Abstract

We present a heterodyne grating interferometer based on a quasi-common-optical-path (QCOP) design for a two-degrees-of-freedom (DOF) straightness measurement. Two half-wave plates are utilized to rotate the polarizations of two orthogonally polarized beams. The grating movement can be calculated by measuring the phase difference variation in each axis. The experimental results demonstrate that our method has the ability to measure two-DOF straightness and still maintain high system stability. The proposed and demonstrated method, which relies on heterodyne interferometric phase measurement combined with the QCOP configuration, has the advantages of high measurement resolution, relatively straightforward operation, and high system stability.

© 2011 Optical Society of America

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    [CrossRef]
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  18. H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
    [CrossRef]
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    [CrossRef]
  21. K. Matsuda, M. Roy, T. Eiju, J. W. O’Byrne, and C. J. R. Sheppard, “Straightness measurements with a reflection confocal optical system—an experimental study,” Appl. Opt. 41, 3966–3970 (2002).
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  22. C. M. Wu, “Periodic nonlinearity resulting from ghost reflection in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
    [CrossRef]
  23. S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26, 448–455(2002).
    [CrossRef]
  24. S. Y. Lee, J. F. Lin, and Y. L. Lo, “Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer,” Opt. Lasers Eng. 43, 704–720 (2005).
    [CrossRef]
  25. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
    [CrossRef]
  26. N. George and J. W. Matthews, “Holographic diffraction grating,” Appl. Phys. Lett. 9, 212–215 (1966).
    [CrossRef]
  27. G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
    [CrossRef]

2010

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

2009

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

2008

S. S. Aphale, S. Devasia, and S. O. R. Moheimani, “High-bandwidth control of a piezoelectric nanopositioning stage in the presence of plant uncertainties,” Nanotechnology 19, 125503 (2008).
[CrossRef] [PubMed]

G. Langfelder, A. Longoni, and F. Zaraga, “Low-noise real-time measurement of the position of movable structures in MEMS,” Sens. Actuators A Phys. 148, 401–406 (2008).
[CrossRef]

2007

S.-K. Kuo, C.-C. Hung, C.-C. Lin, and W.-H. Yang, “Development of a nano-displacement measurement system,” Meas. Sci. Technol. 40, 256–263 (2007).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137, 185–191 (2007).
[CrossRef]

2005

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

S. J. Friedman, B. Barwick, and H. Batelaan, “Focused-laser interferometric position sensor,” Rev. Sci. Instrum. 76, 123106 (2005).
[CrossRef]

S. Y. Lee, J. F. Lin, and Y. L. Lo, “Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer,” Opt. Lasers Eng. 43, 704–720 (2005).
[CrossRef]

2004

C. M. Wu, “Heterodyne interferometer system with subnanometer accuracy for measurement of straightness,” Appl. Opt. 43, 3812–3816 (2004).
[CrossRef] [PubMed]

S. Yoo and S. W. Kim, “Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages,” Int. J. Mach. Tools Manuf. 44, 767–774 (2004).
[CrossRef]

F. Felten, G. A. Schneider, J. Muñoz Saldaña, and S. V. Kalinin, “Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy,” J. Appl. Phys. 96, 563–568 (2004).
[CrossRef]

2003

C. M. Wu, “Periodic nonlinearity resulting from ghost reflection in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
[CrossRef]

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47–54 (2003).
[CrossRef]

2002

K. Matsuda, M. Roy, T. Eiju, J. W. O’Byrne, and C. J. R. Sheppard, “Straightness measurements with a reflection confocal optical system—an experimental study,” Appl. Opt. 41, 3966–3970 (2002).
[CrossRef] [PubMed]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26, 448–455(2002).
[CrossRef]

2001

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

2000

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

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

1999

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

1998

J. H. Zhang and L. L. Cai, “Interferometric straightness measurement system using triangular prisms,” Opt. Eng. 37, 1785–1789 (1998).
[CrossRef]

1996

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

1993

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

1966

N. George and J. W. Matthews, “Holographic diffraction grating,” Appl. Phys. Lett. 9, 212–215 (1966).
[CrossRef]

Alavli, Y.

