光电工程

References	Type	Array	Uniformity/%	Precision of AOA
[18]	Discrete optical element	1×2	−	2.1°
[32]	Beam splitting film	1×4	90	−
Ours	Cascaded grating beam splitter	2×2	>95	1.34°

References	Type	Array	Uniformity/%	Precision of AOA
[18]	Discrete optical element	1×2	−	2.1°
[32]	Beam splitting film	1×4	90	−
Ours	Cascaded grating beam splitter	2×2	>95	1.34°

基于多光束里德堡原子接收机的信号到达角估计

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赵冯婷 , 安强 ^*^,^* , 张金颢 , 陈泓锦 , 李洋 , 孙占山 , 付云起

光电工程 | 科研论文 2026,53(7): 250354-1

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光电工程 |科研论文 2026 , 53 (7) : 250354 -1

基于多光束里德堡原子接收机的信号到达角估计

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赵冯婷, 安强^*^,^*, 张金颢, 陈泓锦, 李洋, 孙占山, 付云起

作者信息

国防科技大学电子科学学院，湖南长沙 410072

通讯作者:

安强，anqiang18@nudt.edu.cn

作者简介:

作者贡献

赵冯婷：理论分析，实验设计及数据处理，论文写作；安强，付云起：指导论文选题、论文修改；张金颢，陈泓锦：数据处理；李洋：研究资料的收集。

赵冯婷 (2001-)，女，硕士研究生，研究方向为量子微波理论与技术。E-mail：zhaofengting@nudt.edu.cn zhaofengting@nudt.edu.cn

Angle of arrival estimation based on multi-beam Rydberg atomic receivers

Fengting Zhao, Qiang An, Jinhao Zhang, Hongjin Chen, Yang Li, Zhanshan Sun, Yunqi Fu

Affiliations

College of Electronic Science and Technology, National University of Defense Technology, Changsha, Hunan 410072, China

Corresponding Author:

anqiang18@nudt.edu.cn

出版时间: 2026-07-25 doi: 10.12086/oee.2026.250354

文章导航

摘要

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里德堡原子接收机利用激光缀饰原子能级实现射频场信息获取，具有高灵敏度和宽频带的射频电场探测能力，有望成为精准导航和高分遥感的重要工具。本文提出并展示了一种面向射频信号到达角估计的多光束里德堡原子接收机方案，利用里德堡原子的电磁诱导透明效应与超外差技术，在气室内不同位置同步测量来波信号的相位差进而实现信号到达角的精确估计。为验证方案可行性，文中使用多光束里德堡原子接收机对X波段 (8.57 GHz)来波信号到达角进行仿真与实验研究，两者具有很好的一致性。结果表明，基于原子的亚波长多光束相位测量方案可以用于射频信号到达角的精确估计，并具备拓展至三维接收阵列的能力。

关键词

到达角 / 多光束 / 里德堡原子 / 液晶偏振光栅

Abstract

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Objective

Rydberg atom is a kind of alkali atoms whose outermost valence electrons are in the highly excited state with a large electric dipole moment and a very high polarization rate, which exhibits extreme sensitivity to external electric field and be utilized in microwave quantum sensing. Rydberg atom-based sensors have developed rapidly and have shown extensive applications in the fields of precise navigation, quantum metrology, communication and high-resolution remote sensing owing to its distinct advantages including high sensitivity, broad frequency bandwidth (DC-THz), SI traceability and self-calibration capability that are not available in conventional antenna-based receivers. As an emerging quantum sensor, the Rydberg atomic receiver employs laser-excited atoms to convert radio frequency (RF) fields into an optical signal that can be read out on a photodetector at baseband to detect the relevant information of the RF field. In Rydberg atom-based electrometry, under the effect of an intense coupling laser, the dispersion property of the medium changes, resulting in the absorption of the weak probe laser being reduced, which is the definition of electromagnetically induced transparency (EIT). Furthermore, when a RF field is applied near resonance using two Rydberg energy levels, the corresponding Rydberg energy levels split, resulting in a two-peak spectrum, known as Autler–Townes splitting (EIT-AT splitting). The EIT-AT splitting interval is proportional to the amplitude of the RF field, which can obtain a direct measurement of the external field by measuring the splitting interval. However, this practical deployment of this promising technology, particularly for advanced functionalities like direction positioning, faces numerous significant challenges. On the one hand, the existing single-beam detection architecture is incapable of acquiring the spatial phase differences critical for Angle of Arrival (AOA) estimation, which the multi-beam architecture could conceptually essential to overcome this limitation. On the other hand, the traditional optical beam splitters suffer from structural complexity and poor stability, which limit the application of this technology in reality positioning.

