Design theory and method of off-axis four-mirror telescope for space-based gravitational-wave mission

Fan Zichao; Tan Hao; Mo Yan; Wang Haibo; Zhao Lujia; Ji Huiru; Jiang Zhiyu; Peng Ruyi; Fu Liping; Ma Donglin

doi:10.12086/oee.2023.230194

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Fan Z C, Tan H, Mo Y, et al. Design theory and method of off-axis four-mirror telescope for space-based gravitational-wave mission[J]. Opto-Electron Eng, 2023, 50(11): 230194. doi: 10.12086/oee.2023.230194

Citation:

Fan Z C, Tan H, Mo Y, et al. Design theory and method of off-axis four-mirror telescope for space-based gravitational-wave mission[J]. Opto-Electron Eng, 2023, 50(11): 230194. doi: 10.12086/oee.2023.230194

Design theory and method of off-axis four-mirror telescope for space-based gravitational-wave mission

1.
School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
2.
School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
3.
Shenzhen Huazhong University of Science and Technology, Shenzhen, Guangdong 518057, China
4.
The National Space Science Center (NSSC) of the Chinese Academy of Sciences (CAS), Beijing 100190, China

Fund Project: Project supported by the National Natural Science Foundation of China (12274156), Technology and Innovation Commission of Shenzhen Municipality (JCYJ20210324115812035), and Key Research Program of the Chinese Academy of Sciences (JCPYJJ-22007)

More Information

^*Corresponding author: madonglin@hust.edu.cn

Received Date 08 August 2023

Revised Date 18 October 2023

Accepted Date 19 October 2023

Published Date 29 December 2023

Abstract

Abstract

The telescopes for space-based gravitational wave detection are used to transmit the laser beam between spacecraft to support the precise interference measurement system. Therefore, the optical path stability of the telescope has become a crucial technical parameter. In this system, pupil aberrations provide deeper insights compared to traditional image plane aberrations in understanding optical path stability requirements, evaluating telescope imaging quality, and suppressing tilt-to-length coupling noise. Based on the theory of traditional imaging aberration and pupil aberration theory, the initial structure of the telescope is established, and the automatic correction of pupil aberration and image plane aberration is achieved through macro programming in the commercial optical software Zemax, thus achieving the design of a high-performance spaceborne telescope. Simulation results demonstrate that the design can meets the requirements of the TianQin mission.
- space gravitational wave detection /
- optical telescope design /
- wavefront error /
- optical length noise

