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Abstract
The space time frequency transfer plays a crucial role in applications such as space optical clock networks, navigation, satellite ranging, and space quantum communication. Here, we propose a high-precision space time frequency transfer and time synchronization scheme based on a simple intensity modulation/direct detection (IM/DD) laser communication system, which occupies a communication bandwidth of approximately 0.2%. Furthermore, utilizing an optical-frequency comb time frequency transfer system as an out-of-loop reference, experimental verification was conducted on a 113 km horizontal atmospheric link, with a long-term stability approximately 8.3 × 10−16 over a duration of 7800 seconds. Over an 11-hour period, the peak-to-peak wander is approximately 100 ps. Our work establishes the foundation of the time frequency transfer, based on the space laser communication channel, for future ground-to-space and inter-satellite links.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The space time frequency transfer enables clock synchronization among distant nodes and is the foundation for many applications, such as space optical clock networks [1], geodesy [2], and navigation [3]. Currently, space time frequency transfer technologies primarily include the GPS Code-phase two-way satellite time and frequency transfer(TWSTFT) technique [4], GPS Carrier-phase two-way satellite time and frequency transfer (TWSTFT) Technique [4,5], and optical-comb-based optical two-way time-frequency transfer (O-TWTFT) [6–8]. The GPS-based time-frequency transfer technology is relatively mature, but its transfer accuracy is limited, with the best precision currently around $\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 16}}}$@ 10,000 seconds [4]. The performance of the optical-comb-based O-TWTFT system is currently the best so far, achieving stability up to $\textrm{4} \times \textrm{1}{\textrm{0}^{\textrm{ - 19}}}$@ 10,000 seconds [6]. However, its drawback lies in the complexity of the system, requiring three frequency combs for a point-to-point link and high-fidelity transmission of analog frequency comb pulses. Additionally, many applications do not necessitate such high transfer accuracy, such as radar at low GHz carrier frequencies or sub-cm positioning.
After decades of development, space laser communication has transitioned from the experimental stage to the application stage, as evidenced by projects such as the European Data Relay System (EDRS) [9], NASA's Laser Communications Relay Demonstration (LCRD) [10–12], and the Lunar Laser Communications Demonstration (LLCD) [13,14]. Laser communication has gradually become a standard configuration for spacecraft, including scientific experiment satellites [15], navigation satellites [16], and communication satellites [9–11]. Currently, satellites from Space Exploration Technologies Corporation’s (SpaceX) Starlink [17], Terran Orbital’s Space Networks [18,19], and Amazon’s Kuiper Satellite Networks [20] are already equipped with or planning to carry laser communication terminals. In the foreseeable future, more satellites are expected to be equipped with laser communication terminals. Therefore, long-distance time frequency transfer based on space laser communication systems, namely lasercom-based O-TWTFT, holds significant potential and promising applications.
Currently, free-space optical time frequency transfer has undergone some in-orbit experiment tests, including sub-nanosecond time transfer based on bouncing optical pulses off a target [21]and pulse-based bidirectional time transfer [22,23], with a daily time offset of approximately 10 ps. These time transfer methods offer the advantages of simplicity and reliability but monopolize the optical spectrum resources, making direct integration with laser communication challenging. ISAAC KHADER and others employed a spectral spreading approach in a 4 km free-space atmospheric link based on laser communication channels for lasercom-based O-TWTFT [24]. They utilized a binary phase shift keying (BPSK) laser communication encoding scheme, with the transmitter and receiver telescopes positioned at the same location. The distant end used a flat mirror for reflection, operating in a half-duplex mode. The time frequency transfer stability achieved was approximately $\textrm{4} \times \textrm{1}{\textrm{0}^{\textrm{ - 16}}}$ @ 10,000 seconds.
The optical-comb-based O-TWTFT and lasercom-based O-TWTFT both are based on the propagation delay of optical signals of bidirectional transmission, the comparison between optical-comb-based O-TWTFT and lasercom-based O-TWTFT as shown in Table 1.
