顧乃庭，王小勇，汶德勝，饒長輝，周澤兵，葉賢基

1中國科學院大學，北京 100049；

2中國科學院光電技術研究所，四川 成都 610209；

3中國科學院自適應光學重點實驗室，四川 成都 610209；

4北京空間機電研究所，北京 100094；

5中國科學院西安光學精密機械研究所，陜西 西安 710019；

6華中科技大學物理學院，湖北 武漢 430074；

7華中科技大學物理學院引力中心，精密重力測量國家重大科技基礎設施，基本物理量測量教育部重點實驗室， 湖北 武漢 430074；

8“天琴計劃”教育部重點實驗室，天琴中心 &物理與天文學院，天琴前沿科學中心，國家航天局引力波研究中心，中山大學(珠海校區(qū))，廣東 珠海 519082

引力波自2015 年被直接探測到以來，為人類認識宇宙提供了新的視角[1]。三位美國科學家因在LIGO 探測器和引力波觀測方面的決定性貢獻而獲得了2017 年的諾貝爾物理學獎[2]。繼地面干涉儀的手段實現高頻引力波探測之后，空間引力波探測將是下一階段的重點發(fā)展方向，其大空間尺度可突破地面探測的頻段限制從而實現低頻引力波探測。目前比較知名的空間引力波探測計劃包括歐空局主導的LISA 計劃[3]，我國的“天琴計劃”[4-5]和“太極計劃”[6]等?？臻g引力波探測均采用三星六鏈路結構設計，其中星載激光干涉儀是引力波探測計劃的核心測量儀器，相應的研究成果也比較多，技術進展較快。相對而言，星載望遠鏡作為激光發(fā)射和接收端擴束系統(tǒng)，其性能要求遠高于常規(guī)光學設備，比如雜散光和光程穩(wěn)定性等性能指標將直接影響引力波信號探測的信噪比。目前，針對引力波探測星載望遠鏡相關關鍵技術的研究還較少?！豆怆姽こ獭反舜谓M織的“空間引力波探測星載望遠鏡”專題，圍繞空間引力波探測星載望遠鏡設計與分析、核心指標優(yōu)化與測試等方面介紹該領域的現狀與發(fā)展趨勢，共收到了來自中山大學“天琴計劃”教育部重點實驗室、浙江大學、北京理工大學、華中科技大學，以及北京空間機電研究所、中國科學院西安光學精密機械研究所、中國科學院光電技術研究所等高校和科研院所的十多篇相關論文，將分批刊出。

2023 年第11 期出版的“空間引力波探測星載望遠鏡專題(一)”包括1 篇綜述和7 篇科研論文。論文《空間引力波探測望遠鏡研究進展》圍繞望遠鏡設計、研制與測試，對星載望遠鏡的光學系統(tǒng)、光機結構、空間熱環(huán)境與熱控、雜散光仿真與抑制、穩(wěn)定性測量等方面的研究進展進行了綜述[7]。此外，還有7 篇研究論文，主要圍繞星載望遠鏡光程穩(wěn)定性、雜散光、波前與指向等核心技術指標的實現，從理論計算、仿真模擬，實驗測試等多種途徑開展研究，探討星載望遠鏡設計與研制的最優(yōu)解?！兑Σㄌ綔y望遠鏡超低熱變形桁架支撐結構設計技術》通過設計CFRP 鋪層改變材料熱脹系數的方法，進而解決了桁架支撐結構熱變形問題，同時針對望遠鏡裝調性能的要求，給出了結構的分段式設計方案[8]?！锻h鏡光程穩(wěn)定性測量方案設計及噪聲理論分析》基于外差干涉測量原理，設計了高共模抑制干涉測量方案，建立了光程噪聲理論模型，并根據1 pm/Hz1/2@1 mHz光程穩(wěn)定性指標需求，分配測量系統(tǒng)組成部分光程噪聲水平[9]?！犊臻g引力波望遠鏡內部光場計算方法研究》論證了采用基于矢量光線追跡的衍射積分算法建立仿真算法的必要性，基于該算法建立了仿真程序，進行了波前計算精度的驗證，并展示了矢量光場仿真計算結果[10]?！痘陔x軸四反的空間引力波探測激光發(fā)射望遠鏡設計》從傳統(tǒng)像平面像差理論和光瞳像差理論出發(fā)，建立了望遠鏡的初始結構，然后利用Zemax 的宏編程實現了光瞳像差和像平面像差的自動校正，實現了高性能星載望遠鏡的設計[11]?！痘谙目?哈特曼傳感器的星載望遠鏡波前測量技術研究》提出了一種基于夏克-哈特曼波前傳感器原理的星載望遠鏡波前像差測量方法，該方法采用經過頻域閾值去噪處理后的頻域上的互相關算法[12]。《空間引力波探測系統(tǒng)中超光滑光學元件表面散射特性分析》針對超光滑光學元件，建立了一種能快速準確地分析和預測其表面散射特性的非傍軸標量散射模型，并研究了各種因素對不同表面統(tǒng)計分布特征下的角分辨散射分布的影響[13]?！犊臻g引力波望遠鏡超前瞄準機構致動器電荷驅動位移行為研究》提出等效電容量計算方法定量分析壓電致動器在電荷驅動下的位移響應特性，并通過仿真和實驗驗證了計算方法的準確性和可行性，為空間引力波探測望遠鏡超前瞄準機構的高精度指向控制提供了可能的分析方法和實現途徑[14]。

