标题： 从二维有限孔径散射场数据中检索小物体的直接采样方法 显示英文标题

标题： Direct sampling method to retrieve small objects from two-dimensional limited-aperture scattered field data

摘要： 在这项研究中，我们探讨了直接采样法（DSM）在有限 aperture 逆散射问题中识别小介电物体的应用。与以往的研究不同，我们考虑了对应于发射器位置的双基地测量配置，并为单个源和多个源设计了指示函数，同时将未知的测量数据转换为固定非零常数。为了阐明物体检测的适用性和局限性，我们证明了指示函数可以通过物体的无穷级数贝塞尔函数、材料属性、双基地角度以及转换后的常数来表达。基于理论结果，我们解释了双基地角度和转换常数如何影响 DSM 的成像性能。此外，我们的分析结果显示，较小的双基地角度可以提高成像精度，而转换常数的最佳选择对于实现可靠的物体检测至关重要。使用二维 Fresnel 数据集进行的数值模拟结果验证了理论发现，并展示了为小物体设计的指示函数的有效性和局限性。 显示英文摘要

摘要： In this study, we investigated the application of the direct sampling method (DSM) to identify small dielectric objects in a limited-aperture inverse scattering problem. Unlike previous studies, we consider the bistatic measurement configuration corresponding to the transmitter location and design indicator functions for both a single source and multiple sources, and we convert the unknown measurement data to a fixed nonzero constant. To explain the applicability and limitation of object detection, we demonstrate that the indicator functions can be expressed by an infinite series of Bessel functions, the material properties of the objects, the bistatic angle, and the converted constant. Based on the theoretical results, we explain how the imaging performance of the DSM is influenced by the bistatic angle and the converted constant. In addition, the results of our analyses demonstrate that a smaller bistatic angle enhances the imaging accuracy and that optimal selection of the converted constant is crucial to realize reliable object detection. The results of the numerical simulations obtained using a two-dimensional Fresnel dataset validated the theoretical findings and illustrate the effectiveness and limitations of the designed indicator functions for small objects.