From The Near-field Data To Reconstruct The Non-uniform Scattering Body Inverse Scattering Problem

The inverse scattering theory researches focused on the reconstruction of scat-terer from far-field data according to the far-field equation, since the inverse scattering problem appeared . The far-field observation data was more vulnerable to noise and other factors, therefore the observers gained the observation data by near-field data primarily in engineering practical, and the researchers hoped to reconstruct the scatterer through the near field data, which made the study on inverse scattering problem using near-field data becoming more important. However, the archives about this aspect were few until now, the solving process (or reconstructing process) of the existing methods was complex and difficult to achieve. This dissertation conducted the research in view of the above these questions. In the dissertation, the research object was the penetration inhomogeneous medium which was prevalence in the objective worlds; the actuation source was point source which was actual widely used in the engineering practical. The two-dimensional mathematical model of reconstruction by point source and near-field was established, the reconstruction method was designed base-on the model, finally, the scatterer reconstruction was implemented.The article structure is as follows:The first chapter is an introduction, this chapter emphasises on the introduction of research background, the present situation and the development trend in domestic and abroad and research contents, gives the structure of this dissertation .The second chapter is the basic theory, this chapter focuses on introducting of the theoretical knowledge involved by this dissertation , provides the theory support for the following research process.In the third chapter, the mixed reciprocity principle is proved under the circumstance of point source and plane wave based-on A. Kirsch's improved linear sampling method, and then a operator F which maps the near-field data to far-field data is constructed, and the relationship between far-field operator and near-field operator is established on the basis of obtained mixed reciprocity principle. Furthermore, the method of reconstructing inhomogeneous scatterer is obtained. In the numerical experiments part of this chapter, the near field E is approximated by PML method, this technique adopted here transformed the unbounded region problems to the bounded region problems, which obviously reduces the difficulty of adding boundary manually, computation load, obtains a good computing effect.In the forth chapter, the scatter is reconstructed by Born approximated method and using far-field data directly.This method takes advantage of the properties of point-source, and then the approxition of Fourier transformation of inhomogeneous scatterer's m(x) is presented. Furthermore, the m(x) is gained through the Fourier inverse transformation.