Abstract

We present a new method of volumetric interferometer, which is intended to measure the three-dimensional coordinates of a moving object in a simultaneous way with a single optical setup. The method is based on the principles of phase-measuring interferometry with phase shifting. Two diffraction point sources, which are made of the polished ends of single-mode optical fibers are embedded on the object. Two spherical wavefronts emanate from the diffraction point sources and interfere with each other within the measurement volume. One wavefront is phase-shifted by elongating the corresponding fiber using a PZT extender. A CCD array sensor fixed at the stationary measurement station detects the resulting interference field. The measured phases are then related to the three-dimensional location of the object with a set of non-liner equations of Euclidean distance, from which the complete set of three-dimensional spatial coordinates of the object is determined through rigorous numerical computation based upon the least square error minimization.

© 2001 Optical Society of Korea

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  1. J. B. Bryan, Precision Eng. 1, 129 (1979)
    [CrossRef]
  2. O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, and T. Kurosawa, Ann. CIRP 40, 523 (1991)
    [CrossRef]
  3. O. Nakamura and M. Goto, Appl. Opt. 33, 31 (1994)
    [CrossRef]
  4. E. B. Hughes, A Wilson, and G. N. Peggs, Ann. CIRP 49, 391 (2000)
    [CrossRef]
  5. A. Ishimaru, Electromagnetic wave propagation, radiation, and scattering (Prentice-Hall, Inc., 1991), 156
  6. S. Kimura and T. Wilson, Appl. Opt. 30, 2143 (1991)
    [CrossRef]
  7. I. B. Kong and S. W. Kim, Opt. Eng. 34, 183 (1995)
    [CrossRef]
  8. A. D. Belegundu and T. R. Chandrupatla, Optimization concepts and applications in engineering (Prentice-Hall, Inc., 1999),74
  9. P. E. Gill and W. Murray, J. Inst. Maths. Applns. 9, 91 (1972)
    [CrossRef]
  10. J. E. Dennis and R. B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations (Prentice-Hall, Inc., 1983), 1163
  11. T. R. Chandrupatla, Computer Methods in Applied Mechanics and Engineering 152, 211 (1999)
    [CrossRef]

2000 (1)

E. B. Hughes, A Wilson, and G. N. Peggs, Ann. CIRP 49, 391 (2000)
[CrossRef]

1999 (2)

A. D. Belegundu and T. R. Chandrupatla, Optimization concepts and applications in engineering (Prentice-Hall, Inc., 1999),74

T. R. Chandrupatla, Computer Methods in Applied Mechanics and Engineering 152, 211 (1999)
[CrossRef]

1995 (1)

I. B. Kong and S. W. Kim, Opt. Eng. 34, 183 (1995)
[CrossRef]

1994 (1)

O. Nakamura and M. Goto, Appl. Opt. 33, 31 (1994)
[CrossRef]

1991 (3)

A. Ishimaru, Electromagnetic wave propagation, radiation, and scattering (Prentice-Hall, Inc., 1991), 156

S. Kimura and T. Wilson, Appl. Opt. 30, 2143 (1991)
[CrossRef]

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, and T. Kurosawa, Ann. CIRP 40, 523 (1991)
[CrossRef]

1983 (1)

J. E. Dennis and R. B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations (Prentice-Hall, Inc., 1983), 1163

1979 (1)

J. B. Bryan, Precision Eng. 1, 129 (1979)
[CrossRef]

1972 (1)

P. E. Gill and W. Murray, J. Inst. Maths. Applns. 9, 91 (1972)
[CrossRef]

Applied Optics (2)

O. Nakamura and M. Goto, Appl. Opt. 33, 31 (1994)
[CrossRef]

S. Kimura and T. Wilson, Appl. Opt. 30, 2143 (1991)
[CrossRef]

CIRP Annals - Manufacturing Technology (2)

E. B. Hughes, A Wilson, and G. N. Peggs, Ann. CIRP 49, 391 (2000)
[CrossRef]

O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, and T. Kurosawa, Ann. CIRP 40, 523 (1991)
[CrossRef]

Computer Methods in Applied Mechanics and Engineering (1)

T. R. Chandrupatla, Computer Methods in Applied Mechanics and Engineering 152, 211 (1999)
[CrossRef]

IMA Journal of Applied Mathematics (1)

P. E. Gill and W. Murray, J. Inst. Maths. Applns. 9, 91 (1972)
[CrossRef]

Opt. Eng. (1)

I. B. Kong and S. W. Kim, Opt. Eng. 34, 183 (1995)
[CrossRef]

Precision Engineering (1)

J. B. Bryan, Precision Eng. 1, 129 (1979)
[CrossRef]

Other (3)

A. Ishimaru, Electromagnetic wave propagation, radiation, and scattering (Prentice-Hall, Inc., 1991), 156

A. D. Belegundu and T. R. Chandrupatla, Optimization concepts and applications in engineering (Prentice-Hall, Inc., 1999),74

J. E. Dennis and R. B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations (Prentice-Hall, Inc., 1983), 1163

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