The Research On The Tilt To Length Coupling Noise In Inter-satellite Interference Link For The Space-based Gravitational Wave Detection

In the space gravitational wave detection represented by the Taiji Program,three spacecraft form an equilateral triangle,and each spacecraft is equipped with two tele-scopes.While the telescope receives the beam,it emits the local beam to the far space-craft through the free transmission of millions of kilometers.Even with such a long inter-satellite laser interference link,the accuracy requirements for distance change mea-surement are still extremely demanding,and the total measurement displacement accu-racy needs to be in the 10^-12m order.In the space environment,the attitude of the spacecraft will inevitably shake due to the disturbance of the solar wind,solar radiation,and non-conservative forces.This kind of jitter will cause the beam jitter when the tele-scope receives or emits the beam.Due to the processing,assembly and adjustment error of the telescope and the temperature gradient in orbit,the wavefront of the beam will be severely distorted after passing through the telescope system.When the receiving beam and the local beam are used for interferometric ranging,the mismatched wavefront be-tween the two interfering beams will coupled with jitter to cause additional optical path noise.At the same time,when the emitted beam is expanded by the telescope,the wave-front distortion of the beam coupled with the pointing jitter between the two spacecraft and will also cause additional optical path noise.The above two kinds of noise are col-lectively referred to as the tilt to length coupling noise(TTL)of the inter-satellite laser link.In view of the above-mentioned research content,we first investigates the current research status of laser interferometric gravitational wave detection and the related tech-nology research of TTL coupling noise.Then,based on the characteristics of the space gravitational wave detection system,a simulation link for the space interferometric op-tical system is established,which realizes the optical modeling and optical-mechanical thermal integration simulation link for the interferometric signal.And use the design and engineering of an all-glass fiber collimator to verify the effectiveness of the link.Aiming at the TTL coupling noise of the scientific interferometer in the inter-satellite laser link,firstly,a detailed theoretical analysis of the interference model of the flat-top beam and the Gaussian beam is carried out,and a new method eliminating the TTL coupling noise is proposed based on the analytical solution.And then Fringe Zernike polynomials are used to fit wavefront error to analyze the optical path noise under LPF(LISA Pathfinder)optical path definition and AP(Average Phase)optical path definition.The results show that for the LPF signal,the wavefront error between the two interfering beams needs to be at least better than/20 to make the average value of 10,000 Monte Carlo samples lower than the required 25 pm/?rad.But for AP optical path signals,the wavefront error can be relaxed to be/10.For the far-field beam transmission,the theoretical model of the optical path noise of the far-field beam transmission is first established.Based on it,the analysis of the far-field phase noise of the exit pupil wavefront of the prototype telescope and the influence of wavefront error on far-field phase noise are completed.The results show that in 10⁴random samples,if the average value of the pointing jitter optical path noise is needed to be less than 0.1 pm/nrad,the RMS of the exit pupil wavefront error of the telescope needs to be better than/50,if the average value is less than 1 pm/nrad,the RMS needs to be better than 0.07.Aiming at the wavefront distortion caused by the thermal deformation of the tele-scope in orbit temperature gradient,firstly,it is found that the C/Si C material has the best in-orbit thermal performance by analyzing the telescope frame made of different mate-rials in the orbit environment.Therefore,a prototype of the telescope support frame was designed and processed using C/Si C materials.A high-precision thermal defor-mation interferometry system that can measure multiple channels at the same time is designed and built.And the system is used to conduct multiple thermal expansion ex-perimental measurements on the telescope support frame prototype.The results show the axial CTE of the C/Si C material is approximately-8.3×10^-7/K,the horizontal CTE is approximately 3.3×10^-5/K.The designed picometer-level multi-channel ther-mal deformation interferometry system designed can be used for the subsequent thermal performance measurement of the telescope prototype.On the basis of the above research,the transmission model of the full link and the transfer function of the TTL coupling noise are established.And the imaging system that can suppress the TTL coupling noise is optimized in the scientific interferometer.Based on the above transmission model,the magnitude of the TTL couping noise of the entire inter-satellite interference link under the ideal design and under the on-orbit temperature gradient is analyzed.The average value of 10⁴random samples under the ideal design is about 3?10^-3pm/nrad,the average value of 10⁴random samples under the on-orbit temperature gradient is about 0.05 pm/nrad.The results show that the designed inter-satellite interference optical system meets the system requirements.