“空間引力波探測星載望遠鏡”專題依托國家重點研發(fā)計劃“引力波探測”2021 年度重點專項“超穩(wěn)和超高雜散光抑制能力的星載望遠鏡系統(tǒng)設計研究”、“星載望遠鏡研制與裝調技術研究”以及“超高精度星載望遠鏡性能測試與評估技術研究”等項目，專題出版的部分論文源自該專項項目的重要學術會議，以及后續(xù)依托該會議精神衍生出的研究成果。希望通過該專題對引力波探測星載望遠鏡相關理論、技術現狀和前沿進展的探討，促進該領域新理論、新技術和新方法的產生與迭代，并逐步發(fā)展成熟，為我國空間引力波探測計劃提供有效手段和有力支撐，也為廣大同行開展相關技術研究、合作交流提供重要參考。

當然，本專題的形成只是一個開始，在理論、方法和技術覆蓋面、成熟度與預期目標仍然存在較大差距，我們將持續(xù)不懈努力、力臻完善，也期望廣大相關領域科研工作者能夠為我們提供寶貴意見和發(fā)展建議，不勝感激！

Special issue on satellite telescope for space gravitational wave detection

Gu Naiting1,2,3,Wang Xiaoyong4,Wen Desheng1,5,Rao Changhui1,2,3,Zhou Zebing6,Ye Xianji7

1University of Chinese Academy of Sciences,Beijing 100049,China;

2Institute of Optics and Electronics,Chinese Academy of Sciences,Chengdu,Sichuan 610209,China;

3Key Laboratory of Adaptive Optics,Chinese Academy of Sciences,Chengdu,Sichuan 610209,China;

4Beijing Institute of Space Mechanical and Electrical Engineering,Beijing 100094,China;

5Xi'an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi' an,Shaanxi 710019,China;

6School of Physics,Huazhong University of Science and Technology,Wuhan,Hubei 430074,China;

7MOE Key Laboratory of TianQin Mission,TianQin Research Center for Gravitational Physics &School of Physics and Astronomy,Frontiers Science Center for TianQin,Gravitational Wave Research Center of CNSA,Sun Yat-sen University(Zhuhai Campus),Zhuhai,Guangdong 519082,China

Since gravitational waves were directly detected in 2015,a new perspective was provided for human to explore the universe.In 2017,three American scientists have won the 2017 Nobel Prize in Physics for their outstanding contributions to the LIGO detector and gravitational wave observations.After the realization of high-frequency gravitational wave detection by employing a ground-based interferometer,the space gravitational wave detection will be the focus of the next stage,which can break through the frequency band limitation of ground-based detection because of the large spatial scale,and can realize low-frequency gravitational wave detection.Currently,the well-known space gravitational wave detection programs include the LISA program led by the European Space Agency,China's TianQin program and Taiji program,etc.And these programs all employ the three-satellite and six-link structure,in which the satellite-based laser interferometer is the core measurement instrument of the detection program,and corresponding research results are relatively numerous and the technology is advancing rapidly.Relatively speaking,the satellite telescope,as the laser emission and receiving beam expansion system,have much higher performance requirements than conventional optical equipment,such as stray light and optical path stability,and other performance indicators will directly affect the signal-to-noise ratio of the gravitational wave detection.At present,little research has been done on key technologies of satellite telescopes for gravitational wave detection.Therefore,the journal ofOpto-Electronic Engineeringorganizes the special issue on "satellite telescope for space gravitational wave detection",which focuses on the design and analysis,and the optimization and testing of core indicators of the satellite telescopes for space gravitational wave detection,and introduces the current situation and development trend of the field.A total of more than ten relevant papers have been received from the key laboratory of the Ministry of Education of the "TianQin Program" of Sun Yat-sen University,Zhejiang University,Beijing Institute of Technology,Huazhong University of Science and Technology,as well as Beijing Institute of Space Mechanics &Electricity,Xi'an Institute of Optics and Precision Mechanics of CAS,Institute of Optics and Electronics of CAS and other universities and research institutes,and will be published in batches.

