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Abstract
To meet the requirement of high-accuracy pointing of quantum signals in satellite-to-ground quantum communication, this paper proposes a flexible satellite-based pointing method that changes the fine tracking point to solve the problem from point-ahead angle and ground beacon laser offset. This method does not require the use of a point-ahead mechanism and can detect the pointing angle in real time. Detailed algorithms and analysis are given. The method has been verified in orbit on the quantum science satellite Micius. The satellite-to-ground test results show that the quantum signal pointing accuracy is between 0.5∼1.0 µrad, which meets the efficiency requirements of satellite-to-ground quantum communication.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum communication uses the principle of quantum mechanics to manipulate quantum states, it is a physically unconditionally secure communication method [1,2]. Although the use of quantum communication via ground fiber channels is relatively mature, the communication distance in fiber optic media is only on the order of hundreds of kilometers, due to fiber channel loss and polarization change [3–5]. Satellite-based quantum communication is an effective way to solve the global quantum communication problem, and it is also a research hotspot in this field [6–12]. The quantum science satellite Micius is one of the first scientific satellites of the Strategic Priority Research Program on Space Science, the Chinese Academy of Sciences. The satellite is in a solar synchronous orbit with an altitude of 500 km. By establishing a quantum channel between a satellite and a quantum optical ground station, several satellite-to-ground quantum science experiments have been completed, including satellite-to-ground high-speed quantum key distribution experiments, quantum entanglement distribution experiments over 1200 km, and ground-to-satellite quantum teleportation experiments [13–15].
Since the quantum signal is very weak and cannot be amplified, the divergence angle is generally very small. For example, the divergence angle of the quantum signal emitted by Micius is less than 12 µrad. Therefore, the establishment of a high-precision quantum signal link is the key to achieving satellite-to-ground quantum communication. In satellite-to-ground quantum communication, it is necessary to use acquisition, tracking, and pointing (ATP) technology. As one important part of the ATP technology, the ‘pointing’ refers to transmitting the communication signal to the receiving aperture of the other terminal accurately on the basis of precise tracking, which mainly needs to compensate for the point-ahead angle caused by the high-speed relative movement of the terminals [16]. The ATP technology has been verified and improved numerous times in satellite-to-ground and inter-satellite laser communications [17–20]. However, the ‘pointing’ method still has the opportunity to be improved. In reported and successfully verified satellite laser communication experiments, such as the European Space Agency’s SILEX and Japan’s OICETS [21,22], the pointing method generally uses a special point-ahead mechanism to achieve the deviation between the emission and reception optical axes. This extra mechanism is subject to open-loop control on the optical path, so the execution error cannot be monitored or compensated in real time, and depends heavily on the execution accuracy of the mechanism itself. Moreover the algorithms needed satellite orbit prediction as input, which increased complexity of the system implementation.
In Ref. [23], the authors discussed a design of the transmitter (for uplink) at ground station in Tibet, without special point-ahead actuator. However, the Earth's angular rotation and the offset between beacon laser and receiving aperture have not been considered. In the case of the uplink, the contributions of these two parts can be ignored. However, it cannot be ignored in the case of downlink (satellite to ground), which requires higher pointing accuracy.
According to the practical problems mentioned above, we propose a high-precision pointing method for downlink quantum signals, with a specific algorithm based on the requirements and hardware configuration of the quantum science satellite Micius. This method has three main features. First, it does not require an extra point-ahead mechanism but generates a deviation between the tracking and emission optical axes by changing the fine tracking point in real time, which achieves the same effect as a point-ahead mechanism. As the tracking and emission optical axes are both connected to the fine tracking camera, the deflection angle of the pointing optical axis can be accurately monitored while tracking. Second, the algorithm considers both the Earth's angular rotation and the offset between beacon laser and receiving aperture, covering most of the error sources. Third, the algorithm does not need the advanced satellite orbit prediction, but only the fixed GPS position of the ground station and real-time GPS data of the satellite, which further reduces implementation complexity. Through in-orbit test of the Micius quantum experiment, we have confirmed that this method can achieve a total pointing error less than 1 µrad, which meets the link efficiency requirements of quantum communication signals.
