Abstract

As the phase delay between the carrier component of the detected interference signal and the carrier has adverse effect for phase generated carrier (PGC) demodulation, it is essential to compensate the phase delay to improve the accuracy of precision displacement measurement in sinusoidal phase-modulation interferometer (SPMI). In this paper, a real-time phase delay compensation method is proposed by regulating a compensating phase introduced to the carrier to maximize the output of the low pass filter so as to make the carrier synchronize with the interference signal. The influence of phase delay for PGC demodulation is analyzed and the method for real-time phase delay compensation is described in detail. The simulation of the method was performed to verify the validity of the phase delay compensation algorithm. A SPMI using an EOM was constructed and several comparative experiments were carried out to demonstrate the feasibility of the proposed method. The experimental results show that the phase delay can be compensated accurately in real time, and nanometer accuracy is achieved for precision displacement measurement.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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  4. S.-C. Huang, Y.-F. Huang, and F.-H. Hwang, “An improved sensitivity normalization technique of PGC demodulation with low minimum phase detection sensitivity using laser modulation to generate carrier signal,” Sensor Actuat A. 191, 1–10 (2013).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
    [Crossref]
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    [Crossref]
  9. O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
    [Crossref]
  10. T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38(34), 7069–7075 (1999).
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    [Crossref] [PubMed]
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    [Crossref]

2015 (3)

O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
[Crossref]

W. Xia, Q. Liu, H. Hao, D. Guo, M. Wang, and X. Chen, “Sinusoidal phase-modulating self-mixing interferometer with nanometer resolution and improved measurement velocity range,” Appl. Opt. 54(26), 7820–7827 (2015).
[Crossref] [PubMed]

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

2013 (2)

K. Wang, M. Zhang, F. Duan, S. Xie, and Y. Liao, “Measurement of the phase shift between intensity and frequency modulations within DFB-LD and its influences on PGC demodulation in a fiber-optic sensor system,” Appl. Opt. 52(29), 7194–7199 (2013).
[Crossref] [PubMed]

S.-C. Huang, Y.-F. Huang, and F.-H. Hwang, “An improved sensitivity normalization technique of PGC demodulation with low minimum phase detection sensitivity using laser modulation to generate carrier signal,” Sensor Actuat A. 191, 1–10 (2013).
[Crossref]

2012 (1)

B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
[Crossref]

2010 (1)

2009 (1)

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (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).

2007 (1)

2005 (1)

2003 (1)

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[Crossref]

2000 (1)

1999 (1)

1998 (1)

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

1997 (1)

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

1994 (1)

C. McGarrity and D. A. Jackson, “Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensors,” Opt. Commun. 109(3), 246–248 (1994).
[Crossref]

1991 (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]

1987 (1)

W. Mikhael and S. Michael, “Composite operational amplifiers: Generation and finite-gain applications,” IEEE Trans. Circ. Syst. 34(5), 449–460 (1987).
[Crossref]

1986 (1)

1982 (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE Trans. Microw. Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

Bönsch, G.

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

Bu, P.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (2009).
[Crossref]

Chen, B.

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

Chen, X.

Choi, S.

O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
[Crossref]

Dandridge, A.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE Trans. Microw. Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

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]

Duan, F.

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. G.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE Trans. Microw. Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

Guo, D.

Hao, H.

He, J.

Huang, B.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (2009).
[Crossref]

Huang, S. C.

Huang, S.-C.

S.-C. Huang, Y.-F. Huang, and F.-H. Hwang, “An improved sensitivity normalization technique of PGC demodulation with low minimum phase detection sensitivity using laser modulation to generate carrier signal,” Sensor Actuat A. 191, 1–10 (2013).
[Crossref]

Huang, Y.-F.

S.-C. Huang, Y.-F. Huang, and F.-H. Hwang, “An improved sensitivity normalization technique of PGC demodulation with low minimum phase detection sensitivity using laser modulation to generate carrier signal,” Sensor Actuat A. 191, 1–10 (2013).
[Crossref]

Hwang, F.-H.

S.-C. Huang, Y.-F. Huang, and F.-H. Hwang, “An improved sensitivity normalization technique of PGC demodulation with low minimum phase detection sensitivity using laser modulation to generate carrier signal,” Sensor Actuat A. 191, 1–10 (2013).
[Crossref]

Jackson, D. A.

C. McGarrity and D. A. Jackson, “Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensors,” Opt. Commun. 109(3), 246–248 (1994).
[Crossref]

Kobayashi, K.

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).

Li, 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).

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, Z.

B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
[Crossref]

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (2009).
[Crossref]

Liao, Y.

Lin, H.

Liu, Q.

Liu, Y.

J. He, L. Wang, F. Li, and Y. Liu, “An Ameliorated Phase Generated Carrier Demodulation Algorithm With Low Harmonic Distortion and High Stability,” J. Lightwave Technol. 28(22), 3258–3265 (2010).