Methods

In this work, in order to achieve the probe laser array and meet the exact alignment requirements of the Rydberg atoms for both the probe laser and coupling laser, we report and present a multi-beam Rydberg atomic receiver for AOA estimation utilizing a cascade liquid crystal polarization grating (LCPG), achieving a 2×2 two-dimensional (2D) collimated laser beam with an interval of 2.42 mm. First, we utilized the polarization-selective properties of the LCPG to design a beam-splitting grating with a period of 21.32 μm, which can split the incident laser into a 2×2 array of beams with deflection angles. Second, to achieve a collimated array output, we further proposed a four-zone collimating grating with a period of 14.95 μm which can collimate the four beams separately. This cascaded gratings optical system has a compact structure with beam power uniformity better than 95% and the effective collimation is over a distance greater than 15 cm, overcoming the inherent shortcomings of discrete optical components effectively. Moreover, we employ the EIT in Rydberg atomic vapor cell in conjunction with a atomic superheterodyne technology to measure the phase difference at different locations of the incident RF signal simultaneously, realizing the estimation of the angle of arrival.

Results and Discussions

To demonstrate this approach, we simulated and measured phase differences of an incident X-band wave at 8.57 GHz by fixing the local oscillator signal (E_LO) and rotating the signal source (E_SIG) within the incident range of -40° to +40°. To simplify the complexity of the adjustment, we expanded the coupling laser to 5 mm to ensure full coverage of the 2×2 probe laser array and apply different photodetectors (PDs) to receive signals from each probe laser simultaneously and connect them to a multi-channel oscilloscope to obtain the phase difference $ \Delta \phi $ of the beat-note signal, thereby enabling precise determination of the AOA of the incident signal. The experimental results show that the functional relationship between the measured phase difference $ \Delta \phi $ and the AOA is highly consistent with the theoretical model and electromagnetic simulation results with the error less than 1.5°, indicating that the proposed atomic-based subwavelength multi-beam receiver can be used to determine the AOA of the RF signal.

Conclusions

This work not only validates the fundamental principle of quantum-based RF direction positioning using Rydberg atom-based sensors but also establishes a practical and robust foundational unit for future advanced systems. The proposed integrated beam array scheme is highly scalable and versatile, and the 2D configuration can be directly extended to full three-dimensional (3D) arrays for omnidirectional sensing. Furthermore, the inherent design of the 2×2 laser array allows for the arbitrary combination of any three beams within a larger array to perform AOA estimation, providing redundancy and flexibility. This capability paves the way for developing sophisticated quantum sensor networks capable of multi-parameter estimation and multi-target recognition in complex spectral environments. By integrating miniaturized photonic components with atomic sensing, this research opens up new, viable avenues for the development of next-generation navigation systems, adaptive radar, and non-cooperative remote sensing technologies, marking a transition from laboratory demonstration towards practical quantum-enabled instrumentation.

Key words

angle of arrival / multi-beam / Rydberg atoms / liquid crystal polarization grating

引用本文

赵冯婷, 安强, 张金颢, 陈泓锦, 李洋, 孙占山, 付云起. 基于多光束里德堡原子接收机的信号到达角估计. 光电工程, 2026 , 53 (7) : 250354 -1 . DOI: 10.12086/oee.2026.250354

Fengting Zhao, Qiang An, Jinhao Zhang, Hongjin Chen, Yang Li, Zhanshan Sun, Yunqi Fu. Angle of arrival estimation based on multi-beam Rydberg atomic receivers[J]. Opto-Electronic Engineering, 2026 , 53 (7) : 250354 -1 . DOI: 10.12086/oee.2026.250354

