Abstract

This paper proposes a novel reflectometry based on the frequency modulation pulse-compression technology, called optical pulse compression reflectometry (OPCR). Linear frequency modulation (LFM) pulse is taken as an example to implement the OPCR. Its working principle and theoretical analysis are demonstrated. The spatial resolution is determined by the sweeping range of the LFM rather than the pulse width, which overcomes the tradeoff between spatial resolution and measurement range in the conventional pulse-based optical time domain reflectometry. The influence of the laser’s phase noise on the integrated side lobe ratio and peak side lobe ratio is theoretically studied. Thanks to the continuous acquisition nature of the OPCR, time averaging is valid to eliminate the influence and results in the measurement range of the OPCR beyond a few times of the source coherent length. A proof-of-concept experiment of the OPCR is carried out to verify the spatial resolution and measurement range.

© 2015 Optical Society of America

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References

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  1. M. K. Barnoski, M. D. Rourke, S. M. Jensen, and R. T. Melville, “Optical time domain reflectometer,” Appl. Opt. 16(9), 2375–2379 (1977).
    [Crossref] [PubMed]
  2. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
    [Crossref] [PubMed]
  3. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
    [Crossref]
  4. D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. 3(5), 971–977 (1985).
    [Crossref]
  5. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
    [Crossref] [PubMed]
  6. S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol. 11(10), 1694–1700 (1993).
    [Crossref]
  7. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. 32(22), 3227–3229 (2007).
    [Crossref] [PubMed]
  8. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency-domain reflectometry,” J. Quantum Electron. 45(6), 594–602 (2009).
    [Crossref]
  9. F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. 30(8), 1015–1024 (2012).
    [Crossref]
  10. M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill Education, 2005).
  11. S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
    [Crossref]
  12. P. Healey, “Pulse compression coding in optical time domain reflectometry,” in Proc. 7th Eur. Conf. Opt. Comun. (1981), pp. 5.2–1.
  13. M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
    [Crossref]
  14. R. Goldman, A. Agmon, and M. Nazarathy, “Direct detection and coherent optical time-domain reflectometry with Golay complementary codes,” J. Lightwave Technol. 31(13), 2207–2222 (2013).
    [Crossref]
  15. M. A. Soto, G. Bolognini, and F. Di Pasquale, “Analysis of optical pulse coding in spontaneous Brillouin-based distributed temperature sensors,” Opt. Express 16(23), 19097–19111 (2008).
    [Crossref] [PubMed]
  16. K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” High Spectral Density Optical Communication Technologies. (Springer Berlin Heidelberg, 2010).
  17. A. Hartog and M. P. Gold, “On the theory of backscattering in single-mode optical fibers,” J. Lightwave Technol. 2(2), 76–82 (1984).
    [Crossref]
  18. A. Moreira, “Real-time synthetic aperture radar (SAR) processing with a new subaperture approach,” IEEE Trans. Geosci. Rem. Sens. 30(4), 714–722 (1992).
    [Crossref]
  19. N. Levanon and E. Mozeson, Radar Signals (John Wiley & Sons, 2004).
  20. J. Armstrong, “Theory of interferometric analysis of laser phase noise,” J. Opt. Soc. Am. 56(8), 1024–1028 (1966).
    [Crossref]
  21. R. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
    [Crossref]
  22. K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” J. Quant. Electron. 17(6), 862–868 (1981).
    [Crossref]
  23. L. R. Varshney and D. Thomas, “Side lobe reduction for match filter range processing,” in Radar Conference, 2003. Proceedings of the 2003 IEEE (2003), pp.446–451.
  24. M. Kashiwagi and K. Hotate, “Long range and high resolution reflectometry by synthesis of optical coherence function at region beyond the coherence length,” IEICE Electron. Express 6(8), 497–503 (2009).
    [Crossref]
  25. L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
    [Crossref]
  26. F. J. Duarte, Tunable Lasers Handbook (Academic Press Inc., 1995).
  27. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).
  28. Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
    [Crossref] [PubMed]

