In this study, we propose a sampling-type algorithm for a real-time identification of a set of short, linear perfectly conducting cracks in a two-dimensional bistatic measurement configuration. The indicator function is defined based on the asymptotic formula of the far-field pattern of the scattered field due to cracks. To clarify the applicability of the proposed algorithm, we investigate the mathematical structure of the indicator function using the Jacobi–Anger expansion formula. In particular, we derive an asymptotic formula for the indicator function in terms of the Bessel functions of the first kind and the parameters that depend on the bistatic measurement configuration. This asymptotic structure reveals intrinsic properties of the indicator function. We validate the theoretical results via various simulation results with synthetic and experimental data.

在这项研究中，我们提出了一种采样型算法，用于在二维双基测量配置中实时识别一组短的、线性的完美导电裂纹。指示函数是根据裂纹引起的散射场远场模式的渐近公式定义的。为了阐明所提出算法的适用性，我们使用 Jacobi-Anger 展开公式研究了指示函数的数学结构。特别地，我们根据第一类贝塞尔函数和依赖于双基地测量配置的参数推导出指示函数的渐近公式。这种渐近结构揭示了指示函数的内在特性。