Abstract

A precision PGC demodulation for homodyne interferometer modulated with a combined sinusoidal and triangular signal is proposed. Using a triangular signal as additional modulation, a continuous phase-shifted interference signal for ellipse fitting is generated whether the measured object is in static or moving state. The real-time ellipse fitting and correction of the AC amplitudes and DC offsets of the quadrature components in PGC demodulation can be realized. The merit of this modulation is that it can eliminate thoroughly the periodic nonlinearity resulting from the influences of light intensity disturbance, the drift of modulation depth, the carrier phase delay, and non-ideal performance of the low pass filters in the conversional PGC demodulation. The principle and realization of the signal processing with the combined modulation signal are described in detail. The experiments of accuracy and rate evaluations of ellipse fitting, nanometer, and millimeter displacement measurements were performed to verify the feasibility of the proposed demodulation. The experimental results show that the elliptical parameters of the quadrature components can be achieved precisely in real time and nanometer accuracy was realized in displacement measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (7)

S. Zhang, L. Yan, B. Chen, Z. Xu, and J. Xie, “Real-time phase delay compensation of PGC demodulation in sinusoidal phase-modulation interferometer for nanometer displacement measurement,” Opt. Express 25(1), 472–485 (2017).
[Crossref] [PubMed]

C. Ni, M. Zhang, Y. Zhu, C. Hu, S. Ding, and Z. Jia, “Sinusoidal phase-modulating interferometer with ellipse fitting and a correction method,” Appl. Opt. 56(13), 3895–3899 (2017).
[Crossref] [PubMed]

M. Zhang, C. Ni, Y. Zhu, C. Hu, J. Hu, L. Wang, and S. Ding, “Sinusoidal phase-modulating laser diode interferometer for wide range displacement measurement,” Appl. Opt. 56(20), 5685–5691 (2017).
[Crossref] [PubMed]

X. Wang, S. Piao, J. Fu, and X. Li, “Automatic carrier signal track algorithm in all-digital PGC demodulation scheme for optical interferometric sensors,” J. Opt. Technol. 84(4), 265–269 (2017).
[Crossref]

L. Yan, B. Chen, and B. Wang, “A differential Michelson interferometer with orthogonal single frequency laser for nanometer displacement measurement,” Meas. Sci. Technol. 28(4), 045001 (2017).
[Crossref]

L. Yan, B. Chen, Z. Chen, J. Xie, E. Zhang, and S. Zhang, “Phase-modulated dual-homodyne interferometer without periodic nonlinearity,” Meas. Sci. Technol. 28(11), 115006 (2017).
[Crossref]

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

2016 (1)

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

2015 (2)

S. Zhang, A. Zhang, and H. Pan, “Eliminating light intensity disturbance with reference compensation in interferometers,” IEEE Photonics Technol. Lett. 27(17), 1888–1891 (2015).
[Crossref]

P. Hu, Y. Bai, J. Zhao, G. Wu, and J. Tan, “Toward a nonlinearity model for a heterodyne interferometer: not based on double-frequency mixing,” Opt. Express 23(20), 25935–25941 (2015).
[Crossref] [PubMed]

2014 (2)

R. Köing, G. Wimmer, and V. Witkovský, “Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase,” Meas. Sci. Technol. 25(11), 115001 (2014).
[Crossref]

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

2012 (2)

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

2011 (1)

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22(8), 085301 (2011).
[Crossref]

2010 (2)

2009 (2)

M. Ishige, M. Aketagawa, T. Banh Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[Crossref]

G. He and X. Wang, “Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry,” Optik (Stuttg.) 120(3), 101–105 (2009).
[Crossref]

2008 (1)

T. Lan, C. Zhang, L. Li, G. Luo, and C. Li, “Carrier phase advance technique for digital PGC demodulation,” Opto-Electronic Eng. 35(7), 49–52 (2008).

2005 (1)

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44(12), 125602 (2005).
[Crossref]

1994 (1)

T. R. Christian, P. A. Frank, and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[Crossref]

1991 (2)

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

1982 (1)

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18(10), 1647–1653 (1982).
[Crossref]

1981 (1)

Aketagawa, M.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

M. Ishige, M. Aketagawa, T. Banh Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[Crossref]

Aleynik, A. S.

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

Bai, Y.