2014 (1)

S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (1)

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
[Crossref]

2009 (2)

X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency-domain reflectometry,” J. Quantum Electron. 45(6), 594–602 (2009).
[Crossref]

M. Kashiwagi and K. Hotate, “Long range and high resolution reflectometry by synthesis of optical coherence function at region beyond the coherence length,” IEICE Electron. Express 6(8), 497–503 (2009).
[Crossref]

2008 (2)

2007 (1)

2005 (1)

1993 (2)

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol. 11(10), 1694–1700 (1993).
[Crossref]

1992 (1)

A. Moreira, “Real-time synthetic aperture radar (SAR) processing with a new subaperture approach,” IEEE Trans. Geosci. Rem. Sens. 30(4), 714–722 (1992).
[Crossref]

1989 (1)

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

1986 (1)

R. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[Crossref]

1985 (1)

D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. 3(5), 971–977 (1985).
[Crossref]

1984 (1)

A. Hartog and M. P. Gold, “On the theory of backscattering in single-mode optical fibers,” J. Lightwave Technol. 2(2), 76–82 (1984).
[Crossref]

1981 (2)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” J. Quant. Electron. 17(6), 862–868 (1981).
[Crossref]

1977 (1)

1966 (1)

Agmon, A.

Aoyama, K.

K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” J. Quant. Electron. 17(6), 862–868 (1981).
[Crossref]

Armstrong, J.

Bao, X.

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
[Crossref] [PubMed]

Barnoski, M. K.

Bolognini, G.

Chen, J.

S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
[Crossref]

Chen, L.

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
[Crossref] [PubMed]

Chraplyvy, A. R.

R. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[Crossref]

Culshaw, B.

D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. 3(5), 971–977 (1985).
[Crossref]

Di Pasquale, F.

Eickhoff, W.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Fan, X.

Foster, S.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Froggatt, M.

Furukawa, S.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Giffard, R. P.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Gifford, D.

Gold, M. P.

A. Hartog and M. P. Gold, “On the theory of backscattering in single-mode optical fibers,” J. Lightwave Technol. 2(2), 76–82 (1984).
[Crossref]

Goldman, R.

Hartog, A.

A. Hartog and M. P. Gold, “On the theory of backscattering in single-mode optical fibers,” J. Lightwave Technol. 2(2), 76–82 (1984).
[Crossref]

He, Z.

Healey, P.

P. Healey, “Pulse compression coding in optical time domain reflectometry,” in Proc. 7th Eur. Conf. Opt. Comun. (1981), pp. 5.2–1.

Horiguchi, T.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Hotate, K.

M. Kashiwagi and K. Hotate, “Long range and high resolution reflectometry by synthesis of optical coherence function at region beyond the coherence length,” IEICE Electron. Express 6(8), 497–503 (2009).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
[Crossref] [PubMed]

Ito, F.

Itoh, T.

K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” J. Quant. Electron. 17(6), 862–868 (1981).
[Crossref]

Izumita, H.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Jensen, S. M.

Kashiwagi, M.

M. Kashiwagi and K. Hotate, “Long range and high resolution reflectometry by synthesis of optical coherence function at region beyond the coherence length,” IEICE Electron. Express 6(8), 497–503 (2009).
[Crossref]

Koshikiya, Y.

Koyamada, Y.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Kurashima, T.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Long, X.

S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
[Crossref]

Maleki, L.

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
[Crossref]

Melville, R. T.

Mizuno, Y.

Moberly, D. S.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Moreira, A.

A. Moreira, “Real-time synthetic aperture radar (SAR) processing with a new subaperture approach,” IEEE Trans. Geosci. Rem. Sens. 30(4), 714–722 (1992).
[Crossref]

Nakagawa, K.

K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” J. Quant. Electron. 17(6), 862–868 (1981).
[Crossref]

Nazarathy, M.

