Abstract

A novel and efficient method for fiber transfer delay measurement is demonstrated. Fiber transfer delay measurement in time domain is converted into the frequency measurement of the modulation signal in frequency domain, accompany with a coarse and easy ambiguity resolving process. This method achieves a sub-picosecond resolution, with an accuracy of 1 picosecond, and a large dynamic range up to 50 km as well as no measurement dead zone.

© 2016 Optical Society of America

1. Introduction

Due to its low attenuation, high reliability and accessibility, optical fiber has become an attractive transmission medium for different application areas, such as optical communication [1], fiber-optic sensing [2], and many large-scale scientific or engineering facilities [3–6 ]. Fiber transmission induced time delay measurement is indispensable in these applications. For the application of phased array antenna, fiber transfer delay (FTD) measurement accuracy directly affects its control accuracy, and further affects the beam forming results [7–10 ]. For time and frequency synchronization network, FTD measurement is a key step to realize clock synchronization [11–14 ]. Ordinarily, the time delay is measured in time domain, such as using the time interval counter (TIC) [15] or optical time domain reflectometer (OTDR) [16], but they have drawbacks of low accuracy and existing dead zones. Recently, efforts have been made to meet requirements of large dynamic range and high accuracy based on propagation delay measurement in frequency domain [17–20 ]. The common method is converting the FTD measurement into the longitudinal mode spacing measurement of a mode-locked fiber laser or the beating frequency measurement of a ring cavity. A mode-locked fiber laser based FTD measurement method was demonstrated. It achieved a resolution of a few centimeters with a dynamic range of hundreds of kilometers [21]. In another report, a technique that included the fiber under test (FUT) as a part of a ring-cavity fiber laser and measured the high-order harmonic beating frequency without mode locking, offers an accuracy of 10−8 for a fiber length of 100km and of 10−6 for a several-meters-long one [22]. Although there is no need for mode locking or laser stabilization, the difficulty of its ambiguity resolving process increases with the FUT length growth, which makes the measurement time-consuming and inconvenient.

In this Letter, we propose and demonstrate a novel and simple technique for FTD measurement by transferring a microwave signal modulated laser light. In this way, the FTD measurement is converted into the precision measurement of microwave signal’s frequency, accompany with a coarse and easy ambiguity resolving process. Compared with previous methods, this is far more convenient and the ambiguity resolving procedure no longer depends on the fiber length. When the microwave signal is frequency-locked to the transfer delay, the long-term and real-time FTD measurement can be implemented through continuous frequency measurement. We demonstrate an FTD measurement system with a large dynamic range up to 50 km as well as no measurement dead zone. The FTD measurement resolution of 0.2 ps and accuracy of 1 ps are obtained.

2. Methods

Figure 1 shows the schematic of the FTD measurement system which consists of FTD measurement loop (Fig. 1(a)) and system delay control (SDC) loop (Fig. 1(b)). In FTD measurement loop, one end of the FUT is connected to a Faraday mirror, and the other end is connected to the FTD measurement system through a fiber circulator. In this way, the FUT is included as a part of the FTD measurement loop, and the FUT will be double-passed by aprobe light. Here, the probe light is a microwave signal modulated 1550 nm laser light. The microwave signal is provided by an oscillator, which consists of a 100MHz voltage control oscillator (VCO) and a frequency multiplier ( × 12). Through mixing and filtering operations on the microwave signals before and after transmission, an error signal Vecos(ϕp) is obtained. Here ϕp denotes the phase delay induced by transmission and can be expressed as