正文

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1　引　言

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量子精密测量技术采用具有分立能级的物质、量子相干或者量子纠缠效应^[1,2]等量子资源构造量子传感器来实现超越经典极限的高精度物理量测量。相较于经典物理理论的传感器，量子传感器有望实现对经典物理学框架的突破，进而实现测量性能质的提升。近年来，量子信息技术飞速发展，国内外研究团队利用电子、光子、声子等量子体系已经在时间、频率^[3]、重力、加速度、磁场^[4]等物理量方面实现了超越经典传感器的高精度测量，诞生了原子钟^[5]、原子重力仪^[6]、陀螺仪、原子磁力计^[7]等精密计量仪器。在微波电场测量领域，基于里德堡原子的量子微波测量技术利用激光缀饰原子探测射频电磁场信息，因其具有超高灵敏度、超宽带宽、自校准^[8]、可溯源至普朗克常量^[9-11]等传统基于天线的接收机所不具备的优势而引起了学者们的广泛关注。

里德堡原子是最外层电子处于大主量子数 (n) 能级的高激发态原子, 具有较大的电偶极矩和极大的极化率^[12-13]。因此，对外电场的响应极为敏感，通过测量外电场对里德堡原子能级的微扰即可实现射频电磁场参数的获取。基于里德堡原子的电场测量技术利用光、微波与碱金属原子相互作用时产生的电磁诱导透明^[13-14] (electromagnetically induced transparency, EIT)和Autler Townes (AT)分裂^[15]等量子相干效应实现对入射微波场参数的光学测量，伴随超外差探测架构的引入，对电场幅度测量的灵敏度达到55 nV·cm^-1·Hz^-1/2[16]。随着量子传感器研究的深入，里德堡原子传感器不仅可以测量电场强度，还实现了电场极化、相位和到达角 (angle of arrival, AOA)^[17-18]等参数的测量以及调幅 (amplitude modulation, AM)^[19-20]、调频 (frequency modulation, FM)^[21] 和相位调制 (phase modulation, PM)^[22] 信号的接收。然而，目前针对入射电磁波信号到达角的测量研究仍相对较少。一方面，到达角估计依赖多通道空间相位的比较，以获取入射微波场的波前相位差从而实现方位估计。现有典型探测方式大多采用单一激光光束作为探测场，无法直接提供用于计算到达角的空间差分相位信息。另一方面，传统光学分束准直方案依赖分立光学元器件往往导致系统结构复杂、体积庞大、光路难以稳定，且各光束之间的相对位置及其准直度^[23] 不易精确控制和保持，严重制约了高精度到达角测量的多光束里德堡原子接收机的实现与发展。

本文利用级联偏振光栅实现了光斑间隔为2.42 mm的一体化2×2二维准直光束阵列，结合原子超外差技术实现X波段 (8.57 GHz)入射射频信号到达角的测量与估计，测量误差小于1.5°。所提出的使用里德堡原子接收器阵列的定位系统是对最基本单元的验证，可以通过系统的组合嵌套来实现更高精度的时空定位和实时速度或位姿响应，为未来构建基于里德堡原子传感器的三维接收阵列奠定了技术基础。

2　原理分析

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2.1　分束准直器件的设计原理

根据量子微波测量技术的机理及实验方案，缀饰原子的探测光 (852 nm)和耦合光 (510 nm)反向共线传播激发里德堡原子以消除多普勒效应^[24]。因此，激光分束后的准直度尤为重要。我们采用级联液晶偏振光栅实现2×2准直光束阵列的产生，主要分为两部分：一是激光分束；二是激光准直。液晶偏振光栅 (Liquid crystal polarization grating, LCPG)具有偏振可调性，可控制入射光经过光栅后的正负一级的能量比值以及入射光的偏振状态^[25-27]。根据光学偏振理论，任何一束光均可看作由左旋圆偏振光和右旋圆偏振光组成，当一束光入射到LCPG后，左旋圆偏振光和右旋圆偏振光将分别偏转到光栅的正负一级。通过改变入射光束偏振态，LCPG能够使出射光在两个偏转方向之间切换；通过制备不同周期的 LCPG 可实现不同的偏转角。LCPG的液晶分子的排列方向随空间坐标线性变化，且在一个光栅周期内，液晶分子的方位角变化了180°，假定排列方向沿x轴变化，液晶分子的方位角