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Alayli, Y.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Aphale, S. S.

S. S. Aphale, S. Devasia, and S. O. R. Moheimani, “High-bandwidth control of a piezoelectric nanopositioning stage in the presence of plant uncertainties,” Nanotechnology 19, 125503 (2008).
[CrossRef] [PubMed]

Barwick, B.

S. J. Friedman, B. Barwick, and H. Batelaan, “Focused-laser interferometric position sensor,” Rev. Sci. Instrum. 76, 123106 (2005).
[CrossRef]

Batelaan, H.

S. J. Friedman, B. Barwick, and H. Batelaan, “Focused-laser interferometric position sensor,” Rev. Sci. Instrum. 76, 123106 (2005).
[CrossRef]

Blaize, S.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Bobroff, N.

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

Bruvant, A.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Cai, L. L.

J. H. Zhang and L. L. Cai, “Interferometric straightness measurement system using triangular prisms,” Opt. Eng. 37, 1785–1789 (1998).
[CrossRef]

Charlaix, E.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Chassagne, L.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Chen, H. Y.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137, 185–191 (2007).
[CrossRef]

Chen, J. C.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Chen, Q.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

Chiu, M. H.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Chu, C. L.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47–54 (2003).
[CrossRef]

Cosijns, S. J. A. G.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26, 448–455(2002).
[CrossRef]

Crassous, J.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Deturche, R.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Devasia, S.

S. S. Aphale, S. Devasia, and S. O. R. Moheimani, “High-bandwidth control of a piezoelectric nanopositioning stage in the presence of plant uncertainties,” Nanotechnology 19, 125503 (2008).
[CrossRef] [PubMed]

Eiju, T.

Fan, K. C.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47–54 (2003).
[CrossRef]

Felten, F.

F. Felten, G. A. Schneider, J. Muñoz Saldaña, and S. V. Kalinin, “Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy,” J. Appl. Phys. 96, 563–568 (2004).
[CrossRef]

Friedman, S. J.

S. J. Friedman, B. Barwick, and H. Batelaan, “Focused-laser interferometric position sensor,” Rev. Sci. Instrum. 76, 123106 (2005).
[CrossRef]

George, N.

N. George and J. W. Matthews, “Holographic diffraction grating,” Appl. Phys. Lett. 9, 212–215 (1966).
[CrossRef]

Haitjema, H.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26, 448–455(2002).
[CrossRef]

Henschel, W.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

Hocken, R.

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

Hsiao, W. H.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Hsieh, H. L.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Hsu, C. C.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137, 185–191 (2007).
[CrossRef]

Hung, C.-C.

S.-K. Kuo, C.-C. Hung, C.-C. Lin, and W.-H. Yang, “Development of a nano-displacement measurement system,” Meas. Sci. Technol. 40, 256–263 (2007).
[CrossRef]

Juncar, P.

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Kaars, P.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

Kalinin, S. V.

F. Felten, G. A. Schneider, J. Muñoz Saldaña, and S. V. Kalinin, “Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy,” J. Appl. Phys. 96, 563–568 (2004).
[CrossRef]

Kim, S. W.

S. Yoo and S. W. Kim, “Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages,” Int. J. Mach. Tools Manuf. 44, 767–774 (2004).
[CrossRef]

Kuo, S.-K.

S.-K. Kuo, C.-C. Hung, C.-C. Lin, and W.-H. Yang, “Development of a nano-displacement measurement system,” Meas. Sci. Technol. 40, 256–263 (2007).
[CrossRef]

Kurz, H.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

Langfelder, G.

G. Langfelder, A. Longoni, and F. Zaraga, “Low-noise real-time measurement of the position of movable structures in MEMS,” Sens. Actuators A Phys. 148, 401–406 (2008).
[CrossRef]

Lee, C. F.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Lee, C. K.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Lee, J. Y.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137, 185–191 (2007).
[CrossRef]

Lee, S. Y.

