Taiji Program Research Articles

Research on High-Precision Resonant Capacitance Bridge Based on Multiple Transformers.

The Taiji program is dedicated to the detection of middle and low-frequency gravitational waves, targeting the 0.1 mHz to 1 Hz frequency band. The project requires an acceleration residual sensitivity of 3 × 10-15 ms-2/Hz1/2, which necessitates a capacitance sensing resolution of 1 aF/Hz1/2 for the capacitive sensing system within the specified frequency range. The noise level of the resonant bridge significantly influences the resolution. Addressing the challenges in enhancing transformer performance parameters in existing resonant capacitance bridges and the constraints on improving the characteristics of resonant capacitance bridges, this study introduces a novel approach to reduce bridge thermal noise without optimizing existing parameters. The simulation results demonstrate that this scheme can reduce the noise to 0.7 times the original level and further reduce bridge thermal noise when other parameters affecting noise are optimized. This not only mitigates the demands for other performance parameters but also increases the range of maximum acceptable resonant frequency deviations and reduces its sensitivity to such variations. Experimental validation confirms that the proposed scheme effectively reduces noise by 0.7 times and improves the resolution of capacitance sensing to 0.6 aF/Hz1/2, thereby advancing the Taiji program gravitational wave detection capabilities.

Sensor Head Temperature Distribution Reconstruction of High-Precision Gravitational Reference Sensors with Machine Learning.

Temperature fluctuations affect the performance of high-precision gravitational reference sensors. Due to the limited space and the complex interrelations among sensors, it is not feasible to directly measure the temperatures of sensor heads using temperature sensors. Hence, a high-accuracy interpolation method is essential for reconstructing the surface temperature of sensor heads. In this study, we utilized XGBoost-LSTM for sensor head temperature reconstruction, and we analyzed the performance of this method under two simulation scenarios: ground-based and on-orbit. The findings demonstrate that our method achieves a precision that is two orders of magnitude higher than that of conventional interpolation methods and one order of magnitude higher than that of a BP neural network. Additionally, it exhibits remarkable stability and robustness. The reconstruction accuracy of this method meets the requirements for the key payload temperature control precision specified by the Taiji Program, providing data support for subsequent tasks in thermal noise modeling and subtraction.

Study on the Effect of Micro-Force Perturbations and Temperature Fluctuation on Interferometer for the Taiji Program.

To increase the interferometric measurement resolution in the Taiji program, we present a noise suppression method in this paper. Taking the specific micro-force perturbation and temperature fluctuation in the Taiji-1 interferometer as an example, we set up and experimentally verified the corresponding transfer function to quantify the effect of both noise sources on the interferometric results. Consistent results were obtained between the numerical and experimental results for the transfer function. It is instructive to eliminate the micro-force perturbations and temperature fluctuations during on-orbit interferometric measurement for as long as the acquisition of the force or temperature distribution of related surfaces and the corresponding transfer functions. This indicates that the method can be used for noise sensing and more in the field of noise elimination and measurement resolution improvement for future Taiji program interferometers.

Enhanced Detection Precision of the Taiji Program by Frequency Setting Strategy Based on a Hierarchical Optimization Algorithm

For space-based gravitational wave detection, a laser interferometric measurement system composed of a three-spacecraft formation offers the most rewarding bandwidth of astrophysical sources. There are no oscillators available that are stable enough so that each spacecraft could use its own reference frequency. The conversion between reference frequencies and their distribution between all spacecrafts for the synchronization of the different metrology systems is the job of the inter-spacecraft frequency setting strategy, which is important for continuously acquiring scientific data and suppressing measurement noise. We propose a hierarchical optimization algorithm to solve the frequency setting strategy. The optimization objectives are minimum total readout displacement noise and maximum beat-note frequency feasible range. Multiple feasible parameter combinations were obtained for the Taiji program. These optimized parameters include lower and upper bounds of the beat note, sampling frequency, pilot tone signal frequency, ultrastable clock frequencies, and modulation depth. Among the 20 Pareto optimal solutions, the minimum total readout displacement noise was 4.12 pm/Hz, and the maximum feasible beat-note frequency range was 23 MHz. By adjusting the upper bound of beat-note frequency and laser power transmitted by the telescope, we explored the effects of these parameters on the minimum total readout displacement noise and optimal local laser power in greater depth. Our results may serve as a reference for the optimal design of laser interferometry system instrument parameters and may ultimately improve the detection performance and continuous detection time of the Taiji program.

