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The Taiji programme is a Chinese space-based laser interferometer gravitational wave detection mission and the differential wavefront sensing (DWS) technique is introduced to reduce the effect of t...

Most of the space gravitational wave detection missions, such as the Taiji program, use space-based laser interferometer to sense the gravitational waves. However, to obtain the interference signal, the inter-satellite laser acquisition scheme is firstly required to establish the laser link. Traditional acquisition sensors are CCD cameras, which cause a serious heating problem and call for high alignment precision. To avoid these questions, a high-speed, high-precision, fully automatic acquisition scheme with quadrant photodetectors (QPD) is proposed in this paper. Incoherent measurement method of the QPD is introduced to fulfill high-speed acquisition, while a dedicated imaging system is involved for automatic acquisition. Also, an improved differential power sensing (DPS) signal is developed. Combined with the down-sampling algorithm and the match filter algorithm, the acquisition scheme can achieve 1 µrad resolution with total scanning time less than 220 s.

The space-based gravitational wave detection programs, like the Laser Interferometer Space Antenna (LISA) or the Taiji program, aim to detect gravitational waves in space with a triangular constellation of three spacecraft. The unavoidable jitters of the spacecraft and the pointing will couple with the misalignment of the interfering beams into the longitudinal path length readout. This effect is called tilt-to-length (TTL) coupling, which is one of the keys to achieving the required measuring accuracy of 1 p m / H z . In terms of two phase definitions (the LISA Pathfinder (LPF) signal and the Average Phase (AP) signal), we implement the comprehensive theoretical analysis concerning the effect of aberrations on TTL coupling noise. In addition, we analytically derive that the proper lateral shift of the interfering beams relative to the detector can partly cancel out the TTL noise coupled with aberrations, especially coma and trefoil aberrations for the AP signal. Based on the above results, the meaningful guidance can be provided for the design and construction of the optical system in LISA or Taiji.

In the acquisition stage of many space applications, such as the Taiji program, the spot center of weak laser light must be accurately determined. Under weak light conditions, the precision of most traditional positioning methods is greatly affected. In this paper, we present a high-precision laser spot center positioning method based on the theoretical analysis of influence factors of precision. It is shown through experimental study that the method’s precision can fulfill the requirement of the Taiji program.

A brief progress report is presented on the interferometer prototype of the Chinese gravitational wave detection pathfinder mission. After careful consideration of the temperature fluctuation induced noise and the electronic noise, the noise spectra density of the interferometer prototype reached 100 pm / Hz at 1 mHz and achieved 15 pm / Hz in high frequency region. However, in some frequency range from 3 mHz to 30 mHz, further improvement is still needed. Possible improvement is also discussed.

The idea of using space laser interferometer to measure the relative displacement change between two satellites has been considered for space gravitational waves detection and Earth gravity filed mapping in recent years. Some investigations on the key issues of laser interferometer in our working team have been presented in this paper. An on-ground laser interferometer prototype used for the demonstration of satellite-to-satellite ranging has been constructed, which is equipped with phasemeter, laser pointing modulation and laser phase-locking control. The experimental results show that path-length measurement sensitivity of the laser interferometer reaches 200 pm/√ Hz, and phase measurement precision achieves 2π × 10− 5 rad/√ Hz, and laser pointing modulation precision is better than 80 nrad/√ Hz, and laser phase-locking control precision attains 2π × 10− 4 rad/√ Hz within the frequency regime of 1 mHz–1 Hz. All of these demonstrate that the proposed laser interferometer has very promising feasibility to meet the requirement of the Taiji, TianQin and Space Advanced Gravity Measurement (SAGM) missions which are put forward by Chinese scientists.

Taiji space gravitational wave detection utilizes the laser interferometer to convert the tiny distance change into the phase fluctuation of the beat note. As to realize the sensitivity of 1 pm/√ Hz, the phasemeter needs to calculate the phase with the precision of 2πμ rad/√ Hz in the frequency range of 0.1 mHz and 1 Hz. In this paper, we report recent progress of the phasemeter for Taiji. Noises which possibly affect the measurement sensitivity are tested and discussed, especially the sampling noise and the frequency jitter. Finally, the accuracy of the phasemeter is calibrated. The result shows that the sensitivity has reached the requirement of Taiji in the frequencies between 0.01 Hz and 1 Hz, 0.1 mHz–1 mHz. Noises in the range of 1 mHz and 0.01 Hz, which have not yet depressed well, are dominated by the clocking jitter and the thermal fluctuation.

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.

