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.

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.

Using DWS Optical Readout to Improve the Sensitivity of Torsion Pendulum.

In space gravitational wave detection missions, a drag-free system is used to keep the test mass (TM) free-falling in an ultralow-noise environment. Ground verification experiments should be carried out to clarify the shielding and compensating capabilities of the system for multiple stray force noises. A hybrid apparatus was designed and analyzed based on the traditional torsion pendulum, and a technique for enhancing the sensitivity of the torsion pendulum system by employing the differential wavefront sensing (DWS) optical readout was proposed. The readout resolution experiment was then carried out on an optical bench that was designed and established. The results indicate that the angular resolution of the DWS signal in optical readout mode can reach the level of 10 nrad/Hz1/2 over the full measurement band. Compared with the autocollimator, the sensitivity of the torsional pendulum is noticeably improved, and the background noise is expected to reach 4.5 × 10-15 Nm/Hz1/2@10 mHz. This method could also be applied to future upgrades of similar systems.

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.

Two-step algorithm for removing the rotationally asymmetric systemic errors on grating lateral shearing interferometer.

The grating lateral shearing interferometer may achieve ultra-high accuracy absolute testing after eliminating the systemic errors from the interferometer itself and the orthogonality problem between two shearing directions. Aiming at the interferometer, we proposed a two-step algorithm for removing the rotationally asymmetric systemic errors from our shearing setup. This rotation method provides a new approach for acquiring the wavefront aberration by choosing the rotation angles with the minimum decentration and to satisfy the immune of systemic errors at the same time. Simulation and experiment verified that it is more propitious to eliminate the systemic errors when it is applied to our shearing setup.

An 11-frame phase shifting algorithm in lateral shearing interferometry.

In order to eliminate zeroth order effect and to make the phase shifting algorithm insensitive to phase shifting error, an 11-frame phase shifting algorithm is proposed in this paper. The analytical expression of phase-restoration error function is derived. The principle of phase shifting error compensation and the capability of suppressing zeroth order effect are explained, in comparison of existing algorithm. The analytical results show that this algorithm's phase-restoration error is proportional to sine of double shearing phase and to biquadratic of phase shifting error. Finally, we generate the interference patterns of 11-frame algorithm and existing algorithm, restore the shearing phases and calculate the phase-restoration errors by simulations. The simulation results verify the theoretical analyses.