The remaining sections of this paper are arranged as follows: Section 2 explains the point-ahead angle and ground station beacon laser requirements for satellite pointing and explains the design and principle of the payload system for link establishment. Section 3 gives specific methods and algorithms for high-precision pointing. Section 4 evaluates the validity and accuracy of the method based on the measured results of the Micius quantum satellite. Section 5 discusses and summarizes the results.
2. Requirements analysis and configuration
2.1 Pointing requirements analysis
In satellite-to-ground quantum communication, the pointing of quantum signal needs to compensate for two sources of error: one is the point-ahead angle, and the other is the installation offset of the ground beacon laser.
When there is high-speed relative motion between the satellite and the ground station, if the satellite transmits a quantum signal along the ground position detected at the current moment, due to the constant speed of light, the signal will deviate from the ground station by a certain amount when it reaches the ground station. To compensate for this error, the optical axis of the transmitted signal needs to be offset from the optical axis of the tracking signal by a certain angle, which is called the point-ahead angle. The point-ahead angle can be expressed as ${\theta _{pa}} = {{2{v_\tau }} \mathord{\left/ {\vphantom {{2{v_\tau }} c}} \right.} c}$, where c is the speed of light, and ${v_\tau }$ is the component of the ground station velocity relative to the satellite in the direction perpendicular to the connection between the two [16,23]. The graphical explanation is shown in Fig. 1(a). In low-orbit satellite communications, the vertical speed of the ground station relative to the satellite can reach a maximum of 7.8 km/s; thus, the point-ahead angle can reach a maximum value of 52 µrad, which exceeds the divergence angle of the quantum signal. So it is necessary to perform accurate point-ahead angle compensation.
Fig. 1. The pointing requirements. (a) Point-ahead requirement. The inertial coordinate system is established with the satellite as the reference. At time t0, the red beacon light is emitted by the ground station, and reaches the satellite terminal at time t0+Δt . The green beacon light and quantum light emitted by the satellite need to deviate from the red beacon light direction by a certain angle so they can point to the ground station at time t0 + 2Δt. The angle of deviation is related to the vertical velocity component of the ground station relative to the satellite and the speed of light. (b) Pointing requirement caused by the offset between beacon laser and receiving aperture.
In an actual satellite-to-ground quantum communication system, a satellite determines the position of a ground station by tracking the uplink beacon light of the ground station. In some scenarios, to suppress the influence of atmospheric turbulence, the optical ground station is equipped with multiple beacon light lasers, but in general, only one beacon light laser needs to be configured. The beacon laser is deviated from the center of the ground optical receiving antenna, which will cause link loss and must be compensated. As shown in Fig. 1(b), the compensation angle can be expressed as ${\theta _{bias}} = {{{l_b}} \mathord{\left/ {\vphantom {{{l_b}} L}} \right.} L}$, where ${l_b}$ is the distance of the beacon light from the center of the optical antenna and $L$ is the distance between the satellite and the ground station. Generally, the diameter of a typical ground station antenna is greater than 1 m, and ${l_b}$ is approximately 0.8 m. When the satellite-to-ground distance is 500 km, $|{\theta _{bias}}|$ reaches 1.6 µrad, which cannot be ignored given that the divergence angle of the quantum signal is only 12 µrad.
2.2 On-satellite tracking and pointing system configuration
The on-satellite tracking and pointing system uses a composite control architecture of coarse tracking and fine tracking. Figure 2 shows the principle block diagram of the tracking and pointing system in the quantum science satellite Micius. The system is divided into three parts: a scanning head, a two-axis turntable mechanism and an internal optical unit.
