Abstract

We report on a novel compact interferometery system for measuring parasitic motions of a precision stage. It is a combination of a Michelson interferometer with an auto-collimator, of which full physical dimension is mere 70 mm×80 mm×35 mm (W×L×H) including optical components, photo-detectors, and electronic circuits. Since the beams, which measure displacement and angle, can be directed at the same position on the moving mirror, the system is applicable for testing small nano-stages where commercial interferometers are not able to be used. And thus, errors from nano-scale deformation of the moving mirror can be minimized. We find that the residual errors of linear and angular motion measurements are 2.5 nm in peak-to-peak and 0.2″, respectively.

© 2007 Optical Society of America

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References

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  1. R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
    [Crossref]
  2. J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
    [Crossref]
  3. S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Meas. Sci. Technol. 10, 986–993 (1999).
    [Crossref]
  4. M. Holmes, R. Hocken, and D. Trumper, “The long-range scanning stage: a novel platform for scanned-probe microscopy,” Prec. Eng. 24, 191–209 (2000).
    [Crossref]
  5. W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
    [Crossref]
  6. A. Bergamin, G. Cavagnero, and G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3080 (1993).
    [Crossref]
  7. G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
    [Crossref] [PubMed]
  8. J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
    [Crossref]
  9. P. R. Yoder, E. R. Schlesinger, and J. L. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14, 1890–1895 (1975).
    [Crossref] [PubMed]
  10. J. Yuan, X. Long, and K. Yang, “Temperature-controlled autocollimator with ultrahigh angular measuring precision,” Rev. Sci. Instrum. 76, 125106 (2005).
    [Crossref]
  11. G. R, Fowles, Introduction to Modern Optics (Dover Publications, 1989), Chap. 2.
  12. C.-M. Wu, C.-S. Su, and G.-S. Peng, “Correction of nonlinearity in one-frequency optical interferometry,” Meas. Sci. Technol. 7, 520–524 (1996).
    [Crossref]
  13. T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferomerer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443–2448 (2004).
    [Crossref] [PubMed]
  14. T. Eom, D. Chung, and J. Kim, “A small angle generator based on a laser angle interferometer,” International Journal of Precision Engineering and Manufacturing 8, 20–23 (2007).

2007 (1)

T. Eom, D. Chung, and J. Kim, “A small angle generator based on a laser angle interferometer,” International Journal of Precision Engineering and Manufacturing 8, 20–23 (2007).

2006 (3)

J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
[Crossref]

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
[Crossref]

2005 (1)

J. Yuan, X. Long, and K. Yang, “Temperature-controlled autocollimator with ultrahigh angular measuring precision,” Rev. Sci. Instrum. 76, 125106 (2005).
[Crossref]

2004 (1)

2001 (1)

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

2000 (1)

M. Holmes, R. Hocken, and D. Trumper, “The long-range scanning stage: a novel platform for scanned-probe microscopy,” Prec. Eng. 24, 191–209 (2000).
[Crossref]

1999 (1)

S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Meas. Sci. Technol. 10, 986–993 (1999).
[Crossref]

1996 (1)

C.-M. Wu, C.-S. Su, and G.-S. Peng, “Correction of nonlinearity in one-frequency optical interferometry,” Meas. Sci. Technol. 7, 520–524 (1996).
[Crossref]

1993 (1)

A. Bergamin, G. Cavagnero, and G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3080 (1993).
[Crossref]

1975 (1)

1974 (1)

Arai, Y.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

Bae, E. D.

J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
[Crossref]

Bergamin, A.

A. Bergamin, G. Cavagnero, and G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3080 (1993).
[Crossref]

Cavagnero, G.

A. Bergamin, G. Cavagnero, and G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3080 (1993).
[Crossref]

Chapman, G. D.

Chickvary, J. L.

Chung, D.

T. Eom, D. Chung, and J. Kim, “A small angle generator based on a laser angle interferometer,” International Journal of Precision Engineering and Manufacturing 8, 20–23 (2007).

Eom, T.

