Abstract

The performance of distributed optical fiber acoustic sensor as a function of parameters such as the linewidth of the laser, the probe pulse width, and the amplitude and frequency of perturbation is experimentally studied. The aim of this study is to experimentally confirm the outcome of the simulation results obtained previously. It is shown that the experimental and simulation results are in good agreement, and the precision of the sensing system depends on the pulse width and linewidth of the probe pulse, as well as the frequency and amplitude of the perturbation. It is shown that the sensing precision of the system can be enhanced by reducing the width of the probe pulse while increasing the linewidth of the laser.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article
OSA Recommended Articles
Analysis of distributed optical fibre acoustic sensors through numerical modelling

Ali Masoudi and Trevor P. Newson
Opt. Express 25(25) 32021-32040 (2017)

Distributed acoustic sensor based on a two-mode fiber

Mengmeng Chen, Ali Masoudi, Francesca Parmigiani, and Gilberto Brambilla
Opt. Express 26(19) 25399-25407 (2018)

References

  • View by:
  • |
  • |
  • |

  1. J. P. Dakin and C. Lamb, “Distributed fibre optic sensor system,” GB patent No. 2222247A (1990).
  2. A. H. Hartog, An Introduction to Distributed Optical Fibre Sensors, CRC Press (2017).
  3. J. C. Juarez, E. W. Maier, K. N. Choi, and H. F. Taylor, “Distributed Fiber-Optic Intrusion Sensor System,” J. Lightwave Technol. 23(6), 2081–2087 (2005).
    [Crossref]
  4. Y. Rao and J. Li, “Distributed intrusion detection based on combination of φ-OTDR and P-OTDR,” Proc. The 19th International Conference on Optical Fiber Sensors (OFS-19), Perth, Australia, 700461 (2008).
    [Crossref]
  5. S. Liehr, Y. S. Muanenda, S. Münzenberger, and K. Krebber, “Relative change measurement of physical quantities using dual-wavelength coherent OTDR,” Opt. Express 25(2), 720–729 (2017).
    [Crossref] [PubMed]
  6. A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
    [Crossref]
  7. X. He, S. Xie, F. Liu, S. Cao, L. Gu, X. Zheng, and M. Zhang, “Multi-event waveform-retrieved distributed optical fiber acoustic sensor using dual-pulse heterodyne phase-sensitive OTDR,” Opt. Lett. 42(3), 442–445 (2017).
    [Crossref] [PubMed]
  8. A. Masoudi and T. P. Newson, “Contributed Review: Distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87(1), 011501 (2016).
    [Crossref] [PubMed]
  9. A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
    [Crossref]
  10. R. I. Crickmore and D. J. Hill, “Traffic sensing and monitoring apparatus,” US patent No. 7652245B2, (2010).
  11. A. H. Hartog and K. Kader, “Distributed fiber optic sensor system with improved linearity,” US patent No. 9170149B2 (2012).
  12. Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016).
    [Crossref] [PubMed]
  13. J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016).
    [Crossref] [PubMed]
  14. D. Chen, Q. Liu, and Z. He, “Phase-detection distributed fiber-optic vibration sensor without fading-noise based on time-gated digital OFDR,” Opt. Express 25(7), 8315–8325 (2017).
    [Crossref] [PubMed]
  15. Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
    [Crossref]
  16. G. Fang, T. Xu, S. Feng, and F. Li, “Phase-Sensitive Optical Time Domain Reflectometer Based on Phase-Generated Carrier Algorithm,” J. Lightwave Technol. 33(13), 2811–2816 (2015).
    [Crossref]
  17. A. Masoudi and T. P. Newson, “High spatial resolution distributed optical fiber dynamic strain sensor with enhanced frequency and strain resolution,” Opt. Lett. 42(2), 290–293 (2017).
    [Crossref] [PubMed]
  18. A. Masoudi and T. P. Newson, “Analysis of distributed optical fibre acoustic sensors through numerical modelling,” Opt. Express 25(25), 32021–32040 (2017).
    [Crossref] [PubMed]
  19. W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
    [Crossref]
  20. M. J. Murray, A. Davis, and B. Redding, “Multimode fiber Φ-OTDR with holographic demodulation,” Opt. Express 26(18), 23019–23030 (2018).
    [Crossref] [PubMed]
  21. M. Chen, A. Masoudi, F. Parmigiani, and G. Brambilla, “Distributed acoustic sensor based on a two-mode fiber,” Opt. Express 26(19), 25399–25407 (2018).
    [Crossref] [PubMed]
  22. Y. Muanenda, C. J. Oton, S. Faralli, and F. Di Pasquale, “A φ-OTDR sensor for high-frequency distributed vibration measurements with minimal post-processing,” presented at 19th Italian National Conference on Photonic Technologies, Padua, Italy, 11–18 June 2017.
    [Crossref]
  23. K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. 17(5), 1065–1069 (2006).
    [Crossref]

2018 (3)

2017 (6)

2016 (3)

2015 (1)

2014 (1)

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

2013 (1)

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

2006 (1)

K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. 17(5), 1065–1069 (2006).
[Crossref]

2005 (1)

Alekseev, A. E.