Fig. 2. The on-satellite tracking and pointing system based on a two-axis turntable. The system comprises a scanning head (a), a two-axis turntable mechanism (b) and an internal optical unit (c). In the system there are three different lights, including the transmitting beacon light at 532 nm, the receiving beacon light at 671 nm and the quantum light at 810 nm and 850 nm.
The scanning head includes an off-axis telescope system and a coarse tracking camera. The off-axis telescope system realizes the expansion of the quantum signal and narrows the divergence angle. The diameter of the telescope is 180 mm. The divergence angle of the finally emitted quantum signal is less than 12 µrad $({1 \mathord{\left/ {\vphantom {1 {{e^2}}}} \right.} {{e^2}}})$. Together with the telescope, the coarse tracking camera rotates with the two-axis turntable.
The two-axis turntable mechanism drives the scanning head to achieve a wide pointing range for communication with the moving ground station. The azimuth axis scan range is ±90°, and the elevation axis is −30°∼+75°. The mechanism uses an optical shafting solution to realize the optical transmission connection between the internal optical unit and the scanning head. The two-axis turntable mechanism and the coarse tracking camera form a closed-loop control system. The control bandwidth is greater than 3 Hz and the control error is less than 50 µrad (1σ).
In the internal optical unit, a piezoelectric ceramic actuator-based fast steering mirror (FSM) is used as a fine tracking mechanism, and an optical closed-loop system is formed with a fine tracking camera. The detection frequency is better than 2 kHz, and the control bandwidth of the tracking system is greater than 250 Hz. Dichroic mirrors are used to realize the isolation of beacon light transmitting signal (532 nm), beacon light receiving signal (671 nm) and quantum transmitting signal (810 and 850 nm). The power of beacon light emitted on the satellite is greater than 50 mW, and the emission divergence angle is about 600 µrad. The detailed system parameters are shown in Table 1.
Table 1. Supplementary Performance of the ATP system on-satellite
3. Implementation method and algorithm
3.1 Implementation method
As discussed in Section 2, due to the effect of point-ahead angle and the beacon laser offset of the ground station, it is necessary to deviate the payload transmitting optical axis from the receiving optical axis by an angle, which is calculated based on the above factors. The conventional method is to use a point-ahead mechanism, and the receiving and emission axes are deviated by the deflection mechanism. In Micius, we adopt the method of changing the fine tracking point in real time, which can achieve the same effect. In addition, the position of the ground beacon spot on the fine tracking camera reflects the angle of compensation, which eliminates the execution error that may be caused by the point-ahead mechanism.
The implementation principle is shown in Fig. 3. In the tracking system, there is a reference point; when the beacon light spot position of the ground station coincides with the reference point, the tracking optical axis and the emission optical axis coincide, as shown in Fig. 3(a). If the ground beacon light spot position (actual tracking point) is deviated from the reference point by adjusting the deflection angle of the FSM, the emission optical axis (pointing axis) and the tracking optical axis will not coincide, leading to the pointing and compensation effect, as shown in Fig. 3(b).
Fig. 3. Principles of the optical axis deviation of pointing and tracking. The blue line is the tracking optical axis, and the red line is the emission optical axis.
