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提出了一种适用于高对比度目标的超分辨成像方法，通过结合对比度源反演方法与基于轨道角动量的超分辨技术，实现对高对比度目标的超分辨成像.首先采用基于轨道角动量的成像方法求解出对比度函数，将其作为对比度源反演方法的迭代初值，虽然初值结果与实际目标相差较大，但是由于初值中已经包含了关于目标的倏逝波信息，再利用这个初值开始迭代便可以得到超分辨重建结果，这种方法具有一定的抗噪声能力.本文研究表明，为了实现超分辨成像，一方面需要将目标对应的倏逝波信息转化到测量数据中，另一方面还要保证成像算法能够充分利用这些信息.本文所引申出的关于超分辨信息的概念对于逆散射超分辨成像的研究具有一定的借鉴意义.A method for the super-resolution imaging of two-dimensional (2D) high-contrast targets is presented. There are two main methods to reconstruct unknown targets with super resolution. One is to illuminate the targets with specific incident fields and transform the information about the evanescent waves into the propagation waves, and the other is to adopt non-linear inversion methods where the multiple scattering within the objects are considered. For the specific-incident-field method, it has been proved that the orbital-angular-momentum (OAM)-carrying electromagnetic (EM) waves can be employed to image unknown targets with super resolution. In fact, OAM-carrying EM waves can transform the information about the evanescent waves into the propagation waves. Thus the resolution of imaging results can break the Rayleigh limit, namely super resolution. At present, the application of OAM-based super-resolution algorithm is only valid for weak scatters based on Born approximation. For the non-linear inversion methods, the contrast source inversion (CSI) is widely used to reconstruct unknown targets, including large-contrast or complex ones. In the CSI method, the information about the evanescent waves is naturally involved since the EM coupling within the objects is taken into account. Thus super resolution can also be achieved by the CSI method. This paper demonstrates a novel algorithm for super resolution of large-contrast targets by combining the OAM-based super-resolution technique and the CSI method. And the better resolution is achieved than by the CSI method. Firstly, 2D OAM EM waves are generated using uniform circular array of line source, and the region of interest is illuminated by the OAM beams of different topological charges. So the information about the evanescent waves can be converted into the propagation waves. Secondly, Born approximation is used to obtain the starting value of the contrast. In the process of evaluating the contrast, the super-resolution information is fully utilized. Thirdly, the starting value of the contrast source is evaluated using the starting value of the contrast. Then the CSI method starts to be iterated. Since the information about the evanescent waves is always involved in the iterating process, super-resolution reconstruction can be obtained and is better than that obtained by the CSI method. Numerical experiments show the accuracy of the algorithm by testing different scenarios. The resolution and outline of the target are reconstructed accurately even when the measurement data are corrupted by noise. To sum up, to reconstruct unknown targets with super resolution, one should firstly transform the information about the evanescent waves into the propagation waves, and secondly make full use of the super-resolution information in the inversion methods. The conclusion of this paper may provide an insight into the super resolution in EM inverse scattering.
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Keywords:
- inverse scattering /
- super resolution /
- orbital angular momentum /
- electromagnetic imaging
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[1] Kirsch A 2016 An Introduction to the Mathematical Theory of Inverse Problems Second Edition (Beijing: World Publishing Corporation) pp191-195
[2] Yang J G, Huang X T, Jin T 2014 Compressed Sensing Radar Imaging (Beijing: Science Press) p5 (in Chinese) [杨俊刚, 黄晓涛, 金添 2014 压缩感知雷达成像(北京: 科学出版社) 第5页]
[3] Gao F Q, van Veen B D, Hagness S C 2015 IEEE Trans. Antennas Propag. 63 3540
[4] Rubæk T, Meaney P M, Meincke P, Paulsen K D 2007 IEEE Trans. Antennas Propag. 55 2320
[5] Slaney M, Kak A C, Larsen L E 1984 IEEE Trans. Microwave Theory Tech. 32 860
[6] Wang Y M, Chew W C 1989 Int. J. Imaging Syst. Technol. 1 100
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[8] van den Berg P M, Kleinman R E 1997 Inverse Prob. 13 1607
[9] van den Berg P M, Van Broekhoven A L, Abubakar A 1999 Inverse Prob. 15 1325
[10] van den Berg P M, Abubakar A, Fokkema J T 2003 Radio Sci. 38 8022
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[17] Huang F M, Zheludev N I 2009 Nano Lett. 9 1249
[18] Wong A M H, Eleftheriades G V 2015 Sci. Rep. 5 8449
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[20] Cui T J, Chew W C, Yin X X, Hong W 2004 IEEE Trans. Antennas Propag. 52 1398
[21] Aharonov Y, Anandan J, Popescu S, Vaidman L 1990 Phys. Rev. Lett. 64 2965
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[24] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
[25] Mair A, Vaziri A, Weihs G, Zeilinger A 2001 Nature 412 313
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[29] Lerosey G, Rosney J D, Tourin A, Fink M 2007 Science 315 1119
[30] Zelenchuk D, Fusco V 2013 IEEE Antennas Wirel. Propag. Lett. 12 284
[31] Mohammadi S M, Daldorff L K S, Bergman J E S, Karlsson R L, Thidé B, Forozesh K, Carozzi T D, Rsham B 2010 IEEE Trans. Antennas Propag. 58 565
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