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Article(id=1253994379987841843, tenantId=1146029695717560320, journalId=1251234571887362144, issueId=1253994374069682477, articleNumber=null, orderNo=null, doi=10.20249/j.cnki.2096-5974.2025.05.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=null, receivedDateStr=null, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1776905158269, onlineDateStr=2026-04-23, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1776905158269, onlineIssueDateStr=2026-04-23, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1776905158269, creator=13041195026, updateTime=1776905158269, updator=13041195026, issue=Issue{id=1253994374069682477, tenantId=1146029695717560320, journalId=1251234571887362144, year='2025', volume='8', issue='5', pageStart='1', pageEnd='114', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1776905156856, creator=13041195026, updateTime=1777355348378, updator=13041195026, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1255882614297248384, tenantId=1146029695717560320, journalId=1251234571887362144, issueId=1253994374069682477, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1255882614301442689, tenantId=1146029695717560320, journalId=1251234571887362144, issueId=1253994374069682477, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=70, endPage=80, ext={EN=ArticleExt(id=1253994383058072384, articleId=1253994379987841843, tenantId=1146029695717560320, journalId=1251234571887362144, language=EN, title=Analysis of the Influence of Grating Diffraction Efficiency on the Angle Measurement of Interferometric Star Tracker, columnId=1253994375617380656, journalTitle=Flight Control & Detection, columnName=Photoelectric Detection and Guidance Technology, runingTitle=null, highlight=null, articleAbstract=

Aiming at the application requirements of high attitude measurement accuracy of interferometric star tracker,the influence of grating diffraction efficiency on the measurement accuracy of starlight interferometry is analyzed. Based on the angular spectrum propagation theory,the im aging angle measurement model of the interferometric star tracker is constructed,and the energy distribution of the interference star point is simulated by numerical calculation. At the same time, the influence of the diffraction efficiency change caused by the change of the incident angle and the wavelength on the angle measurement accuracy of the starlight is analyzed respectively. The results show that the change of grating diffraction efficiency caused by the change of incident angle has little effect on the accuracy of starlight interferometry in the field of view of star sensor. The change of diffraction efficiency caused by wavelength change has a great influence on the accuracy of starlight interferometry. With the increase of spectral width,the accuracy of starlight interferometry decreases as a whole. When the starlight changes from monochromatic light to polychromatic light with spectral width of 300nm,the accuracy of starlight interferometry decreases from about 0.01″to about 0.3″.The analysis results of this paper can provide theoretical basis and technical support for the engineering application of interferometric star tracker.

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面向干涉式星敏感器高姿态测量精度的应用需求，分析了光栅衍射效率对星光干涉测量精度产生的影响。基于角谱传播理论，构建了干涉式星敏感器成像测角模型，并通过数值计算仿真了干涉星点的能量分布，同时，分别分析了入射角及波长改变引起的衍射效率变化对星光测角精度的影响。结果表明，在星敏感器视场内，入射角改变引起的光栅衍射效率变化对星光干涉测量精度几乎没有影响；而波长变化引起的衍射效率变化对星光干涉测量精度的影响较大，且随着谱宽的增加，星光干涉测量精度整体呈下降趋势，当星光由单色光变为谱宽为300nm的复色光时，星光干涉测量精度由约0.01″下降至约0.3″。分析结果可为干涉式星敏感器的工程应用提供理论基础与技术支持。

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通信作者简介：汪洪源，男，博士，教授，博士生导师。
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姚帅，男，博士生。