Balling, P.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Bancone, N.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Banh Quoc, T.

M. Ishige, M. Aketagawa, T. Banh Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[Crossref]

Basile, G.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Bergamin, A.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Birlikseven, C.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Cavagnero, G.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Çelik, M.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Chen, B.

Chen, Z.

L. Yan, B. Chen, Z. Chen, J. Xie, E. Zhang, and S. Zhang, “Phase-modulated dual-homodyne interferometer without periodic nonlinearity,” Meas. Sci. Technol. 28(11), 115006 (2017).
[Crossref]

Christian, T. R.

T. R. Christian, P. A. Frank, and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[Crossref]

Dandridge, A.

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18(10), 1647–1653 (1982).
[Crossref]

Ding, S.

Docchio, F.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

Dong, W.

Estler, W. T.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Flügge, J.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Forbes, A.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Frank, P. A.

T. R. Christian, P. A. Frank, and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[Crossref]

Fu, J.

Füßl, R.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Galetto, M.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Gelmini, E.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

Giallorenzi, T.

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18(10), 1647–1653 (1982).
[Crossref]

Goch, G.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Hamid, R.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Härtig, F.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Hausotte, T.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

He, G.

G. He and X. Wang, “Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry,” Optik (Stuttg.) 120(3), 101–105 (2009).
[Crossref]

He, J.

Heydemann, P. L. M.

Hoshino, Y.

M. Ishige, M. Aketagawa, T. Banh Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[Crossref]

Houston, B. H.

T. R. Christian, P. A. Frank, and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[Crossref]

Hu, C.

Hu, J.

Hu, P.

Hughes, B.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Ishige, M.

M. Ishige, M. Aketagawa, T. Banh Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[Crossref]

Jäger, G.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Jia, Z.

Knapp, W.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Köchert, P.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Köing, R.

R. Köing, G. Wimmer, and V. Witkovský, “Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase,” Meas. Sci. Technol. 25(11), 115001 (2014).
[Crossref]

Kren, P.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Kuetgens, U.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Kumagai, T.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Lan, T.

T. Lan, C. Zhang, L. Li, G. Luo, and C. Li, “Carrier phase advance technique for digital PGC demodulation,” Opto-Electronic Eng. 35(7), 49–52 (2008).

Lassila, A.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Li, C.

Li, D.

Li, F.

Li, L.

T. Lan, C. Zhang, L. Li, G. Luo, and C. Li, “Carrier phase advance technique for digital PGC demodulation,” Opto-Electronic Eng. 35(7), 49–52 (2008).

Li, X.

Liu, Y.

Luo, G.

T. Lan, C. Zhang, L. Li, G. Luo, and C. Li, “Carrier phase advance technique for digital PGC demodulation,” Opto-Electronic Eng. 35(7), 49–52 (2008).

Madden, M.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Maeda, Y.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Mana, G.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Manske, E.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Marioli, D.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

Masutomi, T.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44(12), 125602 (2005).
[Crossref]

Mekhrengin, M. V.

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

Minoni, U.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

Miroshnichenko, G. P.

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

Morse, E.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Možina, J.

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22(8), 085301 (2011).
[Crossref]

Ni, C.

Okuyama, E.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Pan, H.

S. Zhang, A. Zhang, and H. Pan, “Eliminating light intensity disturbance with reference compensation in interferometers,” IEEE Photonics Technol. Lett. 27(17), 1888–1891 (2015).
[Crossref]

Peterek, M.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Piao, S.

Picotto, G. B.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Pisani, M.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Plotnikov, M. Y.

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

Požar, T.

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22(8), 085301 (2011).
[Crossref]

Sahin, E.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Sardini, E.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

Sasaki, O.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44(12), 125602 (2005).
[Crossref]

Schmitt, R. H.

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

Seppä, J.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Suzuki, T.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44(12), 125602 (2005).
[Crossref]

Tan, J.

Tang, W.

Tedaldi, M.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Tveten, A.

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18(10), 1647–1653 (1982).
[Crossref]

Volkov, A. V.

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

Wang, B.

L. Yan, B. Chen, and B. Wang, “A differential Michelson interferometer with orthogonal single frequency laser for nanometer displacement measurement,” Meas. Sci. Technol. 28(4), 045001 (2017).
[Crossref]

Wang, L.