The Special issue "Satellite telescope for space gravitational wave detection (I)",published in No.11,2023,includes one review and seven articles.The paper "Research progress of telescopes for space-based gravitational wave missions"provides an overview of research progress in optical systems,opto-mechanical structures,space thermal environments and thermal control,stray light simulation and suppression,and stability measurements for satellite telescopes.In addition,the other seven research articles explore the optimal solutions for the design and development of satellite telescopes from theoretical calculations,simulations and experimental tests,which mainly focus on the core technical indexes such as optical path stability,stray light,wavefront and pointing of satellite telescopes.In "Design technology of the truss support structure of the ultra-low thermal deformation gravitational wave detection telescope",the problem of thermal deformation for the truss support structure is solved by designing a CFRP layer to change the thermal expansion coefficient of the material.Meanwhile,this paper gives a segmented design plan of the support structure for the requirements of telescope mounting performance.In "Design of optical path stability measurement scheme and theoretical analysis of noise in telescope",a high common mode suppression interferometry program based on heterodyne interferometry is proposed,a theoretical model for the optical path noise is built,and optical path noise levels to the components of the measurement system is assigned according to the 1 pm/Hz1/2@1 mHz optical path stability metrics requirements.In "Research on optical field calculation methods in the space gravitational wave telescope",the wavefront calculation simulation program is built utilizing a diffraction integration algorithm based on vector light tracing,and the simulation results of vector optical field are displayed.In "Design theory and method of offaxis four-mirror telescope for space-based gravitational-wave mission",the initial telescope structure is built up based on the traditional focal plane aberration theory and the optical pupil aberration theory,and then the automatic correction of optical pupil aberration and focal plane aberration was realized by employing Zemax macro programming,and finally a high-performance satellite telescope is designed.In "Research on wavefront measurement technology of space-based telescope using Shack-Hartmann wavefront sensor",the wavefront aberration measurement method for satellite telescopes based on the Shack-Hartmann wavefront sensor is proposed,which employs a mutual correlation algorithm with threshold denoising processing in the frequency domain.In "Analysis of surface scattering characteristics of ultrasmooth optical components in gravitational wave detection system",a non-equatorial scalar scattering model is built,which can quickly and accurately analyze and predict their surface scattering characteristics for ultra-smooth optical elements,and the effects of various factors on the angularly resolved scattering distributions under different surface statistical distribution characteristics are analyzed.In "Study on the charge driven displacement behavior of the actuator of the point ahead angle mechanism of a space gravitational wave telescope",an equivalent capacitance calculation method is proposed to quantitatively analyze the displacement response characteristics of piezoelectric actuators driven by electric charge,and the accuracy and feasibility of the method is verified experimentally and simulationally,which provides a possible analytical method and implementation approach for the high-precision pointing control of the overtargeting mechanism of the space gravitational wave detection telescope.

The Special issue on "Satellite telescope for space gravitational wave detection" is supported by numerous programs,including the National Key Research and Development Program "Gravitational wave detection",the 2021 Key Special Program "Design and investigation of the satellite telescope system with ultra-stable and ultra-high stray light suppression capability","Investigation of satellite telescope development and adjustment techniques",and "Investigation of ultra-high-precision satellite telescope performance testing and evaluation techniques",etc.Some papers published on this issue originated from the major academic conferences of these programs and subsequent research results derived from the spirit of the conferences.We hope that through the discussion of this special issue on the theory and technology status and frontier progress of the satellite telescope for gravitational wave detection,promoting the generation and iteration of new theories,technologies and methods in this field,and gradually developing and maturing them,meanwhile,also providing effective ways and strong support for China's space gravitational wave detection program,and also providing the important reference for the majority of colleagues to carry out related technical research,cooperation and exchange.

Certainly,this special issue is just a beginning,there are still big gaps in the theory,methodology and technology coverage,and maturity and the expected goal.We will continue to make unremitting efforts to improve,and also hope that the majority of researchers in this field can provide us with valuable advice and development ideas,we would be grateful!