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姚帅，男，博士生。

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tableContent=null), ArticleFig(id=1253994405015253274, tenantId=1146029695717560320, journalId=1251234571887362144, articleId=1253994379987841843, language=EN, label=Fig.10, caption=The deviation of incident angle solution under different spectral widths of K-type stars, figureFileSmall=0XhjGdtaAZyezxbcC9jDbQ==, figureFileBig=uUXgNmyl9LKm8Zn8lNVF1A==, tableContent=null), ArticleFig(id=1253994405099139357, tenantId=1146029695717560320, journalId=1251234571887362144, articleId=1253994379987841843, language=CN, label=图10, caption=K类恒星不同谱宽下的入射角解算偏差, figureFileSmall=0XhjGdtaAZyezxbcC9jDbQ==, figureFileBig=uUXgNmyl9LKm8Zn8lNVF1A==, tableContent=null), ArticleFig(id=1253994405178831136, tenantId=1146029695717560320, journalId=1251234571887362144, articleId=1253994379987841843, language=EN, label=Fig.11, caption=The deviation of incident angle solution under different spectral widths of M-type stars, figureFileSmall=9yiJrsFPBbNsRZoc5Q+7zw==, figureFileBig=hmx2qpYdCAneUJTL1lHMog==, tableContent=null), ArticleFig(id=1253994405266911522, tenantId=1146029695717560320, journalId=1251234571887362144, articleId=1253994379987841843, language=CN, label=图11, caption=M类恒星不同谱宽下的入射角解算偏差, figureFileSmall=9yiJrsFPBbNsRZoc5Q+7zw==, figureFileBig=hmx2qpYdCAneUJTL1lHMog==, tableContent=null), ArticleFig(id=1253994405342408994, tenantId=1146029695717560320, journalId=1251234571887362144, articleId=1253994379987841843, language=EN, label=Tab.1, caption=

The root mean square deviation of the incident angle solution for different types of stars and different spectral widths is calculated

, figureFileSmall=null, figureFileBig=null, tableContent=
谱宽/nm入射角解算均方根偏差/（″）
G类恒星K类恒星M类恒星
500.0150.0150.016
1000.1290.1260.122
1500.1880.1920.204
2000.2150.1880.143
2500.3540.3430.339
3000.3120.2420.156
), ArticleFig(id=1253994405430489380, tenantId=1146029695717560320, journalId=1251234571887362144, articleId=1253994379987841843, language=CN, label=表1, caption=

不同类型恒星、不同谱宽下的入射角解算均方根偏差

, figureFileSmall=null, figureFileBig=null, tableContent=
谱宽/nm入射角解算均方根偏差/（″）
G类恒星K类恒星M类恒星
500.0150.0150.016
1000.1290.1260.122
1500.1880.1920.204
2000.2150.1880.143
2500.3540.3430.339
3000.3120.2420.156
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光栅衍射效率对干涉式星敏感器测角影响分析
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姚帅 1 , 张徐玮 2, 3 , 叶志龙 2, 3 , 孙朔冬 2, 3 , 汪洪源 1 , 武少冲 1 , 廖真 1 , 臧云朝 1
飞控与探测 | 光电探测与制导技术 2025,8(5): 70-80
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飞控与探测 | 光电探测与制导技术 2025, 8(5): 70-80
光栅衍射效率对干涉式星敏感器测角影响分析
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姚帅1, 张徐玮2, 3, 叶志龙2, 3, 孙朔冬2, 3, 汪洪源1, 武少冲1, 廖真1, 臧云朝1
作者信息
  • 1哈尔滨工业大学 空间光学工程研究中心·哈尔滨·150001
  • 2上海航天控制技术研究所·上海·201109
  • 3上海市空间智能控制技术重点实验室·上海·201109

    • 姚帅，男，博士生。

通讯作者:

通信作者简介：汪洪源，男，博士，教授，博士生导师。
Analysis of the Influence of Grating Diffraction Efficiency on the Angle Measurement of Interferometric Star Tracker
Shuai YAO1, Xuwei ZHANG2, 3, Zhilong YE2, 3, Shuodong SUN2, 3, Hongyuan WANG1, Shaochong WU1, Zhen LIAO1, Yunzhao ZANG1
Affiliations
  • 1Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001
  • 2Shanghai Aerospace Control Technology Institute, Shanghai 201109
  • 3Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai 201109
doi: 10.20249/j.cnki.2096-5974.2025.05.008
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摘要
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面向干涉式星敏感器高姿态测量精度的应用需求，分析了光栅衍射效率对星光干涉测量精度产生的影响。基于角谱传播理论，构建了干涉式星敏感器成像测角模型，并通过数值计算仿真了干涉星点的能量分布，同时，分别分析了入射角及波长改变引起的衍射效率变化对星光测角精度的影响。结果表明，在星敏感器视场内，入射角改变引起的光栅衍射效率变化对星光干涉测量精度几乎没有影响；而波长变化引起的衍射效率变化对星光干涉测量精度的影响较大，且随着谱宽的增加，星光干涉测量精度整体呈下降趋势，当星光由单色光变为谱宽为300nm的复色光时，星光干涉测量精度由约0.01″下降至约0.3″。分析结果可为干涉式星敏感器的工程应用提供理论基础与技术支持。

