论文标题
从被动测量中唯一确定散射屏幕的形状
Unique determination of the shape of a scattering screen from a passive measurement
论文作者
论文摘要
我们考虑了来自声音柔软的扁平屏幕的固定频率声散射的问题。更确切地说，障碍物仅限于二维平面并与任意事件波相互作用，它将声波散布到三维空间。该模型在反射声纳和天线的研究和设计中尤其重要，因为人们无法假设入射波是平面波。我们的主要结果是，鉴于屏幕所在的平面，任何单个任意入射波产生的远场图案都决定了屏幕的确切形状，只要与平面相对于平面不对称。即使是屏幕，其形状是任意连接的平滑域的屏幕。这与早期的工作形成鲜明对比的是，事件波必须是平面波，或者仅确定多边形散射器的最新工作。
We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to three-dimensional space. The model is particularly relevant in the study and design of reflecting sonars and antennas, cases where one cannot assume that the incident wave is a plane wave. Our main result is that given the plane where the screen is located, the far-field pattern produced by any single arbitrary incident wave determines the exact shape of the screen, as long as it is not antisymmetric with respect to the plane. This holds even for screens whose shape is an arbitrary simply connected smooth domain. This is in contrast to earlier work where the incident wave had to be a plane wave, or more recent work where only polygonal scatterers are determined.
