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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
[7] Kleinman R E, van den Berg P M 1992 J. Comput. Appl. Math. 42 17
[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
[11] Oliveri G, Anselmi N, Massa A 2014 IEEE Trans. Antennas Propag. 62 5157
[12] Anselmi N, Salucci M, Oliveri G, Massa A 2015 IEEE Trans. Antennas Propag. 63 4889
[13] Pu M B, Wang C T, Wang Y Q, Luo X G 2017 Acta Phys. Sin. 66 144101 (in Chinese) [蒲明博, 王长涛, 王彦钦, 罗先刚 2017 66 144101]
[14] Guo C, Zhang Y 2017 Acta Phys. Sin. 66 147804 (in Chinese) [郭畅, 张岩 2017 66 147804]
[15] Betzig E, Trautman J K, Harris T D, Weiner J S, Kostelak R L 1991 Science 251 1468
[16] Hartschuh A, Sanchez E J, Xie X S, Novotny L 2003 Phys. Rev. Lett. 90 095503
[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
[19] Dong X H, Wong A M H, Kim M, Eleftheriades G V 2017 Optica 4 1126
[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
[22] Berry M V 1994 J. Phys. A: Math. Gen. 27 L391
[23] Ferreira P J S G, Kempf A 2006 IEEE Trans. Signal Process. 54 3732
[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
[26] Liu K, Cheng Y Q, Li X, Qin Y L, Wang H Q, Jiang Y W 2016 IEEE Antennas Wirel. Propag. Lett. 15 1873
[27] Liu K, Cheng Y Q, Gao Y, Li X, Qin Y L, Wang H Q 2017 Appl. Phys. Lett. 110 164102
[28] Li L L, Li F 2013 Phys. Rev. E 88 033205
[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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