R. Goldman, A. Agmon, and M. Nazarathy, “Direct detection and coherent optical time-domain reflectometry with Golay complementary codes,” J. Lightwave Technol. 31(13), 2207–2222 (2013).
[Crossref]

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Newton, S. A.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Rourke, M. D.

Sischka, F.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Soller, B.

Sorin, W. V.

S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol. 11(10), 1694–1700 (1993).
[Crossref]

Soto, M. A.

Thomas, D.

L. R. Varshney and D. Thomas, “Side lobe reduction for match filter range processing,” in Radar Conference, 2003. Proceedings of the 2003 IEEE (2003), pp.446–451.

Tkach, R.

R. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[Crossref]

Trutna, W. R.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Ulrich, R.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Uttam, D.

D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. 3(5), 971–977 (1985).
[Crossref]

Varshney, L. R.

L. R. Varshney and D. Thomas, “Side lobe reduction for match filter range processing,” in Radar Conference, 2003. Proceedings of the 2003 IEEE (2003), pp.446–451.

Venkatesh, S.

S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol. 11(10), 1694–1700 (1993).
[Crossref]

Wolfe, M.

Yang, S.

S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
[Crossref]

Zou, W.

S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

IEEE Trans. Geosci. Rem. Sens. (1)

A. Moreira, “Real-time synthetic aperture radar (SAR) processing with a new subaperture approach,” IEEE Trans. Geosci. Rem. Sens. 30(4), 714–722 (1992).
[Crossref]

IEICE Electron. Express (1)

M. Kashiwagi and K. Hotate, “Long range and high resolution reflectometry by synthesis of optical coherence function at region beyond the coherence length,” IEICE Electron. Express 6(8), 497–503 (2009).
[Crossref]

IEICE Trans. Commun. (1)

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

J. Lightwave Technol. (7)

R. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986).
[Crossref]

D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. 3(5), 971–977 (1985).
[Crossref]

S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol. 11(10), 1694–1700 (1993).
[Crossref]

F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. 30(8), 1015–1024 (2012).
[Crossref]

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

R. Goldman, A. Agmon, and M. Nazarathy, “Direct detection and coherent optical time-domain reflectometry with Golay complementary codes,” J. Lightwave Technol. 31(13), 2207–2222 (2013).
[Crossref]

A. Hartog and M. P. Gold, “On the theory of backscattering in single-mode optical fibers,” J. Lightwave Technol. 2(2), 76–82 (1984).
[Crossref]

J. Opt. Soc. Am. (1)

J. Quant. Electron. (1)

K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” J. Quant. Electron. 17(6), 862–868 (1981).
[Crossref]

J. Quantum Electron. (1)

X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency-domain reflectometry,” J. Quantum Electron. 45(6), 594–602 (2009).
[Crossref]

Nat. Photonics (1)

L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

S. Yang, W. Zou, X. Long, and J. Chen, ““Pulse-compression optical time domain reflectometer,” in the 23rd International Conference on Optical Fiber Sensors,” Proc. SPIE 9157, 915736 (2014).
[Crossref]

Sensors (Basel) (1)

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
[Crossref] [PubMed]

Other (6)

M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill Education, 2005).

P. Healey, “Pulse compression coding in optical time domain reflectometry,” in Proc. 7th Eur. Conf. Opt. Comun. (1981), pp. 5.2–1.

K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” High Spectral Density Optical Communication Technologies. (Springer Berlin Heidelberg, 2010).

F. J. Duarte, Tunable Lasers Handbook (Academic Press Inc., 1995).

L. R. Varshney and D. Thomas, “Side lobe reduction for match filter range processing,” in Radar Conference, 2003. Proceedings of the 2003 IEEE (2003), pp.446–451.