Let the vector direction of the emitted optical axis be ${\boldsymbol {PA}}$ and the vector direction of the tracking optical axis be ${\boldsymbol {PT}}$, then the additional pointing offset angle is:
The effect of the tracking optical system on the beam transmission direction conforms to the linear transformation. Let the vector corresponding to ${\boldsymbol {PA}}$ be ${\boldsymbol P}{{\boldsymbol A}^{\boldsymbol n}}$ and the vector corresponding to ${\boldsymbol {PT}}$ be ${\boldsymbol P}{{\boldsymbol T}^{\boldsymbol n}}$, when converted to the front of the fine tracking camera, as in Fig. 3. There is:3.2 Detailed algorithm derivation
The specific steps of the pointing algorithm are shown in Fig. 4. The initial reference coordinate system is the WGS84 ground-fixed coordinate system. The calculation inputs are the ground station position, the satellite position, the satellite velocity in the WGS84 coordinate system, and the satellite attitude. Based on these inputs, the values of the point-ahead vector and the beacon light offset vector are calculated under WGS84 coordinate system. Next, the transformation matrix from the WGS84 coordinate system to the payload coordinate system, and the internal optical path transmission transformation matrix of the payload are calculated. Based on the above information, the tracking point changes corresponding to the pointing vector of the fine tracking camera are obtained. The reason why the WGS84 coordinate system was chosen instead of the commonly used J2000 inertial coordinate system is that the WGS84 coordinate system can directly use the output information of the navigation system on the satellite platform without the need for additional conversion, which reduces error sources and complexity.
Calculate the point-ahead angle vector
According to the analysis in Section 2.1, the point-ahead angle vector is related to the velocity of the ground station relative to the satellite. The velocity here refers to the relative velocity in inertial space. The velocity vector of the ground station in the ground-fixed coordinate system is zero, but this is not the case in inertial space. According to the Galileo relative velocity principle, the velocity of the ground station relative to the satellite can be obtained as:
Fig. 5. Relative relationship between ground station and satellite. The Xw-Yw-Zw rectangular coordinate system is the WGS84 coordinate system, the Xo-Yo-Zo coordinate system is the satellite centroid orbit coordinate system, O is the center of the Earth, G is the ground station, and S is the satellite. VSG is the velocity of the ground station relative to the satellite in inertial space, and Vτ is its vertical component.
Then, the point-ahead angle vector in the WGS84 coordinate system can be found as:
Calculate the beacon laser offset vector
The beacon laser offset vector is the position of the ground-emitted beacon light relative to the center of the ground station receiving telescope. Establish a coordinate system, as shown in Fig. 6; Xgt and Ygt are located in the receiving plane of the ground station telescope, and Zgt points to the satellite. Xgt is always parallel to the surface horizontal plane. The projections of the ground beacon light positions on Xgt and Ygt are α and β, respectively. Then, there is the following relationship:
According to the calculation formula in Section 2.1, it can be concluded that the value of the beacon laser offset vector in the WGS84 coordinate system is:
Calculate WGS84 coordinate system transformation to payload coordinate system
The pointing deflection angle, which is solved in WGS84 coordinates must be transformed to the payload coordinate system, and as part of this process, the azimuth and elevation angle of the payload turntable can be obtained, which are necessary for the next calculation of the internal optical path transmission of the payload.
The coordinate transformation process is divided into three steps. The first step is to find the transformation matrix from WGS84 system to the satellite's centroid orbit coordinate system. The second step is to find the transformation from the satellite's centroid orbit coordinate system to the satellite body coordinate system based on the satellite attitude angle. The third transformation is from the satellite body coordinate system to the payload coordinate system.
WGS84 to satellite centroid orbit coordinate system
The satellite's centroid orbit coordinate system is defined such that the Zo axis points to the center of the Earth, and the Xo axis points to the direction of satellite velocity in the orbital plane, as shown in Fig. 6. From this, the vector values of the three axes of the satellite's centroid orbit coordinate system in the WGS84 coordinate system can be calculated [24]:
When the satellite is in orbit, the attitude angle is usually not zero, and some satellites also perform attitude maneuvers. The Euler angle is used to represent the satellite attitude angle, where ψ represents the yaw angle around the Z-axis; φ represents the roll angle around the X-axis; and θ represents the elevation angle around the Y-axis. The satellite adopts the Z-X-Y conversion order, then:
The relationship between the payload and the installation of the satellite can usually be accurately calibrated, which has a fixed transformation matrix. We assume the axes of these two coordinate systems are in the same direction. It can be expressed as a unit matrix in order to simplify the analysis.