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[Crossref]

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).

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]

Maruyama, T.

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38(34), 7069–7075 (1999).
[Crossref] [PubMed]

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

Matsuda, M.

McGarrity, C.

C. McGarrity and D. A. Jackson, “Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensors,” Opt. Commun. 109(3), 246–248 (1994).
[Crossref]

Michael, S.

W. Mikhael and S. Michael, “Composite operational amplifiers: Generation and finite-gain applications,” IEEE Trans. Circ. Syst. 34(5), 449–460 (1987).
[Crossref]

Mikhael, W.

W. Mikhael and S. Michael, “Composite operational amplifiers: Generation and finite-gain applications,” IEEE Trans. Circ. Syst. 34(5), 449–460 (1987).
[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]

Okada, T.

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

Okazaki, H.

Potulski, E.

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35(2), 133–139 (1998).
[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.

O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
[Crossref]

B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
[Crossref]

T. Suzuki, K. Kobayashi, and O. Sasaki, “Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode interferometer,” Appl. Opt. 39(16), 2646–2652 (2000).
[Crossref] [PubMed]

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38(34), 7069–7075 (1999).
[Crossref] [PubMed]

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25(18), 3137–3140 (1986).
[Crossref] [PubMed]

Suzuki, T.

O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
[Crossref]

T. Suzuki, K. Kobayashi, and O. Sasaki, “Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode interferometer,” Appl. Opt. 39(16), 2646–2652 (2000).
[Crossref] [PubMed]

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38(34), 7069–7075 (1999).
[Crossref] [PubMed]

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

Tan, S.

Tveten, A. B.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE Trans. Microw. Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

Wang, B.

B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
[Crossref]

Wang, K.

Wang, L.

Wang, M.

Wang, X.

B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
[Crossref]

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (2009).
[Crossref]

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[Crossref]

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[Crossref]

Xia, W.

Xie, S.

Xin, J.

O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
[Crossref]

Yan, L.

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

Yang, Y.

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

Yu, D.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[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).

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[Crossref]

Zhang, E.

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

Zhang, M.

Zhang, S.

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

Zheng, D.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (2009).
[Crossref]

Appl. Opt. (6)

IEEE Trans. Circ. Syst. (1)

W. Mikhael and S. Michael, “Composite operational amplifiers: Generation and finite-gain applications,” IEEE Trans. Circ. Syst. 34(5), 449–460 (1987).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE Trans. Microw. Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

J. Lightwave Technol. (1)

Metrologia (1)

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

Opt. Commun. (3)

C. McGarrity and D. A. Jackson, “Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensors,” Opt. Commun. 109(3), 246–248 (1994).
[Crossref]

B. Wang, X. Wang, Z. Li, and O. Sasaki, “Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system,” Opt. Commun. 285(18), 3827–3831 (2012).
[Crossref]

O. Sasaki, J. Xin, S. Choi, and T. Suzuki, “Profile measurement of thin films by backpropagation of multiple-wavelength optical fields with two sinusoidal phase-modulating interferometers,” Opt. Commun. 356, 578–581 (2015).
[Crossref]

Opt. Eng. (1)

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35(3), 219–222 (2003).
[Crossref]

Optik (Stuttg.) (1)

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zheng, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source,” Optik (Stuttg.) 120(16), 799–803 (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).

Rev. Sci. Instrum. (2)

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]

L. Yan, B. Chen, E. Zhang, S. Zhang, and Y. Yang, “Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edlén equation estimation,” Rev. Sci. Instrum. 86(8), 085111 (2015).
[Crossref] [PubMed]

Sensor Actuat A. (1)

S.-C. Huang, Y.-F. Huang, and F.-H. Hwang, “An improved sensitivity normalization technique of PGC demodulation with low minimum phase detection sensitivity using laser modulation to generate carrier signal,” Sensor Actuat A. 191, 1–10 (2013).
[Crossref]

Other (2)

T. R. Christian, P. A. Frank, and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proceedings of SPIE - The International Society for Optical Engineering 2191 (1994).
[Crossref]

International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement International Organization for Standardization (Geneva, 1995).

