laser,” Appl. Opt. 38, 5981–5994 (1999).
[CrossRef]

P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
[CrossRef]

Z. Sodnik, E. Fischer, T. Ittner, H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
[CrossRef] [PubMed]

S. Kimura, T. Wilson, “Confocal scanning optical microscope using single-mode fiber for signal detection,” Appl. Opt. 30, 2143–2150 (1991).
[CrossRef] [PubMed]

K. A. Goldberg, J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
[CrossRef]

J. Appl. Phys. (1)

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

J. Opt. Soc. Am. A (1)

Laser Focus (1)

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).

Meas. Sci. Technol. (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993), and references therein.
[CrossRef]

Opt. Eng. (1)

I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).
[CrossRef]

Opt. Lett. (3)

Precis. Eng. (1)

J. B. Bryan, “The Abbe principle revisited: an updated interpretation, Precis. Eng. 1, 129–132 (1979).

Other (6)

International Organization for Standardization, “Guide to the expression of uncertainty in measurement,” in International Vocabulary of Basic and General Terms in Metrology, 2nd ed. (International Organization for Standardization, Geneva, Switzerland, 1993).

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), Chap. 7.

A. D. Belegundu, T. R. Chandrupatla, Optimization Concepts and Applications in Engineering (Prentice-Hall, Upper Saddle River, N.J., 1999), pp. 74–79.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983), pp. 116–133.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 156–161.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Geometry of the absolute distance interferometer.

Fig. 2
Fig. 2

Interference of two spherical wave fronts.

Fig. 3
Fig. 3

Equal-phase contours in the xz plane.

Fig. 4
Fig. 4

Hardware configuration of the absolute distance measuring interferometer.

Fig. 5
Fig. 5

Configuration of fiber optics for phase shifting.

Fig. 6
Fig. 6

Stabilization of frequency and power of the He-Ne laser source.

Fig. 7
Fig. 7

Variation of computation time with the number of photodetectors.

Fig. 8
Fig. 8

Selection of photodetectors from a CCD array.

Fig. 9
Fig. 9

Convergence of the numerical search to the global minimum. The specified iteration numbers indicate the total number of iterations before convergence. (a) Relation for xy. (b) Relation for xz.

Fig. 10
Fig. 10

Experiment for accuracy verification of the absolute distance interferometer.

Fig. 11
Fig. 11

Test results for measurement repeatability for (a) x, (b) y, (c) z. PV, peak-to-valley values.

Fig. 12
Fig. 12

Test results for one-dimensional uncertainty in comparison with a heterodyne He-Ne laser interferometer.

Tables (2)

Tables Icon

Table 1 Error Sources and Their Contributions to the Overall Uncertainty of the Absolute Distance Interferometera

Tables Icon

Table 2 Uncertainty for Three Photodetectors of Different Sizesa

Equations (11)

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

u=Urexp-j2πλ r+ϕ,
I=|u1+u2|2=Π+Γ cosΦ+Δϕ,
ΠU12r12+U22r22, Γ2U1U2r1r2, Φ2πλr1-r2, Δϕϕ1-ϕ2.
Φx, y, z=2πλr1x, y, z-r2x, y, z =2πλx1-x2+y1-y2+z1-z21/2-x2-x2+y2-y2+z2-z21/2,
Φp=Φ-2πn+Δϕ,
Φuk=Φk-2πn0+Δϕ,
Λk=λ2πΦuk-Φu0=λ2πΦk-Φ0-2πn0-n0+Δϕ-Δϕ =λ2πΦk-Φ0.
Λk=λ2πΦk-Φ0,
Φk=2πλx1-xk2+y1-yk2+z1-zk21/2-x2-xk2+y2-yk2+z2-zk21/2, Φ0=2πλx1-x02+y1-y02+z1-z021/2-x2-x02+y2-y02+z2-z021/2.
E=kλ2πΦk-Φ0-Λk2.
Ij=Π+Γ cosΦ+Δϕj for j=0, 1, 2,.

Metrics