ϕp=2πft=2πfLopc,
where f is frequency of the microwave signal, t is the transfer delay, Lop is the optical path length of the FTD measurement loop, and c is the velocity of light in vacuum. Through a phase-locked loop, the frequency of the microwave signal f can be locked onto the transfer delay t, making Vecos(ϕp)=0. To achieve the lock, the frequency shift (δf) induced phase delay shift (δϕp) should be more than π. According to Eq. (1), the following relationship is valid:
δϕp=2πδft.
Here, the 100 MHz VCO has a frequency tuning range of 2 kHz leading to a maximum frequency shift δf = 24 kHz. To obtain enough phase delay shift, the minimum transfer delay can be calculated as t=δϕp/(2πδf)20.8μs, corresponding to a 6.25 km optical path length (4.17 km fiber length). Consequently, for the convenience of frequency locking and eliminating the dead zone, an internal fiber (5 km long) is preset into the FTD measurement loop. When the FTD measurement loop is locked, ϕp is a constant as
ϕp=(N+12)π.
Here, N is an integer and can be considered as an ambiguity of the measurement. According to Eq. (1) and (3) , we can get
t=2N+14f.
The transfer delay t can be obtained as long as f and N are determined. The frequency f can be precisely measured by a frequency counter. In order to get N, a general time delay discrimination method is used for FTD coarse measurement. The same 1550 nm laser light is modulated by a pulse signal transferring through the FTD measurement loop. To rapidly switch between precise and coarse measurement, a double-pole-double-throw electric switch is inserted into the FTD measurement loop (shown in Fig. 1(a)). Pulse signals before and after transmission are used to measure the coarse transfer delay tcoarse by a TIC. Based on Eq. (4), N can be obtained by equation
N=2ftcoarse12.
To evaluate the ambiguity resolution of the method, according to Eq. (5), we can analyze the uncertainty of N
ΔN=2fΔt+2tΔf.
Here, f is 1.2 GHz in our measurement system. Δf is decided by the frequency counter accuracy, which is better than 10−10 for a commercial meter. Δt is determined by coarse FTD measurement accuracy. For common measurement, the FUT length is below 100 km and the transfer delay t will not exceed 1 ms. Consequently, the second term on the right-hand side of Eq. (6) is small enough to be neglected, and the uncertainty of N is mainly limited by the coarse FTD measurement accuracy which deteriorates with the FUT length growth. In order to obtain sufficient enough accuracy of N, i.e. ΔN0.5, Δt should be less than 210 ps, which is easy to realize using commercial TIC.

 

Fig. 1 Schematic of FTD measurement system. VCO, 100 MHz voltage control oscillator; FPD, fast photo detector with a typical 3dB bandwidth of 16 GHz; FUT, fiber under test; PLL, phase locked loop; TIC, time interval counter; WDM, 1547/1550 nm wavelength division multiplexer; REF, reference signal; PI, proportional integral controller. (a) FTD measurement loop. The microwave signal and the pulse signal are switched to modulate the amplitude of a 1550 nm laser light. After transferred in the 5 km long internal fiber, the laser light is coupled into the FUT through an optical circulator. The reflected light is detected by FPD1. The pulse signals before and after transmission are used for coarse FTD measurement by a TIC. The microwave signals before and after transmission are used to generator an error signal through frequency filtering and mixing operations. The PLL uses the error signal to control the frequency of the VCO, making the microwave signal frequency-locked to the transfer delay. (b) SDC loop. A 1547 nm laser light modulated by a 1 GHz signal is coupled into the internal preset fiber together with the 1550 nm laser light through a 50/50 optical coupler. Two laser lights are separated by a WDM. The 1547 nm laser light is detected by FPD2. Via frequency mixing and filtering operations, an error signal proportional to the system phase delay is obtained. Through changing the temperature of a part of the internal fiber (2 km long), a PI controller uses the error signal to cancel out the variation of the system delay.

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Once N is determined, t can be obtained according to Eq. (4). Here, the measured FTD t contains not only double-passed FUT delay, but also the propagation delays of internal fiber, electronic circuits, cables, fiber pigtails of the measurement system, which belong to system delay (t0). Consequently, to get one-way FUT delay (tF), we need to calibrate the system delay. When no FUT is connected, the modulated laser light entering into the port 1 of fiber circulator is reflected by the end face of the port 2 (FC/PC connector) and transferred back to measurement system. In this way, the system delay t0 is measured and the one-way FUT delay tF can be obtained by following relation

tF=12(tt0).

