Abstract

We report on measurement of small displacements with sub-nanometer precision using an optoelectronic oscillator (OEO) with an intra-loop Michelson interferometer. In comparison with conventional homodyne and heterodyne detection methods, where displacement appears as a power change or a phase shift, respectively, in the OEO detection, the displacement produces a shift in the oscillation frequency. In comparison with typical OEO sensors, where the frequency shift is proportional to the OEO oscillation frequency in radio-frequency domain, the frequency shift in our method with an intra-loop interferometer is proportional to an optical frequency. We constructed a hybrid apparatus and compared characteristics of the OEO and heterodyne detection methods.

© 2016 Optical Society of America

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References

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  1. G. Cella and A. Giazotto, “Invited review article: Interferometric gravity wave detectors,” Rev. Sci. Instrum. 82(10), 101101 (2011).
    [Crossref] [PubMed]
  2. J. N. Dukes and G. B. Gordon, “A two-hundred-foot yardstick with graduations every microinch,” Hewlett-Packard J. 21, 2–8 (1970). http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1970-08.pdf
  3. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
    [Crossref]
  4. R. T. Kersten, “Ein optisches Nachrichtensystem mit Bauelementen der integrierten Optik für die Übertragung hoher Bitraten,” Arch. Elektrotech. 60(6), 353–359 (1978).
    [Crossref]
  5. X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
    [Crossref]
  6. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
    [Crossref]
  7. L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photonics Technol. Lett. 22(12), 857–859 (2010).
    [Crossref]
  8. F. Kong, W. Li, and J. Yao, “Transverse load sensing based on a dual-frequency optoelectronic oscillator,” Opt. Lett. 38(14), 2611–2613 (2013).
    [Crossref] [PubMed]
  9. Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  14. V. N. Konopsky, “A new type of optical gyro via electro-optic oscillator,” Opt. Commun. 126(4-6), 236–239 (1996).
    [Crossref]
  15. A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
    [Crossref]
  16. S. H. Yim, D. Cho, and J. Park, “Two-frequency interferometer for a displacement measurement,” Am. J. Phys. 81, 153–156 (2012).
  17. G. E. Sommargren, “Apparatus to transform a single frequency, linearly polarized laser beam into a beam with two, orthogonally polarized frequencies,” United States Patent 4684828 (1987).
  18. C. H. Lee and S. H. Yim, “Optoelectronic oscillator for a measurement of acoustic velocity in acousto-optic device,” Opt. Express 22(11), 13634–13640 (2014).
    [Crossref] [PubMed]

2016 (1)

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

2015 (1)

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

2014 (3)

2013 (2)

2012 (1)

S. H. Yim, D. Cho, and J. Park, “Two-frequency interferometer for a displacement measurement,” Am. J. Phys. 81, 153–156 (2012).

2011 (1)

G. Cella and A. Giazotto, “Invited review article: Interferometric gravity wave detectors,” Rev. Sci. Instrum. 82(10), 101101 (2011).
[Crossref] [PubMed]

2010 (1)

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photonics Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

1998 (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

1996 (2)

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
[Crossref]

V. N. Konopsky, “A new type of optical gyro via electro-optic oscillator,” Opt. Commun. 126(4-6), 236–239 (1996).
[Crossref]

1991 (1)

T. V. Babkina, V. V. Grigor’yants, Y. B. Il’in, and A. A. Lobanov, “Use of a laser oscillator heterodyne interferometer as an optical sensor of microdisplacements,” Sov. J. Quantum Electron. 21(12), 1384–1387 (1991).
[Crossref]

1978 (1)

R. T. Kersten, “Ein optisches Nachrichtensystem mit Bauelementen der integrierten Optik für die Übertragung hoher Bitraten,” Arch. Elektrotech. 60(6), 353–359 (1978).
[Crossref]

1958 (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[Crossref]

Babkina, T. V.

T. V. Babkina, V. V. Grigor’yants, Y. B. Il’in, and A. A. Lobanov, “Use of a laser oscillator heterodyne interferometer as an optical sensor of microdisplacements,” Sov. J. Quantum Electron. 21(12), 1384–1387 (1991).
[Crossref]

Cella, G.

G. Cella and A. Giazotto, “Invited review article: Interferometric gravity wave detectors,” Rev. Sci. Instrum. 82(10), 101101 (2011).
[Crossref] [PubMed]

Chi, H.

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Cho, D.