Wang, X.

X. Wang, S. Piao, J. Fu, and X. Li, “Automatic carrier signal track algorithm in all-digital PGC demodulation scheme for optical interferometric sensors,” J. Opt. Technol. 84(4), 265–269 (2017).
[Crossref]

G. He and X. Wang, “Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry,” Optik (Stuttg.) 120(3), 101–105 (2009).
[Crossref]

Weichert, C.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Wimmer, G.

R. Köing, G. Wimmer, and V. Witkovský, “Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase,” Meas. Sci. Technol. 25(11), 115001 (2014).
[Crossref]

Witkovský, V.

R. Köing, G. Wimmer, and V. Witkovský, “Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase,” Meas. Sci. Technol. 25(11), 115001 (2014).
[Crossref]

Wu, G.

Xie, J.

S. Zhang, L. Yan, B. Chen, Z. Xu, and J. Xie, “Real-time phase delay compensation of PGC demodulation in sinusoidal phase-modulation interferometer for nanometer displacement measurement,” Opt. Express 25(1), 472–485 (2017).
[Crossref] [PubMed]

L. Yan, B. Chen, Z. Chen, J. Xie, E. Zhang, and S. Zhang, “Phase-modulated dual-homodyne interferometer without periodic nonlinearity,” Meas. Sci. Technol. 28(11), 115006 (2017).
[Crossref]

Xu, Z.

Yacoot, A.

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Yan, L.

Yang, T.

Yao, X.

Zhang, A.

S. Zhang, A. Zhang, and H. Pan, “Eliminating light intensity disturbance with reference compensation in interferometers,” IEEE Photonics Technol. Lett. 27(17), 1888–1891 (2015).
[Crossref]

Zhang, C.

T. Lan, C. Zhang, L. Li, G. Luo, and C. Li, “Carrier phase advance technique for digital PGC demodulation,” Opto-Electronic Eng. 35(7), 49–52 (2008).

Zhang, E.

L. Yan, B. Chen, Z. Chen, J. Xie, E. Zhang, and S. Zhang, “Phase-modulated dual-homodyne interferometer without periodic nonlinearity,” Meas. Sci. Technol. 28(11), 115006 (2017).
[Crossref]

Zhang, M.

Zhang, S.

S. Zhang, B. Chen, L. Yan, and Z. Xu, “Real-time normalization and nonlinearity evaluation methods of the PGC-arctan demodulation in an EOM-based sinusoidal phase modulating interferometer,” Opt. Express 26(2), 605–616 (2018).
[Crossref] [PubMed]

L. Yan, B. Chen, Z. Chen, J. Xie, E. Zhang, and S. Zhang, “Phase-modulated dual-homodyne interferometer without periodic nonlinearity,” Meas. Sci. Technol. 28(11), 115006 (2017).
[Crossref]

S. Zhang, L. Yan, B. Chen, Z. Xu, and J. Xie, “Real-time phase delay compensation of PGC demodulation in sinusoidal phase-modulation interferometer for nanometer displacement measurement,” Opt. Express 25(1), 472–485 (2017).
[Crossref] [PubMed]

S. Zhang, A. Zhang, and H. Pan, “Eliminating light intensity disturbance with reference compensation in interferometers,” IEEE Photonics Technol. Lett. 27(17), 1888–1891 (2015).
[Crossref]

Zhao, J.

Zhao, X.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44(12), 125602 (2005).
[Crossref]

Zhu, Y.

Appl. Opt. (3)

CIRP Ann- Manuf. Techn. (1)

R. H. Schmitt, M. Peterek, E. Morse, W. Knapp, M. Galetto, F. Härtig, G. Goch, B. Hughes, A. Forbes, and W. T. Estler, “Advances in Large-Scale Metrology-Review and future trends,” CIRP Ann- Manuf. Techn. 65(2), 643–665 (2016).