干涉式星敏感器  /  星光成像测量  /  测角  /  朗奇光栅  /  衍射效率

Aiming at the application requirements of high attitude measurement accuracy of interferometric star tracker,the influence of grating diffraction efficiency on the measurement accuracy of starlight interferometry is analyzed. Based on the angular spectrum propagation theory,the im aging angle measurement model of the interferometric star tracker is constructed,and the energy distribution of the interference star point is simulated by numerical calculation. At the same time, the influence of the diffraction efficiency change caused by the change of the incident angle and the wavelength on the angle measurement accuracy of the starlight is analyzed respectively. The results show that the change of grating diffraction efficiency caused by the change of incident angle has little effect on the accuracy of starlight interferometry in the field of view of star sensor. The change of diffraction efficiency caused by wavelength change has a great influence on the accuracy of starlight interferometry. With the increase of spectral width,the accuracy of starlight interferometry decreases as a whole. When the starlight changes from monochromatic light to polychromatic light with spectral width of 300nm,the accuracy of starlight interferometry decreases from about 0.01″to about 0.3″.The analysis results of this paper can provide theoretical basis and technical support for the engineering application of interferometric star tracker.

interferometric star tracker  /  starlight imaging measurement  /  angle measurement  /  Ronchi grating  /  diffraction efficiency
姚帅, 张徐玮, 叶志龙, 孙朔冬, 汪洪源, 武少冲, 廖真, 臧云朝. 光栅衍射效率对干涉式星敏感器测角影响分析. 飞控与探测, 2025 , 8 (5) : 70 -80 . DOI: 10.20249/j.cnki.2096-5974.2025.05.008
Shuai YAO, Xuwei ZHANG, Zhilong YE, Shuodong SUN, Hongyuan WANG, Shaochong WU, Zhen LIAO, Yunzhao ZANG. Analysis of the Influence of Grating Diffraction Efficiency on the Angle Measurement of Interferometric Star Tracker[J]. Flight Control & Detection, 2025 , 8 (5) : 70 -80 . DOI: 10.20249/j.cnki.2096-5974.2025.05.008
