Abstract

We describe a method of absolute xyz-coordinates measurement based on the two-point diffraction interferometer. In this paper we use a new optimization algorithm to the interferometer. Experimental results show that the systematic error of the interferometer is less than 1 μm (peak-to-valley value) within a 60 mm by 60 mm by 20 mm working volume. To extract the systematic error and verify the absolute performance of the interferometer we applied the Fourier self-calibration concept.

©2007 Optical Society of America

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References

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  9. J. Ye, “Absolute measurement of long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29, 1153–1155 (2004).
    [Crossref] [PubMed]
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    [Crossref]
  11. K. Lau, R. J. Hocken, and W. C. Haight, “Automatic laser tracking interferometer system for robot metrology,” Prec. Eng. 8, 3–8 (1986).
    [Crossref]
  12. O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura, and T. Kurosawa, “Development of a coordinate measuring system with tracking laser interferometer,” Annals of CIRP 40, 523–526 (1991).
    [Crossref]
  13. E. B. Hughes, A Wilson, and G. N. Peggs, “Design of a high-accuracy CMM based on multi-lateration techniques,” Annals of CIRP 49, 391–394 (2000).
    [Crossref]
  14. H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
    [Crossref]
  15. H.G. Rhee and S.W. Kim, “Absolute distance measurement by two-point diffraction interferometry,” Appl. Opt. 41, 5921–5928 (2002).
    [Crossref] [PubMed]
  16. J. Chu and S. W. Kim, “Absolute distance measurement by lateral shearing interferometry of point-diffracted spherical waves,” Opt. Express 14, 5961–5967 (2006).
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  17. J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
    [Crossref]
  18. A. D. Belegundu and T.R. Chandrupatla, “Simulated annealing (SA),” in Optimization concepts and applications in engineering, M. Horton, ed. (Prentice-Hall, Inc., New Jersey, 1999).
  19. H. Kihm and S. W. Kim, “Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers,” Opt. Lett. 29, 2366–2368 (2004).
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  21. D. G. Cameron, J. K. Kauppinen, D. J. Moffatt, and H. H. Mantsch, “Precision in condensed phase vibrational spectroscopy,” Appl. Spectrosc. 36, 245–250 (1982).
    [Crossref]

2006 (1)

2004 (2)

2002 (2)

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

H.G. Rhee and S.W. Kim, “Absolute distance measurement by two-point diffraction interferometry,” Appl. Opt. 41, 5921–5928 (2002).
[Crossref] [PubMed]

2000 (2)

K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39, 5512–5517 (2000).
[Crossref]

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

1997 (1)

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

1996 (2)

1995 (1)

1993 (1)

1991 (2)

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

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

1988 (1)

1987 (1)

1986 (2)

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

K. Lau, R. J. Hocken, and W. C. Haight, “Automatic laser tracking interferometer system for robot metrology,” Prec. Eng. 8, 3–8 (1986).
[Crossref]

1982 (1)

Belegundu, A. D.

A. D. Belegundu and T.R. Chandrupatla, “Simulated annealing (SA),” in Optimization concepts and applications in engineering, M. Horton, ed. (Prentice-Hall, Inc., New Jersey, 1999).

Berglund, C. N.

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

Cameron, D. G.

Chandrupatla, T.R.

A. D. Belegundu and T.R. Chandrupatla, “Simulated annealing (SA),” in Optimization concepts and applications in engineering, M. Horton, ed. (Prentice-Hall, Inc., New Jersey, 1999).

Chu, J.

Claus, R.

Dandliker, R.

de Groot, P.

Fischer, E.

Fujimoto, J. G.

Goto, M.

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

Haight, W. C.

K. Lau, R. J. Hocken, and W. C. Haight, “Automatic laser tracking interferometer system for robot metrology,” Prec. Eng. 8, 3–8 (1986).
[Crossref]

Hee, M. R.

Hocken, R. J.

K. Lau, R. J. Hocken, and W. C. Haight, “Automatic laser tracking interferometer system for robot metrology,” Prec. Eng. 8, 3–8 (1986).
[Crossref]

Hughes, E. B.

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

Ittner, T.

Iwata, K.

Izatt, J. A.

Jacobson, J. M.

Jiang, H.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

Kauppinen, J. K.

Kihm, H.

Kikuta, H.

Kim, S. W.

Kim, S.W.

Kurosawa, T.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

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

Lau, K.

K. Lau, R. J. Hocken, and W. C. Haight, “Automatic laser tracking interferometer system for robot metrology,” Prec. Eng. 8, 3–8 (1986).
[Crossref]

Li, T.