N. Levanon and E. Mozeson, Radar Signals (John Wiley & Sons, 2004).

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Figures (8)

Fig. 1
Fig. 1 Basic principle of pulse compression with frequency modulation (FM).
Fig. 2
Fig. 2 Schematic configuration of OPCR based on LFM pulse compression technology. EOM: electro-optic modulator, FUT: fiber under test.
Fig. 3
Fig. 3 Qualitative description of pulse-compression process. (a) Time-domain profile of LFM pulse and (b) compressed pulse with a 3-dB width equal to 1/KT. (c) Zoomed-in compressed pulse for definition of two parameters of ISLR and PSLR.
Fig. 4
Fig. 4 Numerical simulation of the influence of phase noise. The compressed pulse without (a) and with (b) phase noise. (c) The compressed pulse after 10,000 time averaging.
Fig. 5
Fig. 5 (a) Dependence of both ISLR and PSLR on the phase noise. The effect of time-averaging process on (b) ISLR and (c) PSLR.
Fig. 6
Fig. 6 Proof-of-concept experiment of the OPCR system. The inset (a) shows the LFM spectrum with 221 MHz sweeping range. DFB-LD: distributed feedback laser diode, SSBM: single sideband modulator, VCO: voltage-controlled oscillator, AWG: arbitrary waveform generator, MZM: Mach-Zehnder modulator, PC: polarization control, EDFA: Erbium-doped fiber amplifier, OSC: oscilloscope.
Fig. 7
Fig. 7 Comparison between the proof-of-concept measurement (a) and numerical simulation (b). The insets show the magnified curves at the near and far ends of the FUT, respectively.
Fig. 8
Fig. 8 (a) Schematic of the ideal backscattered trace starting at τ = 0 (i.e. the location of the circulator in Fig. 6) where no any reflection exists except for Rayleigh backscatter. (b) A compressed pulse to convolute the ideal backscattered trace. Demonstration of the accumulation process of the real component (c) and imaginary component (d) of the compressed pulse. The real part (e), imaginary part (f), and (g) amplitude of the OPCR’s trace after matched filtering.

Equations (13)

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

h( t )= x * (t) F H( ω )= X * ( ω ),
Y( ω )=X( ω )H( ω )= | X( ω ) | 2 ,
E s ( t )= A 1 ( t )*{ rect( t T )exp[ j2π f c ( t )+jπK t 2 ] }, E local ( t )= A 2 exp( j2π f c t ),
i s ( t )2Re{ E s E local * }=2 A 2 0 T s A 1 ( τ )rect( tτ T )cos[ πK ( tτ ) 2 2π f c τ ]dτ ,
s( t )=A( t )*x(t), A( t )=2 A 2 A 1 ( τ )exp( j2π f c τ ), x(t)={ rect( t T )exp[ jπK t 2 ] }.
h( t )= x * (t)=rect( t T )exp( jπK t 2 ).
y( t )=s( t )*h( t )=[A( t )*x(t)]*h(t)=A( t )*[x(t)*h(t)]=A( t )*C( t ) C( t )=x(t)*h(t)={ rect( t 2T ) Tsin[ πK( T| t | )( t ) ] πKT( t ) }
R= c 2nKT = c 2nB ,
SNR P s N 0 ,
ISLR=10 log 10 a b | C( τ ) | 2 dτ a | C( τ ) | 2 dτ+ b | C( τ ) | 2 dτ , PSLR=10 log 10 I m I s ,
E s ( t )= A 1 ( t )*{ rect( t T )exp[ j2π f c ( t )+jπK t 2 +jϕ( t ) ] }, E local ( t )= A 2 exp[ j2π f c t+jϕ( t ) ],
s ( t )= 0 T s A( τ ) x τ ( t )dτ , x τ ( t )=x(tτ)exp[ jϕ( t )jϕ( tτ ) ],
x τ ( t )=rect( tτ T )exp[ jπK ( tτ ) 2 ]exp[ jΔϕ( τ ) ], C τ ( t )= x τ ( t )*h(t)=C( t )exp[ jΔϕ( τ ) ].

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