For the case of long-term, continuous measurement, temperature variations may cause fluctuation of the system delay. Consequently, SDC loop (shown in Fig. 1(b)) is used to monitor and compensate the system delay fluctuation, making it stable during the measurement. In SDC loop, another 1547 nm laser light is modulated by a 1 GHz signal referenced by Hydrogen-Maser. The modulated 1547 nm laser light is coupled into the internal preset fiber and transfers together with the 1550 nm laser light. After transmission, two laser lights are separated by a wavelength division multiplexer (WDM). The 1547 nm laser light is detected by a fast photo detector (FPD2). Via frequency mixing and filtering operations on the 1 GHz signals before and after transmission, an error signal proportional to the system phase delay is obtained. A part of the internal fiber (2 km long) is wrapped around a copper wheel. A PI controller uses the error signal to cancel out the variation of the system delay by changing the spool’s temperature. Within the control period of 1 s, through changing the duty cycle of the heating and cooling durations, the system reaches a sensitivity of 87 ps/°C and a total dynamic range of 1.7 ns. In this way, the fluctuation of the system delay is well compensated.

During measurement, when the SDC loop is locked, the system delay is stabilized. When the FTD measurement loop is locked, N is fixed as a constant. In this way, a long-term, real-time FTD measurement can be implemented by continuous measurement of frequency.

3. Results and discussion

To evaluate the system delay stability, we performed a series of system delay measurementswithout connecting FUT. Figure 2 shows the measured system delay fluctuations and the converted system stability via time deviation (TDEV). The black line is the result when the system internal fiber is running freely, and the red line is the result when the system delay fluctuation is compensated. We observed the fluctuation of ±100 ps for the uncompensated loop. While, for the compensated loop, it is reduced to ±1 ps, shown in Fig. 2(a). A significant improvement can be clearly observed in the corresponding TDEV plot, shown in Fig. 2(b). The values of compensated loop are always below 210 fs, whereas in freely running system, the TDEV reaches 30 ps for averaging times of 103 s. It indicates that with system delay compensation, the long-term stability is kept at sub-picosecond level. Meanwhile, it can be seen from Fig. 2(b) that the response time of the SDC loop is around 20 s, corresponding to an effective bandwidth of 0.05 Hz. Because of the specific heat capacity of the copper wheel, the response time is longer than the temperature control period (1s). As a comparison, we used TIC to measure the stabilized system delay by transferring a pulse signal. The result is shown in Fig. 3 (black line). A delay fluctuation of ±25 ps can be seen. Comparing measurement results of two methods, we note that the uncertainty of the measurement using the present method is reduced by more than one order of magnitude compared to that of using TIC.

 

Fig. 2 Measurement results of the uncompensated and compensated system delays. (a) The system delay fluctuation. The black line is the result when the system internal fiber is running freely, showing a fluctuation of ±100 ps. The red line is the result with the system delay fluctuation compensated, showing a fluctuation of ±1 ps. (b) The time deviation of the system delay derived from the measured system delay fluctuation.

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Fig. 3 Measurement results of the compensated system delay fluctuations using two methods. The black line is the result measured by TIC, showing a fluctuation of ±25 ps. The red line is the result measured by proposed method, showing a fluctuation of ±1 ps.

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To further verify the accuracy of the FTD measurement system, we used it to measure the FTD of a 2 m long fiber which can be considered as a constant. We repeated tests at different times of a day. The result is shown in Fig. 4 . It can be seen that, the means of all measured FTDs using two methods are well overlapped. The statistical error of the proposed method is below 0.2 ps and the long-term fluctuation of it is below ±1 ps. In the measurement using commercial TIC, the statistical error reaches approximately 20 ps and the long-term fluctuation increases to ±20ps. It indicates that using the proposed method the FTD measurement resolution of 0.2 ps and accuracy of 1 ps are obtained. There are two orders of magnitude improvement in the measurement resolution, and the measurement accuracy is obviously improved as well.

