基于旋转多普勒效应的自旋目标转速估计方法

印必还; 何姿; 丁大志

doi:10.7498/aps.72.20230807

摘要

旋转多普勒效应是携带轨道角动量的涡旋电磁波用于旋转目标探测时的一种重要现象. 相比于传统平面波, 旋转多普勒效应使得涡旋电磁波可以沿目标旋转轴方向探测到目标的自旋运动. 然而, 对于特定结构的自旋目标, 利用整数阶轨道角动量波束进行探测仍然存在盲区. 为了拓展基于旋转多普勒效应的探测方案的适用范围, 本文基于时频分析方法, 研究了在分数阶轨道角动量波束正入射和斜入射时自旋目标的转速估计方法. 首先基于理想散射点模型, 推导了其在整数阶和分数阶轨道角动量波束正入射和斜入射时的回波模型, 以及理论时频曲线. 其次, 以三维实际目标为例, 基于矩量法和短时傅里叶变换方法, 得到目标在分数阶轨道角动量波束入射时的回波及其时频图, 并从时频图中提取时频脊及其波动周期, 以此估计目标自旋速度. 结果证明, 分数阶轨道角动量波束无论在正入射还是斜入射情况下均可有效地估计自旋目标的旋转速度, 并且能够克服整数阶轨道角动量波束的探测盲区, 在探测目标自旋运动时具有更广泛的适用性.

关键词:

Abstract

Rotational Doppler effect is an important phenomenon when the vortex electromagnetic wave carrying orbital angular momentum is used to detect a rotating target. Compared with the traditional plane wave case, rotational Doppler effect enables the vortex electromagnetic wave to detect the spin motion along the rotation axis of target. However, there are still some blind zones when the integer orbital angular momentum beams are used to detect specific spinning objects. To expand the application scope of detection scheme based on the rotational Doppler effect, according to the time-frequency analysis, in this paper we study the method of estimating the rotation speed of spinning objects under the normal incidence and oblique incidence of fractional orbital angular momentum beams. Firstly, based on the ideal scattering point model, the echo models are derived under the normal incidence and oblique incidence of integer orbital angular momentum beam and fractional orbital angular momentum beam, respectively, as well as theoretical time-frequency curves. Then taking the three-dimensional practical object for example, the echo under the incidence of fractional orbital angular momentum beams and its time-frequency graph are achieved by using the momentum method and short-time Fourier transform. The time-frequency ridge and its fluctuation period are extracted from the time-frequency graph, thereby estimating the spinning speed of target. The results show that the fractional orbital angular momentum beams can be used to estimate the rotation speed of spinning objects effectively, whether it is normal incidence or oblique incidence, thereby solving the problem about the detection blind zone of integer orbital angular momentum beams, and improving the applicability in detecting spin motion.

Keywords:

作者及机构信息

南京理工大学电子工程与光电技术学院, 南京　210094

通信作者: 何姿, 15850554055@163.com

基金项目: 国家自然科学基金(批准号: 61931021, 62071231)、江苏省自然科学基金(批准号: BK20211571)和中央高校基本科研业务专项资金(批准号: 30921011207)资助的课题.

Authors and contacts

School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Corresponding author: He Zi, 15850554055@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61931021, 62071231), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20211571), and the Fundamental Research Funds for the Central Universities, China (Grant No. 30921011207).

