【摘要】 为了获得散射介质中异质结构信息 ,建立了层状均匀介质中含有一个较小的异质球模型 ,考虑小异质球对光(电磁波 )的传播的影响是微扰的 ,在吸收边界条件下求得漫射方程一级微扰的基本解 .同时考察漫射方程在二维傅里叶空间里形式解的特性 ,提出一种新颖的加权逆傅里叶变换 .在加权傅里叶变换作用下 ,模型的表面数据在异质球位置上存在奇异性 ,结合数据本身的对称性 ,从而可以确定异质球的三维位置更多还原

【Abstract】 Characterization of the structure of spatial inhomogeneities embedded in a highly scattering medium is required in many fields. In this paper, a model of a stratified medium embedded with an inhomogeneous ball is considered. With an assumption that the ball is small enough, a perturbation solution to diffusion equation is obtained with some boundary treatments. According to the characteristics of this solution in the two\|dimensional Fourier space, a new weighted Fourier transform is used to process the surface data. After this process, a singularity appears at the center of the ball. Combining with the symmetry of the surface data, the information of three\|dimensional position of the ball is determined.更多还原