S. H. Yim, D. Cho, and J. Park, “Two-frequency interferometer for a displacement measurement,” Am. J. Phys. 81, 153–156 (2012).

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

Giazotto, A.

G. Cella and A. Giazotto, “Invited review article: Interferometric gravity wave detectors,” Rev. Sci. Instrum. 82(10), 101101 (2011).
[Crossref] [PubMed]

Grigor’yants, V. V.

T. V. Babkina, V. V. Grigor’yants, Y. B. Il’in, and A. A. Lobanov, “Use of a laser oscillator heterodyne interferometer as an optical sensor of microdisplacements,” Sov. J. Quantum Electron. 21(12), 1384–1387 (1991).
[Crossref]

Guo, T.

Il’in, Y. B.

T. V. Babkina, V. V. Grigor’yants, Y. B. Il’in, and A. A. Lobanov, “Use of a laser oscillator heterodyne interferometer as an optical sensor of microdisplacements,” Sov. J. Quantum Electron. 21(12), 1384–1387 (1991).
[Crossref]

Jia, S.

Jin, X.

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Journet, B.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photonics Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

Kersten, R. T.

R. T. Kersten, “Ein optisches Nachrichtensystem mit Bauelementen der integrierten Optik für die Übertragung hoher Bitraten,” Arch. Elektrotech. 60(6), 353–359 (1978).
[Crossref]

Kong, F.

Konopsky, V. N.

V. N. Konopsky, “A new type of optical gyro via electro-optic oscillator,” Opt. Commun. 126(4-6), 236–239 (1996).
[Crossref]

Lee, C. H.

Li, M.

Li, P.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

Li, W.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

F. Kong, W. Li, and J. Yao, “Transverse load sensing based on a dual-frequency optoelectronic oscillator,” Opt. Lett. 38(14), 2611–2613 (2013).
[Crossref] [PubMed]

Liu, X.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

Lobanov, A. A.

T. V. Babkina, V. V. Grigor’yants, Y. B. Il’in, and A. A. Lobanov, “Use of a laser oscillator heterodyne interferometer as an optical sensor of microdisplacements,” Sov. J. Quantum Electron. 21(12), 1384–1387 (1991).
[Crossref]

Luo, B.

Maleki, L.

Miao, W.

Nakatani, K.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photonics Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

Nguyen, L. D.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photonics Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

Pan, W.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

X. Zou, M. Li, W. Pan, B. Luo, L. Yan, and L. Shao, “Optical length change measurement via RF frequency shift analysis of incoherent light source based optoelectronic oscillator,” Opt. Express 22(9), 11129–11139 (2014).
[Crossref] [PubMed]

Park, J.

S. H. Yim, D. Cho, and J. Park, “Two-frequency interferometer for a displacement measurement,” Am. J. Phys. 81, 153–156 (2012).

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[Crossref]

Shao, L.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

X. Zou, M. Li, W. Pan, B. Luo, L. Yan, and L. Shao, “Optical length change measurement via RF frequency shift analysis of incoherent light source based optoelectronic oscillator,” Opt. Express 22(9), 11129–11139 (2014).
[Crossref] [PubMed]

Sun, B.

Townes, C. H.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[Crossref]

Wang, J.

Wang, W.

Wu, Q.

Yan, L.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

X. Zou, M. Li, W. Pan, B. Luo, L. Yan, and L. Shao, “Optical length change measurement via RF frequency shift analysis of incoherent light source based optoelectronic oscillator,” Opt. Express 22(9), 11129–11139 (2014).
[Crossref] [PubMed]

Yao, J.

Yao, X. S.

Ye, S.

Yim, S. H.

C. H. Lee and S. H. Yim, “Optoelectronic oscillator for a measurement of acoustic velocity in acousto-optic device,” Opt. Express 22(11), 13634–13640 (2014).
[Crossref] [PubMed]

S. H. Yim, D. Cho, and J. Park, “Two-frequency interferometer for a displacement measurement,” Am. J. Phys. 81, 153–156 (2012).

Yu, J.

Zhang, T.

Zhang, X.

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Zheng, S.

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Zhou, J.

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Zhu, J.

Zhu, Y.

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Zou, X.

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

X. Zou, M. Li, W. Pan, B. Luo, L. Yan, and L. Shao, “Optical length change measurement via RF frequency shift analysis of incoherent light source based optoelectronic oscillator,” Opt. Express 22(9), 11129–11139 (2014).
[Crossref] [PubMed]

Am. J. Phys. (1)

S. H. Yim, D. Cho, and J. Park, “Two-frequency interferometer for a displacement measurement,” Am. J. Phys. 81, 153–156 (2012).