In Micius, the relationship between the payload coordinate system and the two-axis turntable is shown in Fig. 7. At the reference zero position, the external optical axis points to the Zp direction, and the elevation axis is parallel to Xp. The payload azimuth axis angle is represented by As, and the elevation axis angle is represented by Es.
Fig. 7. Schematic diagram of optical transmission inside the tracking and pointing system. In the figure, Xp-Yp-Zp is the payload coordinate system, and Xb-Yb-Zb is the internal optical unit coordinate system.
The position coordinates of the ground station in the payload structure coordinate system are:
After the angle of the payload turntable is obtained, the optical path transmission transformation within the payload can be performed, which is an important step in calculating the tracking point of the fine tracking camera.
As shown in Fig. 7, the incident light first enters the telescope and the folding mirror, and then passes through the U-shaped frame to fold the optical path and then enters the rear optical path bottom plate. The telescope and folding mirror are equivalent to the reflecting mirror TM; the U-frame reflecting mirrors are UM1, UM2 and UM3; and the internal unit are BM1 and BM2, respectively. We will find four matrices to obtain the final result.
Coordinate transformation of the telescope with the rotation of the two-axis turntable:
First rotate the azimuth As with the U-shaped frame around the azimuth axis (Y axis), and then rotate the yaw angle Es around the elevation axis (X axis) alone. In the equation, k is the magnification of the telescope. Then we can get the transformation matrix:
The reflection of mirror TM turns light 90 degrees, then the light rotates Es angle around the elevation axis. We can get:
Then the light get reflected by mirror UM1, UM2, UM3 in turn. Through the law of reflection, we can get the transformation of coordinates:
At last, light rotates As angle around the azimuth axis, then gets reflected by mirror BM1 and BM2, then into the fine camera. The transmission process can be expressed by matrix:
Based on Eqs. (5), (7), (12) and (19), the pointing vector corresponding to the incident surface of the fine tracking camera is:
4. Realization and results
4.1 Realization
In the above sections, we introduce the principle and detailed algorithm of pointing method. The payload system configuration and main technical parameters are shown respectively in Fig. 2 and Table 1, in Section 3. In this section, we introduce the realization related to the pointing method in Micius, including main control board, fine tracking camera, piezoelectric drive circuit, and FSM, as shown in Fig. 8. The picture of ATP payload system in satellite Micius is shown in Fig. 9.
Fig. 9. The picture of ATP payload system in satellite Micius. The payload comprises a telescope, a coarse camera, a two-axis turntable, communication electronics, and internal optical unit. The FSM, fine tracking camera described in Fig. 8 are sub-units of the internal optical unit.
The algorithm calculation is implemented on a 32-bit floating point digital signal processor (DSP, TMS320C6701). The inputs such as the satellite position, velocity and attitude are directly from the GPS and attitude control system in real time. And the ground station position is uploaded to the payload from the software instructions in advance. The calculation result is transmitted to FPGA (Xilinx XQ2V3000) for tracking control reference. The fine tracking camera detects the beacon spot and calculates target position using centroid algorithm. We use CMOS array detector in the fine tracking camera, and the tracking point is easy to adjust and has a very high linearity with optical angle. Tracking control is implemented on FPGA chip with the inputs. The output control signals are amplified by piezoelectric drive circuit from 0∼5 V to 0∼100 V, and then used to drive the fast steering mirror (FSM). In turn, the direction of the optical axis is affected by FSM and detected by fine tracking camera as feedback. If we change the tacking point, the angle between the transmitting optical axis and the receiving optical axis will change accordingly.
4.2 Algorithm calculation
The Micius is a solar synchronous orbit satellite with an altitude of 500 km. We select the ground station located at Nanshan Observatory (43.47546 N, 87.17669 E, altitude of 2080 m) as the other terminal. Figure 10 shows the tracking point offset value calculated by the satellite payload for the same ground station, where (a) and (b) show the satellite transiting from the east of the ground station (UTC time 18:12:00), and (c) and (d) from the west of the ground station (UTC time 18:42:00). The attitude of the satellite is according to the geocentric pointing mode. Each pixel of the payload fine tracking camera corresponds to 5 µrad, and the maximum aiming offset synthesized in the two directions during the station crossing is 51.3 µrad.