S. Y. Lee, J. F. Lin, and Y. L. Lo, “Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer,” Opt. Lasers Eng. 43, 704–720 (2005).
[CrossRef]

Lerondel, G.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Liao, J. L.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47–54 (2003).
[CrossRef]

Lin, C. C.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Lin, C. T.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Lin, C.-C.

S.-K. Kuo, C.-C. Hung, C.-C. Lin, and W.-H. Yang, “Development of a nano-displacement measurement system,” Meas. Sci. Technol. 40, 256–263 (2007).
[CrossRef]

Lin, D.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

Lin, J. F.

S. Y. Lee, J. F. Lin, and Y. L. Lo, “Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer,” Opt. Lasers Eng. 43, 704–720 (2005).
[CrossRef]

Lin, S. C.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Lin, Y. C.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Lo, Y. L.

S. Y. Lee, J. F. Lin, and Y. L. Lo, “Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer,” Opt. Lasers Eng. 43, 704–720 (2005).
[CrossRef]

Longoni, A.

G. Langfelder, A. Longoni, and F. Zaraga, “Low-noise real-time measurement of the position of movable structures in MEMS,” Sens. Actuators A Phys. 148, 401–406 (2008).
[CrossRef]

Maile, B. E.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

Matsuda, K.

Matthews, J. W.

N. George and J. W. Matthews, “Holographic diffraction grating,” Appl. Phys. Lett. 9, 212–215 (1966).
[CrossRef]

Moheimani, S. O. R.

S. S. Aphale, S. Devasia, and S. O. R. Moheimani, “High-bandwidth control of a piezoelectric nanopositioning stage in the presence of plant uncertainties,” Nanotechnology 19, 125503 (2008).
[CrossRef] [PubMed]

Monchanin, M.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Mou, J. I.

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47–54 (2003).
[CrossRef]

Muñoz Saldaña, J.

F. Felten, G. A. Schneider, J. Muñoz Saldaña, and S. V. Kalinin, “Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy,” J. Appl. Phys. 96, 563–568 (2004).
[CrossRef]

O’Byrne, J. W.

Polman, R.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

Restagno, F.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Rienks, B.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

Rover, P.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Roy, M.

Ruaux, P.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Schellekens, P. H. J.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26, 448–455(2002).
[CrossRef]

Schneider, G. A.

F. Felten, G. A. Schneider, J. Muñoz Saldaña, and S. V. Kalinin, “Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy,” J. Appl. Phys. 96, 563–568 (2004).
[CrossRef]

Sheppard, C. J. R.

Shih, H. C.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Sinno, A.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Su, D. C.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Teng, C. T.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Topcu, S.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Trumper, D.

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

Wakim, M.

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Wang, J. S.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Wu, C. C.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137, 185–191 (2007).
[CrossRef]

Wu, C. M.

C. M. Wu, “Heterodyne interferometer system with subnanometer accuracy for measurement of straightness,” Appl. Opt. 43, 3812–3816 (2004).
[CrossRef] [PubMed]

C. M. Wu, “Periodic nonlinearity resulting from ghost reflection in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
[CrossRef]

Wu, G. Y.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Wu, J.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

Wu, W. J.

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Wu, W. T.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Yan, J.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

Yang, W.-H.

S.-K. Kuo, C.-C. Hung, C.-C. Lin, and W.-H. Yang, “Development of a nano-displacement measurement system,” Meas. Sci. Technol. 40, 256–263 (2007).
[CrossRef]

Yin, C.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

Yoo, S.

S. Yoo and S. W. Kim, “Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages,” Int. J. Mach. Tools Manuf. 44, 767–774 (2004).
[CrossRef]

Zaraga, F.

G. Langfelder, A. Longoni, and F. Zaraga, “Low-noise real-time measurement of the position of movable structures in MEMS,” Sens. Actuators A Phys. 148, 401–406 (2008).
[CrossRef]

Zhang, J. H.