Taiji-1 satellite was successfully launched on 31 August 2019, and it has been operating normally in orbit until now. A series of in-orbit experiments were carried out with the inertial sensor, which included the micro-thrust test, drag-free control test and laser interferometer test. Comprehensive performance simulations and tests of the inertial sensor were also carried out prior to the launch of Taiji-1, including the calibration and drop-tower tests. These tests were one of the preconditions for the success of these experiments. The calibration experiments were conducted in a cave-lab using the gravity-inclination method and the scale factors of the inertial sensor along Y- and Z-axis were measured. In addition, 20 drop-tower tests were carried out in the National Microgravity Laboratory of China (NMLC) drop tower and the control stability of all the axes was tested and optimized. A simulation model was used before each test, and the results showed that an accurate simulation prior to each experiment had an important role in ensuring the efficiency and accuracy of the experiment. The circuit-gain switch was realized for the first time during the drop-tower tests. The test results indicated that the microgravity level of the NMLC drop tower could reach about 13 [Formula: see text]g0 along the horizontal axes, offering an important reference for researchers planning to conduct microgravity experiments in the NMLC drop tower.

Taiji-1, which is the first experimental satellite for space gravitational wave detection in China, relies on key technologies which include the laser interferometer, the gravitational reference sensor (GRS), the micro-thruster and the satellite platform. Similarly to the Laser Interferometer Space Antenna (LISA) pathfinder, except for the science interferometer, the optical bench (OB) of Taiji-1 contains reference and test mass (TM) interferometers. Limited by the lower mechanical strength of the carrier rocket and by the orbit environment, the OB of Taiji-1 is made of invar steel and fused silica, and it is aimed to achieve a sensitivity of the order of 100[Formula: see text]pm/[Formula: see text]. The experimental results from in-orbit tests of Taiji-1 demonstrate that the interferometer can reach a sensitivity of 30[Formula: see text]pm/[Formula: see text] in the frequency range of 0.01–10[Formula: see text]Hz, which satisfies the requirements of Taiji-1 mission.

The laser acquisition-pointing technique is one of the most important techniques for space gravitational wave detection missions, like the Taiji program and the LISA (Laser Interferometer Space Antenna) program. The laser acquisition system suppresses the laser deviation angle to 1 µrad at the receiving aperture. Corresponding to 80 times of telescope magnification, the acquisition accuracy should reach 80 µrad at the acquisition camera. In order to verify the feasibility of the laser acquisition scheme, a laser acquisition ground simulation experimental system is designed and constructed. The experimental system simulates the actual acquisition process of the Taiji from three aspects: optical path, acquisition accuracy and acquisition scanning process. In the experiment, the coupling between the laser acquisition system and the laser pointing system is considered by introducing the DWS (Differential Wave-front Sensing) technique to calibrate the reference position of the acquisition camera and read out the acquisition precision. Due to limited beam propagation distance in the ground experiment, the in-flat top properties of the transmitting beam will greatly affect the acquisition precision. Based on the analysis of the influence, an improved acquisition ground simulation scheme is introduced. The experimental results indicate that the experimental system can achieve the acquisition accuracy of sub-10 µrad magnitude at the acquisition camera. The experimental system realizes methodological demonstration of the acquisition scheme. The results offer the experimental foundation and theoretical basis for the acquisition system of the Taiji/LISA program.

A comprehensive simulation was performed to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for LISA. The result showed that the phase of the slave laser tracked well with the received transmitting light under different noise level, and the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed. This result was then confirmed by a benchtop experimental test. The required LISA noise floor was recovered from the simulation which proved the validity of the simulation program. In order to convert the noise function into real time data with random characteristics, an algorism based on Fourier transform was also invented.

The space gravitational wave (GW) antennae is more sensitive to the lower frequency GW signals compare with the ground-based GW detectors. The space mission Taiji is designed to detect the GW sources within frequencies between 0.1 mHz and 1 Hz. A preliminary study of Taiji was started in 2008. Up to now, a sophisticated mission design of Taiji have gradually taken shape. The research and development of the key technologies for Taiji is now officially launched. A brief introduction to the analysis and the pre-work of the Taiji technology are given here.

Due to high data rates and reliability, inter-satellite laser communication has developed rapidly in these days. However, the stability of the laser beam pointing is still a key technique which needs to be solved; otherwise, the beam pointing jitter noise would reduce the communication quality or, even worse, would make the inter-satellite laser communication impossible. For this purpose, a bench-top of the fine beam pointing control system has been built and tested for inter-satellite laser communication. The pointing offset of more than 100 μrad is produced by the steering mirror. With beam pointing control system turned on, the offset could be rapidly suppressed to lower than 100 nrad in less than 0.5 s. Moreover, the pointing stability can be kept at 40 nrad for yaw motion and 62 nrad for pitch motion, when the received beam jitter is set at 20 μrad.