Error analysis: The algorithm is implemented by a 32-bit DSP, and by comparing the calculation results with the same input of computer, the calculation error of the formulas can be ignored. The algorithm error mainly comes from the accuracy of the input parameters, including the Global Positioning System position and the three-axis attitude angle error of the satellite. The three-axis attitude error of the satellite is always below 0.1 degree and the GPS position accuracy is better than 20 m. Through the comparison of computer calculation the total algorithm error caused by the input parameters is less than 0.3 µrad.
4.3 Verification
To verify the function and accuracy of the pointing method, we carried out two steps of experiments. The first experiment was carried out in the static environment of the laboratory, which is used to test the pointing function and calibrate the precision coefficient. The second experiment was conducted in-orbit, in order to verify the performance of the algorithm and implementation.
The implementation diagram of the first experiment is shown in Fig. 11. The payload was placed in front of a collimator with 17 m focal length and tracks the beacon light. The collimator generates beacon light and receives the quantum signal emitted by the payload. At first, the fine tracking point of the payload is fixed. If we change the tracking point, the optical axis of quantum signal will change and detected by the beam analyzer at the focal plane of collimator. The angle change of the optical axis can be obtained by dividing the spot displacement on the beam analyzer by the focal length of the collimator. Compared with the theoretical analysis, we can verify the pointing function, and accurately calibrate the corresponding coefficient of camera pixel value and optical angle. According to the experimental results shown in Table 2, the function and polarity of this pointing method are correct, and the coefficient of camera pixel to optical angle is 4.94 µrad / pixel (based on repeated measurements).
Table 2. Laboratory experiment results
In-orbit experiment is a sufficient way to test the pointing method, as the point-ahead angle cannot be simulated on ground. The experiments were carried out between satellite Micius and the ground station at Nanshan Observatory in China. In the experiment, the satellite payload emitted quantum signals (40 M photons/s at four polarization directions) which were received by a 1 meter telescope on the ground station. As the received signal is so weak, all the experiments were conducted at mid-night with cloudless weather.
In the near earth orbit, the relative distance and angle between the satellite and the ground station change rapidly, and the visible time of the satellite to the ground station is about 8 minutes at most. Therefore, the strength of the quantum signal received on the ground changes at any time, which makes it difficult to test and verify the pointing of quantum signals. So we used an internationally used signal scanning method for verification [19,22]. In the experiment, the satellite calculates a theoretical pointing curve (tracking point offsets) and then superimposes a rectangular scanning curve. By comparing the satellite's scan value and the number of photons (counts per second) received on the ground at the same time, both the far-field pattern and pointing accuracy of the satellite’s quantum signal can be obtained. If the peak point of the ground received signal is near the scanning center and the result is repeatable, the pointing method should be effective and accurate. On the contrary, if the ground received signal obtained by scanning is irregular and has poor repeatability, the pointing method may be invalid.
The original fine tracking point offset in the experiment and the actual curve after superposing the rectangular scan are shown in Fig. 12. At first, a wide range rectangular scan was performed, covering ±1.2 pixels and a total angular range of ± 6 µrad. The measurement results of the wide range scan are shown in Fig. 13. In the figure, (a) shows the number of photons (counts per second) received by the ground station in two continuous cycles. Since the satellite-to-ground distance changes at the same time during the scanning period, the data is compensated according to the distance square relationship. Figures 13(b) and 13(c) show the processing results of two continuous scanning cycles. The overall distribution of the quantum emission signal on the ground can be obtained. The full width at half maximum (FWHM) of the quantum signal is estimated to be approximately 1.5 pixels, which is 7.5 µrad. At the same time, it can be seen that the pointing accuracy is about 0.3 pixels (1.5 µrad).
