Preliminary design and analysis of telescope for space gravitational wave detection
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摘要:引力波的直接观测已开启引力波天文学的新篇章，爱因斯坦的百年预言终获证实。空间引力波探测器使得探测0.1 mHz~1 Hz频段丰富的引力波源成为可能，与地面引力波探测器互为补充，才可实现更加宽广波段的引力波探测，揭开宇宙早期的更多秘密。空间 干涉引力波探测采用外差干涉测量技术，测量间距百万公里的两自由悬浮测试质量间10 pm量级的变化量。望远镜是 干涉测量系统的重要组成部分，1 pm的光程稳定性及苛刻的杂散光要求，不同于传统的几何成像望远镜。本文根据空间太极计划任务需求，对望远镜的功能及技术要求进行了分析，并完成了原理样机的初步方案设计，针对百万公里远场波前分布，分析了望远镜系统的敏感性，同时完成了在轨光机热集成仿真，为后面原理样机的研制奠定了技术基础。Abstract:The direct detection of gravitational waves opens up a new era of gravitational wave astronomy, and 100-year-old prediction on gravitational wavers by Einstein have been confirmed ultimately. The space gravitational wave detector makes it possible to detect rich sources of gravitational waves in the 0.1 mHz-1 Hz band. The space gravitational wave detector and the ground gravitational wave detector complement each other, and the combination of the two methods can realize the detection of gravitational waves in a broader band, thus uncovering more secrets of the early universe. Spatial laser interferometry gravitational wave detection uses heterodyne interferometry to measure changes in the order of 10 pm between two free-floating test masses that are millions of kilometers apart. Telescope is an important part of the laser interferometry system. Unlike the traditional geometrical imaging telescope, the telescope of the laser interferometry system shall meet the requirements of optical path stability for 1 pm and that of a harsh stray light. Based on the mission requirements of the Taiji Program in Space, this paper analyzes the functions and technical requirements of the telescope and completes the preliminary design of the principle prototype. In this paper, the sensitivity of the telescope system is analyzed according to the wavefront distribution in the far field of one million kilometers. At the same time, the thermal integration simulation in orbit is completed, which lays the technical foundation for the development of the subsequent principle prototypes.
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图 2LISA轨道及航天器编队示意图，航天器组成的平面与黄道面夹角约为60°, 航天器星座质心落后地球约20°，航天器之间的距离为5×106km[3]
Figure 2.Schematic diagram of LISA orbit and spacecraft formation. The angle between the spacecraft plane and the ecliptic plane is about 60°. The constellation trails earth by about 20°, and the distance between spacecraft is 5×106km[3]
图 3引力波经过测试质量组成的三角形编队。三角形编队中3个测试质量代表3个LISA航天器，红色臂长的时变量即需要测量的引力波引起的距离变化量[1]
Figure 3.Gravity waves pass through the triangle formation formed by the test masses. The three test masses in formation represent three LISA spacecraft, the time variable of the red arm length represents the distance variation caused by the gravitational wave that needs to be measured
图 7系统出瞳处波前质量，RMS值0.013λ
Figure 7.Wavefront performance at exit-pupil of telescope, RMS is 0.013λ
图 11发射望远镜波前λ/60，5×106km处强度(a)和波前(b)分布图
Figure 11.Diagrams of intensity and wavefront distributions at 5×106km with telescope wave front ofλ/60
图 12次镜M2在X方向偏心0.5 μm时5×106km处波前分布和变化量
Figure 12.Wavefront distribution and variation at 5×106km withXdecenter of M2 of 0.5 μm
图 13次镜M2在Y方向偏心0.5 μm时5×106km处波前分布和变化量
Figure 13.Wavefront distribution and variation at 5×106km withYdecenter of M2 of 0.5 μm
图 14次镜M2在Z方向偏心0.5 μm时5×106km处波前分布和变化量
Figure 14.Wavefront distribution and variation at 5×106km withZdecenter of M2 of 0.5 μm
图 15次镜M2绕X轴旋转0.4″时5×106km处波前分布和变化量
Figure 15.Wavefront distribution and variation at 5×106km with M2 rotating aroundXby 0.4″
图 16次镜M2绕Y轴旋转0.4″时5×106km处波前分布和变化量
Figure 16.Wavefront distribution and variation at 5×106km with M2 rotating aroundYby 0.4″
图 17次镜M2绕Z轴旋转0.4″时5×106km处波前分布和变化量
Figure 17.Wavefront distribution and variation at 5×106km with M2 rotating aroundZby 0.4″
图 18次镜M2半径变化1 μm时5×106km处波前分布和变化量
Figure 18.Wavefront distribution and variation at 5×106km with radius change of M2 of 1 μm
图 19次镜M2二次曲面系数变化0.001时5×106km处波前分布和变化量
Figure 19.Wavefront distribution and variation at 5×106km with conic change of M2 of 0.001
表 1望远镜关键技术指标
Table 1.Key technology requirements of telescope
Characteristics Requirements Aperture 20 cm Optical efficiency ≥0.853 Field of view acquisition mode 400μrad full angle Science mode(out of plane) ±7 μrad (in plane) ±4.2 μrad in-plane Optical path length stability 
Magnification 40 Far-field wavefront quality λ/20 
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表 2望远镜结构参数变化量
Table 2.Variations of telescope parameters
Type of variations Variations M1 M2 M3 M4 position Xdecenter/μm 0.5 0.5 0.5 0.5 Ydecenter/μm 0.5 0.5 0.5 0.5 Zdecenter/μm 0.5 0.5 0.5 0.5 Xtilt/(″) 0.4 0.4 0.4 0.4 Ytilt/(″) 0.2 0.4 0.4 0.4 Ztilt/(″) 0.4 0.4 - - surface Radius/μm 1 1 1 1 Conic 0.00001 0.001 - - 下载:
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表 35×106km处远场波前变化量PV值
Table 3.Far field wavefront variations(PV) at 5×106km
Type of variations Variations Variation PV(λ) M1 M2 M3 M4 position Xdecenter/μm 8.26×10-6 1.12×10-6 1.33×10-6 1.47×10-6 Ydecenter/μm 4.34×10-7 5.35×10-8 1.05×10-7 2.93×10-6 Zdecenter/μm 4.04×10-7 1.47×10-6 1.31×10-7 2.70×10-8 Xtilt/(″) 3.33×10-6 1.31×10-6 1.10×10-6 6.16×10-7 Ytilt/(″) 2.42×10-7 5.91×10-8 7.94×10-7 6.61×10-8 Ztilt/(″) 3.46×10-9 1.30×10-6 - - surface Radius/mm 8.86×10-7 1.87×10-6 1.26×10-7 1.99×10-8 Conic 4.07×10-7 1.06×10-6 - - 下载:
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表 4各反射镜的平动和转动
Table 4.Translaton and rotation of mirrors
M1 M2 M3 M4 PV/nm 45.721 1.663 0.121 0.711 RMS/nm 8.927 0.503 0.032 0.183 ΔX/μm 0.001 -0.369 -0.005 -0.024 ΔY/μm -0.403 0.977 0.497 -1.271 ΔZ/μm 0.855 1.407 0.540 -0.988 Δθx/(″) -0.363 -0.009 2.570 2.063 Δθy/(″) 0.104 -0.403 0.011 0.027 下载:
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