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摘要
文章主要围绕空间引力波探测中超长空间链路传输部分进行介绍，概述了目前国内外星间传输仿真时采用的计算方法，以及指向抖动引起的相位噪声分析方法。相较于地基引力波探测，空间引力波探测可以有效降低噪声，增加干涉臂长度，从而实现更高精度、更低频率的探测。在长达数百万公里的传输距离，以及皮米量级数值模拟的精度要求下，需要考虑指向角变化引起的相位噪声。研究表明，在2.5×109 m的传输距离下，离焦和像散是影响指向抖动噪声的主要像差。通常情况下，相位驻点位置与原点位置存在一定偏离，需要对望远镜角度进行调整，才能使相位噪声最小化。在相位驻点位置进行引力波探测，可以有效降低相位噪声，并降低望远镜出瞳波前的质量要求。而大的离焦像差与小的彗差可以使相位驻点接近光轴，提高接收到的激光功率。
Abstract
This paper mainly introduces the development of space gravitational wave transmission and laser propagation in space gravitational wave detection. We profile the calculation methods used in the simulation of laser propagation and jitter noise in space-based laser interferometry. Compared with ground detection, space gravitational wave detection can effectively reduce noise and increase the length of the interference arm to realize high-precision gravitational wave detection. Under the distance of millions of kilometers and the precision requirements of the picometer level, it is necessary to consider the phase noise caused by pointing jitter with the telescope. Research has shown that defocus and astigmatism are the main aberrations affecting jitter noise at a distance of 2.5×109 m. There is a deviation between the phase stationary point and the origin position. To minimize the phase noise, the telescope angle needs to be adjusted. The gravitational wave detection at the phase stationary point can effectively reduce the phase noise and the requirements of the telescope exit pupil wavefront RMS. The large defocus and small coma can make the phase stationary point close to the optical axis and increase the received laser power.
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Key words:
- gravitational wave detection /
- space propagation /
- jitter noise /
- phase stationary point
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Overview
Overview: Compared with ground gravitational wave detection, space gravitational wave detection can avoid the low-frequency noise caused by ground vibration and the interference of climate change on the transmission. The space environment can also greatly increase the arm length of laser interference to achieve high-precision gravitational wave detection. However, the ultra-long inter-satellite link transmission distance also puts forward extremely high requirements for pointing accuracy and dynamic measurement capabilities. At a transmission distance of millions of kilometers, the detection accuracy needs to reach the picometer level.
To minimize the influence of noises on the detection, we must simulate the system with high precision. The simulation of inter-satellite transmission can be realized by Hermite Gaussian beam fitting, Fourier transform or numerical integration. The plasma has little effect on inter-satellite transmission under most circumstances. It will thus not affect the detection. Pointing jitter noise is the focus of research in inter-satellite transmission. In the actual system, there are aberrations in the exit pupil wavefront of the telescope, so the far-field wavefront is no longer close to the ideal spherical wave. An angle offset of 10 nrad will cause a position offset of tens of meters in the far field. In the analysis, the far-field origin is usually taken as the object, and the phase part of the telescope exit pupil complex amplitude is expanded to simplify the model in a Taylor series. The coupling coefficients between the far field and the exit pupil Zernike aberration of the telescope can be calculated by the integral calculation or the least square fitting. To satisfy the simulation accuracy of the picometer level, the Taylor expansion and the coupling coefficients should retain at least the second-order term.
Taking the LISA system as a reference, the phase noise of the inter-satellite transmission needs to be less than 1 pm. Research has shown that the defocus and the astigmatism are the main aberrations affecting jitter noise at a distance of 2.5×109 m. There is a deviation between the phase stationary point and the origin position. To minimize the phase noise, the telescope angle needs to be adjusted. The gravitational wave detection at the phase stationary point can effectively reduce the phase noise and the requirements of the telescope exit pupil wavefront RMS. The large defocus and small coma can make the phase stationary point close to the optical axis and increase the received laser power.
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图 4 数值积分与高斯光束解析解相位对比
Figure 4. The comparison between numerical integration method and analytical expression of Gaussian beam
图 6 700 nrad静态角下，耦合系数γ与泽尼克项数的关联
Figure 6. The correlation between the coupling coefficient γ and Zernike indices at 700 nrad static angle.
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