 

Fig. 4 FTD measurement results of a 2 m long fiber. The averaging period is 100 s. The error bar is the standard deviation of each measurement. The black line is the FTD measured by TIC, showing a long-term fluctuation of ±20 ps with a statistical error of 20 ps. The red line is the FTD measured by proposed method. The long-term fluctuation is reduced to ±1 ps with a statistical error below 0.2 ps.

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By analyzing the uncertainty of tF, we also theoretically evaluate the FTD measurement accuracy of the method. According to Eq. (4) and (7) , tF can be expressed as

tF=12(tt0)=12(2N+14ft0).
The uncertainty of tF is mainly determined by the system delay fluctuation (Δt0) and the uncertainty of frequency measurement (Δf). Indeed, the residual phase error of PLL in FTD measurement loop may also make contribution to the total uncertainty. Table 1 gives the uncertainty budget of the FTD measurement, with comments for each affecting quantity.

Tables Icon

Table 1. Uncertainty budget of the FTD measurement.

As a result, the total measurement uncertainty below 1 ps is quite realistic, coinciding well with measurement results in Fig. 4, and the uncertainty of FTD measurement mainly depends on the system delay stabilization. To further improve the measurement accuracy, effort should be mainly focused on the system delay fluctuation compensation.

To demonstrate the measurement range, we also measure the FTD of a 50 km fiber spool. Compared with the 2 m fiber, the FTD of the 50 km fiber will be greatly affected by temperature. The short term FTD fluctuation caused by temperature variation will affect the resolution evaluation of the measurement system. Consequently, the fiber spool is placed in a cotton filled box to decrease its short term FTD fluctuation. Comparison tests using two methods have also been demonstrated at different times of a day. The result is shown in Fig. 5 .

 

Fig. 5 FTD measurement results of a 50 km long fiber. The averaging period is 10 s. The error bar is the standard deviation of the measurement. The long-term fluctuation is around 600 ps. The black line is the FTD measured by TIC, showing a statistical error of about 75 ps. The red line is the FTD measured by proposed method, the statistical error of which is around 0.2 ps.

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It can be seen that, the means at each time using two methods are well overlapped. The long-term fluctuation of 600 ps reflects the temperature fluctuation while taking measurement. In the measurement using commercial TIC, the statistical error increases to 75 ps, whereas using the proposed method, the statistical error is still around 0.2 ps. This result indicates that the proposed method has a large dynamic range of at least up to 50 km, with an extremely high resolution.

4. Conclusion

We have demonstrated a novel and efficient scheme for fiber transfer delay measurement. Using this method, continuously real-time FTD measurement can be realized. More importantly, the method has a sub-picosecond high resolution, with a large dynamic range of more than 50 km, and a high accuracy, as well as no dead zone. Owing to its good repeatability, high reliability, and simple measurement process, the method may find wide applications, particularly in large-scale, phased-array antenna such as the Square Kilometre Array (SKA) for radio astronomy.

Acknowledgments

We acknowledge financial support from the National Key Scientific Instrument and Equipment Development Project (No. 2013YQ09094303) and the Beijing Higher Education Young Elite Teacher Project (No. YETP0088).

References and links

1. B. Mukherjee, “WDM optical communication networks: progress and challenges,” IEEE J. Sel. Areas Comm. 18(10), 1810–1824 (2000). [CrossRef]  

2. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003). [CrossRef]  

3. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012). [CrossRef]   [PubMed]  

4. W. Shillue, “Fiber distribution of local oscillator for Atacama Large Millimeter Array,” in Optical Fiber Communication/National Fiber Optic Engineers Conference (IEEE, 2008), pp. 1–3. [CrossRef]  

5. B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015). [CrossRef]   [PubMed]  

6. https://www.ptb.de/emrp/neatft_publications.html.