$ \varphi $

满足：

$ \varphi =\dfrac{{\text{π}} x}{\varLambda }\;, $

(1)

式中：

$ \varLambda $

为光栅周期。忽略吸收和散射等能量损失，一束光经过偏振光栅后的光波状态可用琼斯矩阵表述^[25]：

$ {\boldsymbol{T}}={\boldsymbol{R}} (-\varphi )\left[\begin{matrix}1 & 0\\0 & \exp (-{\mathrm{i}}\varGamma )\end{matrix}\right]{\boldsymbol{R}} (\varphi )\;, $

(2)

式中：

$ {\boldsymbol{R }}(\varphi )=\left[\begin{matrix}\cos \varphi & \sin \varphi \\-\sin \varphi & \cos \varphi \end{matrix}\right] $

为旋转矩阵；

$ \varGamma =2\text{π}\Delta nd/\lambda_{\mathrm{p}} $

，为液晶层的相位延迟量，d是 LCPG的厚度，

$ \lambda_{\mathrm{p}} $

是工作波长；

$ \Delta n $

是双折射率。输出光在远场的衍射级次可以通过周期傅里叶级数公式^[28]：

$ {\boldsymbol{E}}_{\text {out }}=\frac{1}{\varLambda} \int_0^{\varLambda} {\boldsymbol{T}} \cdot {{E}}_{\text {in }} {\mathrm{e}}^{-{\mathrm{i}} 2 {\text{π}} n x / \varLambda} {\mathrm{d}} x\;, $

(3)

计算得到。线偏振光入射光栅即

$ {{\boldsymbol{E}}}_{{\mathrm{in}}}=\left[\begin{array}{c}1\\0\end{array}\right] $

时，由式 (3)可知，出射光可表示为

$ {\boldsymbol{E}}_{\text {out }}={\boldsymbol{E}}_{\text {in }}\left (x-\lambda _{\mathrm{p}}\frac{f}{\varLambda}\right)\left[\begin{array}{c}1 \\-{\mathrm{i}}\end{array}\right]+{{E}}_{\text {in }}\left (x+\lambda_{\mathrm{p}} \frac{f}{\varLambda}\right)\left[\begin{array}{l}1 \\{\mathrm{i}}\end{array}\right]\;, $

(4)

式中：

$ f $

为焦距，

$ \lambda\mathit{\mathit{_{\mathrm{p}}}} $

本文中为852 nm。式 (4)可知，出射光由左旋圆偏振光 (left-hand circle polarization，LCP)和右旋圆偏振光 (right-hand circle polarization，RCP)组成。此外，正负一级的衍射效率由入射光的偏振态和液晶层的双折射相位延迟量共同决定，可表示为

$ {\eta }_{\pm 1}=\dfrac{ (1\mp S_{3}^{\prime})}{2}{\sin }^{2}\dfrac{\varGamma }{2}\;, $

(5)

式中：

$ S_{3}^{\prime} $

表征入射光圆偏振组分的归一化斯托克斯参量，

$ S_{3}^{\prime}=\pm 1 $

分别表示左旋圆偏振光和右旋圆偏振光。当液晶层的双折射相位延迟量满足半波条件时，左旋圆偏振分量出射到

$ +1 $

级，右旋圆偏振分量出射到

$ -1 $

级。

基于上述分析，本研究针对波长852 nm的探测光设计了级联分束准直器件，包括分束光栅和四分区准直光栅。为实现2×2二维阵列激光输出，分束光栅由两层栅线互相垂直的一级光栅和二级光栅和一层波片组成。线偏振光入射第一层光栅时先经过一级光栅的分束和偏振调制作用，变为两束一维圆偏振光，经过四分之一波片的偏振调制变为带有一定偏转角度的1×2一维线偏振光。经过二级光栅，前级光栅出射的两束激光经过分束和偏振调制产生2×2四束二维圆偏振光，如图1所示。