Table 1. The comparison between optical-comb-based O-TWTFT and lasercom-based O-TWTFT
The main differences between optical-comb-based O-TWTFT and lasercom-based O-TWTFT include, 1) For optical-comb-based O-TWTFT, the optical signal requires polarization maintenance control and single-mode fiber coupling reception. For lasercom-based O-TWTFT, the signal receiver can be either single-mode fiber coupling reception for coherent optical communication and pre-amplified, or multi-mode fiber coupling reception for direct detection, offering higher flexibility. 2) Time measurement for optical-comb-based O-TWTFT is based on linear optical sampling of optical comb signal interference, achieving accuracy up to the femtosecond level. Time measurement for lasercom-based O-TWTFT is generally implemented using time-to-digital converters (TDC), with measurement accuracy at the level of 10 picoseconds. 3) The optical-comb-based O-TWTFT occupies independent spectral resources. However, the lasercom-based O-TWTFT, along with the laser communication system itself, utilizes time-division multiplexing to share the same frequency resources, the lasercom-based O-TWTFT occupies no more than 1% of the laser communication data bandwidth. Compared to optical-comb-based O-TWTFT, lasercom-based O-TWTFT has the advantages of simpler implementation and higher spectral efficiency.
In the context of future space-based time frequency transfer based on laser communication channel, we conducted a demonstration of time frequency transfer on a ground atmospheric link based on an intensity modulation/direct detection (IM/DD) laser communication system. The laser communication operated in full-duplex mode, and TDC utilized a scheme based on an field-programmable gate array (FPGA) delay chain [25]. This significantly simplified the system design, enabling convenient time measurement on existing laser communication hardware without additional components. Additionally, laser communication and time frequency transfer can operate simultaneously, with time transfer occupying approximately 0.2% of the data bandwidth. Using an optical-comb-based O-TWTFT system as an out-of-loop reference, we conducted time frequency transfer on the proposed system over a 113 km atmospheric link. The stability of time frequency transfer over 7800 seconds reached approximately $\textrm{8}\textrm{.3} \times \textrm{1}{\textrm{0}^{\textrm{ - 16}}}$, with a time deviation of about 100 picoseconds over an 11-hour period.
2. Experiment Setup
The experiment was performed in Urumqi, Xinjiang Province. Two terminals (A and B) are located at Nanshan and Gaoyazi with a distance between them of 113 km. The laser communication system is implemented with the simple IM/DD scheme. Each terminal contains, A laser communication processor FPGA for laser communication data frame encoding and decoding, namely encoder and decoder, and FPGA-based TDC. A laser communication transmitter composed of an electro-optic modulation drive circuit, a laser, and an erbium-doped fiber amplifier (EDFA). And a laser communication receiver consisting of an avalanche photodiode (APD) detector and a data clock recovery circuit. Two dedicated optical transceiver telescopes with automatic direction tracking functions were developed for this experiment. The telescopes in the two laboratory terminals are equipped with a beacon laser for direction tracking at wavelengths of 785 nm and 914 nm, respectively. The primary mirror of each telescope is a Cassegrain reflector with an aperture of 400 mm and a focal length of 1,600 mm. The schematic of the experiment setup as shown in Fig. 1. For the optical-comb-based O-TWTFT system, each terminal mainly consists of an ultra-stable laser (USL), an optical frequency comb (OFC), a linear optical sampling (LOS), and a processor. Additionally, in Fig. 1, tAS and tBR respectively represent the arrival times of the time signal sent from A terminal to B terminal on the clocks of A terminal and B terminal; Correspondingly, tAR and tBS respectively represent the arrival times of the time signal sent from B terminal to A terminal on the clocks of A terminal and B terminal.
Fig. 1. The schematic of the experiment setup. The two terminals of the experiment were separated by about 113 km. At two terminals, the laser communication system and the out-of-loop 1563 nm optical-comb-based O-TWTFT system share the same clock sources, and simultaneously measure the clock deviation of the two terminal clocks.
The laser communication system parameters as shown in Table 2, the laser communication operates with wavelengths of 800 nm and 1600 nm, with transmit powers of 25 dBm and 30 dBm, respectively. The two terminals employ Si APD for receiving the 800 nm signal and InGaAs APD for receiving the 1600 nm signal, with static sensitivities of −45 dBm and −42 dBm, respectively. According to the telescope design specifications, the near-field divergence angles for emissions at 800 nm and 1600 nm are 6 urad and 12 urad respectively. Without considering atmospheric effects, we calculate the attenuation on the 113 km atmospheric link to be 25 dBm and 27 dBm respectively. However, due to atmospheric effects, the measured average attenuation for emissions at 800 nm and 1600 nm on the 113 km atmospheric link during the experiment period were found to be 60 dBm and 60 dBm respectively. For horizontal atmospheric links, the divergence angle of the beam cannot be effectively controlled, which is the main reason for requiring higher transmit power. For horizontal atmospheric link at 113 km, the designed near-field divergence angle of the optical telescope is approximately 10 urad. According to test data, after passing through the 113 km horizontal atmospheric link, the equivalent divergence angle has expanded to the level of 100 urad. The uplink link between the ground and satellite also faces the issue of beam divergence after passing through the atmosphere. However, the advantage is that the transmit terminal of the uplink link is on the ground, and there is no difficulty in achieving higher transmit power. As for the downlink link, the atmospheric part of link is at the end of the optical transmission link, and the divergence angle expansion effect is not significant. For LEO satellites, a transmit power in the order of milliwatts is sufficient for the downlink.