7. W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991). [CrossRef]  

8. B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006). [CrossRef]  

9. D. Dolfi, F. Michel-Gabriel, S. Bann, and J. P. Huignard, “Two-dimensional optical architecture for time-delay beam forming in a phased-array antenna,” Opt. Lett. 16(4), 255–257 (1991). [CrossRef]   [PubMed]  

10. B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006). [CrossRef]  

11. S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997). [CrossRef]  

12. C. Lopes and B. Riondet, “Ultra precise time dissemination system,” in Proceedings of the 1999 Joint Meeting of the European Frequency and Time Forum, 1999 and the IEEE International Frequency Control Symposium,1999 (IEEE, 1999), pp. 296–299. [CrossRef]  

13. M. Rost, M. Fujieda, and D. Piester, “Time transfer through optical fibers (TTTOF): progress on calibrated clock comparisons,” in Proceedings of 24th European Frequency and Time Forum (2010), paper 6.4. [CrossRef]  

14. B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012). [CrossRef]   [PubMed]  

15. J. Kalisz, “Review of methods for time interval measurements with picosecond resolution,” Metrologia 41(1), 17–32 (2004). [CrossRef]  

16. D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982). [CrossRef]  

17. B. Qi, A. Tausz, L. Qian, and H. K. Lo, “High-resolution, large dynamic range fiber length measurement based on a frequency-shifted asymmetric Sagnac interferometer,” Opt. Lett. 30(24), 3287–3289 (2005). [CrossRef]   [PubMed]  

18. L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

19. K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007). [CrossRef]  

20. I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998). [CrossRef]  

21. Y. L. Hu, L. Zhan, Z. X. Zhang, S. Y. Luo, and Y. X. Xia, “High-resolution measurement of fiber length by using a mode-locked fiber laser configuration,” Opt. Lett. 32(12), 1605–1607 (2007). [CrossRef]   [PubMed]  

22. K. Yun, J. Li, G. Zhang, L. Chen, W. Yang, and Z. Zhang, “Simple and highly accurate technique for time delay measurement in optical fibers by free-running laser configuration,” Opt. Lett. 33(15), 1732–1734 (2008). [CrossRef]   [PubMed]  

References

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  1. B. Mukherjee, “WDM optical communication networks: progress and challenges,” IEEE J. Sel. Areas Comm. 18(10), 1810–1824 (2000).
    [Crossref]
  2. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
    [Crossref]
  3. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
    [Crossref] [PubMed]
  4. W. Shillue, “Fiber distribution of local oscillator for Atacama Large Millimeter Array,” in Optical Fiber Communication/National Fiber Optic Engineers Conference (IEEE, 2008), pp. 1–3.
    [Crossref]
  5. B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
    [Crossref] [PubMed]
  6. https://www.ptb.de/emrp/neatft_publications.html .
  7. W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
    [Crossref]
  8. B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
    [Crossref]
  9. D. Dolfi, F. Michel-Gabriel, S. Bann, and J. P. Huignard, “Two-dimensional optical architecture for time-delay beam forming in a phased-array antenna,” Opt. Lett. 16(4), 255–257 (1991).
    [Crossref] [PubMed]
  10. B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006).
    [Crossref]
  11. S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
    [Crossref]
  12. C. Lopes and B. Riondet, “Ultra precise time dissemination system,” in Proceedings of the 1999 Joint Meeting of the European Frequency and Time Forum, 1999 and the IEEE International Frequency Control Symposium,1999 (IEEE, 1999), pp. 296–299.
    [Crossref]
  13. M. Rost, M. Fujieda, and D. Piester, “Time transfer through optical fibers (TTTOF): progress on calibrated clock comparisons,” in Proceedings of 24th European Frequency and Time Forum (2010), paper 6.4.
    [Crossref]
  14. B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
    [Crossref] [PubMed]
  15. J. Kalisz, “Review of methods for time interval measurements with picosecond resolution,” Metrologia 41(1), 17–32 (2004).
    [Crossref]
  16. D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
    [Crossref]
  17. B. Qi, A. Tausz, L. Qian, and H. K. Lo, “High-resolution, large dynamic range fiber length measurement based on a frequency-shifted asymmetric Sagnac interferometer,” Opt. Lett. 30(24), 3287–3289 (2005).
    [Crossref] [PubMed]
  18. L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.
  19. K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007).
    [Crossref]
  20. I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
    [Crossref]
  21. Y. L. Hu, L. Zhan, Z. X. Zhang, S. Y. Luo, and Y. X. Xia, “High-resolution measurement of fiber length by using a mode-locked fiber laser configuration,” Opt. Lett. 32(12), 1605–1607 (2007).
    [Crossref] [PubMed]
  22. K. Yun, J. Li, G. Zhang, L. Chen, W. Yang, and Z. Zhang, “Simple and highly accurate technique for time delay measurement in optical fibers by free-running laser configuration,” Opt. Lett. 33(15), 1732–1734 (2008).
    [Crossref] [PubMed]