IEEE J. Quantum Electron. (1)

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18(10), 1647–1653 (1982).
[Crossref]

IEEE Photonics Technol. Lett. (1)

S. Zhang, A. Zhang, and H. Pan, “Eliminating light intensity disturbance with reference compensation in interferometers,” IEEE Photonics Technol. Lett. 27(17), 1888–1891 (2015).
[Crossref]

IEEE Sens. J. (1)

A. V. Volkov, M. Y. Plotnikov, M. V. Mekhrengin, G. P. Miroshnichenko, and A. S. Aleynik, “Phase Modulation Depth Evaluation and Correction Technique for the PGC Demodulation Scheme in Fiber-Optic Interferometric Sensors,” IEEE Sens. J. 17(13), 4143–4150 (2017).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Technol. (1)

Meas. Sci. Technol. (7)

R. Köing, G. Wimmer, and V. Witkovský, “Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase,” Meas. Sci. Technol. 25(11), 115001 (2014).
[Crossref]

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22(8), 085301 (2011).
[Crossref]

L. Yan, B. Chen, and B. Wang, “A differential Michelson interferometer with orthogonal single frequency laser for nanometer displacement measurement,” Meas. Sci. Technol. 28(4), 045001 (2017).
[Crossref]

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

L. Yan, B. Chen, Z. Chen, J. Xie, E. Zhang, and S. Zhang, “Phase-modulated dual-homodyne interferometer without periodic nonlinearity,” Meas. Sci. Technol. 28(11), 115006 (2017).
[Crossref]

M. Ishige, M. Aketagawa, T. Banh Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[Crossref]

Metrologia (2)

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

M. Pisani, A. Yacoot, P. Balling, N. Bancone, C. Birlikseven, M. Çelik, J. Flügge, R. Hamid, P. Köchert, P. Kren, U. Kuetgens, A. Lassila, G. B. Picotto, E. Şahin, J. Seppä, M. Tedaldi, and C. Weichert, “Comparison of the performance of the next generation of optical interferometers,” Metrologia 49(4), 455–467 (2012).
[Crossref]

Opt. Eng. (1)

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44(12), 125602 (2005).
[Crossref]

Opt. Express (4)

Optik (Stuttg.) (1)

G. He and X. Wang, “Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry,” Optik (Stuttg.) 120(3), 101–105 (2009).
[Crossref]

Opto-Electronic Eng. (1)

T. Lan, C. Zhang, L. Li, G. Luo, and C. Li, “Carrier phase advance technique for digital PGC demodulation,” Opto-Electronic Eng. 35(7), 49–52 (2008).

Proc. SPIE (1)

T. R. Christian, P. A. Frank, and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[Crossref]

Rev. Sci. Instrum. (1)

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62(11), 2579–2583 (1991).
[Crossref]

Other (1)

S. V. Huffel and J. Vandewalle, The Total Least Squares Problem: Computational Aspects and Analysis, (SIMA, 1991).

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Figures (11)

Fig. 1
Fig. 1 System configuration for homodyne interferometer modulated with a combined sinusoidal and triangular signal.
Fig. 2
Fig. 2 Principle of phase demodulation with combined sinusoidal and triangular modulation signal. DDS: direct digital frequency synthesizer, TWG: triangle waveform generator, ADD: adder, MUL: multiplier, LPF: low pass filter, EF: ellipse fitting, ATAN: arctangent operation, PUW: phase unwrapping, RTPA: real-time phase averaging.
Fig. 3
Fig. 3 Scheme of real-time ellipse fitting and correction based on FPGA + ARM. SCS: signal calculation and synchronizing; SUB: subtractor; MUL: multiplier; ACC: accumulator.
Fig. 4
Fig. 4 Principle of signal calculation and synchronizing. DTD: Digital time delayer; D1[…] means delay of one clock; D2[…] means delay of two clocks.
Fig. 5
Fig. 5 Experimental setup.
Fig. 6
Fig. 6 The Lissajous figures of Ix(t) and Iy(t) when M2 was in stationary and moving states. (a) M2 was in stationary state. (b) M2 was in moving state.
Fig. 7
Fig. 7 The real-time drifts of the parameters. (a) The drifts of a(t), b(t). (b) The drifts of x0(t) and y0(t).
Fig. 8
Fig. 8 Result of real-time correction. (a) Lissajous figure of Ix(t) and Iy(t). (b) The comparison between the demodulated displacement and the displacement provided by the P-753.CD stage.
Fig. 9
Fig. 9 Experimental results for nanometer displacement measurement with step of 10 nm. (a) Measurement results of the demodulated displacement, position of the P-753.CD stage and the displacement deviation. (b) FFT analysis of the displacement deviation.
Fig. 10
Fig. 10 Experimental results for nanometer displacement measurement with step of 20 nm. (a) Measurement results of the demodulated displacement, position of the P-753.CD stage and the displacement deviation. (b) FFT analysis of the displacement deviation.
Fig. 11
Fig. 11 Comparison experiment of dynamic displacement measurements. (a) Measurement results and deviations of the proposed and Renishaw interferometers. The black triangle line is shifted by 10 mm to make the plots visible. (b) Difference between the proposed and Renishaw interferometers.