Table 2. The laser communication system parameters
In order to conduct an out-of-loop comparison of the time-transfer performance based on laser communication channels, an optical-comb-based O-TWTFT system and our proposed system share the same pair of telescopes [6], ensuring consistency in experimental environments and share the same clock source. Laser communication data frame format, time signal encoding, transmission, and measurement diagram as showed in Fig. 2(a). The working process of lasercom-based O-TWTFT includes, 1) Laser communication data transmission utilizes the synchronized clock source driver, enabling the clock information needed for transmission to be modulated into the laser communication data stream. 2) At the receiving terminal, clock and data recovery (CDR) technology is employed to obtain the clock from the data stream, which is the clock from the transmitting terminal. 3) Due to limitations in the measurement rate of the TDC, which is typically around 10 Msps, it's necessary to perform low-speed sampling on the received clock. The specific approach involves encoding the clock signal positions that need to be sampled at the receiving end using Syn code at the transmitting terminal. Upon detecting the Syn code, the receiving terminal extracts the corresponding clock signals and outputs them to the TDC for measurement. To simplify the system, we employ a TDC based on FPGA delay chains for measuring time-frequency transfer signals. The resolution of this TDC is approximately 25 ps. The bidirectional laser communication speed is 156.25 Mbps. The physical layer frame length of the data is 2048 bytes, and physical frames are continuously sent regardless of whether there is application data to transmit. We insert 4 bytes time-frequency transfer information, Syn code, near the header of each physical layer frame, occupying a communication bandwidth of approximately 0.2%. The time-frequency transfer information includes a timestamp number of the moment of transmission at the sending terminal, along with corresponding checksum information. The corresponding transfer frequency or physical layer frame frequency is 9537 Hz.
Fig. 2. (a) Laser communication data frame format, time signal encoding, transmission, and TDC measurement diagram. (b)The O-TWTFT timestamp number diagram. The timestamp number increases sequentially, and the timestamp nusssmber sent by the terminal B is based on the received timestamp number from terminal A. Here, tASn and tBRn respectively represent the arrival times of the n-th time signal sent from A terminal to B terminal on the clocks of A terminal and B terminal; Correspondingly tARn and tBSn respectively represent the arrival times of the n-th time signal sent from B terminal to A terminal on the clocks of A terminal and B terminal.
The O-TWTFT timestamp number diagram as showed in Fig. 2(b). According to the TWTFT protocol, four timestamps are required to calculate the clock difference between the two terminals. These timestamps represent the arrival times of the time signal sent from the A terminal to the B terminal on the clocks of the A terminal and B terminal, as well as the arrival times of the time signal sent from the B terminal to the A terminal on the clocks of the A terminal and B terminal. These timestamps are denoted as ${t_{ASn}}$, ${t_{ARn}}, {t_{BSn}}$ and ${t_{BRn}}$ respectively. To ensure reciprocity, both signals are required to be transmitted in reverse simultaneously through the link. We encode each signal using a 4 bytes and the encoding of the signal sent from the B terminal to A terminal be adjusted based on the received signal's encoding to ensure that signals with the same identifier are transmitted simultaneously through the channel. After adopting this approach, the process of calculating the clock difference between the two terminals using timestamp matching will be simple.
At both terminals, TDCs based on the local clock are separately used to measure the transmitted and received timestamps, resulting in four measured times, namely ${t_{ASn}}$, ${t_{ARn}}, {t_{BSn}}$ and ${t_{BRn}}$, the four timestamps with the same identifier form a set. Assuming the time deviation between the two terminal clocks at TDCs is ${x_{m\_n}}$, with clock A ahead of clock B. Based on the bidirectional signal propagation delay, the following formulas can be derived
The measured clock deviation, ${x_{m\_n}},$ includes both the inherent deviation, ${x_{comb\_n}},$ between two terminal clocks and the errors, ${x_n},$ introduced by the measurement system, then.