2015 (1)

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

2012 (2)

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

2008 (1)

2007 (2)

K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007).
[Crossref]

Y. L. Hu, L. Zhan, Z. X. Zhang, S. Y. Luo, and Y. X. Xia, “High-resolution measurement of fiber length by using a mode-locked fiber laser configuration,” Opt. Lett. 32(12), 1605–1607 (2007).
[Crossref] [PubMed]

2006 (2)

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006).
[Crossref]

2005 (1)

2004 (1)

J. Kalisz, “Review of methods for time interval measurements with picosecond resolution,” Metrologia 41(1), 17–32 (2004).
[Crossref]

2003 (1)

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

2000 (1)

B. Mukherjee, “WDM optical communication networks: progress and challenges,” IEEE J. Sel. Areas Comm. 18(10), 1810–1824 (2000).
[Crossref]

1998 (1)

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[Crossref]

1997 (1)

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

1991 (2)

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

D. Dolfi, F. Michel-Gabriel, S. Bann, and J. P. Huignard, “Two-dimensional optical architecture for time-delay beam forming in a phased-array antenna,” Opt. Lett. 16(4), 255–257 (1991).
[Crossref] [PubMed]

1982 (1)

D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
[Crossref]

Alnis, J.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Bai, Y.

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Bann, S.

Bell, E. W.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

Bernstein, N.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Chen, L.

Chen, W. L.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Dalmases, F.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

Dilla, S.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

Dolfi, D.

Dong, J. W.

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

Droste, S.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Feng, Y. Y.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Fujima, I.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[Crossref]

Gao, C.

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Grosche, G.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Hänsch, T. W.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Holzwarth, R.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Hu, Y. L.

Huignard, J. P.

Ibánez-López, C.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

Iwasaki, S.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[Crossref]

Jefferts, S. R.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

Jofre, L.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

Journet, B.

L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

Kalisz, J.

J. Kalisz, “Review of methods for time interval measurements with picosecond resolution,” Metrologia 41(1), 17–32 (2004).
[Crossref]

Kim, H. D.

K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007).
[Crossref]

Kuhl, J. F.

D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
[Crossref]

Ledoux-Rak, I.

L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

Lee, B.

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

Lee, J. J.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Legero, T.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Levine, J.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

Li, J.

Li, T. C.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Lo, H. K.

Luc, V. V.

L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

Luo, S. Y.

Marti, J.

B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006).
[Crossref]

Martí, J.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

McKenzie, I.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

Mengual, T.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006).
[Crossref]

Mettler, S. C.