T. Eom, D. Chung, and J. Kim, “A small angle generator based on a laser angle interferometer,” International Journal of Precision Engineering and Manufacturing 8, 20–23 (2007).

Eom, T. B.

J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
[Crossref]

Fowles, G. R,

G. R, Fowles, Introduction to Modern Optics (Dover Publications, 1989), Chap. 2.

Gao, W.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

Gonda, S.

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferomerer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443–2448 (2004).
[Crossref] [PubMed]

S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Meas. Sci. Technol. 10, 986–993 (1999).
[Crossref]

Haycocks, J.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Hocken, R.

M. Holmes, R. Hocken, and D. Trumper, “The long-range scanning stage: a novel platform for scanned-probe microscopy,” Prec. Eng. 24, 191–209 (2000).
[Crossref]

Holmes, M.

M. Holmes, R. Hocken, and D. Trumper, “The long-range scanning stage: a novel platform for scanned-probe microscopy,” Prec. Eng. 24, 191–209 (2000).
[Crossref]

Huang, Q.

Jackson, K.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Keem, T.

J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
[Crossref]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferomerer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443–2448 (2004).
[Crossref] [PubMed]

Kim, J.

T. Eom, D. Chung, and J. Kim, “A small angle generator based on a laser angle interferometer,” International Journal of Precision Engineering and Manufacturing 8, 20–23 (2007).

Kim, J. W.

J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
[Crossref]

Kim, J.-A.

J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
[Crossref]

Kim, S.-W.

J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
[Crossref]

Kiyono, S.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

Kurosawa, T.

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferomerer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443–2448 (2004).
[Crossref] [PubMed]

S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Meas. Sci. Technol. 10, 986–993 (1999).
[Crossref]

Leach, R.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Lewis, A.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Long, X.

J. Yuan, X. Long, and K. Yang, “Temperature-controlled autocollimator with ultrahigh angular measuring precision,” Rev. Sci. Instrum. 76, 125106 (2005).
[Crossref]

Mana, G.

A. Bergamin, G. Cavagnero, and G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3080 (1993).
[Crossref]

Misumi, I.

Oh, J, S.

J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
[Crossref]

Oldfield, S.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Park, B. C.

J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
[Crossref]

Park, C. H.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

Peng, G.-S.

C.-M. Wu, C.-S. Su, and G.-S. Peng, “Correction of nonlinearity in one-frequency optical interferometry,” Meas. Sci. Technol. 7, 520–524 (1996).
[Crossref]

Schlesinger, E. R.

Shibuya, A.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

Su, C.-S.

C.-M. Wu, C.-S. Su, and G.-S. Peng, “Correction of nonlinearity in one-frequency optical interferometry,” Meas. Sci. Technol. 7, 520–524 (1996).
[Crossref]

Tanimura, Y.

S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Meas. Sci. Technol. 10, 986–993 (1999).
[Crossref]

Trumper, D.

M. Holmes, R. Hocken, and D. Trumper, “The long-range scanning stage: a novel platform for scanned-probe microscopy,” Prec. Eng. 24, 191–209 (2000).
[Crossref]

Wu, C.-M.

C.-M. Wu, C.-S. Su, and G.-S. Peng, “Correction of nonlinearity in one-frequency optical interferometry,” Meas. Sci. Technol. 7, 520–524 (1996).
[Crossref]

Yacot, A.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Yang, K.

J. Yuan, X. Long, and K. Yang, “Temperature-controlled autocollimator with ultrahigh angular measuring precision,” Rev. Sci. Instrum. 76, 125106 (2005).
[Crossref]

Yoder, P. R.

Yuan, J.

J. Yuan, X. Long, and K. Yang, “Temperature-controlled autocollimator with ultrahigh angular measuring precision,” Rev. Sci. Instrum. 76, 125106 (2005).
[Crossref]

Appl. Opt. (3)

International Journal of Machine Tools and Manufacture (1)

J, S. Oh, E. D. Bae, T. Keem, and S.-W. Kim, “Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman-Green interferometry,” International Journal of Machine Tools and Manufacture 46, 1748–1752 (2006).
[Crossref]

International Journal of Precision Engineering and Manufacturing (1)

T. Eom, D. Chung, and J. Kim, “A small angle generator based on a laser angle interferometer,” International Journal of Precision Engineering and Manufacturing 8, 20–23 (2007).

