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
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 , fiber-optic sensing , 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)  or optical time domain reflectometer (OTDR) , 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 . 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 . 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.
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 is obtained. Here denotes the phase delay induced by transmission and can be expressed asEq. (1), the following relationship is valid:Eq. (1) and (3) , we can getFig. 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 equationEq. (5), we can analyze the uncertainty of N 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. , should be less than 210 ps, which is easy to realize using commercial TIC.
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
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 ps for the uncompensated loop. While, for the compensated loop, it is reduced to 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 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.
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 ps. In the measurement using commercial TIC, the statistical error reaches approximately 20 ps and the long-term fluctuation increases to ps. 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.
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 asTable 1 gives the uncertainty budget of the FTD measurement, with comments for each affecting quantity.
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 .
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.
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.
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).
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