J. H. Zhang and L. L. Cai, “Interferometric straightness measurement system using triangular prisms,” Opt. Eng. 37, 1785–1789 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

N. George and J. W. Matthews, “Holographic diffraction grating,” Appl. Phys. Lett. 9, 212–215 (1966).
[CrossRef]

Int. J. Mach. Tools Manuf.

S. Yoo and S. W. Kim, “Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages,” Int. J. Mach. Tools Manuf. 44, 767–774 (2004).
[CrossRef]

J. Appl. Phys.

F. Felten, G. A. Schneider, J. Muñoz Saldaña, and S. V. Kalinin, “Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy,” J. Appl. Phys. 96, 563–568 (2004).
[CrossRef]

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruvant, S. Topcu, P. Rover, and Y. Alayli, “Enlarged near field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Jpn. J. Appl. Phys.

B. E. Maile, W. Henschel, H. Kurz, B. Rienks, R. Polman, and P. Kaars, “Sub-10 nm linewidth and overlay performance achieved with a fine-tuned EBPG-5000 TFE electron beam lithography system,” Jpn. J. Appl. Phys. 39, 6836–6842 (2000).
[CrossRef]

C. K. Lee, G. Y. Wu, C. T. Teng, W. J. Wu, C. T. Lin, W. H. Hsiao, H. C. Shih, J. S. Wang, S. C. Lin, C. C. Lin, C. F. Lee, and Y. C. Lin, “A high performance Doppler interferometer for advanced optical storage systems,” Jpn. J. Appl. Phys. 38, 1730–1741(1999).
[CrossRef]

Meas. Sci. Technol.

L. Chassagne, M. Wakim, S. Topcu, P. Ruaux, P. Juncar, and Y. Alavli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimeter displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16, 2030–2037(2005).
[CrossRef]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

S.-K. Kuo, C.-C. Hung, C.-C. Lin, and W.-H. Yang, “Development of a nano-displacement measurement system,” Meas. Sci. Technol. 40, 256–263 (2007).
[CrossRef]

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

K. C. Fan, C. L. Chu, J. L. Liao, and J. I. Mou, “Development a high-precision straightness measuring system with DVD pick-up head,” Meas. Sci. Technol. 14, 47–54 (2003).
[CrossRef]

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

Nanotechnology

S. S. Aphale, S. Devasia, and S. O. R. Moheimani, “High-bandwidth control of a piezoelectric nanopositioning stage in the presence of plant uncertainties,” Nanotechnology 19, 125503 (2008).
[CrossRef] [PubMed]

Opt. Commun.

C. M. Wu, “Periodic nonlinearity resulting from ghost reflection in heterodyne interferometry,” Opt. Commun. 215, 17–23 (2003).
[CrossRef]

Opt. Eng.

J. H. Zhang and L. L. Cai, “Interferometric straightness measurement system using triangular prisms,” Opt. Eng. 37, 1785–1789 (1998).
[CrossRef]

Opt. Lasers Eng.

S. Y. Lee, J. F. Lin, and Y. L. Lo, “Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer,” Opt. Lasers Eng. 43, 704–720 (2005).
[CrossRef]

Precis. Eng.

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

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng. 26, 448–455(2002).
[CrossRef]

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Rev. Sci. Instrum.

S. J. Friedman, B. Barwick, and H. Batelaan, “Focused-laser interferometric position sensor,” Rev. Sci. Instrum. 76, 123106 (2005).
[CrossRef]

A. Sinno, P. Ruaux, L. Chassagne, S. Topcu, Y. Alayli, G. Lerondel, S. Blaize, A. Bruvant, and P. Rover, “Enlarged atomic force microscopy scanning scope: novel sample-holder device millimeter range,” Rev. Sci. Instrum. 78, 095107 (2007).
[CrossRef] [PubMed]

Sens. Actuators A Phys.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137, 185–191 (2007).
[CrossRef]

G. Langfelder, A. Longoni, and F. Zaraga, “Low-noise real-time measurement of the position of movable structures in MEMS,” Sens. Actuators A Phys. 148, 401–406 (2008).
[CrossRef]

Other

Hewlett-Packard, “5526A laser measurement systems user’s guide,” http://www.home.agilent.com/agilent/product.jspx?cc=US&lc=eng&nid=-536900389.536898115&pageMode=PL.