Design and Construction of the Optical Bench Interferometer for the Taiji Program.

A kind of full-function two-sided optical bench interferometer (OBI) is designed to meet the practical requirements of the Taiji Program for space gravitational wave detection. The main optical paths are arranged on the A-side for transmission and interference, and other optical paths and electronic devices are placed on the B-side. According to the design scheme, we successfully constructed two OBIs by using hydrogen-oxygen catalytic stress-free bonding technology. When the OBI is installed and adjusted, the position and Angle error of the interference beam are controlled within 30 μm and 50 μrad through the self-designed precision mechanical clamping mechanism and beam position measuring device. The built OBI was placed on the vibration isolation platform in the vacuum tank for the stability test. The test results show that the noise of the OBI is less than 10 pm/√Hz in the frequency band of 0.1 Hz to 1 Hz, which meets the noise budget requirements of the Taiji Pathfinder in the middle- and high-frequency band.

A Systematic Approach for Inertial Sensor Calibration of Gravity Recovery Satellites and Its Application to Taiji-1 Mission

High-precision inertial sensors or accelerometers can provide references for free-falling motion in gravitational fields in space. They serve as the key payloads for gravity recovery missions such as CHAMP, the GRACE-type missions, and the planned Next-Generation Gravity Missions. In this work, a systematic method for electrostatic inertial sensor calibration of gravity recovery satellites is suggested, which is applied to and verified with the Taiji-1 mission. With this method, the complete operating parameters including the scale factors, the center of mass offset vector, and the intrinsic biased acceleration can be precisely calibrated with only two sets of short-term in-orbit experiments. This could reduce the gaps in data that are caused by necessary in-orbit calibrations during the lifetime of related missions. Taiji-1 is the first technology-demonstration satellite of the “Taiji Program in Space”, which, in its final extended phase in 2022, could be viewed as operating in the mode of a high–low satellite-to-satellite tracking gravity mission. Based on the principles of calibration, swing maneuvers with time spans of approximately 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. Given the data of the actuation voltages of the inertial sensor, satellite attitude variations, precision orbit determinations, the inertial sensor’s operating parameters are precisely re-calibrated with Kalman filters and are relayed to the Taiji-1 science team. The relative errors of the calibrations are <1% for the linear scale factors, <3% for center of mass, and <0.1% for biased accelerations. Data from one of the sensitive axes are re-processed with the updated operating parameters, and the resulting performance is found to be slightly improved over the former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the Next-Generation Gravity Missions. This could also create some insight into the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.

Advanced inter-spacecraft offset frequency setting strategy for the Taiji program based on a two-stage optimization algorithm.

For space-based gravitational wave (GW) detection, the continuity of detection data acquisition is crucial to the inversion of wave sources and the realization of scientific goals. To control the inter-spacecraft beat-note frequency in an appropriate range for continuous gravitational wave detection and to reduce the upper bound of the beat-note frequency for improving the detection capability, a two-stage optimization algorithm is proposed to solve the offset frequency setting strategy in the Taiji program. The optimization objectives are the maximum offset frequency duration and minimum upper bound of the beat-note frequency. Considering all feasible phase-locked schemes, Doppler frequency shift, and the bandwidth of the phasemeter, a series of offset frequency setting strategies satisfying the conditions was obtained. The solution results show that the upper bound can be reduced to 16MHz and, in this case, the offset frequency changes nine times with a minimum and maximum offset frequency duration of 90days and 713days, respectively. If the Doppler frequency shift is constrained, the minimum upper bound can be reduced to 14MHz. When the minimum duration is increased, the minimum upper bound is increased. These results show that, by varying the offset frequency a limited number of times, the data continuity requirements of the Taiji program can be satisfied, and the phasemeter development difficulty and detection capability can be balanced, and may provide a reference for the phasemeter design, the setting of phase-locking schemes, and inter-spacecraft offset frequency in the Taiji program.