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0　引言
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星敏感器是以恒星为参照物、输出在惯性系下姿态信息的仪器，其姿态解算精度高，且无累积误差，目前已广泛应用于卫星、导弹、舰船等平台[1-5]。随着航天技术的快速发展，平台对星敏感器姿态测量精度的要求越来越高，传统星敏感器为提高测量精度所付出的质量、功耗等代价也随之剧增。干涉式星敏感器在传统星敏感器前引入干涉组件及分光组件，其可将星光的相位信息耦合至像点能量中，在传统星敏感器质心定位算法的基础上，二次利用像点能量，应用相应的相位解调方法解算星光入射角，实现在测量范围不变的前提下大幅提升测量精度，最终突破传统星敏感器的星光入射角测量精度极限。
干涉式星敏感器的概念最早由Held[6]于1971年提出。直到2008年，美国光学物理公司（Optical Physics Company，OPC）开始研究这一技术，并于2011年提出了一种基于朗奇光栅的干涉式星敏感器[7]，并指出干涉式星敏感器的星点质心定位精度可达到1/1000像素，远超传统星敏感器1/10～1/50像素的星点质心定位精度，随后在2014年完成了干涉式星敏感器原理样机（Mist-IR[8]）的研制。近年来，国内也开始了相关的理论研究。2017年，中国科学院院长春光机所的董磊团队[9]基于Held的专利，对干涉探测技术进行了理论分析和数学建模，验证了利用恒星相干特性实现星光测量的技术可行性。2018年，浙江大学的杜娟等[10]基于OPC的专利，提出了一种基于交叉相位光栅的干涉式星敏感器结构。2021年，董磊团队[11]从频域出发，对星光复振幅在干涉式星敏感器内部的传播过程进行了建模，并提出了单星测量精度的计算方法。2023年，该团队进一步分析了干涉条纹分割误差对测角精度的影响[12]。在国内外学者对干涉式星敏感器测角机理的研究过程中，均进行了一些假设，例如衍射效率不随波长、入射角改变，而实际应用过程中，这些因素均会影响干涉星点的能量分布，进而影响星光的测角精度。因此，有必要深入分析在考虑入射角及波长变化时，这些因素对干涉式星敏感器测角精度的影响。
面向干涉式星敏感器高姿态测量精度的应用需求，分析了光栅衍射效率对干涉式星敏感器测角精度的影响。首先，阐述了以光栅为干涉组件的干涉式星敏感器系统结构组成，并基于角谱传播理论，对星光经过干涉组件、分光组件及聚焦组件后在探测器上的成像过程进行建模；其次，基于夫琅禾费衍射理论，构建了透射式矩形光栅的衍射效率计算模型；最后，仿真计算了在不同入射角、不同波长下的透射式矩形光栅衍射效率，以及考虑入射角、波长影响下的干涉星点能量分布，基于干涉式星敏感器成像测角机理和仿真星图，对星光入射角进行了解算，并通过角度解算均方根偏差对结果进行定量评估。
1　干涉式星敏感器成像测角模型
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基于衍射光栅的干涉式星敏感器结构如图1所示，该系统由干涉组件（为两块衍射光栅，平行光经过光栅后将发生衍射，不同级次的衍射光之间在光栅G2的后表面产生干涉，光栅G1与光栅G2的刻线方向均与光轴方向垂直，且与y轴有一数值相同、方向相反的夹角）、分光组件（为4块光楔沿y轴并排分布的光楔阵列，使得入射光方向分别发生上、下、左、右4个方向的偏转）、聚焦组件构成，星光经过由G1，G2组成的干涉仪后产生白光干涉条纹，最终经过分光组件分光、聚焦组件成像后在探测器处形成多个像点。
星点的角直径很小，因此可以将其当作平行光考虑，基于角谱传播理论及透镜的傅里叶变化性质，分析星光在干涉星敏感器中的传播过程，单束星光经干涉式星敏感器内部传播后在像面上的复振幅可表示为
式中：λ表示星光波长；j表示虚数单位；f表示聚焦组件的焦距；d0表示G2与分光组件的间隔；xf，yf表示像面坐标；[（Ustar*UG1）（H*UG2*T）]表示星光经过分光组件后的角谱；Ustar表示入射星光的角谱，即复振幅的傅里叶变换，具体形式如式（2)；UG1，UG2分别表示光栅G1，G2复振幅透过率的傅里叶变换，具体形式如式（3)、式（4)；H表示星光在光栅间传播的传递函数，由亥姆霍兹方程确定，具体形式如式（5)；T表示光楔阵列透过率的傅里叶变换，具体形式如式（6)；*表示卷积，复振幅在时域的乘积对应角谱在频域的卷积。
