摘要
对恢复三维空间中的两层物体进行了研究,使用无相位远场方法确定三维物体形状的唯一性。远场相位信息难以获取,而无相位远场信息更容易测量,使用无相位远场确定多层散射体形状更加方便有效。首先运用Helmholtz方程建立问题模型,为克服平面波的平移不变性,选择3个叠加平面波作为入射波,获得物体更为丰富的信息,引入与模型相对应的格林函数揭示物体与入射波的相互作用,最终证明只知无相远场信息情况下可以唯一确定两层散射体形状,即其边界和材料系数可被唯一确定。
The uniqueness of the shape of the three-dimensional object is determined by using the phaseless far field method.The far field phase information is difficult to obtain,but the phaseless far field information is easier to measure,and it is more convenient and effective to use the phaseless far field to determine the shape of multilayer scatterers.In order to overcome the translational invariance of plane waves,three superimposed plane waves are selected as incident waves to obtain more abundant information about the object.Green s function corresponding to the model is introduced to reveal the interaction between the object and the incident wave.Finally,it is proved that the shape of the two-layer scatterer can be uniquely determined when the far field information of the phase is unknown.In addition,its material coefficient can also be uniquely determined.
作者
胡双霞
李金红
赵琳琳
王岩
HU Shuangxia;LI Jinhong;ZHAO Linlin;WANG Yan(Mathematics and Artificial Intelligence Division,Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China)
出处
《齐鲁工业大学学报》
2025年第4期40-45,共6页
Journal of Qilu University of Technology
基金
山东省科技型中小企业创新能力提升工程(2021TSGC1017)。