Ground-based principle verification of clock noise transfer for the Taiji program

摘要: 太极计划是中国科学院提出的空间引力波探测任务，利用激光差分干涉的方法学探测卫星间由引力波引起的pm级位移波动。为消除由卫星间因时钟不同步而产生的测量误差，拟采用边带倍频时钟噪声传递的方法进行星间时钟噪声测量与消除。本文讨论太极计划星间时钟噪声传递的需求、原理、方法，并设计实验进行原理验证。通过搭建电子学实验测试两个系统时钟噪声的极限值，确定实验相关参数，进一步光学实验验证边带倍频传递方案的原理。实验结果表明，本文提出的时钟噪声消除方案及相关参数合理可行，适用于太极计划的需求。在0.05 Hz~1 Hz频段，星间时钟噪声的抑制效果优于2π×10-5 rad/Hz1/2，满足太极探路者的噪声需求，为未来太极计划的时钟噪声传递的方案与参数设计奠定实验和理论的基础。

Research on Simulated Laser Link Construction Control System of Taiji Program

Research on Simulated Laser Link Construction Control System of Taiji Program

Analysis of Telescope Wavefront Aberration and Optical Path Stability in Space Gravitational Wave Detection

Space-based gravitational wave detection programs, such as the Laser Interferometer Space Antenna (LISA) or Taiji program, obtain gravitational wave signals by measuring the change in the distance between three satellites by laser. The telescope is an important part of the measurement system, and its function is to transmit and receive laser signals. Due to changes in the space environment, the telescope will inevitably introduce additional dynamic aberrations, which will bring optical path errors to the inversion of gravitational wave signals. Taking LISA as an example, to achieve pm-level measurement accuracy at the detection frequency of 0.1 mHz–1 Hz, the stability requirements of the telescope are less than 1 pm/Hz1/2. This paper theoretically deduces the aberration types that affect the telescope’s stability and conducts simulation analysis according to the actual phase demodulation method, which verifies the theory’s correctness. In addition, using this theory, it can be concluded that under the condition that the total size of the telescope aberration is determined to be stable, reducing the ratio of rotationally symmetric aberrations such as “spherical aberration” and “defocusing” among common aberrations can significantly improve the stability of the telescope. The conclusion guides the optical system design of LISA or Taiji.

Preliminary simulation of intersatellite laser interference link for the Taiji program

Laser interferometry is used in the Taiji program to detect gravitational waves ranging from 0.1 mHz to 1 Hz, and picometer-level ranging accuracy needs to be achieved. Limited by the interference of ground environment and the length of ground test baseline, it is difficult to carry out the experimental verification of key technologies and indicators on the ground. Therefore, implementing a computer simulation based on detection principles is crucial. The simulation method of combining the geometric and wave optics is adopted, and corresponding models, including the Gaussian beam and its propagation model, diffraction model, telescope model, and readout signal model are implemented and validated by comparing with analytical methods and other simulator. Afterward, the intersatellite laser interference link based on split interferometry detection applied by the Taiji program is simulated. The results are verified by theoretical analysis. This work can provide a foundation for the simulator development and further be applied in the optimal design of interferometer for the Taiji program.

Global Gravity Field Model from Taiji-1 Observations

Taiji-1 is the first technology demonstration satellite of the Taiji program of China’s space-borne gravitational wave antenna. After the demonstration of the key individual technologies, Taiji-1 continues collecting the data of the precision orbit determinations, satellite attitudes, and non-conservative forces exerted on the S/C. Therefore, during its free-fall, Taiji-1 can be viewed as operating in the high-low satellite-to-satellite tracking mode of a gravity recovery mission. In this work, we have selected and analyzed the one month data from Taiji-1’s observations, and developed the techniques to resolve the long term interruptions and disturbances in the data due to the scheduled technology demonstration experiments. The first global gravity model TJGM-r1911, that independently derived from China’s own satellite mission, is successfully built from Taiji-1’s observations. Compared with gravity models from CHAMP and other satellite gravity missions, the accuracy discrepancies exist, which is mainly caused by the data discontinuity problem. As the extended free-falling phase been approved, Taiji-1 could serve as a gravity recovery mission for China since 2022 and it will provide us the independent measurement of both the static and the monthly time-variable global gravity field.

The Micro-Deformation Monitoring Based on the All-Fiber-Optic Sensor in Taiji Program

The Micro-Deformation Monitoring Based on the All-Fiber-Optic Sensor in Taiji Program

Inter-spacecraft offset frequency setting strategy in the Taiji program.