式中：A0表示星光复振幅；α表示星光沿子午方向的入射角；fx，fy分别表示入射光沿子午、弧矢方向的空间频率；δ表示冲激函数。
式中，Cm表示光栅G1的m级次衍射系数，Cm′表示光栅G2的m′级次衍射系数，p表示光栅周期，ε表示光栅G1绕光轴的旋转角。
式中，z表示两光栅的间距。
式中：a，b分别表示每块光楔的长和宽；θxn，θyn表示第n块光楔沿子午、弧矢方向的偏转角。
将式（1）化简得到焦平面的复振幅分布为
φm为G1的m级衍射光经自由空间传播附加的相位，具体形式如下
最终可得到焦平面的能量分布为
令每块光楔的短边满足下式
当只考虑两光栅的0，±1级衍射，且光栅的0级衍射效率为零时，星光经过第n块光楔偏转后形成像点的能量为
由式（8）可知φ+1 -φ-1近似为一常量
最终得到如下关系
式中。
相位项与星点能量满足如下关系
即可以通过4个像点的能量解算高精度的星光入射角。
2　透射式光栅衍射效率计算模型
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光栅的种类繁多，可按调制方式分为相位光栅和振幅光栅，相位光栅与振幅光栅相比可透过更多能量的光，故本文将以结构简单的透射式矩形光栅作为干涉式星敏感器的干涉组件。透射式矩形光栅的局部微结构如图2所示，槽宽为τ，占空比为ρ=τ/d，刻蚀深度为h1，基底厚度为h2，折射率为n。
设光线1和光线2以入射角α入射到光栅上，ε为折射角，易知光线1通过光栅附加的相位为
光线2通过光栅附加的相位为
则光线1和2通过光栅时产生的相位差为
于是，光栅的复振幅透过率可写为
式中，l表示光栅沿x方向的第l个光栅周期。
单位平行光经过光栅后，复振幅可表示为
可将上式以傅里叶级数的形式展开，得到
易知Cm即为光栅的各级次衍射系数，基于夫琅禾费衍射理论，可得到衍射图样的强度分布为
式中，A为光栅后表面的复振幅分布。
联立式（17)、式（19)、式（20）即可得到各级衍射系数为
最终得到斜入射下矩形光栅衍射效率的一般形式如下
干涉式星敏感器进行星光角度解算时，默认光栅衍射效率不随波长及入射角发生改变。而由上述推导可知，光栅各级次衍射效率随入射光的入射角及波长的变化均发生改变，因此本文将重点分析星光波长及入射角对星点定位精度产生的影响。
3　仿真实验及结果分析
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本部分共开展3组仿真实验，分别仿真理想情况、考虑衍射效率随星光入射角发生改变、考虑衍射效率随波长发生改变下的干涉星点能量分布。
3.1　仿真条件
基本仿真参数设置如下：1）模拟的星光中心波长为690nm，采样间隔为5nm，谱宽分别为50nm，100nm，150nm，200nm，250nm，300nm，恒星选为G，K，M类恒星（取三类恒星的色温分别为5500K，4450K，3050K）；2）光楔组件的整体尺寸为48mm×48mm（4块光楔的尺寸均为48mm×12mm）；3）光栅为朗奇光栅，材料选择阿贝数较大的熔石英（折射率为1.4548)，刻蚀深度为759.6nm（可保证光栅在星光中心波长处的0级衍射效率为0)，光栅周期为50 μm，光栅间隔为50mm，光栅夹角为0.0298°，只考虑光栅的0，±1级衍射光；4）聚焦组件的焦距为50mm，探测器阵列数为1024×1024，像元尺寸为5.5μm，视场约为6°×6°，单个像点能量随入射角度每变化一个周期，对应的能量细分数为1000。
3.2　光栅衍射效率仿真结果
基于光栅各级次衍射效率计算方法，可得到不同入射角、不同波长下的各级次衍射系数如图3所示。
由以上分析结果可知，在星敏感器视场内，星光入射角对光栅各级次衍射系数的影响较小，而波长对光栅各级次衍射系数的影响较大。同时光栅的零级衍射系数在690nm处取得最小值，为0；在347nm处取得最大值，为1。为了提升星敏感器的探测能力，星敏感器的工作波段一般较宽，因此波长对干涉式星敏感器的影响将较大。
3.3　星点能量分布仿真结果
基于光学系统基本参数、生成的星光入射角及式（9）仿真3组星点能量分布如下。
1）入射光为690nm，不考虑衍射效率随入射角的变化，以0.001°为步长仿真了0°～6°的干涉星点能量分布，如图4所示。
由图4可以看出，等效零级星点（即光栅G1的+m级衍射光与光栅G2的-m级衍射光叠加得到的星点）的能量随入射角的增加呈现周期性变化，与第1章的理论相符，等效+2级与等效-2级星点的能量随入射角的增加不发生改变，故可应用等效零级星点的能量关系解算星光入射角。
2）入射光中心波长为690nm，考虑衍射效率随入射角的变化，以0.001°为步长仿真了0°～6°的干涉星点能量分布，如图5所示。
