Locating satellites, spacecraft, and other objects in space with high precision generally requires a telescope system large enough to collect significant quantities of light. One example is the Five hundred meter Aperture Spherical Telescope (FAST), which will be the world's largest and most sensitive single-aperture spherical telescope when it begins operations in 2016.1 Although the project is physically vast (it will cover an area the equivalent of 30 football fields), giant telescope systems are not the only way to achieve accurate space measurements.
In this work we demonstrate that, by connecting several smaller radio dishes, we can achieve a very high angular resolution that corresponds to a virtual aperture with diameter equal to the longest distance between any two dishes (the interferometer).2 We use two coherently connected dishes, so that radio-frequency (RF) signals from an object are received by both dishes, and are synthesized together in phase (see Figure 1). We are thus able to locate satellites or spacecraft tens of kilometers away, with greater precision than FAST.
Figure 1. General phase-locking versus ‘tunable-wavelength- (λ) dispersion’ delay stabilizing techniques for connecting radio telescope dishes. In phase-locking, the reference frequency phase of the fiber link connecting control rooms is locked. With tunable-λ-dispersion delay stabilizing, the delay of the dish-to-dish fiber link is stabilized. LO: Local oscillation. RF: Radio frequency (signal).
The carrier signal for our system is generally a few GHz (the period is less than 1ns), therefore synchronization is critical. As carriers, optical fibers have a small loss and excellent short-time stability, but their transmission delay varies with temperature changes (about 30ps/°C/km) or vibrations. To overcome these issues, the reference frequency (10 or 100MHz) is generally phased-locked at each end of the fiber.3 The received RF signals are thus down-converted to baseband before long-distance delivery. There are, however, more steps involved in the synchronization of our system. First, the clock needs to be synchronized. This cannot be achieved through phase-locking because the timing signal is broadband. Second, the fiber link usually ends at the control room. This means that the RF front end, which connects the control room and dish, and which performs the reference frequency delivery, local oscillation (LO) synthesis, and down-conversion mixing, is actually out of the locking loop. This results in significant phase change, even though the front end (external to the control room) is just tens of meters long. To solve these problems, we are working on a new scheme to deliver multiple LOs and the timing signal directly to the dish (or to deliver any broadband signal) through a delay-stabilized fiber.
The key to our approach is locking the fiber delay—rather than the phase—of a particular reference frequency (see Figure 1). Fiber dispersion (about 17ps/nm/km for standard single mode fibers) causes the signal to undergo a different time delay if it is carried at a different wavelength (λ). By adjusting a wavelength tunable laser, we can fix the delivery delay.4 This ‘tunable-λ-dispersion’ scheme has two advantages. First, we achieve an adjustable delay range that is proportional to fiber length, which supports long-distance delivery. Second, although we still phase lock a reference RF tone, the fiber is actually time-delay-locked (so the delays of other RF signals, as long as they are all carried by the same lightwave, are stabilized). With our scheme, we can therefore simultaneously deliver stabilized LOs, as well as time and RF signals in one fiber link (see Figure 2).
Figure 2. In the tunable-λ-dispersion scheme, multiple LOs and the timing signal are delay-stabilized and delivered to the remote end. The broadband RF signal is also obtained. WTL: Wavelength tunable laser. E/O: Electro-optic conversion. OC: Optical coupler. O/E: Opto-electronic conversion.
We conducted experiments in the laboratory, where the temperature varied more than for the actual conditions (underground) where the fibers are buried. Our results indicated improved transfer stability for both the short- and long-terms (see Figure 3). After transferring a 1.21GHz LO down a 45km fiber link, we measured its stability and the broadband timing signal. The frequency stability reached 2.8 × 10−13 (averaging over 1s) and 2× 10−15 (averaging over 103s), with a time deviation of 40ps and 2.3ps, respectively.5 In another experiment, we transferred two LOs (2.46 and 8GHz) to a remote location 30km away. The delay fluctuation of both LOs was 3ps, and showed a squeeze ratio of about 400 during the total 104s recording time.6 We also fetched a 2.5GHz RF tone from a remote location 45km away. The stability reached 3.3 × 10−13 when we averaged over 1s and 7.5 × 10−17 when averaged over 104s. Before our stabilization, the peak-to-peak delay variation was as large as 2.3ns.7
Figure 3. Experimental results from laboratory testing of the tunable-λ-dispersion technique with (w) and without (w/o) phase-locking. (a) Delivering a broadband timing signal to a remote end 45km away. (b) Simultaneously delivering a 2.46GHz LO and a 8GHz LO to the remote end 30km away. (c) Fetching a 2.5GHz RF tone from the remote end 45km away. ps: Picoseconds.
Our long-distance synchronization approach has several applications. For instance, we had the opportunity to conduct a lunar radio measurement (LRM) when the China National Space Administration's Chang'E-3 spacecraft made a soft landing on the Moon in 2013. Compared with laser ranging (where several observation stations measure the travel length of a light pulse), in our LRM we used the phase of the carrier to estimate a high-precision relative range for orbit determination. Such measurements are unaffected by weather conditions or lunar phase. Our integrated equipment and our tunable-λ-dispersion technique were used to directly deliver three stabilized LOs (at different RF bands) from the control room to the dish 100m away (see Figure 4). We were thus able to eliminate the RF front end's phase change. The X-band carrier frequency estimation of the Chang'E-3 lander was 9.8mHz.
Figure 4. The antenna used for a lunar radio measurement is 100m away from the control room, and is equipped with the integrated delay-stabilized fiber link remote end (shown in inset).
Another important application of our phase-stable transmission technique is in a 5.5km connected element interferometry system built at the Beijing Aerospace Control Center. This system is now being used to track an S-band geostationary Earth-orbit satellite. A navigation satellite with high-accuracy ephemeris is also being used for calibration. Recent results indicate an accuracy of 0.5ns for the differential interferometry. We can therefore obtain an accuracy of 0.0022° for the angle position. If we were to use a single antenna to measure an angle position with such accuracy, the size of the dish would be more than 100m.
In summary, we have demonstrated a novel method for making accurate aerospace measurements. We use a broadband, delay-stabilized optical fiber link to support dish-to-dish connections. The success of our approach has been experimentally verified and has been used for a lunar radio measurement and tracking of a geostationary satellite. We are now carrying out field experiments, with the future aim of further improving the accuracy of our technique.
This work was supported by the National Program on Key Basic Research, (project 973), under contract 2012CB315705, and by the National Natural Science Foundation of China, under contract 61302016.
Yitang Dai, Zhongze Jiang, Kun Xu
Beijing University of Posts and Telecommunications
Yitang Dai is an associate professor with the State Key Laboratory of Information Photonics and Optical Communications. His research interests include microwave photonics, optical fiber communications, as well as fiber-based and integrated devices.
Tianpeng Ren, Geshi Tang
Beijing Aerospace Control Center
The 54th Research Institute of China Electronic Technology Group Corporation
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