For controlling the beat frequency of heterodyne interferometry so that the Taiji program can detect gravitational waves in space, an offset frequency setting strategy based on a linear programming algorithm is proposed. Considering factors such as Doppler frequency shift, phase-locking scheme, laser relative intensity noise, and phase detector bandwidth, inter-spacecraft offset frequency setting results suitable for the Taiji program are obtained. During the six years of running the detection process, the use of frequency bounds in the range of [5 MHz, 25 MHz] showed that offset frequencies will remain unchanged for a maximum of 1931 days. If the upper and lower bounds are adjusted, and the relative motion between spacecraft is further constrained, the offset frequencies do not need to change during the time of the mission. These results may provide insights into selecting the phase detector and designing operation parameters such as orbit and laser modulation frequency in the Taiji program.

Ground electronics verification of inter-satellites laser ranging in the Taiji program

The predecessor of China Optics was China Optics and Applied Optics Digest, which was founded in 1985. At that time, it was the only retrieval journal in the field of optics in China. At the end of 2008, China Optics and Applied Optics Digest was renamed

Recent Status of Taiji Program in China

Recent Status of Taiji Program in China

A low-noise analog frontend design for the Taiji phasemeter prototype.

The Taiji program plans to utilize the laser interferometer to measure the movement at the picometer level between free-floating test masses. As the phase readout equipment, the phasemeter needs to obtain the beat note with an accuracy of μrad/Hz. The main source of noise in the phasemeter is the analog frontend of the analog to digital converter. A self-designed phasemeter prototype with a low-noise analog frontend, which includes the theme of the pilot tone correction, has been developed and tested for the Taiji program in this Note. The experimental results show that the performance of the developed phasemeter can satisfy the Taiji sensitivity requirement in the whole frequency range. The sensitivity of the board can reach 0.5 μrad/Hz in the frequency range of 0.1-1Hz. Therefore, the prototype gives us a good model for the fully functional Taiji phasemeter.

Taiji program in space for gravitational universe with the first run key technologies test in Taiji-1

Taiji program in space for gravitational universe with the first run key technologies test in Taiji-1

Ground performance tests and evaluation of RF ion microthrusters for Taiji-1 satellite

The “Taiji-1” satellite is a test satellite for the verification of those key technologies involved in the “Taiji Program in Space”, China’s space gravitational wave detection project; and the spacecraft drag-free control technology is one of its key technologies used to improve the microgravity level of spacecraft. Thus, a demand for a high-precision and continuously adjustable micronewton-level thrust has been proposed on the spacecraft micro-propulsion system. In allusion to such a task, a set of micronewton-level RF ion propulsion system was designed based on the principle of self-sustained discharge of RF plasma so as to conduct studies on the parameter optimization and engineering of RF ion thruster, and an engineering prototype of the micronewton-level continuously adjustable RF ion thruster was successfully developed to meet the design index requirements. The operating parameters have been solidified through further studies on the extreme operating conditions of the engineering prototype, and a series of ground simulation tests of space environment were successfully passed. The ground test and calibration experiment results of the micro-propulsion engineering prototype show that the engineering prototype has fully met the requirements of the Taiji-1 mission, thus having laid a solid foundation for the successful space verification of the key technologies for the “Taiji-1” satellite.

System modeling in data processing of Taiji-1 mission

Taiji-1 is the first technology demonstration satellite of the Taiji Program in Space, which, served as the pre-PathFinder mission, had finished its nominal science operational phase and successfully accomplished the mission goal. The gravitational reference sensor (GRS) on-board Taiji-1 is one of the key science payloads that coupled strongly to other instruments, sub-systems and also the satellite platform itself. Fluctuations of the physical environment inside the satellite and mechanical disturbances of the platform generate important noises in the GRS measurements, therefore their science data can also be used to evaluate the performance of the [Formula: see text]-thrusters and the stability of the platform. In this work, we report on the methods employed in Taiji-1 GRS data processing in the systematical modelings of the spacecraft orbit and attitude perturbations, mechanical disturbances, and internal environment changes. The modeled noises are then removed carefully from the GRS science data to improve the data quality and the GRS in-orbit performance estimations.