Development and test of the Point Ahead Angle Mechanism for space gravitational wave detection

  Objective   To detect low-frequency gravitational waves, it is necessary to eliminate the interference of geo-noise and build a laser interference gravitational wave detection device in space. Taiji, LISA, Tianqin and other space gravitational wave detection missions have been planning to achieve pm-sensitivity on the arm length of several million kilometers to meet the requirements of gravitational wave detection. Because of orbit evolution and time delay in the interferometer arms, the direction of transmitted laser beam changes, consequently, a remote telescope cannot receive the laser beam to complete the inter-satellite laser interference. Aiming at the need for the point ahead angle of the emission beam, a beam pointing mechanism that provides the point ahead angle in the laser interference link is designed and developed for the space gravitational wave detection device, called the Point Ahead Angle Mechanism.

  Methods   Based on the design concept of aligning the rotary axis on the mirror surface, the Point Ahead Angle Mechanism employs the structural form of flexible hinges and lever (Fig.2), and the control scheme of piezoelectric ceramic self-closing loops to achieve one-dimensional high-precision beam rotation (Fig.3). Mechanical properties are verified by the simulation analysis (Fig.4-5). Rotary range of the mechanism is verified by the simulation analysis (Fig.6). Under the condition of normal temperature and pressure with a relative humidity of 60%, the rotary characteristic test is carried out by using an autocollimator (Fig.7). And under the conditions of normal temperature (24 ℃) and vacuum environment (less than 50 Pa), a special interferometer is built to test the optical path difference (Fig.9).

  Results and Discussions   A series of experiments are conducted on the mechanism, and the results show that the rotary range of the mechanism is \rm709.4\; \textμ \rmrad , rotary accuracy is \rm0.44\; \textμ \rmrad , and the results meet the requirements (Fig.8). The optical path differences are better than 10\; \mathrmpm / \sqrt\mathrmHz when the frequency is between 1 Hz and 10 Hz, and the results meet the requirement (Fig.10). But when the frequency was between 1 mHz and 1 Hz, the optical path differences are greater than 10 \;\mathrmpm / \sqrt\mathrmHz. After simulation analysis, they are mainly related to the influence of temperature changes in the experimental environment (Fig.11). This is also the direction of further research. In short, it is proven that the principal design of the mechanism is feasible, and it is a reasonable reference for achieving ultra-stable and high-precision beam rotation.

  Conclusions   In this study, the Point Ahead Angle Mechanism for space gravitational wave detection is designed and developed, and the corresponding index tests are completed, which verify the rationality of the mechanism design. The mechanism is a one-dimensional and two-way rotation, the maximum rotary range can reach about 709.4 μrad, and the rotary accuracy can reach about 0.44 μrad, all of which meet the expected design requirements. When the frequency is between 1 Hz and 10 Hz, the optical path difference caused by the mechanism is better than 10\; \mathrmpm / \sqrt\mathrmHz , and when the frequency is between 1 mHz and 1 Hz , the optical path difference is greater than 10\; \mathrmpm / \sqrt\mathrmHz . The optical path difference of the Point Ahead Angle Mechanism developed in this paper still has a gap with the foreign advanced level and design requirements, and the mechanism needs to be optimized. At the same time, the influence of temperature on the optical path difference test should be considered in further research.