D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
[Crossref]

Miao, J.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Michel-Gabriel, F.

Mukherjee, B.

B. Mukherjee, “WDM optical communication networks: progress and challenges,” IEEE J. Sel. Areas Comm. 18(10), 1810–1824 (2000).
[Crossref]

Nam, L.

L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

Newberg, I. L.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Ng, W.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Nguyen, L. D.

L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

Parker, T. E.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

Philen, D. L.

D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
[Crossref]

Predehl, K.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Qi, B.

Qian, L.

Raupach, S. M. F.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Santamaría, J.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

Schnatz, H.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Seta, K.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[Crossref]

Song, J. W.

K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007).
[Crossref]

Tangonan, G. L.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Tausz, A.

Terra, O.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Udem, T.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Vez, E.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

Vidal, B.

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006).
[Crossref]

Walston, A. A.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Wang, B.

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Wang, L. J.

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Weiss, M. A.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

White, I. A.

D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
[Crossref]

Xia, Y. X.

Yang, W.

Yoon, K. H.

K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007).
[Crossref]

Yun, K.

Zhan, L.

Zhang, G.

Zhang, J. W.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Zhang, Z.

Zhang, Z. X.

Zhu, X.

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Zyss, J.

L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

IEEE J. Sel. Areas Comm. (1)

B. Mukherjee, “WDM optical communication networks: progress and challenges,” IEEE J. Sel. Areas Comm. 18(10), 1810–1824 (2000).
[Crossref]

IEEE Photonics Technol. Lett. (2)

B. Vidal, T. Mengual, C. Ibáňez-López, J. Martí, I. McKenzie, E. Vez, J. Santamaría, F. Dalmases, and L. Jofre, “Simplified WDM optical beamforming network for large antenna arrays,” IEEE Photonics Technol. Lett. 18(10), 1200–1202 (2006).
[Crossref]

B. Vidal, T. Mengual, and J. Marti, “Optical beamforming network based on fiber-optical delay lines and spatial light modulators for large antenna arrays,” IEEE Photonics Technol. Lett. 18(24), 2590–2592 (2006).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas. 46(2), 209–211 (1997).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

D. L. Philen, I. A. White, J. F. Kuhl, and S. C. Mettler, “Single-mode fiber OTDR: experiment and theory,” IEEE Trans. Microw. Theory Tech. 30(10), 1487–1496 (1982).
[Crossref]

J. Lightwave Technol. (1)

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, and N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).
[Crossref]

Jpn. J. Appl. Phys. (1)

K. H. Yoon, J. W. Song, and H. D. Kim, “Fiber length measurement technique employing self-seeding laser oscillation of fabry–perot laser diode,” Jpn. J. Appl. Phys. 46(1), 415–416 (2007).
[Crossref]

Meas. Sci. Technol. (1)

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[Crossref]

Metrologia (1)

J. Kalisz, “Review of methods for time interval measurements with picosecond resolution,” Metrologia 41(1), 17–32 (2004).
[Crossref]

Opt. Fiber Technol. (1)

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

Opt. Lett. (4)

Sci. Rep. (2)

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10-19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhu, C. Gao, Y. Bai, J. W. Dong, and L. J. Wang, “Square kilometer array telescope - precision reference frequency synchronisation via 1f-2f dissemination,” Sci. Rep. 5, 13851 (2015).
[Crossref] [PubMed]

Science (1)

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref] [PubMed]

Other (5)

W. Shillue, “Fiber distribution of local oscillator for Atacama Large Millimeter Array,” in Optical Fiber Communication/National Fiber Optic Engineers Conference (IEEE, 2008), pp. 1–3.
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L. D. Nguyen, B. Journet, I. Ledoux-Rak, J. Zyss, L. Nam, and V. V. Luc, “Opto-electronic oscillator: applications to sensors,” in Proceedings of IEEE International Meeting on Microwave Photonics/2008 Asia-Pacific Microwave Photonics Conference (IEEE, 2008), pp. 131–134.