光栅相关参数可由光栅方程确定，其中

$ {\theta }_{0} $

是经过分束光栅后出射光的偏转角，这里m取±1。

$ (a+b)\sin\theta_0=\pm m\lambda_{\mathrm{p}}\; , $

(6)

$ \tan {\theta }_{0}= (\Delta x/2)/L\;, $

(7)

式中：

$ \Delta x $

是预设分束间隔2.42 mm；L为分束光栅与四分区准直光栅间隔即带有偏转角的阵列光的工作距离。综上，可计算出四束光的偏转角以及分束光栅的周期。分束之后经过四分区准直光栅对四束圆偏振阵列光进行准直，根据上述分析，左旋圆偏振分量出射到+1级，右旋圆偏振分量出射到

$-1 $

级。本文创新提出四分区分束光栅，同时对四束光分别准直形成准直的光束阵列，再经过四分之一波片的偏振调制变为带偏转角度为0°的2×2线偏振光阵列，其原理可由激光斜入射光栅的光栅方程给出^[29-30]：

$ (a+b) (\sin {\theta }_{{\mathrm{out}}}+\sin {\theta }_{{\mathrm{in}}})=\pm m\lambda_{\mathrm{p}} \;. $

(8)

为实现准直输出，

$ {\theta }_{\text{out}}={0}^{\circ } $

，

$ \theta\mathrm{_{in}} $

为入射准直光栅时的角度，由几何关系可知，

$ \tan {\theta }_{{\mathrm{in}}}=\sqrt{2}\Delta x/(2L )$

。

基于上述理论分析，在光学仿真软件中采用光线追迹法仿真计算得到准直光栅的周期为14.95 μm，分束光栅的周期为21.32 μm，加工得到一体化设计的光栅分束器。

2.2　多光束里德堡原子接收机测向原理

为确定入射电磁波的到达角，需要在至少两个不同位置上测量信号的相位。假定入射波为平面波，且测量平面与入射波方向垂直，如图2所示，则不同位置之间的相位差

$ \Delta {\phi }_{2,1} $

与到达角之间

$ \theta $

的关系可表述为^[31]

$ \Delta {\phi }_{2,1}={\phi }_{1}-{\phi }_{2}\approx kd\sin \theta\;, $

(9)

$ \theta\approx\mathrm{arcsin}\left(\frac{\Delta\phi_{2,1}}{kd}\right)\; , $

(10)

式中：

$ \phi_1 $

、

$ \phi_2 $

分为测量点1、2处测量信号的相位，

$ k=2\text{π}/ \lambda$

是波数；

$ \lambda $

是入射信号的波长；d是光束之间的间距。若测量位置的形成的平面与来波方向不垂直且光束间的相对高度为h，则其关系可表示为

$ \begin{split} \Delta \phi_{3,1}=& \phi_{\mathrm{ref} 3}-\phi_{\mathrm{refl}} \\\approx & k \sqrt{d^2+h^2} \sin \left[\theta+{\mathrm{arctan}} (h / d)\right]\end{split}\;, $

(11)

$ \theta\approx\mathrm{arcsin}\left(\dfrac{\Delta\phi_{3,1}}{k\sqrt{d^2+h^2}}\right)-\mathrm{arctan}\left(\frac{h}{d}\right)\; . $

(12)

3　实验装置

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为测量入射射频信号的方位，采用上述设计的一体化分束器件产生的光束阵列在铯原子气室内形成多个激发通道，完成入射电磁波的到达角测量，实验装置如图3所示。波长为852 nm的探测光从外腔半导体激光出射由光纤耦合头耦合产生空间光，经过偏振分光棱镜 (polarization beam splitter, PBS)和半波片 (half wave plate, HWP)按照极化分量比例分为两束激光。其中一束线偏振光经过PBS反射和平板分束镜的分束被一分为二，大部分功率透射过分束镜形成强泵浦光，经过高反射率反射镜 (high reflectivity, HR)和一个分束镜的两次反射进入原子气室1中，入射到平板分束镜的另一束弱探测光经过分束镜和反射镜的反射与强泵浦光共线反向传输产生铯原子饱和吸收谱用于探测光频率锁定。耦合光频率采用电磁诱导透明 (electromagnetically induced transparency, EIT)光谱进行锁定，上述透射过PBS的探测光再经PBS和半波片调整分为两束，其中一束反射进入原子气室2，与激光器出射的耦合光共线反向传播形成EIT光谱用于耦合光频率锁定。透射过PBS的耦合光和探测光经由反射镜或二向色镜的反射进入原子气室3形成测量光路用于信号的测量。构成超外差探测架构的本振信号与待测信号的频率分别为8.57 GHz和8.57 GHz+