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参考文献

[1]	Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185 Google Scholar
[2]	Courtial J, Dholakia K, Robertson D A, Allen L, Padgett M J 1998 Phys. Rev. Lett. 80 3217 Google Scholar
[3]	Courtial J, Robertson D A, Dholakia K, Allen L, Padgett M J 1998 Phys. Rev. Lett. 81 4828 Google Scholar
[4]	Mohammadi S M, Daldorff L K S, Bergman J E S, Karlsson R L, Thide B, Forozesh K, Carozzi T D, Isham B 2010 IEEE Trans. Antennas Propag. 58 565 Google Scholar
[5]	Yin B H, He Z, Chen R S 2019 Appl. Comput. Electromagn. Soc. J. 34 1637
[6]	Thide B, Then H, Sjoholm J, Palmer K, Bergman J, Carozzi, T D, Istomin Ya N, Ibragimov N H, Khamitova R 2007 Phys. Rev. Lett. 99 087701 Google Scholar
[7]	Liu K, Cheng Y Q, Yang Z C, Wang H Q, Qin Y L, Li X 2015 IEEE Antennas Wirel. Propag. Lett. 14 711 Google Scholar
[8]	Zhang C, Chen D, Jiang X F 2017 Sci. Rep. 7 15412 Google Scholar
[9]	Zhao M Y, Gao X L, Xie M T, Zhai W S, Xu W J, Huang S G, Gu W Y 2016 Opt. Lett. 41 2549 Google Scholar
[10]	Zheng J Y, Zheng S L, Shao Z L, Shao Z L, Zhang X M 2018 J. Appl. Phys. 124 164907 Google Scholar
[11]	Gong T, Cheng Y Q, Li X, Chen D C 2018 IEEE Microwave Wireless Compon. Lett. 28 843 Google Scholar
[12]	Zhou Z L, Cheng Y Q, Liu K, Wang H Q, Qin Y L 2019 IEEE Sens. Lett. 3 1 Google Scholar
[13]	Yin B H, He Z, Chen R S 2022 IEEE Trans. Antennas Propag. 70 9971 Google Scholar
[14]	Luo Y, Chen Y J, Zhu Y Z, Li W Y, Zhang Q 2019 IET Radar Sonar Navig. 14 2 Google Scholar
[15]	李瑞, 李开明, 张群, 梁佳, 罗迎 2021 电子与信息学报 43 547 Google Scholar Li R, Li K M, Zhang Q, Liang J, Luo Y 2021 J. Electron. Inf. Technol. 43 547 Google Scholar
[16]	王煜, 刘康, 王建秋, 王宏强, 程永强 2021 雷达学报 10 740 Google Scholar Wang Y, Liu K, Wang J Q, Wang H Q, Cheng Y Q 2021 J. Radars 10 740 Google Scholar
[17]	Lavery M P J, Speirits F C, Barnett S M, Padgett M J 2013 Science 431 537 Google Scholar
[18]	Zheng S L, Hui X N, Jin X F, Chi H, Zhang X M 2015 IEEE Trans. Antennas Propag. 63 1530 Google Scholar
[19]	Berry M V 2004 J. Opt. A:Pure Appl. Opt. 6 259 Google Scholar
[20]	Liu H Y, Wang Y, Wang J Q, Liu K, Wang H Q 2021 IEEE Antennas Wirel. Propag. Lett. 20 948 Google Scholar

施引文献

图 1 波束轴指向目标旋转中心并垂直于旋转平面的理想入射情况

Fig. 1. The ideal illumination with the beam axis pointing to the center of rotation and perpendicular to the plane of rotation.

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图 2 DBoR散射中心分布情况

Fig. 2. The distribution of scattering centers for the DBoR.

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图 3 目标旋转平面的偏转

Fig. 3. The deflection of the rotating plane.

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图 4 回波频谱　(a) FFT频谱; (b) 理论时频曲线

Fig. 4. The frequency spectrum of echo: (a) FFT spectrum; (b) theoretical time-frequency curve.

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图 5 当$N = 1$时的回波频谱　(a) $l = 0.5$; (b) $l = 1.5$ (c) $l = 2.5$; (d) $l = 3.5$

Fig. 5. Echo frequency spectrums with $N = 1$: (a) $l = 0.5$ ; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$.

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图 6 当$N = 2$时的回波频谱　(a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

Fig. 6. Echo frequency spectrums with $N = 2$: (a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$.

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图 7 当$N = 3$时的回波频谱　(a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

Fig. 7. Echo frequency spectrums with $N = 3$ and: (a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$.

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图 8 目标旋转平面偏转时的非理想入射情况

Fig. 8. The unideal illumination with the deflection of the rotating plane.

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图 9 当$N = 3$时, 旋转平面偏转后的回波频谱　(a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

Fig. 9. Echo frequency spectrums after the tilt of rotation plane with $N = 3$: (a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

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图 10 旋转平面偏转后模式1.5回波时频图及其局部放大

Fig. 10. Echo frequency time-frequency graphs of mode 1.5 after the tilt of rotation plane and its local zoom

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图 11 旋转平面偏转后模式2.5回波时频图及其局部放大

Fig. 11. Echo frequency time-frequency graphs of mode 2.5 after the tilt of rotation plane and its local zoom

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图 12 风速仪模型

Fig. 12. The anemoscope model.

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图 13 辐射电场的相位梯度以及模式谱　(a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

Fig. 13. Phase gradients and mode spectrums of the radiation electric field with: (a) $l = 0.5$ (b) $l = 1.5$ (c) $l = 2.5$ (d) $l = 3.5$.

