We present monostatic sampling methods for limited-aperture scattering problems in two dimensions. The direct sampling method (DSM) is well known to provide a robust, stable, and fast numerical scheme for imaging inhomogeneities from multistatic measurements even with only one or two incident fields. However, in practical applications, monostatic measurements in limited-aperture configuration are frequently encountered. A monostatic sampling method (MSM) was studied in full-aperture configuration in recent literature. In this paper, we develop MSM in limited-aperture configuration and derive an asymptotic formula of the corresponding indicator function. Based on the asymptotic formula, we then analyze the imaging performance of the proposed method depending on the range of measurement directions and the geometric, material properties of inhomogeneities. Furthermore, we propose a modified numerical scheme with multi-frequency measurements that improve imaging performance, especially for small anomalies. Numerical simulations are presented to validate the analytical results.
翻译:我们对有限孔径散射问题采用了两个层面的单一抽样方法。众所周知,直接抽样方法(DSM)为多静态测量的成像异同性提供了一个稳健、稳定、快速的数字方法,即使只有一两个事故场。然而,在实际应用中,往往会遇到有限孔径构造的单一测量。在最近的文献中,以全孔配置方式研究了一种单一抽样方法(MSM)。在本文中,我们开发了有限孔径配置的MSM,并得出了相应指标函数的无症状公式。根据无孔径公式,我们随后根据测量方向和异差的几何和物质特性的范围,分析了拟议方法的成像性能。此外,我们提出了一个修改的数字方法,用多频率测量方法改进成像性能,特别是小异常的成像性。提出了数值模拟,以验证分析结果。