C. Lopes and B. Riondet, “Ultra precise time dissemination system,” in Proceedings of the 1999 Joint Meeting of the European Frequency and Time Forum, 1999 and the IEEE International Frequency Control Symposium,1999 (IEEE, 1999), pp. 296–299.
[Crossref]

M. Rost, M. Fujieda, and D. Piester, “Time transfer through optical fibers (TTTOF): progress on calibrated clock comparisons,” in Proceedings of 24th European Frequency and Time Forum (2010), paper 6.4.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic of FTD measurement system. VCO, 100 MHz voltage control oscillator; FPD, fast photo detector with a typical 3dB bandwidth of 16 GHz; FUT, fiber under test; PLL, phase locked loop; TIC, time interval counter; WDM, 1547/1550 nm wavelength division multiplexer; REF, reference signal; PI, proportional integral controller. (a) FTD measurement loop. The microwave signal and the pulse signal are switched to modulate the amplitude of a 1550 nm laser light. After transferred in the 5 km long internal fiber, the laser light is coupled into the FUT through an optical circulator. The reflected light is detected by FPD1. The pulse signals before and after transmission are used for coarse FTD measurement by a TIC. The microwave signals before and after transmission are used to generator an error signal through frequency filtering and mixing operations. The PLL uses the error signal to control the frequency of the VCO, making the microwave signal frequency-locked to the transfer delay. (b) SDC loop. A 1547 nm laser light modulated by a 1 GHz signal is coupled into the internal preset fiber together with the 1550 nm laser light through a 50/50 optical coupler. Two laser lights are separated by a WDM. The 1547 nm laser light is detected by FPD2. Via frequency mixing and filtering operations, an error signal proportional to the system phase delay is obtained. Through changing the temperature of a part of the internal fiber (2 km long), a PI controller uses the error signal to cancel out the variation of the system delay.
Fig. 2
Fig. 2 Measurement results of the uncompensated and compensated system delays. (a) The system delay fluctuation. The black line is the result when the system internal fiber is running freely, showing a fluctuation of ± 100 ps. The red line is the result with the system delay fluctuation compensated, showing a fluctuation of ± 1 ps. (b) The time deviation of the system delay derived from the measured system delay fluctuation.
Fig. 3
Fig. 3 Measurement results of the compensated system delay fluctuations using two methods. The black line is the result measured by TIC, showing a fluctuation of ± 25 ps. The red line is the result measured by proposed method, showing a fluctuation of ± 1 ps.
Fig. 4
Fig. 4 FTD measurement results of a 2 m long fiber. The averaging period is 100 s. The error bar is the standard deviation of each measurement. The black line is the FTD measured by TIC, showing a long-term fluctuation of ± 20 ps with a statistical error of 20 ps. The red line is the FTD measured by proposed method. The long-term fluctuation is reduced to ± 1 ps with a statistical error below 0.2 ps.
Fig. 5
Fig. 5 FTD measurement results of a 50 km long fiber. The averaging period is 10 s. The error bar is the standard deviation of the measurement. The long-term fluctuation is around 600 ps. The black line is the FTD measured by TIC, showing a statistical error of about 75 ps. The red line is the FTD measured by proposed method, the statistical error of which is around 0.2 ps.

Tables (1)

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Table 1 Uncertainty budget of the FTD measurement.

Equations (8)

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ϕ p = 2 π f t = 2 π f L o p c ,
δ ϕ p = 2 π δ f t .
ϕ p = ( N + 1 2 ) π .
t = 2 N + 1 4 f .
N = 2 f t c o a r s e 1 2 .
Δ N = 2 f Δ t + 2 t Δ f .
t F = 1 2 ( t t 0 ) .
t F = 1 2 ( t t 0 ) = 1 2 ( 2 N + 1 4 f t 0 ) .

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