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

Barfoot, D. A.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Belal, M.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Brambilla, G.

Cao, S.

Chen, D.

Chen, M.

Choi, K. N.

da Silva Chaves, R.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Dai, H.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Davis, A.

de Campos, M. L. R.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

De Souza, K.

K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. 17(5), 1065–1069 (2006).
[Crossref]

Ellmauthaler, A.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Fan, M.

Fang, G.

Feng, S.

Garcia-Ruiz, A.

Gonzalez-Herraez, M.

Gorshkov, B. G.

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

Gu, L.

He, X.

He, Z.

Jin, X.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Juarez, J. C.

Krebber, K.

Li, F.

Li, J.

Y. Rao and J. Li, “Distributed intrusion detection based on combination of φ-OTDR and P-OTDR,” Proc. The 19th International Conference on Optical Fiber Sensors (OFS-19), Perth, Australia, 700461 (2008).
[Crossref]

Liehr, S.

Liu, F.

Liu, L.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Liu, Q.

Lordelo, C. P. V.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Maier, E. W.

Martin-Lopez, S.

Martins, H. F.

Martins, W. A.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Masoudi, A.

Muanenda, Y. S.

Münzenberger, S.

Murray, M. J.

Newson, T. P.

A. Masoudi and T. P. Newson, “High spatial resolution distributed optical fiber dynamic strain sensor with enhanced frequency and strain resolution,” Opt. Lett. 42(2), 290–293 (2017).
[Crossref] [PubMed]

A. Masoudi and T. P. Newson, “Analysis of distributed optical fibre acoustic sensors through numerical modelling,” Opt. Express 25(25), 32021–32040 (2017).
[Crossref] [PubMed]

A. Masoudi and T. P. Newson, “Contributed Review: Distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87(1), 011501 (2016).
[Crossref] [PubMed]

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Nunes, L. O.

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Parmigiani, F.

Pastor-Graells, J.

Peng, F.

Potapov, V. T.

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

Qi, G.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Qian, X.

Rao, J.

Rao, Y.

Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016).
[Crossref] [PubMed]

Y. Rao and J. Li, “Distributed intrusion detection based on combination of φ-OTDR and P-OTDR,” Proc. The 19th International Conference on Optical Fiber Sensors (OFS-19), Perth, Australia, 700461 (2008).
[Crossref]

Redding, B.

Simikin, D. E.

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

Sun, W.

Taylor, H. F.

Vdovenko, V. S.

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

Wang, G.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Wang, S.

Wang, Z.

Xie, S.

Xu, T.

Xue, N.

Yu, Z.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Zhang, J.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Zhang, L.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016).
[Crossref] [PubMed]

Zhang, M.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

X. He, S. Xie, F. Liu, S. Cao, L. Gu, X. Zheng, and M. Zhang, “Multi-event waveform-retrieved distributed optical fiber acoustic sensor using dual-pulse heterodyne phase-sensitive OTDR,” Opt. Lett. 42(3), 442–445 (2017).
[Crossref] [PubMed]

Zhang, Q.

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

Zheng, X.

Appl. Phys. B (1)

Z. Yu, Q. Zhang, M. Zhang, H. Dai, J. Zhang, L. Liu, L. Zhang, X. Jin, G. Wang, and G. Qi, “Distributed optical fiber vibration sensing using phase-generated carrier demodulation algorithm, ” Appl. Phys. B 124(5), 84 (2018).
[Crossref]

J. Lightwave Technol. (2)

Laser Phys. (1)

A. E. Alekseev, V. S. Vdovenko, B. G. Gorshkov, V. T. Potapov, and D. E. Simikin, “A phase-sensitive optical time-domain reflectometer with dual-pulse phase modulated probe signal,” Laser Phys. 24(11), 115106 (2014).
[Crossref]

Meas. Sci. Technol. (2)

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. 17(5), 1065–1069 (2006).
[Crossref]

Opt. Express (7)

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

A. Masoudi and T. P. Newson, “Contributed Review: Distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87(1), 011501 (2016).
[Crossref] [PubMed]

SENS. J. (1)

W. A. Martins, M. L. R. de Campos, R. da Silva Chaves, C. P. V. Lordelo, A. Ellmauthaler, L. O. Nunes, and D. A. Barfoot, “Communication Models for Distributed Acoustic Sensing for Telemetry,” SENS. J. 17(15), 4677–4688 (2017).
[Crossref]

Other (6)

Y. Muanenda, C. J. Oton, S. Faralli, and F. Di Pasquale, “A φ-OTDR sensor for high-frequency distributed vibration measurements with minimal post-processing,” presented at 19th Italian National Conference on Photonic Technologies, Padua, Italy, 11–18 June 2017.
[Crossref]

R. I. Crickmore and D. J. Hill, “Traffic sensing and monitoring apparatus,” US patent No. 7652245B2, (2010).

A. H. Hartog and K. Kader, “Distributed fiber optic sensor system with improved linearity,” US patent No. 9170149B2 (2012).