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Figures (9)

Fig. 1
Fig. 1 Schematic of the PGC demodulation.
Fig. 2
Fig. 2 Principle of the phase delay compensator.
Fig. 3
Fig. 3 Simulation results of displacement measurement for 950 nm with phase delay of 30°. (a) Amplitude of the quadrature components before compensation. (b) Amplitude of the quadrature components after compensation. (c) Displacement measurement results before compensation. To make the plots visible, the red dash line is shifted by 50 nm from the actual values. (d) Displacement measurement results after compensation. The red dash line is shifted by 50 nm from the actual values.
Fig. 4
Fig. 4 Schematic of the SPMI with an EOM.
Fig. 5
Fig. 5 Experimental setup.
Fig. 6
Fig. 6 Displacement measurement results of 950 nm without additional phase delay. (a) Amplitude of the quadrature components before compensation. (b) Amplitude of the quadrature components after compensation. (c) Displacement measurement results before compensation. To make the plots visible, the red dot line is shifted by 50 nm from the actual values. (d) Displacement measurement results after compensation. The red dot line is shifted by 50 nm from the actual values.
Fig. 7
Fig. 7 Displacement measurement results of 950 nm with additional phase delay of 30°. (a) Amplitude of the quadrature components before compensation. (b) Amplitude of the quadrature components after compensation. (c) Displacement measurement results before compensation. To make the plots visible, the red dot line is shifted by 50 nm from the actual values. (d) Displacement measurement results after compensation. The red dot line is shifted by 50 nm from the actual values.
Fig. 8
Fig. 8 Displacement measurement results of 950 nm with additional phase delay of 90°. (a) Amplitude of the quadrature components before compensation. (b) Amplitude of the quadrature components after compensation. (c) Displacement measurement results before compensation. (d) Displacement measurement results after compensation. To make the plots visible, the red dot line is shifted by 50 nm from the actual values.
Fig. 9
Fig. 9 Experimental results for stepping displacement measurement. (a) Measurement results with the step of 20 nm. (b) Measurement results with the step of 0.5 μm.

Tables (1)

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Table 1 Experimental Data with Additional Phase Delay of 0°, 30° and 90°.

Equations (26)

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V ω c (t)=Acos ω c t,
S( t )= S 0 + S 1 cos[ zcos ω c t+φ(t) ],
S( t )= S 0 + S 1 cosφ(t)[ J 0 ( z )+2 m=1 ( 1 ) m J 2m ( z )cos2m ω c t ] + S 1 sinφ(t)[ 2 m=1 ( 1 ) m J 2m1 ( z )cos( 2m1 ) ω c t ],
V 2 ω c (t)=Acos2 ω c t,
P 1 =LPF[ S( t ) V ω c ( t ) ]= K 1 S 1 A J 1 ( z )sinφ(t),
P 2 =LPF[ S( t ) V 2 ω c ( t ) ]= K 2 S 1 A J 2 ( z )cosφ(t)
Y(t)= K 1 K 2 S 1 2 A 2 J 1 (z) J 2 (z)φ(t).
φ( t )=arctan( P 1 / J 1 ( z ) P 2 / J 2 ( z ) )=arctan( K 1 sinφ(t) K 2 cosφ(t) )
S( t )= S 0 + S 1 cos[ zcos ω c ( tΔt )+φ(t) ] = S 0 + S 1 cos[ zcos( ω c tθ )+φ(t) ],
P 1 =LPF[ S( t ) V ω c ( t ) ]= K 1 S 1 A J 1 ( z )cosθsinφ(t),
P 2 =LPF[ S( t ) V 2 ω c ( t ) ]= K 2 S 1 A J 2 ( z )cos2θcosφ(t)
Y(t)= K 1 K 2 S 1 2 A 2 J 1 (z) J 2 (z)cosθcos2θφ(t).
φ( t )=arctan( P 1 / J 1 ( z ) P 2 / J 2 ( z ) )=arctan( K 1 cosθsinφ(t) K 2 cos2θcosφ(t) ).
V ω c (t)=Acos( ω c tα ).
P 1 =LPF[ S( t ) V ω c ( t ) ] = K 1 S 1 A J 1 ( z )cos( θα )sinφ(t)= B 1 cos( θα ),
P 2 =LPF[ S( t ) V 2 ω c ( t ) ] = K 2 S 1 A J 2 ( z )cos2( θα )cosφ(t)= B 2 cos2( θα ),
P 1 / J 1 ( z ) = K 1 S 1 Acos( θα )sinφ(t),
P 2 / J 2 ( z ) = K 2 S 1 Acos2( θα )cosφ(t).
V(t)=β V ω c (t)=βAcos ω c t
φ EOM = π V π V(t)= πβA V π cos ω c t
S( t )= S 0 + S 1 cos[ φ EOM + 4π λ ( l o l r +d(t) ) ] = S 0 + S 1 cos[ πβA V π cos ω c t+ 4π λ ( l o l r +d(t) ) ] = S 0 + S 1 cos[ zcos ω c t+φ(t) ]
φ( t )= 4π λ d( t )+ φ 0 ,
D=d( t 2 )d( t 1 )= λ 2 ( N+ Δφ 2π ),
u( D )= ( D u(λ) λ ) 2 + ( λ 2 u(Δφ) 2π ) 2 ,
u( Δφ )= 2 u[ φ(t) ],
u( D )= ( 0.61nm ) 2 + ( 2.65× 10 4 D ) 2 .

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