Meas. Sci. Technol. (3)

C.-M. Wu, C.-S. Su, and G.-S. Peng, “Correction of nonlinearity in one-frequency optical interferometry,” Meas. Sci. Technol. 7, 520–524 (1996).
[Crossref]

J.-A. Kim, J. W. Kim, B. C. Park, and T. B. Eom, “Measurement of microscope calibration standards in nanometrology using a metrological atomic force microscope,” Meas. Sci. Technol. 17, 1792–1800 (2006).
[Crossref]

S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Meas. Sci. Technol. 10, 986–993 (1999).
[Crossref]

Nanotechnology (1)

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1–R6 (2001).
[Crossref]

Prec. Eng. (2)

M. Holmes, R. Hocken, and D. Trumper, “The long-range scanning stage: a novel platform for scanned-probe microscopy,” Prec. Eng. 24, 191–209 (2000).
[Crossref]

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Prec. Eng. 30, 96–103 (2006).
[Crossref]

Rev. Sci. Instrum. (2)

A. Bergamin, G. Cavagnero, and G. Mana, “A displacement and angle interferometer with subatomic resolution,” Rev. Sci. Instrum. 64, 3076–3080 (1993).
[Crossref]

J. Yuan, X. Long, and K. Yang, “Temperature-controlled autocollimator with ultrahigh angular measuring precision,” Rev. Sci. Instrum. 76, 125106 (2005).
[Crossref]

Other (1)

G. R, Fowles, Introduction to Modern Optics (Dover Publications, 1989), Chap. 2.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of basic structure of MICA. LS: light source; BS: beam splitter; QPD: quadratic photo diode; CL: collimating lens; PBS: polarizing beam splitter; M1 and M2: mirrors; Q1 and Q2: quarter wave plates: P: polarizer; L: lens; PD: photo diode.

Fig. 2.
Fig. 2.

The (a) schematic diagram and (b) photograph of MICA. OI: optical isolator; BS1 and BS2: beam splitters; L and CL: lens; PBS1 and PBS2: polarizing beam splitter; W1 and W2: half-wave plate; Q1, Q2, and Q3: quarter-wave plates; CC1 and CC2: cube-corner prisms; M, M1, and M2: mirrors; PD1, PD2, and PD3: photo detectors; RP: right angle prism; PMSMF: polarization maintaining single mode fiber; QPD: quadratic photo detector; P: polarizer.

Fig. 3.
Fig. 3.

Residual nonlinearity of the laser interferometer

Fig. 4.
Fig. 4.

Setup for calibration of autocollimator part of MICA. M: Mirror; CA and CB: cube-corner prism; S: spring, MM: micrometer; D: photo detector; O: pivot point of rotational arm.

Fig. 5.
Fig. 5.

(a) Calibration of the auto-collimator part in MICA and (b) the residuals.

Fig. 6.
Fig. 6.

Test results of a nano-stage. (a) Parasitic motion and (b) residual of capacitance sensor

Equations (6)

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

Q ( θ ) = ( cos 2 θ + i sin 2 θ ( 1 i ) sin θ cos θ ( 1 i ) sin θ cos θ sin 2 θ + i cos 2 θ ) .
Q ( θ ) R Q ( θ ) ( 1 0 ) = ( sin 2 θ cos 2 θ sin 2 θ )
θ Y = r Y 2 f and θ P = r P 2 f ,
θ Y = K Y Θ Y and θ P = K P Θ P
Θ Y = V 1 V 2 + V 3 V 4 V 1 + V 2 + V 3 + V 4
Θ P = V 1 + V 2 V 3 V 4 V 1 + V 2 + V 3 + V 4 .

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