The inherent deviation between two terminal clocks ${x_{comb\_n}}$ is by the optical frequency comb time transfer system [6], to eliminate the inherent deviation between the two terminal clock, namely out-of-loop comparison. Then, time transfer frequency stability, based on the laser communication system, Allan deviation is calculated [26],
Here N is the number of measurement samples for clock deviation, ideally sampled at a frequency of approximately 9537 Hz. In practice, due to scintillation in the atmospheric link, some timestamps may be lost. By sequentially encoding each transmitted timestamp, we can identify the missing timestamp data. Subsequently, the received timestamps data can be arranged in the predetermined order, and the calculation of the stability Allan deviation can then be performed. Upon obtaining the bidirectional laser transmission delay, we can directly calculate the range between the two terminals, according to formula (1) and formula (2),
Here, the distance refers to the separation between the focal points of the two terminal telescopes. Since both telescopes are fixed on the Earth, in a short period, assuming the Earth remains stationary, the spatial distance between these two focal points can be considered constant. For bidirectional ranging with 9537 Hz, the stability of two terminal clocks is maintained within 1ppb, the inherent deviation of the clocks at both terminals does not affect the ranging results.
3. Results
From 23:11:35 on October 2nd, 2023, China Standard Time (CST), to 10:11:35 on the 3rd, we conducted a continuous 11-hour time-frequency transfer experiment. The experiment involved the simultaneous operation of a lasercom-based O-TWTFT and an optical-comb-based O-TWTFT, the latter is used to eliminate the inherent deviation between the two terminals clocks. The clock deviation between the two terminals, as measured by the lasercom-based O-TWTFT system, is shown in Fig. 3(a). The peak-to-peak wander over 11 hours is approximately 100 ps. It should also be noted that there is a fixed time deviation of approximately 23.95 ns between the reference points of the lasercom-based O-TWTFT system and the optical-comb-based O-TWTFT system. This inherent deviation is introduced by the inconsistent lengths of optical fiber paths and electronic circuit in the telescope backend and can be eliminated through actual measurement or calculation. The inherent deviation is retained here but does not affect the measurement results.
Fig. 3. (a) The clock deviation measured through the lasercom-based O-TWTFT after eliminating the inherent clock deviation using the optical-comb-based O-TWTFT. Data is resampled to 1 Hz for visualization. (b) Time transfer frequency stability Allan deviation at 113 km (blue) and over a shorted fiber link (green) and over a shorted fiber link with received power disturbance (red).
The fractional frequency uncertainty given by the modified Allan deviation (MDEV) is shown Fig. 3(b). Over 113 km horizontal atmospheric link, at 7800 s, the frequency stability reaches $\textrm{8}\textrm{.3} \times \textrm{1}{\textrm{0}^{\textrm{ - 16}}}$ level. Compared to shorted fiber links, the performance decreases by approximately four times. Under conditions of a shorted fiber link, the detector receives a power of approximately −30 dBm. Under conditions of a shorted fiber link with received power disturbance, the detector's average received power is approximately −33 dBm. The disturbance is achieved through an electrically controlled attenuator (models Thorlabs V800A and V1550A for 800 nm and 1600 nm, repectively), driven by a 250 Hz random intensity signal, with disturbance magnitude of approximately 15 dB peak-to-peak. Under atmospheric conditions with a 113 km optical link, the peak-to-peak fluctuation of optical received power in laser communication is approximately 20 dB, which is about 5 dB higher than fiber analog disturbances. Moreover, the fluctuation spectrum is higher than 250 Hz. This is one reason why the performance under atmospheric conditions over a 113 km link is worse than fiber disturbances. Additionally, compared to the direct interconnection scheme with the same source clock in the fiber test system, the clock distribution network between lasercom-based O-TWTFT system and the optical-comb-based O-TWTFT system is slightly more complex, including the conversion from optical frequency domain clock to microwave domain clock, which also degrades the time transfer performance. Furthermore, during the time transfer process, we measured the time transmission delay of bidirectional optical signals. Using formula (3), the pseudorange between the two terminals can be directly calculated based on the time transmission delay of bidirectional optical signals. The pseudorange between the two terminals and the corresponding temperatures measured during the 11 hours experiment, without considering atmospheric refractive index, are showed in Fig. 4(a). For long-duration ranging data, there is significant fluctuation due to variations in atmospheric refractive index with environmental conditions such as temperature and pressure. Generally, over short duration, such as one second, atmospheric refractive index can be considered constant. Analyzing ranging data within one second allows us to assess the inherent ranging performance of the system. The ranging jitter in 1 second is shown in Fig. 4(b), the standard deviation of jitter in 1 second is approximately 1 cm.