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Figures (9)

Fig. 1
Fig. 1

Heterodyne light source and beam expanding system.

Fig. 2
Fig. 2

Different phase retardations in the different quarters of the HWP (PR, retardation and FA, fast axis).

Fig. 3
Fig. 3

Diffracted light region is comprised of part A with B and part A with C.

Fig. 4
Fig. 4

Scheme of the QCOP heterodyne grating straightness interferometer: 1, laser; 2, electro-optic modulator; 3, beam expander; 4, half-wave plate 1; 5, half-wave plate 2; 6, mirror; 7, focus lens; 8, 2D grating; 9, detector, D 1 ; 10, detector, D 2 ; 11, detector, D 3 ; 12, polarizer, P 1 ; 13, polarizer, P 2 ; 14, polarizer, P 3 ; 15, two-axis piezoelectric stage; 16, two-axis stepper; and 17, rotation stage.

Fig. 5
Fig. 5

Straightness measurements along the x direction (with and without the curve fitting method).

Fig. 6
Fig. 6

Straightness measurements along the y direction (with and without the curve fitting method).

Fig. 7
Fig. 7

Experimental results of resolution testing.

Fig. 8
Fig. 8

System stability test (by the QCOP heterodyne grating interferometer).

Fig. 9
Fig. 9

Influences of the straightness measurement resulting from the pitch, yaw, and roll of the XY linear stepper.

Equations (16)

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

E 0 = ( e i ω t / 2 e i ω t / 2 ) .
J ( 0 ) = J ( 360 ) = ( 1 0 0 1 ) , J ( 180 ) = ( 0 1 1 0 ) .
A = D = J ( 0 ) · E 0 = ( e i ω t / 2 e i ω t / 2 ) , B = C = J ( 180 ) · E 0 = ( e i ω t / 2 e i ω t / 2 ) .
ϕ q m = 2 m π s q / p ,
A q m = D q m = ( e i ω t / 2 e i ω t / 2 ) exp ( i ϕ q m ) , B q m = C q m = ( e i ω t / 2 e i ω t / 2 ) exp ( i ϕ q m ) .
I 1 = | P 1 ( 0 ) · ( A 0 + B x 1 ) | 2 = | ( 1 0 0 0 ) · [ ( e i ω t / 2 e i ω t / 2 ) exp ( i ϕ x 0 ) + ( e i ω t / 2 e i ω t / 2 ) exp ( i ϕ x 1 ) ] | 2 = 2 + 2 cos [ ω t ( ϕ x 1 ϕ x 0 ) ] .
I 2 = | P 2 ( 0 ) · ( A 0 + C y 1 ) | 2 = 2 + 2 cos ( ω t ϕ y 1 ) .
I 3 cos ( ω t ) .
ϕ q 1 = 2 π s q / p ,
s q = p × ϕ q 1 / 2 π .
D ( s q ) = tan θ s · s q + D s t ,
E = P ( α , θ p ) · [ HWP ( δ , θ h ) ( e i ω t 2 e i ω t 2 ) + ( e i ω t 2 e i ω t 2 ) e i ϕ q 1 ] ,
I = | E | 2 A C cos ( ω t + Φ ) ,
Δ Φ = Φ ( α , θ p , δ , θ h ) ϕ q 1 .
| Δ p | = α T × p × Δ T ,
E x ( β ) b sin c [ b π ( 1 p + sin ( θ roll ) λ sin ( β ) λ ) ] · e i 2 π s x / p ,

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