Tables (2)

Tables Icon

Table 1 Accuracy evaluation of ellipse fitting

Tables Icon

Table 2 Efficiency test result of ellipse fitting

Equations (17)

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

S ( t ) = I 0 + I 1 cos [ 4 π λ d ( t ) + V e o m V π π ] ,
S ( t ) = I 0 + I 1 cos [ 4 π λ d ( t ) + A c cos ( ω c t ) + B t T r i ( ω t t ) V π π ] , = I 0 + I 1 cos [ C cos ( ω c t ) + ϕ ( t ) ]
S ( t ) = I 0 + I 1 { [ J 0 ( C ) + 2 n = 1 ( 1 ) n J 2 n ( C ) cos ( 2 n ω c t ) ] cos ϕ ( t ) , + [ 2 n = 1 ( 1 ) n J 2 n - 1 ( C ) cos [ ( 2 n - 1 ) ( ω c t ) ] ] sin ϕ ( t ) }
I x ( t ) = LPF 1 [ S ( t ) × cos ( ω c t ) ] = - K 1 I 1 J 1 ( C ) sin ϕ ( t ) ,
I y ( t ) = LPF 2 [ S ( t ) × cos ( 2 ω c t ) ] = - K 2 I 1 J 2 ( C ) cos ϕ ( t ) ,
I x ( t ) = a ( t ) sin ϕ ( t ) + x 0 ( t ) ,
I y ( t ) = b ( t ) cos ϕ ( t ) + y 0 ( t ) ,
I x ( t ) = sin [ ϕ ( t ) ] = [ I x ( t ) x 0 ( t ) ] / a ( t ) ,
I y ( t ) = cos [ ϕ ( t ) ] = [ I y ( t ) y 0 ( t ) ] / b ( t ) .
ϕ ( t ) = P U W [ arc tan sin [ ϕ ( t ) ] cos [ ϕ ( t ) ] ] = arc tan I x ( t ) I y ( t ) + 2 π M ,
I x ( t ) = a n sin ϕ ( t ) + x 0 n ,
I y ( t ) = b n cos ϕ ( t ) + y 0 n .
I x 2 ( t ) + A 1 I y 2 ( t ) + A 2 I x ( t ) + A 3 I y ( t ) + A 4 = 0 ,
{ A 1 = a n 2 / b n 2 A 2 = 2 x 0 n A 3 = ( 2 a n 2 y 0 n ) / b n 2 A 4 = ( b n 2 x 0 n 2 + a n 2 y 0 n 2 a n 2 b n 2 ) / b n 2 .
Ω = i = 1 N σ i 2 = i = 1 N [ I x 2 ( i ) + A 1 I y 2 ( i ) + A 2 I x ( i ) + A 3 I y ( i ) + A 4 ] 2 ,
Ω A 1 = Ω A 2 = Ω A 3 = Ω A 4 = 0.
[ i = 1 N I y 4 ( i ) i = 1 N I x ( i ) I y 2 ( i ) i = 1 N I y 3 ( i ) i = 1 N I y 2 ( i ) i = 1 N I x ( i ) I y 2 ( i ) i = 1 N I x 2 ( i ) i = 1 N I x ( i ) I y ( i ) i = 1 N I x ( i ) i = 1 N I y 3 ( i ) i = 1 N I x ( i ) I y ( i ) i = 1 N I y 2 ( i ) i = 1 N I y ( i ) i = 1 N I y 2 ( i ) i = 1 N I x ( i ) i = 1 N I y ( i ) 1 ] [ A 1 A 2 A 3 A 4 ] = [ i = 1 N I x 2 ( i ) I y 2 ( i ) i = 1 N I x 3 ( i ) i = 1 N I x 2 ( i ) I y ( i ) i = 1 N I x 2 ( i ) ] .

Metrics