Fig. 4. The pseudorange results of our experiments. (a) The pseudorange. Pseudorange data is resampled to 1 Hz for visualization. Temperature data is sampled at every minute. (b) The ranging jitter in one second, assuming no measurable atmospheric changes within one second.
In practice, ranging in ground-to-ground or ground-to-satellite laser links inevitably involves traversing the atmosphere, requiring consideration of atmospheric refractivity effects. In the field of ranging, particularly in scenarios involving atmospheric conditions, correcting for atmospheric refractive index and calibrating reference points are both time-consuming and challenging tasks. Even more challenging is the lack of an absolute reference standard for atmospheric correction accuracy. Currently in the field of Satellite Laser Ranging (SLR), after correcting ranging data using atmospheric models, multiple ranging stations cross-validate and further refine the corrections. Currently, the normal point (NP) residuals for ranging to the LAGEOS satellites are around ±5 cm [27]. To analyze the atmospheric influence on ranging, we utilized the National Institute of Standards and Technology's Engineering Metrology Toolbox [28] for atmospheric refractive index calculations. During the 11-hour experiment, we measured the atmospheric environment temperature along the link, as shown in the Fig. 4. Other parameters were kept constant, with atmospheric pressure set at 101.325 kPa, carbon dioxide content at 450 ppm, and air humidity at 50% relative humidity. At temperatures of 0 °C and 5 °C, the atmospheric refractive indices at 800 nm were 1.000290082 and 1.000284799 respectively, while at 1600 nm, they were 1.000288152 and 1.000282903 respectively. At a distance of 113 km, temperature-induced refractive index changes resulted in distance variations were 0.596635956 m and 0.592798431 m for 800 nm and 1600 nm respectively, with a difference of approximately 3.8 mm between the two wavelengths, corresponding to a delay difference of approximately 13 ps. Therefore, for ranging with centimeter-level accuracy, the difference in using 800 nm or 1600 nm wavelengths can be neglected.
Furthermore, we have carefully considered some factors that affect time transfer and ranging performance. When further enhancing the system's time transfer and ranging capabilities in the future, special attention should be paid to these factors. The first factor is reciprocity. Therefore, when laser communication systems are used for ranging and time-frequency transfer, it is recommended to keep the wavelength separation within 10 nm (resulting in an optical path difference of approximately 0.9 mm, or 3 ps, over a 113 km atmospheric link). The second factor is time walk effect. Time walk refers to the delay of the detector changing with the variation of received optical power. The time walk characteristics of the two APDs in our lasercom-based O-TWTFT system are shown in the Fig. 5.
Fig. 5. (a) The time walk of 800 nm receiving detector. (b) The time walk of 1600 nm receiving detector.
For the 800 nm receiving detector, the time walk is approximately 270 ps when the power changes from −43 dBm to −23 dBm. From −23 dBm to −20 dBm, the time walk is approximately 250 ps. For the 1600 nm receiving detector, the time walk is approximately 100 ps when the power changes from −40 dBm to −22 dBm. From −22 dBm to −20 dBm, the time walk is approximately 950 ps. In the 113 km atmospheric link environment, we compensated for the APD low-frequency, approximately 10 Hz, time walk using the detected average power. Currently, there are no particularly effective measures to address the time walk caused by high-frequency fluctuations, which is also part of the work we plan to do in the future.
The last factor is temperature. Temperature change is a major contributor to low-frequency errors in time transfer and ranging, primarily by affecting the delay of the atmospheric link, APD detector, and the performance parameters of the FPGA-based TDC. For the APD detector and FPGA TDC-based systems, we power on the equipment two hours before the experiment, allowing the equipment and environment to reach thermal equilibrium before conducting experimental tests. Meanwhile, The room, where the equipment is placed, temperature is controlled within a range of 20 ± 1 °C using air conditioning. For the delay of the atmospheric link, we record the environmental temperature of the atmospheric link at the B terminal, which can be used as input parameters for atmospheric correction in ranging.