Mantsch, H. H.

Matsumoto, H.

Merphy, K.

Minoshima, K.

Moffatt, D. J.

Nagata, R.

Nakamura, O.

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

Noguchi, H.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

Osawa, S.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

Owen, G.

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

Pease, R. F.

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

Peggs, G. N.

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

Prongue, D.

Rhee, H.G.

Schnell, U.

Sodnik, Z.

Swanson, E. A.

Takac, M.

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

Takatsuji, T.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

Tanimura, Y.

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

Thalmann, R.

Tiziani, H. J.

Toyoda, K.

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

Wang, A.

Wilson, A

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

Ye, J.

J. Ye, “Absolute measurement of long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29, 1153–1155 (2004).
[Crossref] [PubMed]

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

Annals of CIRP (2)

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

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

Appl. Opt. (5)

Appl. Spectrosc. (1)

Opt. Eng. (1)

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulation mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41, 632–637 (2002).
[Crossref]

Opt. Express (1)

Opt. Lett. (7)

Prec. Eng. (2)

K. Lau, R. J. Hocken, and W. C. Haight, “Automatic laser tracking interferometer system for robot metrology,” Prec. Eng. 8, 3–8 (1986).
[Crossref]

J. Ye, M. Takac, C. N. Berglund, G. Owen, and R. F. Pease, “An exact algorithm for self-calibration of two-dimensional precision metrology stages,” Prec. Eng. 20, 16–32 (1997).
[Crossref]

Other (2)

A. D. Belegundu and T.R. Chandrupatla, “Simulated annealing (SA),” in Optimization concepts and applications in engineering, M. Horton, ed. (Prentice-Hall, Inc., New Jersey, 1999).

ISO, “Guide to the expression of uncertainty in measurement,” in International vocabulary of basic and general terms in metrology, International Organization for Standardization ed. (International Organization for Standardization, Switzerland, 1993).

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Figures (8)

Fig. 1.
Fig. 1. Optical configuration of the two-point diffraction phase-measuring interferometer.

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Fig. 2.
Fig. 2. Photographic view of the two-dimensional performance test setup.

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Fig. 3.
Fig. 3. Deviation map between the readings of the optical scale and the results of the proposed interferometer. The blue lines mean the intentionally exaggerated deviation.

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Fig. 4.
Fig. 4. Designed artifact plate for self-calibration.

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Fig. 5.
Fig. 5. Two-dimensional self-calibration procedure using an artifact.

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Fig. 6.
Fig. 6. Extracted systematic error of (a) the conventional optical scale, and (b) the proposed interferometer. The measured y-coordinate is about −1.12 mm.

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Fig. 7.
Fig. 7. Three-dimensional performance test scheme. (a) Target setup on block gauges, and (b) the actual test plane.

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Fig. 8.
Fig. 8. Results of the Fourier self-calibration. (a) The error of the optical scale at y = −11.12, (b) the error of the proposed interferometer at y = −11.12, (c) the error of the optical scale at y = -21.12, and (d) the error of the proposed interferometer at y = −21.12.

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Tables (2)

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Table 1. Performance comparison between the BFGS and the new algorithm. The stopping criterion was 0.006 μn2 and the average calculation times were estimated when the cost function was successfully converged.

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Table 2. Error budget of the two point-diffraction phase-measuring interferometer. X represents the wavelength of the laser source.

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Equations (7)

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I = ∣ u 1 + u 2 ∣ 2 = Π + Γ cos ⁡ ( Φ + Δ ϕ ) ,
where Π = U 1 2 r 1 2 + U 2 2 r 2 2 , Γ = 2 U 1 U 2 r 1 r 2 , Φ = 2 π λ ( r 1 − r 2 ) , and Δ ϕ = ( ϕ 1 − ϕ 2 ) .
Φ x y z = 2 π λ [ r 1 x y z − r 2 x y z ]
= 2 π λ [ ( x 1 − x ) 2 + ( y 1 − y ) 2 + ( z 1 − z ) 2 − ( x 2 − x ) 2 + ( y 2 − y ) 2 + ( z 2 − z ) 2 ] .
Λ k = λ 2 π [ ( Φ k + Δ ϕ ) − ( Φ 0 + Δ ϕ ) ] = λ 2 π [ Φ k − Φ 0 ] .
E = ∑ k [ λ 2 π ( Φ k − Φ 0 ) − Λ ̑ k ] 2 ,
d 2 = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 + ( z 1 − z 2 ) 2 = constant ,

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