In this study, we consider the application of orthogonality sampling method (OSM) with single and multiple sources for a fast identification of small objects in limited-aperture inverse scattering problem. We first apply the OSM with single source and show that the indicator function with single source can be expressed by the Bessel function of order zero of the first kind, infinite series of Bessel function of nonzero integer order of the first kind, range of signal receiver, and the location of emitter. Based on this result, we explain that the objects can be identified through the OSM with single source but the identification is significantly influenced by the location of source and applied frequency. For a successful improvement, we then consider the OSM with multiple sources. Based on the identified structure of the OSM with single source, we design an indicator function of the OSM with multiple sources and show that it can be expressed by the square of the Bessel function of order zero of the first kind an infinite series of the square of Bessel function of nonzero integer order of the first kind. Based on the theoretical results, we explain that the objects can be identified uniquely through the designed OSM. Several numerical experiments with experimental data provided by the Institute Fresnel demonstrate the pros and cons of the OSM with single source and how the designed OSM with multiple sources behave.

翻译：本研究考虑将单源及多源正交采样法（OSM）应用于有限孔径逆散射问题中微小物体的快速识别。我们首先应用单源正交采样法，并证明该单源指示函数可表示为第一类零阶贝塞尔函数、第一类非零整数阶贝塞尔函数的无穷级数、信号接收器范围及发射源位置等参数的表达式。基于此结果，我们阐明虽然可通过单源正交采样法识别物体，但识别效果显著受源位置及工作频率影响。为有效改进，我们进一步考虑多源正交采样法。基于单源正交采样法的结构分析，我们设计了多源正交采样法的指示函数，并证明其可表示为第一类零阶贝塞尔函数的平方与第一类非零整数阶贝塞尔函数平方的无穷级数。根据理论结果，我们证明所设计的正交采样法能够唯一识别物体。利用菲涅耳研究所提供的实验数据进行多次数值实验，展示了单源正交采样法的优缺点及所设计多源正交采样法的性能表现。