Additionally, for extending the lasercom-based O-TWTFT system to non-stationary operation, such as satellite platforms, the main challenges include, 1) The Doppler effect causing frequency variations in received data clocks, requiring control of the CDR frequency tracking bandwidth and delay. For orbits of 10,000-20,000 km, Doppler-induced errors are approximately 2.5 mm. 2) The Sagnac effect, which can disrupt link reciprocity. 3) Atmospheric refractive index correction, requiring fusion of atmospheric models and atmospheric monitoring data. Currently, we are conducting analyses related to Doppler shifts and ground verification experiments for extending the lasercom-based O-TWTFT system to non-stationary operation.
4. Conclusion
Over 113 km horizontal atmospheric link, we conducted time frequency transfer and ranging using a mature IM/DD laser communication system. In a continuous 11 hours experiment, the time frequency transfer achieved frequency stability approximately $\textrm{8}\textrm{.3} \times \textrm{1}{\textrm{0}^{\textrm{ - 16}}}$ for 7800 seconds, and the ranging accuracy was approximately 1 centimeters. Thanks to the high-performance optical-comb-based O-TWTFT system, we were able to perform out-of-loop comparisons of the test results over long distances, testing the inherent time transfer performance of the system without considering measurement errors introduced by the clocks themselves.
In the current landscape of growing space laser communication resources, time-frequency transfer and ranging based on laser communication channels offer advantages of low implementation cost and high spectrum resource utilization. This method can easily achieve time-frequency transfer and ranging on existing laser communication links without the need for additional hardware resources and costs. Our experiments have explored and accumulated experience for the future implementation of time frequency transfer and ranging on space laser communication links.
Funding
Innovation Program for Quantum Science and Technology (2021ZD0300104); Youth Innovation Promotion Association of the Chinese Academy of Sciences (Y2021119); Natural Science Foundation of Anhui Province (2008085J03); National Key Research and Development Program of China (2020YFA0309701).
Acknowledgements
We thank professor Qiang Zhang for providing the optical frequency comb time transfer system used for out-of-loop comparison.
Disclosures
The authors declare that they have no competing interests.
Authors’ contributions. The study was conceived by Yu-Xiang Cheng and Meng Yang, Sheng-Kai Liao, Juan Yin and Cheng-Zhi Peng providing planning and logistical support. The test procedure was developed by Yu-Xiang and Meng Yang, supervised by Sheng-Kai Liao and Qi Shen. Yu-Xiang Cheng, Meng Yang and Jian-Yu Guan conducted the experiment, assisted by Zhen-Jie Lu and Wen-Shuai Tang. Yu-Xiang Cheng and Meng Yang analysed the data and prepared the manuscript, assisted by Sheng-Kai Liao. All the authors have read and approved the final manuscript.
Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.
References
1. F. Riehle, “Optical clock networks,” Nat. Photonics 11(1), 25–31 (2017). [CrossRef]
2. W. McGrew, X. Zhang, R. J. Fasano, et al., “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018). [CrossRef]
3. G. Giorgi, T.D. Schmidt, C. Trainotti, et al., “Advanced technologies for satellite navigation and geodesy,” Adv. Space Res. 64(6), 1256–1273 (2019). [CrossRef]
4. J. Achkar, B. Chupin, Y.-J. Huang, et al., “Study and characterization of a two-way satellite time and frequency transfer link using software-defined radio solutions to both code and carrier-phase signals,” in 2021 XXXIVth General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), (IEEE, 2021), 1–4.
5. J. Yao and J. Levine, “Long-term GPS carrier-phase time transfer noise: a study based on seven GPS receivers at NIST,” in 2016 IEEE International Frequency Control Symposium (IFCS), (IEEE, 2016), 1–5.
6. Q. Shen, J.-Y. Guan, J.-G. Ren, et al., “Free-space dissemination of time and frequency with 10− 19 instability over 113 km,” Nature 610(7933), 661–666 (2022). [CrossRef]
7. H. Bergeron, L. C. Sinclair, W. C. Swann, et al., “Tight real-time synchronization of a microwave clock to an optical clock across a turbulent air path,” Optica 3(4), 441–447 (2016). [CrossRef]
8. E. D. Caldwell, J.-D. Deschenes, J. Ellis, et al., “Quantum-limited optical time transfer for future geosynchronous links,” Nature 618(7966), 721–726 (2023). [CrossRef]
9. H. Hauschildt, S. Mezzasoma, H. Ludwig, et al., “European data relay system goes global,” in 2017 IEEE International Conference on Space Optical Systems and Applications (ICSOS), (IEEE, 2017), 15–18.