Fig. 12. Pointing offset curve and scanning mode of the satellite-ground joint scanning. (a) is the payload fine tracking point offset curve, the dashed line is the reference curve when no scanning is applied, and the solid line is the actual curve after increased scanning. (b) is a diagram of a wide range rectangular scanning mode, where the scanning range is ±1.2 pixels in both directions.
Fig. 13. Satellite-ground wide range scanning results. (a) is the number of photons received by the ground station during two scanning cycles, (b) is the processing result of the first cycle, showing the distribution of quantum emission spots near the ground station, and (c) is the processing result of the second cycle.
From Fig. 13, we can also see that the pointing center of the quantum signal has a relative fixed bias with about 0.3 pixels in X and Y axis, which is a common phenomenon caused by launch process and space environment. At the same time, due to the large step angle, which is 0.4 pixels, more detailed beam distribution cannot be obtained. So we performed another scan test. In this time, the 0.3 pixels pointing bias was compensated, and the scanning range was narrowed down to ±0.4 pixels. The measurement result of the narrow range scan is shown in Fig. 14(a), and the fine tracking error is shown in Fig. 14(b). As the tracking error (beam pointing random jitter) is about 0.5 µrad (1σ), the shape of light spot has a little deformation. From Fig. 14(a), we can evaluate that the distance between the peak point of scanned image and the scanning center is between 0.1∼0.2 pixel after compensation, corresponding to 0.5∼1.0 µrad.
5. Conclusions
We propose a method for high-accuracy pointing of the quantum signals of satellite terminals for the needs of satellite-to-ground quantum communication. This method adopts the means of flexibly changing the precise tracking points, and uses Earth fixed coordinate system as calculation basis, which can reduce the complexity of the tracking system and improve reliability and measurability. A specific calculation method is given in this paper, and was realized in the quantum science satellite Micius. We performed special designed in-orbit test by joint scanning of the satellite and the ground station. The result proves that the method can achieve a pointing accuracy of 0.5∼1.0 µrad, which guarantees the long-distance transmission efficiency of quantum signals. Although this method is designed for quantum communication, it is also applicable to bi-directional satellite laser communication, especially for the multimode optical fiber receiving system. In summary, the method in this article provides a design reference for a high-precision, light and small space tracking and pointing system.
Funding
Strategic Priority Research Program on Space Science, the Chinese Academy of Sciences (XDA04000000); Shanghai Rising-Star Program (19QA1410400); Key Technologies Research and Development Program (2017YFA0303900); Youth Innovation Promotion Association of the Chinese Academy of Sciences.
Acknowledgments
We thank many colleagues at the University of Science and Technology of China, Shanghai Engineering Center for Microsatellites, and the National Space Science Center.
Disclosures
The authors declare no conflicts of interest.
References
1. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, (IEEE Press, New York, 1984), pp.175–179.