由图5可知，在考虑光栅衍射效率受入射角的影响后，各级次星点能量分布随入射角的变化关系与忽略光栅衍射效率受入射角的影响时基本保持一致。
3）入射光中心波长为690nm，恒星光谱类型分别为G，K，M，谱宽分别为50nm，100nm，150nm，200nm，250nm，300nm时，考虑各级次衍射效率随波长的变化，以0.001°为步长仿真了0°～6°的干涉星点能量分布，G类恒星、谱宽为50nm时的像点能量分布如图6所示。
由图6可知，考虑宽谱段入射光后的等效高级次衍射星点沿衍射方向的色散较明显（若考虑的谱段更宽，则色散更明显），导致探测难度增加，且出现了两星点混叠的现象。而等效零级星点不会因谱段变宽而出现色散，能量密度仍较高，且4个像点的能量随入射角的增加仍呈周期性变化。
3.4　星光角度解算结果
基于干涉式星敏感器成像测角原理，分别解算以上3种情况下的星光入射角，并对测角精度进行统计。
1）基于干涉式星敏感器入射角解算原理及仿真得到的星点能量分布，得到理想情况下入射角解算偏差如图7所示。
由以上统计结果可知，视场内角度解算偏差最大约为0.02″，应用入射角解算均方根偏差作为评价干涉式星敏感器测角精度的指标，具体形式如下
式中，N表示统计的样本数，εi为第i个样本的角度解算偏差值。
基于式（24)，得到不考虑衍射效率随入射角的变化、只考虑星光为单色光时的入射角解算均方根偏差为0.0076″。
2）基于干涉式星敏感器入射角解算原理及仿真得到的星点能量分布，解算得到考虑光栅衍射效率随入射角发生改变时的入射角解算偏差如图8所示。
由以上统计结果可知，考虑衍射效率受入射角的影响后，入射角解算偏差与未考虑入射角影响时的结果几乎保持一致，应用式得到考虑衍射效率随入射角变化时的入射角解算均方根偏差为0.0077″。
3）基于干涉式星敏感器入射角解算原理及仿真得到的星点能量分布，分别得到考虑光栅衍射效率随波长发生变化时不同类型恒星、不同谱宽下的入射角解算偏差，如图9～图11所示。
基于式（24)，计算得到不同类型恒星、不同谱宽下的入射角解算均方根偏差如表1所示。
由以上统计结果可知，考虑星光为复色光时，星光入射角解算偏差较大，与仅考虑星光为单色光时的解算精度相比甚至超过一个数量级，且随着谱宽的增加，入射角解算偏差基本呈现增大的趋势；即使谱宽相同，恒星也会由色温的不同导致入射角解算偏差有所不同。
针对以上仿真结果可知，光栅衍射效率随入射角变化对干涉式星敏感器测角精度产生的影响较小，可忽略不计，而各级次衍射效率随波长变化对测角精度产生的影响巨大。同时，本文仅针对3种典型的恒星类型开展仿真分析，并未考虑滤光片、透镜材料以及探测器的光谱特性。因此，在干涉式星敏感器设计阶段，应充分考虑以上因素的影响，从而保证干涉式星敏感器的高星光测量精度。
4　结论
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面向干涉式星敏感器的高姿态测量精度需求，基于构建的干涉式星敏感器成像模型，通过数值仿真的方法分析了光栅衍射效率对星光测量精度产生的影响。分析结果表明：1）由入射角增加引起的光栅衍射效率变化对星光角度测量产生的影响极小，可忽略不计；2）由波长改变导致的光栅衍射效率变化对测角精度产生的影响较大，当谱宽为300nm时，测角精度约为0.3″。本文尚未考虑滤光片、透镜材料、探测器的光谱特性以及光栅高阶衍射对干涉式星敏感器测角精度的影响，后续研究将针对以上因素不可忽略时的成像测角模型构建及其测角影响分析等问题进行深入探讨。
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2025年第8卷第5期
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doi: 10.20249/j.cnki.2096-5974.2025.05.008
  • 首发时间：2026-04-23
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    1哈尔滨工业大学 空间光学工程研究中心·哈尔滨·150001
    2上海航天控制技术研究所·上海·201109
    3上海市空间智能控制技术重点实验室·上海·201109

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通信作者简介：汪洪源，男，博士，教授，博士生导师。
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