10. D. J. Israel, B. L. Edwards, R. L. Butler, et al., “Early results from NASA’s laser communications relay demonstration (LCRD) experiment program,” in Free-Space Laser Communications XXXV, (SPIE, 2023), 10–24.
11. B. Edwards, T. Randazzo, N. Babu, et al., “Challenges, lessons learned, and methodologies from the LCRD optical communication system AI&T,” in 2022 IEEE International Conference on Space Optical Systems and Applications (ICSOS), (IEEE, 2022), 22–31.
12. S. A. Hamilton, D. M. Borosona, P. B. Dixon, et al., “Overview of NASA’s national space quantum laboratory program,” in 70th International Astronautical Congress (IAC), 2019), 21–25.
13. D. M. Boroson, J. J. Scozzafava, D. V. Murphy, et al., “The lunar laser communications demonstration (LLCD),” in 2009 Third IEEE International Conference on Space Mission Challenges for Information Technology, (IEEE, 2009), 23–28.
14. D. M. Boroson and B. S. Robinson, “The lunar laser communication demonstration: NASA’s first step toward very high data rate support of science and exploration missions,” The lunar atmosphere and dust environment explorer mission (LADEE) , 185, 115–128 (2015). [CrossRef]
15. W. Chen, J. Sun, X. Hou, et al., “5.12 Gbps optical communication link between LEO satellite and ground station,” in 2017 IEEE International Conference on Space Optical Systems and Applications (ICSOS), (IEEE, 2017), 260–263.
16. Z. Huang, W. Gong, F.-W. Shao, et al., “A Beidou laser link allocation scheme based on network throughput optimization,” in China Satellite Navigation Conference (CSNC 2021) Proceedings: Volume II, (Springer, 2021), 505–514.
17. A. U. Chaudhry and H. Yanikomeroglu, “Temporary laser inter-satellite links in free-space optical satellite networks,” IEEE Open J. Commun. Soc. 3, 1413–1427 (2022). [CrossRef]
18. K. Riesing, C. Schieler, B. Bilyeu, et al., “Operations and results from the 200 Gbps TBIRD laser communication mission,” in 37th Annual Small Satellite Conference, 2023).
19. C. M. Schieler, K. M. Riesing, B. C. Bilyeu, et al., “On-orbit demonstration of 200-Gbps laser communication downlink from the TBIRD CubeSat,” in Free-Space Laser Communications XXXV, (SPIE, 2023), 1241302.
20. M. Toyoshima, “Recent trends in space laser communications for small satellites and constellations,” J. Lightwave Technol. 39(3), 693–699 (2021). [CrossRef]
21. J. Anderson, A. Jeremy, B. Nathan, et al., “Sub-nanosecond ground-to-space clock synchronization for nanosatellites using pulsed optical links,” Adv. Space Res. 62(12), 3475–3490 (2018). [CrossRef]
22. K. U. Schreiber, I. Prochazka, P. Lauber, et al., “Ground-based demonstration of the European Laser Timing (ELT) experiment,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 57(3), 728–737 (2010). [CrossRef]
23. E. Samain, P. Exertier, Ph. Guillemot, et al., “Time transfer by laser link—T2L2: current status and future experiments,” in 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings, (IEEE, 2011), 1–6.
24. I. Khader, H. Bergeron, L. C. Sinclair, et al., “Time synchronization over a free-space optical communication channel,” Optica 5(12), 1542–1548 (2018). [CrossRef]
25. Y. Wang, J. Kuang, C. Liu, et al., “A flexible 32-channel time-to-digital converter implemented in a Xilinx Zynq-7000 field programmable gate array,” Nucl. Instrum. Methods Phys. Res., Sect. A 847, 61–66 (2017). [CrossRef]
26. W. J. Riley and D. A. Howe, “Handbook of frequency stability analysis,” (2008). [CrossRef]
27. D. Dequal, C. Agnesi, D. Sarrocco, et al., “100 kHz satellite laser ranging demonstration at Matera Laser Ranging Observatory,” J. Geod. 95(2), 26 (2021). [CrossRef]
28. J. Stone and J.H. Zimmerman, “Refractive index of air calculator,” NIST (2023). https://emtoolbox.nist.gov/Wavelength/Ciddor.asp
