Research On Electromagnetic Inverse Scattering Problems Based On TSOM

Solving of the inverse problems, as the words suggest, is a study method to find the reasons with results. The inverse scattering problems of electromagnetic is an important non-touch and non-destructive detection technique. Recently, it has been widely used in many fields, including the location, the microwave remote sensing, the geographical detection, the non-destruction detec-tion, the biological imaging. In common, the inverse scattering problems of electromagnetic is to retrieve or reconstruct the unknown objects’s physical and geometric information, including the location, size, quantity, boundary and distribution of permittivity, with the measured scattered field or far field outside of the unknown objects, due to the incidence to the unknown objects.The main topic of this thesis is the inverse scattering imaging with electromagnetic wave, we analyzed the model of the inverse scattering problems, and introduced a Sub-space based Opti-mization Method (SOM). The characteristics of the SOM algorithm is the analysis of the induced current in its space spectrum. The induced current is decomposed into deterministic current and ambiguous current. The deterministic current applies to the space spectrum with high singular val-ue and is obtained by directly calculation. But the ambiguous current is very sensitive to the noise or other interference and has to be obtained by the optimization method. Thus, this method not only improved the robust against noise, but reduced the space of solution and favours the stabili-ty. Based on the FFT method in matrix calculation, we introduced a FFT-SOM algorithm, which could heavily increase the calculation efficiency. Based on the spectrum analysis of the mapping function of the induced current into the region under detection, a two-fold SOM algorithm could further reduced the space of solution. In the numerical simulations, the SOM algorithm showed fast convergence and high noise robust advantages.Then, the inverse scattering problem of PEC scatterers were investigated. The inverse scatter-ing problems of PEC scatterers under transverse electric (TE) wave has been a difficult problem in computational electromagnetics. Applied the TSOM algorithm, we realized the reconstruction of PEC scatterers with any location, any quantities and any boundary. Moreover, the algorithm did not need any prior information of the scatterers. Then, the TSOM algorithm was further verified with the measured scattered field and obtained good reconstruction results. The influence of mul-tiple scattering effect to the SOM algorithm was discussed by introducing a known PEC circular cylinder beside the region under detection. It is seen that the reconstruction results (both the objec- tive function and relative error of permittivity) were not a monotonic function of either the radius of cylinder or the separation distance; the auxiliary cylinder is not always helpful in the inverse scattering problems.At last,we designed a measurement system of scattered field and realized the reconstruction with experimental data. The measured data suffered from the noise and other disturbance, the TSOM algorithm was especially excellent in dealing with experimental data, due to its high robust against noise. The influence from the outside objects, including the coupling effect between the antennas, could be decreased by analyzing the difference between the theoretical incident field and the analytical incident field. And the introduce of correction method,based on the comparison between a theoretical scattered field and analytical scattered field from a known scatterer, could improve the inherent error due to the non ideality of the scatterers and incident fields in two-dimensional measurement.