The space laser interferometer has been considered the most promising means for detecting gravitational waves and improving the accuracy and spatial resolution of the Earth’s gravity model. An on-ground polarizing laser interferometer prototype equipped with one reference interferometer and two measurement interferometers having equal-length arms is presented in the paper. The laser interferometer prototype is designed as the demonstration of a Chinese space laser interferometer antenna in the future, of which the path-length measurement performance evaluation and preliminary noise analysis are investigated here. The results show that the path-length measurement sensitivity is better than 200 pm/Hz½ in the frequency band of 10 mHz–1 Hz, and the sensitivity of measuring the motion of a sinusoidally driven testmass is better than 100 pm within the frequency regime of 1 mHz–1 Hz. In this way, laboratory activities have demonstrated the feasibility of this prototype to measure tiny path-length fluctuations of the simulated testmass. As a next step, adopting an integrated design of optics and optical substrate to enhance the stability of the laser interferometer is being planned, and other key techniques included in the space laser interferometer such as laser pointing modulation and laser phase-locking control are to be implanted into this prototype are under consideration.

Weak-light phase locking is a key technology for Taiji space gravitational wave detection and its pathfinder mission. Previously, the phase locking was achieved by a complicated technique, which controls the frequency of the laser via a piezo-electric actuator (kHz range or more) and a temperature actuator (sub-Hz range). We propose an easy phase-locking strategy, which is based on the electro-optic modulator (EOM). Compared with the traditional way, this strategy only needs to modulate the driven voltage of the EOM, and the frequency bandwidth can cover all ranges. An experiment is also established to prove the feasibility of the method. The results show that the noises are

An alternative acquisition scheme is introduced. The principle is to modulate power of the laser at a frequency within the photodiode’s bandwidth so that the photodiode in each satellite can detect the laser signal from the other satellite incoherently. Therefore, we can disentangle the degrees of freedom, two laser pointing directions per space craft and one frequency offset. Despite the employment of downlink and uplink data transferring, the total scanning time could be reduced from several hours to 160 s.

Heterodyne laser interferometry is considered as the most promising readout scheme for future space gravitational wave detection missions, in which the gravitational wave signals disguise as small phase variances within the heterodyne beat note. This makes the phasemeter, which extracts the phase information from the beat note, the key device to this system. In this paper, a prototype of phasemeter based on digital phase-locked loop technology is developed, and the major noise sources which may contribute to the noise spectra density are analyzed in detail. Two experiments are also carried out to evaluate the performance of the phasemeter prototype. The results show that the sensitivity is achieved 2π μrad/√Hz in the frequency range of 0.04 Hz-10 Hz. Due to the effect of thermal drift, the noise obviously increases with the frequencies down to 0.1 mHz.

The present work reports on a feasibility study commissioned by the Chinese Academy of Sciences of China to explore various possible mission options to detect gravitational waves in space alternative to that of the eLISA/LISA mission concept. Based on the relative merits assigned to science and technological viability, a few representative mission options descoped from the ALIA mission are considered. A semi-analytic Monte Carlo simulation is carried out to understand the cosmic black hole merger histories starting from intermediate mass black holes at high redshift as well as the possible scientific merits of the mission options considered in probing the light seed black holes and their coevolution with galaxies in early Universe. The study indicates that, by choosing the armlength of the interferometer to be three million kilometers and shifting the sensitivity floor to around one-hundredth Hz, together with a very moderate improvement on the position noise budget, there are certain mission options capable of exploring light seed, intermediate mass black hole binaries at high redshift that are not readily accessible to eLISA/LISA, and yet the technological requirements seem to within reach in the next few decades for China.

In space laser interferometer gravitational wave (G.W.) detection missions, the stability of the laser beam pointing direction has to be kept at 10 nrad/√Hz. Otherwise, the beam pointing jitter noise will dominate the noise budget and make the detection of G.W. impossible. Disturbed by the residue non-conservative forces, the fluctuation of the laser beam pointing direction could be a few μrad/√Hz at frequencies from 0.1 mHz to 10 Hz. Therefore, the laser beam pointing control system is an essential requirement for those space G.W. detection missions. An on-ground test of such beam pointing control system is performed, where the Differential Wave-front Sensing technique is used to sense the beams pointing jitter. An active controlled steering mirror is employed to adjust the beam pointing direction to compensate the jitter. The experimental result shows that the pointing control system can be used for very large dynamic range up to 5 μrad. At the interested frequencies of space G.W. detection missions, between 1 mHz and 1 Hz, beam pointing stability of 6 nrad/√Hz is achieved.

A Chinese satellite gravity mission called SAGM (Space Advanced Gravity Measurements) is now taken into consideration. To meet its designed requirement, the measurement precision of the laser ranging system used to measure the inter-satellite distance change has to be better than 100nm/Hz1/2 within a broad bandwidth from 0.1 mHz to 1 Hz. An equal arm heterodyne Mach-Zehnder interferometer has been built on ground to demonstrate the measurement principle of a laser ranging system, which potentially can be used for both SAGM and future GW (gravitational wave) space antennas. Because of the equal arm length, the laser frequency noise has been significantly suppressed in the interferometer. Thus, the sensitivity better than 1nm/Hz1/2 in a frequency range of 0.15 mHz–0.375 Hz has been achieved. The result shows that the proposed methodology has very promising feasibility to meet the requirements of SAGM and of GW space antennas as well.