2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993). [CrossRef]
3. M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11(7), 075001 (2009). [CrossRef]
4. T.-Y. Chen, J. Wang, H. Liang, W.-Y. Liu, Y. Liu, X. Jiang, Y. Wang, X. Wan, W.-Q. Cai, L. Ju, L.-K. Chen, L.-J. Wang, Y. Gao, K. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Metropolitan all-pass and inter-city quantum communication network,” Opt. Express 18(26), 27217–27225 (2010). [CrossRef]
5. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legre, S. Robyr, P. Trinkler, L. Monat, J.-B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Langer, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19(11), 10387–10409 (2011). [CrossRef]
6. J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground–satellite quantum key distribution,” Nat. Photonics 7(5), 387–393 (2013). [CrossRef]
7. S. Nauerth, M. Furst, T. Schmitt-Manderbach, H. Weier, and H. Weinfurter, “Information leakage via side channels in freespace BB84 quantum cryptography,” New J. Phys. 11(6), 065001 (2009). [CrossRef]
8. R. Bedington, J. M. Arrazola, and A. Ling, “Progress in satellite quantum key distribution,” npj Quantum Inf. 3(1), 30 (2017). [CrossRef]
9. R. Bedington, X. Bai, E. Truong-Cao, Y.-C. Tan, K. Durak, A. V. Zafra, J. A. Grieve, D. K. Qi, and A. Ling, “Nanosatellite experiments to enable future space-based QKD missions,” EPJ Quantum Technol. 3(1), 12 (2016). [CrossRef]
10. K. Gunthner, I. Khan, D. Elser, B. Stiller, O. Bayraktar, C. R. Mueller, K. Saucke, D. Trondle, F. Heine, S. Seel, P. Greulich, H. Zech, B. Gutlich, S. Philipp-May, C. Marquardt, and G. Leuchs, “Quantum-limited measurements of optical signals from a geostationary satellite,” Optica 4(6), 611–616 (2017). [CrossRef]
11. H. Takenaka, A. Carrasco-Casado, M. Fujiwara, M. Kitamura, M. Sasaki, and M. Toyoshima, “Satellite-to-ground quantum communication using a 50-kg-class micro-satellite,” Nat. Photonics 11(8), 502–508 (2017). [CrossRef]
12. J. P. Bourgoin, B. L. Higgins, N. Gigov, C. Holloway, C. J. Pugh, S. Kaiser, M. Cranmer, and T. Jennewein, “Free-space quantum key distribution to a moving receiver,” Opt. Express 23(26), 33437–33447 (2015). [CrossRef]
13. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017). [CrossRef]
14. J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Ling, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1180–1184 (2017). [CrossRef]
15. J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017). [CrossRef]
16. J. H. Shapiro, “Point-ahead limitation on reciprocity tracking,” J. Opt. Soc. Am. 65(1), 65–68 (1975). [CrossRef]
17. M. Toyoda, M. Toyoshima, T. Takahashi, M. Shikatani, Y. Arimoto, K. Araki, and T. Aruga, “Ground-to-ETS-VI narrow laser beam transmission,” Proc. SPIE 2699, 71–80 (1996). [CrossRef]
18. M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. Reyes, A. Alonso, Z. Sodnik, and B. Demelenne, “Ground-to-satellite optical link tests between Japanese laser communications terminal and European geostationary satellite ARTEMIS,” Proc. SPIE 5338, 1–15 (2004). [CrossRef]
19. T. Tolker-Nielsen and G. Oppenhauser, “In-orbit test result of an operational optical intersatellite link between ARTEMIS and SPOT4,” Proc. SPIE 4635, 1–15 (2002). [CrossRef]
20. S. Bai, J. Qiang, L. Zhang, and J.-Y. Wang, “Optimization of spatial acquisition systems for low-light-level robustness in space optical communications,” Opt. Lett. 40(16), 3750–3753 (2015). [CrossRef]
21. T. Jono, M. Toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition, tracking, and pointing systems of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999). [CrossRef]
22. M. Toyoshima and K. Araki, “Far-field pattern measurement of an onboard laser transmitter by use of a space-to-ground optical link,” Appl. Opt. 37(10), 1720–1730 (1998). [CrossRef]
23. X. Han, H.-L. Yong, P. Xu, W.-Y. Wang, K.-X. Yang, H.-J. Xue, W.-Q. Cai, J.-G. Ren, C.-Z. Peng, and J.-W. Pan, “Point-ahead demonstration of a transmitting antenna for satellite quantum communication,” Opt. Express 26(13), 17044–17054 (2018). [CrossRef]
24. Y. Liu, D.-Y. Yi, and Z.-M. Wang, “Coordinate Transformation Methods from the Inertial System to the Centroid Orbit System,” Aerosp Contrl 25(2), 6–10 (2007).