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References

[1]	Abbott B P, Abbott R, Abbott T D, et al. Observation of gravitational waves from a binary black hole merger[J]. Phys Rev Lett, 2016, 116(6): 061102. doi: 10.1103/PhysRevLett.116.061102 CrossRef Google Scholar
[2]	Acernese F, Agathos M, Agatsuma K, et al. Advanced Virgo: a second-generation interferometric gravitational wave detector[J]. Class Quantum Gravity, 2015, 32(2): 024001. doi: 10.1088/0264-9381/32/2/024001 CrossRef Google Scholar
[3]	Wanner G. Complex optical systems in space: numerical modelling of the heterodyne interferometry of LISA Pathfinder and LISA[D]. Hannover: Leibniz University Hannover, 2010: 1–106. Google Scholar
[4]	Danzmann K. LISA mission overview[J]. Adv Space Res, 2000, 25(6): 1129−1136. doi: 10.1016/S0273-1177(99)00973-4 CrossRef Google Scholar
[5]	Cornelisse J W. Lisa mission and system design[J]. Class Quantum Gravity, 1996, 13(11A): A251−A258. doi: 10.1088/0264-9381/13/11A/034 CrossRef Google Scholar
[6]	Kawamura S, Ando M, Seto N, et al. Current status of space gravitational wave antenna DECIGO and B-DECIGO[J]. Prog Theor Exp Phys, 2021, 2021(5): 05A105. doi: 10.1093/ptep/ptab019 CrossRef Google Scholar
[7]	Luo J, Chen L S, Duan H Z, et al. TianQin: a space-borne gravitational wave detector[J]. Class Quantum Gravity, 2016, 33(3): 035010. doi: 10.1088/0264-9381/33/3/035010 CrossRef Google Scholar
[8]	Luo Z R, Wang Y, Wu Y L, et al. The Taiji program: a concise overview[J]. Prog Theor Exp Phys, 2021, 2021(5): 05A108. doi: 10.1093/ptep/ptaa083 CrossRef Google Scholar
[9]	Schuster S, Wanner G, Tröbs M, et al. Vanishing tilt-to-length coupling for a singular case in two-beam laser interferometers with Gaussian beams[J]. Appl Opt, 2015, 54(5): 1010−1014. doi: 10.1364/AO.54.001010 CrossRef Google Scholar
[10]	Wanner G, Heinzel G, Kochkina E, et al. Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams[J]. Opt Commun, 2012, 285(24): 4831−4839. doi: 10.1016/j.optcom.2012.07.123 CrossRef Google Scholar
[11]	Schuster S, Tröbs M, Wanner G, et al. Experimental demonstration of reduced tilt-to-length coupling by a two-lens imaging system[J]. Opt Express, 2016, 24(10): 10466−10475. doi: 10.1364/OE.24.010466 CrossRef Google Scholar
[12]	Sasso C P, Mana G, Mottini S. The LISA interferometer: impact of stray light on the phase of the heterodyne signal[J]. Class Quantum Gravity, 2019, 36(7): 075015. doi: 10.1088/1361-6382/ab0a15 CrossRef Google Scholar
[13]	Spector A, Mueller G. Back-reflection from a Cassegrain telescope for space-based interferometric gravitational-wave detectors[J]. Class Quantum Gravity, 2012, 29(20): 205005. doi: 10.1088/0264-9381/29/20/205005 CrossRef Google Scholar
[14]	Sankar S R, Livas J. Optical alignment and wavefront error demonstration of a prototype LISA telescope[J]. Class Quantum Gravity, 2020, 37(6): 065005. doi: 10.1088/1361-6382/ab6adf CrossRef Google Scholar
[15]	Livas J C, Arsenovic P, Crow J A, et al. Telescopes for space-based gravitational wave missions[J]. Opt Eng, 2013, 52(9): 091811. doi: 10.1117/1.OE.52.9.091811 CrossRef Google Scholar
[16]	Mi Z X, Li Z X, Zhang X D. Construction of a compact off-axis three-mirror reflective system[J]. Appl Opt, 2022, 61(9): 2424−2431. doi: 10.1364/AO.450953 CrossRef Google Scholar
[17]	Xu S, Cui Z, Qi B. Compensation factors for 3rd order coma in three mirror anastigmatic (TMA) telescopes[J]. Opt Express, 2018, 26(1): 298−310. doi: 10.1364/OE.26.000298 CrossRef Google Scholar
[18]	Ji H R, Zhu Z B, Tan H, et al. Design of a high-throughput telescope based on scanning an off-axis three-mirror anastigmat system[J]. Appl Opt, 2021, 60(10): 2817−2823. doi: 10.1364/AO.421998 CrossRef Google Scholar
[19]	Sankar S R, Livas J C. Optical telescope design for a space-based gravitational-wave mission[J]. Proc SPIE, 2014, 9143: 914314. doi: 10.1117/12.2056824 CrossRef Google Scholar
[20]	田思恒, 黄永梅, 徐杨杰, 等. 利用离焦光斑的离轴望远镜失调校正方法研究[J]. 光电工程, 2023, 50(7): 230040. doi: 10.12086/oee.2023.230040 CrossRef Google Scholar Tian S H, Huang Y M, Xu Y J, et al. Study of off-axis telescope misalignment correction method using out-of-focus spot[J]. Opto-Electron Eng, 2023, 50(7): 230040. doi: 10.12086/oee.2023.230040 CrossRef Google Scholar
[21]	McNamara P W. Development of optical techniques for space-borne laser interferometric gravitational wave detectors[D]. Glasgow: University of Glasgow, 1998: 1–144. Google Scholar
[22]	Kim D, Choi H, Brendel T, et al. Advances in optical engineering for future telescopes[J]. Opto-Electron Adv, 2021, 4(6): 210040. doi: 10.29026/oea.2021.210040 CrossRef Google Scholar
[23]	Livas J, Sankar S, West G, et al. eLISA telescope in-field pointing and scattered light study[J]. J Phys Conf Ser, 2017, 840: 012015. doi: 10.1088/1742-6596/840/1/012015 CrossRef Google Scholar
[24]	牛帅旭, 蒋晶, 唐涛, 等. 望远镜中扰动抑制的Youla控制器优化设计[J]. 光电工程, 2020, 47(9): 190547. doi: 10.12086/oee.2020.190547 CrossRef Google Scholar Niu S X, Jiang J, Tang T, et al. Optimal design of Youla controller for vibration rejection in telescopes[J]. Opto-Electron Eng, 2020, 47(9): 190547. doi: 10.12086/oee.2020.190547 CrossRef Google Scholar
[25]	Wang Z, Yu T, Zhao Y, et al. Research on telescope TTL coupling noise in intersatellite laser interferometry[J]. Photonic Sens, 2020, 10(3): 265−274. doi: 10.1007/s13320-019-0574-5 CrossRef Google Scholar
[26]	Zhao Y, Shen J, Fang C, et al. Far-field optical path noise coupled with the pointing jitter in the space measurement of gravitational waves[J]. Appl Opt, 2021, 60(2): 438−444. doi: 10.1364/AO.405467 CrossRef Google Scholar
[27]	Lehan J P, Howard J M, Li H, et al. Pupil aberrations in the LISA transceiver design[J]. Proc SPIE, 2020, 11479: 114790D. doi: 10.1117/12.2566373 CrossRef Google Scholar
[28]	ESA/SRE 2011 LISA assessment study report (Yellow Book)[EB/OL]. (2011−02)[2023−06]. https://sci.esa.int/documents/35005/36499/1567258681608-LISA_YellowBook_ESA-SRE-2011–3_Feb2011.pdf. Google Scholar
[29]	Mahajan V N. Strehl ratio for primary aberrations in terms of their aberration variance[J]. J Opt Soc Am, 1983, 73(6): 860−861. doi: 10.1364/JOSA.73.000860 CrossRef Google Scholar
[30]	Livas J C, Sankar S R. Optical telescope system-level design considerations for a space-based gravitational wave mission[J]. Proc SPIE, 2016, 9904: 99041K. doi: 10.1117/12.2233249 CrossRef Google Scholar
[31]	Chwalla M, Danzmann K, Barranco G F, et al. Design and construction of an optical test bed for LISA imaging systems and tilt-to-length coupling[J]. Class Quantum Gravity, 2016, 33(24): 245015. doi: 10.1088/0264-9381/33/24/245015 CrossRef Google Scholar
[32]	Gross H. Handbook of Optical Systems[M]. Weinheim: Wiley-VCH, 2005: 1–49. Google Scholar
[33]	Sasián J. Theory of sixth-order wave aberrations[J]. Appl Opt, 2010, 49(16): D69−D95. doi: 10.1364/AO.49.000D69 CrossRef Google Scholar
[34]	Fan Z C, Zhao L J, Cao S Y, et al. High performance telescope system design for the TianQin project[J]. Class Quantum Gravity, 2022, 39(19): 195017. doi: 10.1088/1361-6382/ac8b57 CrossRef Google Scholar
[35]	Lakshminarayanan V, Fleck A. Zernike polynomials: a guide[J]. J Mod Opt, 2011, 58(7): 545−561. doi: 10.1080/09500340.2011.554896 CrossRef Google Scholar

