DEVELOPMENT OF AN EFFICIENT DIFFRACTION TOMOGRAPHY TECHNIQUE WITH FAST-CONVERGENCE AND HIGH-RESOLUTION PROPERTIES APPLIED TO IMAGING OF UNDERGROUND OBJECTS

1.利用修正的MarQuardt方法研究了井间几何中均匀矩形目标的成像问题。数值结果表明，无论接收电场的极化程度如何，迭代格式都能提供高质量的重建结果，且具有快速收敛的特性。此外，我们还研究了自由空间中非均匀立方体目标的逆散射问题。从数值结果可以看出，即使在散射场数据中存在测量误差的情况下，物体的介电常数也能被成功地重建。2.在圆柱体的电磁散射中，我们将物体的介电常数分布展开为小波级数，得到散射场。结果表明，与传统的矩量法相比，该方法可以显著减少内存和计算时间。接下来，我们用FDTD方法处理了脉冲波在双层柱体上的散射问题。数值结果证实了我们可以从散射响应中模拟出物体的内部结构和介质参数。3.研究了用FDTD方法重建两层和四层介质的介电常数。利用修正的拟牛顿法和小波展开，推导了一种迭代算法。从数值结果可以看出，我们可以得到快速收敛和高分辨率的介电常数图像。该算法也适用于介质圆柱的成像。数值例子表明，我们可以成功地估计物体的位置和介电常数，有必要弄清楚物体的性质与散射场的波形之间的关系。此外，利用真实数据进行图像重建是非常重要的。这些都是今后工作的主题。

1.The problem of imaging a homogeneous rectangular object in cross-well geometry is considered using the revised Marquardt method. Numerical results prove that the iterative scheme provides high-quality reconstructions with fast cnvergence property regardless of the polarization of the received electric field. Furthermore we investigate the inverse scattering of an inhomogeneous cubic object, which is located in free space. It is seen from the numerical results that the object's permittivity can be successfully reconstructed even in the presence of measurement error in the scattered field data.2.In the electromagnetic scattering by a circular cylinder, we expand the permittivity profile of the object in a wavelet series to obtain the scattered field. It is shown that the memory storage and the computation time can be cosiderably reduced in comparison with the conventional moment method. Next, we deal with the scattering of a pulsed wave by a two-layred cylinder using the FDTD method. Numerical results confirm the we can esimate the inner structure and the medium parameter of the object from the scattering response.3.We study the reconstructinon of the permittivity of two-and four-layred media using the FDTD method. An iterative algorithm is derived employing the revised quasi-Newton method and wavelet expansion. It is concluded from the numerical results that we can obtain the fast-convergence and high-resolution image of the permittivity. This algorithm is also applied to imaging of a dielectric circular cylinder. Numerical examples demonstrate that we can successfully estimate the position and the permittivity of the object.It is neccessary to clarify the relationship between the object's properties and the waveform of the scattered field. Furthermore image reconstruction using real data is very important. These are the topics for future work.