$ \Delta f $

，其中

$ \Delta f=20 $

kHz。两个信号经由射频传输线分别馈入两个口径为4.6 cm × 3.2 cm的喇叭天线进行辐射，天线位置与气室之间的距离满足远场条件。通过优化信号源输出功率使得探测光产生的拍频信号达到最佳，以便实现信号接收。辐射本振场的喇叭在气室3的正后方并固定位置不变，待测场位于旋转盘上可在一维平面旋转用于测量不同来波处的到达角，当信号场旋转到与本振场位于同一线上时定义为0°。图3(a)为双光子激发里德堡原子的光路示意图，探测光激发铯原子从基态6S_1/2, F=4到中间态 6P_3/2, F=5，耦合光将原子从中间态激发到里德堡态44D_5/2。射频微波作用于44D_5/2→45P_3/2的跃迁，二者之间具有较大的跃迁偶极矩，可实现对射频场信息的高灵敏测量。图3(b)为系统测试图，采用级联分束器件对进入气室3的探测光进行均匀分束准直并与耦合光反向共线传输，分束后的四光束光斑大小一致均为1 mm，耦合光光斑直径为5 mm。探测光穿过气室进入四个相同型号光电探测器，探测器信号输出到四通道示波器以便同时接收不同测量位置处的光信号从而实现相位差的测量。

4　结果分析

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里德堡原子接收系统充当传统接收系统的混频器和低通滤波器响应和接收拍频信号，光束间隔为2.42 mm，在气室内任意光束位置处的电场强度

$ {E}_{\text{atoms}} $

是共极化方向的本振场

$ {E}_{\text{LO}} $

(

$ {E}_{\text{LO}}={E}_{\text{LO}}\cos \left ({\omega }_{\text{LO}}t+{\phi }_{\text{LO}}\right) $

)与信号场

$ {E}_{\text{SIG}} $

(

$ {E}_{\text{SIG}}={E}_{\text{SIG}}\cos \left ({\omega }_{\text{SIG}}t+{\phi }_{\text{SIG}}\right) $

)场强之和。探测光信号在不同位置处的时间函数可表示为

$ \left| {E}_{\text{atoms}}\right| \approx {E}_{\text{LO}}+{E}_{\text{SIG}}\cos \left (\Delta \omega t+{\phi }_{i,j}\right) \;,$

(13)

式中：

$ {\phi }_{i,j} $

对应位置i (

$ i\text{=1,2} $

)和j (

$ j=3,4 $

)处的信号相位；

$ \Delta \omega ={\omega }_{\text{LO}}-{\omega }_{\text{SIG}} $

。不同光电探测器可以测量不同光束位置处的探测光信号携带的相位信息，则相位差可表示为

$ \Delta \phi ={\phi }_{j}-{\phi }_{i} \;.$

(14)

光束阵列中任意两束探测光可进行相位测量，本实验中选取1，3位置处光束进行测量验证。本振位置固定，转动信号场的位置，相位差

$ \Delta \phi $

即本振与信号之间在测量位置处的相位差。综上，对于给定入射角

$ \theta $

，从光电探测器获得不同测量位置处的拍频信号以获得相位差，拍频周期为50 μs (对应中频信号20 kHz)，根据式 (10)或式 (12)即可实AOA的测量。光束1，3的水平间隔和垂直间隔均为2.42 mm，光斑相对位置及该处的拍频信号如图4所示。从图中可见，两个探测器接收到的IF信号具有相移。由于本振信号的喇叭天线是固定的，这种相移是由待测信号喇叭天线的不同入射角