Y. Rao and J. Li, “Distributed intrusion detection based on combination of φ-OTDR and P-OTDR,” Proc. The 19th International Conference on Optical Fiber Sensors (OFS-19), Perth, Australia, 700461 (2008).
[Crossref]

J. P. Dakin and C. Lamb, “Distributed fibre optic sensor system,” GB patent No. 2222247A (1990).

A. H. Hartog, An Introduction to Distributed Optical Fibre Sensors, CRC Press (2017).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 The outline of a typical interferometric DAS setup.
Fig. 2
Fig. 2 Distribution of inhomogeneity along two fixed sections of the sensing fiber before and after longitudinal elongation.
Fig. 3
Fig. 3 Experimental setup. DFB, distributed feedback; EOM, electro-optic modulator; EDFA, erbium-doped fiber amplifier; AOM, acousto-optic modulator; C, Circulator; DWDM, Dense Wavelength Division Multiplexing; PD, photodetector.
Fig. 4
Fig. 4 Linewidth of the directly modulated DFB laser. (a) The frequency spectrum of the DFB laser for different modulated voltages, (b) Relationship between the linewidth of the laser and the amplitude of the modulation signal.
Fig. 5
Fig. 5 Time domain Rayleigh backscattered traces for a probe pulse with 10 MHz linewidth (in blue) and 1 GHz linewidth (in orange).
Fig. 6
Fig. 6 3D representation of the strain distribution along the fiber for a 1 kHz vibration with an amplitude of 10 Vpp and a probe pulse linewidth of 500 MHz. The graphs represent 3D maps of the strain distribution (a) in the time domain, and (b) in the frequency domain.
Fig. 7
Fig. 7 Relationship between the SD of the strain level measured by using φ-OTDR and the probe pulse linewidth. For this diagram, the sensing system was set for a range of linewidths from 10 MHz to 1 GHz for a fixed pulse width of 2m.
Fig. 8
Fig. 8 Relationship between the SD of the strain level measured by using φ-OTDR and the probe pulse width. For this diagram, the sensing system was set by stepping the pulse widths from 50 cm to 2 m in 25 cm steps while the probe pulse linewidth was fixed to 2 MHz.
Fig. 9
Fig. 9 System response to a 1 kHz sinusoidal strain ranging from 50 nε to 350 nε. (a) Experimental results as a function of the induced strain amplitude, (b) SD of different realization of the system model versus the induced strain amplitude.
Fig. 10
Fig. 10 System response to 4 V perturbations for a frequency ranging from 250 Hz to 2250 Hz. (a) System output as a function of the frequency of the induced strain, (b) SD of different realization of the system versus the frequency of the induced strain.

Equations (9)

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

{ I 1 = E A (λ) 2 + E B (λ) 2 +2 E A (λ) E B (λ)cos[ φ A (λ) φ B (λ) 2π 3 ] I 2 = E A (λ) 2 + E B (λ) 2 +2 E A (λ) E B (λ)cos[ φ A (λ) φ B (λ) ] I 3 = E A (λ) 2 + E B (λ) 2 +2 E A (λ) E B (λ)cos[ φ A (λ) φ B (λ)+ 2π 3 ]
{ I 1 = λ 0 λ n { E A (Λ) 2 + E B (Λ) 2 +2 E A (Λ) E B (Λ)cos[ φ A (Λ) φ B (Λ) 2π 3 ] }dΛ I 2 = λ 0 λ n { E A (Λ) 2 + E B (Λ) 2 +2 E A (Λ) E B (Λ)cos[ φ A (Λ) φ B (Λ) ] }dΛ I 3 = λ 0 λ n { E A (Λ) 2 + E B (Λ) 2 +2 E A (Λ) E B (Λ)cos[ φ A (Λ) φ B (Λ)+ 2π 3 ] }dΛ
Δφ= 2πn λ 2l×0.78+ φ 2 φ 1
Δφ ¯ = 2πn λ 2( l+Δl )×0.78+ φ 2 ¯ φ 1 ¯
ΔΦ= Δφ ¯ Δφ= 2πn λ 2(Δl)×0.78+( φ 2 ¯ φ 2 )+( φ 1 ¯ φ 1 )
Δϕ=arctan( I ˙ 2 I ˙ 3 I ˙ 1 )
I= λ 0 λ n   E A ( Λ ) 2 + E B ( Λ ) 2 +2 E A ( Λ ) E B ( Λ )cos( 2πn Λ 2l×0.78+ φ 2 ( Λ ) φ 1 ( Λ ) )dΛ.
I=2 E 2 λ 0 λ n  [ 1+cos( 2πn Λ 2l×0.78+ φ 2 ( Λ ) φ 1 ( Λ ) )  ]dΛ.
f CRN ( V g 4 Δz Δν ) 1 2

Metrics