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图 14 当$N = 3$时的回波频谱　(a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

Fig. 14. Echo frequency spectrums with $N = 3$: (a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

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图 15 当$N = 3$时, 旋转平面偏转后的回波频谱　(a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

Fig. 15. Echo frequency spectrums after the tilt of rotation plane with $N = 3$: (a) $l = 0.5$; (b) $l = 1.5$; (c) $l = 2.5$; (d) $l = 3.5$

下载: 全尺寸图片幻灯片

图 16 模式0.5波束正入射目标时的时频图及时频曲线　(a) 时频图; (b) 时频曲线

Fig. 16. Time-frequency graph and curve under the normal incidence of the beam with mode 0.5: (a) Time-frequency map; (b) time-frequency curve

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图 17 模式2.5波束斜入射目标时(旋转平面绕Y轴倾斜5°)的时频图及时频曲线　(a) 时频图; (b) 时频曲线

Fig. 17. Time-frequency graph and curve under the oblique incidence (the plane of rotation tilts around Y axis with 5°) of the beam with mode 2.5: (a) Time-frequency map; (b) time-frequency curve

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map

[1]	Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185 Google Scholar
[2]	Courtial J, Dholakia K, Robertson D A, Allen L, Padgett M J 1998 Phys. Rev. Lett. 80 3217 Google Scholar
[3]	Courtial J, Robertson D A, Dholakia K, Allen L, Padgett M J 1998 Phys. Rev. Lett. 81 4828 Google Scholar
[4]	Mohammadi S M, Daldorff L K S, Bergman J E S, Karlsson R L, Thide B, Forozesh K, Carozzi T D, Isham B 2010 IEEE Trans. Antennas Propag. 58 565 Google Scholar
[5]	Yin B H, He Z, Chen R S 2019 Appl. Comput. Electromagn. Soc. J. 34 1637
[6]	Thide B, Then H, Sjoholm J, Palmer K, Bergman J, Carozzi, T D, Istomin Ya N, Ibragimov N H, Khamitova R 2007 Phys. Rev. Lett. 99 087701 Google Scholar
[7]	Liu K, Cheng Y Q, Yang Z C, Wang H Q, Qin Y L, Li X 2015 IEEE Antennas Wirel. Propag. Lett. 14 711 Google Scholar
[8]	Zhang C, Chen D, Jiang X F 2017 Sci. Rep. 7 15412 Google Scholar
[9]	Zhao M Y, Gao X L, Xie M T, Zhai W S, Xu W J, Huang S G, Gu W Y 2016 Opt. Lett. 41 2549 Google Scholar
[10]	Zheng J Y, Zheng S L, Shao Z L, Shao Z L, Zhang X M 2018 J. Appl. Phys. 124 164907 Google Scholar
[11]	Gong T, Cheng Y Q, Li X, Chen D C 2018 IEEE Microwave Wireless Compon. Lett. 28 843 Google Scholar
[12]	Zhou Z L, Cheng Y Q, Liu K, Wang H Q, Qin Y L 2019 IEEE Sens. Lett. 3 1 Google Scholar
[13]	Yin B H, He Z, Chen R S 2022 IEEE Trans. Antennas Propag. 70 9971 Google Scholar
[14]	Luo Y, Chen Y J, Zhu Y Z, Li W Y, Zhang Q 2019 IET Radar Sonar Navig. 14 2 Google Scholar
[15]	李瑞, 李开明, 张群, 梁佳, 罗迎 2021 电子与信息学报 43 547 Google Scholar Li R, Li K M, Zhang Q, Liang J, Luo Y 2021 J. Electron. Inf. Technol. 43 547 Google Scholar
[16]	王煜, 刘康, 王建秋, 王宏强, 程永强 2021 雷达学报 10 740 Google Scholar Wang Y, Liu K, Wang J Q, Wang H Q, Cheng Y Q 2021 J. Radars 10 740 Google Scholar
[17]	Lavery M P J, Speirits F C, Barnett S M, Padgett M J 2013 Science 431 537 Google Scholar
[18]	Zheng S L, Hui X N, Jin X F, Chi H, Zhang X M 2015 IEEE Trans. Antennas Propag. 63 1530 Google Scholar
[19]	Berry M V 2004 J. Opt. A:Pure Appl. Opt. 6 259 Google Scholar
[20]	Liu H Y, Wang Y, Wang J Q, Liu K, Wang H Q 2021 IEEE Antennas Wirel. Propag. Lett. 20 948 Google Scholar

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基于旋转多普勒效应的自旋目标转速估计方法