Overview

Overview

The TianQin project is a planned space-based gravitational wave observatory in China, consisting of a formation of three spacecraft, each equipped with two telescopes for laser beam transmission and reception. The TianQin mission utilizes heterodyne interferometry to achieve precise distance measurements between test masses. The optical telescopes transmit measurement beams between the spacecraft, forming the long arms of the heterodyne interferometer. Due to the distinct objectives, the telescope system design for the space-based gravitational-wave observatory have slightly different design criteria compared to ordinary telescopes. In addition to meeting the requirements for diffraction-limited imaging quality, maintaining optical path stability is crucial. Wavefront aberrations caused by the telescopes and angular misalignment due to field of view jitter introduce changes in the optical path signal, inevitably generating tilt-to-length coupling noise. Relevant research indicates that the coordinate offset of the chief rays on the pupil plane will cause the TTL noise to exceed the expected level in the interferometer measurement system. While rarely mentioned in conventional optical systems, this system evidently provides a typical application for pupil aberrations. Specifically, the pupil aberration is the preferred option for evaluating telescope aberrations, understanding the requirements for optical path stability, and suppressing tilt-to-length coupling noise. Based on the theory of traditional imaging aberration and pupil aberration theory, the initial structure of the telescope is established, and the automatic correction of pupil aberration and image plane aberration is achieved through macro programming in the commercial optical software Zemax, enabling the design of a high-performance spaceborne telescope. The design results show that the pupil aberration of the system has been corrected, the RMS wavefront error of the scientific field of view is less than λ/200. The maximum value of tilt-to-length coupling noise within a ±300 μrad field of view is 0.0144 nm/µrad, meeting the requirements of the Tianqin mission. The introduction of the concept of pupil aberrations has led to a rapid convergence of TTL noise, clearly providing designers with a new perspective to address the original design issue. Moreover, the pupil aberration evaluation metrics mentioned in this paper can offer an alternative optimization target for other systems requiring pupil aberration correction. This could potentially evolve into a conventional tool in optical design in the future. We believe that our design approach can provide valuable guidance for other space-based gravitational wave detection projects and the design of similar optical systems for space telescopes.