$ \theta $

引起的，证明了方案的可行性。

采用图3所示实验装置，测量了xoy平面内

$ \theta $

=±40°以5°为步进间隔的入射射频场的到达角。入射波角度用带有刻度的可旋转量角器实现，其精度为1°。定义本振场与待测信号成180°时为测量0°作为校准参考，每组数据取5组数据的平均值，入射角

$ \theta $

对应的相位差的理论值与实测结果如图5(a)所示。根据测量的相位差即可反推出入射电磁波的方位角AOA，如图5(b)所示。此外，考虑到该接收方案中射频场可能在气室内部出现多次反射产生驻波影响测量结果，为探究气室对入射波相位的影响，使用电磁仿真软件分别模拟并计算了有无气室时不同位置处相位差以及对应的AOA。以5°为步进在±40°范围内旋转入射平面波角度，放置水平、垂直间隔均为2.42 mm的电场探针监测相位，气室的尺寸为 25 mm×25 mm×25 mm，与实验中实际使用的气室尺寸一致。将理论计算、仿真结果以及实测

$ \Delta \phi $

和对应的AOA结果如图所示。根据入射角得到的两个测量点的相位差理论值与仿真值 (无气室时)吻合良好 (图中紫色曲线与黄色点线)，测量值 (绿色)分布在理论曲线附近与理论之间有些许偏差。考虑到气室壁可能对测量造成的误差 (蓝色)，可见测量值与考虑气室影响时的理论值吻合较好，说明气室的确对测量会造成影响。消除气室带来的测量误差，根据图5(a)得到的相位差，由式 (12)分别计算入射电磁场AOA，由图可知，修正后的测量值与理论吻合良好且误差在1.5°(1.34°)以内，实现了基于原子的亚波长相位测量方法确定射频信号到达角的估计。此外，本方案中以1, 3两个光斑为例，对理论和测试方案进行了论证。事实上，2×2四光束阵列中任意两个光斑的随机组合均可完成一定方位内的角度测量且任意三个光斑的组合可完成任意到达角的测量。本方案可作为组合、嵌套等多阵列的最基本单元，为三维测量系统以及组合阵元实现多参数测量、多目标识别奠定了理论和实验基础。

目前，在量子微波电场测量领域，以到达角测量的光束阵列产生方式还鲜有研究，与本文所设计的级联光栅分束器的性能比较如表1所示。从表中可以看出，文献[18]和文献[32]的分束方式采用独立光学元件光路复杂且不利于集成，光束间均匀性难以保证。级联光栅分束器能够在保持光束直径不变的情况下实现2×2的分光效果，并可通过调整光栅常数精确控制衍射角，该器件结构紧凑，均匀性达95%，易于集成。因此，本文所设计的分束结构在测量精度及功率均匀性这两个指标上展现出显著优势，彰显其在原子微波测量中的应用潜力。

5　结　论

收起

本文提出了面向射频信号到达角测量的多光束里德堡原子接收机方案，设计了多光束阵列分束准直器件，利用光束阵列结合原子超外差技术实现了X波段 (8.57 GHz)入射射频信号−40°~+40°的到达角估计且误差小于1.5°，从理论和实验上证明了里德堡原子传感器信号到达角的精准估计能力。此外，分束准直器件具有一体化易集成的特点，可产生均匀性>95%、准直距离>15 cm的2×2二维阵列，任意三个光束组合即可实现任意方位角的测量，是构建三维测量系统以及组合阵元实现多参数测量、多目标识别系统的基础单元。利用其亚波长相位测量和高灵敏度特性，可在实现高精度定位的同时实现系统小型化，为开发新一代导航和遥感技术发展开辟新路径。

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2026年第53卷第7期

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doi: 10.12086/oee.2026.250354

接收时间：2025-11-18
首发时间：2026-10-22
出版时间：2026-07-25

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收稿日期：2025-11-18
修回日期：2026-01-29
录用日期：2026-02-02

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国防科技大学电子科学学院，湖南长沙 410072

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安强，anqiang18@nudt.edu.cn

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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