Appl. Opt. (1)

Arch. Elektrotech. (1)

R. T. Kersten, “Ein optisches Nachrichtensystem mit Bauelementen der integrierten Optik für die Übertragung hoher Bitraten,” Arch. Elektrotech. 60(6), 353–359 (1978).
[Crossref]

IEEE J. Quantum Electron. (1)

X. Zou, X. Liu, W. Li, P. Li, W. Pan, L. Yan, and L. Shao, “Optoelectronic oscillators to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 0601116 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (1)

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photonics Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

Microw. Opt. Technol. Lett. (1)

Y. Zhu, J. Zhou, X. Jin, H. Chi, X. Zhang, and S. Zheng, “An optoelectronic oscillator-based strain sensor with extended measurement range,” Microw. Opt. Technol. Lett. 57(10), 2336–2339 (2015).
[Crossref]

Opt. Commun. (1)

V. N. Konopsky, “A new type of optical gyro via electro-optic oscillator,” Opt. Commun. 126(4-6), 236–239 (1996).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[Crossref]

Rev. Sci. Instrum. (1)

G. Cella and A. Giazotto, “Invited review article: Interferometric gravity wave detectors,” Rev. Sci. Instrum. 82(10), 101101 (2011).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

T. V. Babkina, V. V. Grigor’yants, Y. B. Il’in, and A. A. Lobanov, “Use of a laser oscillator heterodyne interferometer as an optical sensor of microdisplacements,” Sov. J. Quantum Electron. 21(12), 1384–1387 (1991).
[Crossref]

Other (2)

J. N. Dukes and G. B. Gordon, “A two-hundred-foot yardstick with graduations every microinch,” Hewlett-Packard J. 21, 2–8 (1970). http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1970-08.pdf

G. E. Sommargren, “Apparatus to transform a single frequency, linearly polarized laser beam into a beam with two, orthogonally polarized frequencies,” United States Patent 4684828 (1987).

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Figures (11)

Fig. 1
Fig. 1 Optoelectronic oscillator. f c is the carrier frequency of the laser and f s is the frequency of the sideband produced by the modulator.
Fig. 2
Fig. 2 Heterodyne detection scheme. NPBS: non-polarizing beam splitter; PBS: polarizing beam splitter; PD: photodetector.
Fig. 3
Fig. 3 OEO detection scheme.
Fig. 4
Fig. 4 (a) Measurement of phase shift in heterodyne detection and (b) measurement of frequency shift in OEO detection.
Fig. 5
Fig. 5 Modulator to produce an orthogonally polarized sideband. AOM: acousto-optic modulator; M: mirror; HWP: half-wave plate. Polarization states of the carrier (red) and the sideband (blue) are shown.
Fig. 6
Fig. 6 Apparatus configured for OEO detection in a phase-locked loop (PLL) scheme. DC: directional coupler; DPD: digital phase detector.
Fig. 7
Fig. 7 (a) Output spectrum of the OEO. Free spectral range is 1.8 MHz. (b) Comparison of OEO spectra before and after the phase lock.
Fig. 8
Fig. 8 Standard deviation of the error signal for heterodyne detection and the correction signal for OEO detection. Each results are average values of 50 measurements.
Fig. 9
Fig. 9 Displacement noise of heterodyne and OEO detections.
Fig. 10
Fig. 10 Bode plot of heterodyne detection.
Fig. 11
Fig. 11 Bode plot of OEO detection.

Equations (14)

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K q ( L s + l a )+ k ¯ l d =2πq,
F q = c L q l d L f ¯ ,
Δ F q = 2Δl L f ¯ .
Δ F q = ΔL L F q .
P(Δz)= P o (1+coskΔz),
δ(Δz)= λ 2π ω P o τ .
P(t)= P o (1+cos( ω m t+Δϕ)),
P ¯ j = 1 Δt jΔt (j+1)Δt P(t)dt ,
1 ( δ(Δϕ) ) 2 = j=1 n 1 ( (Δϕ) P j δ P j ) 2 ,
δ(Δϕ)= ω P o τ .
δ F OEO = 1 2π ω P o t r 2 ,
δ(ΔF)= δ F OEO 2πτ .
δ(Δz)= λδt τ T .
δ(Δz)=L F q δt f 0 τ .

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