Real-time detection of small objects in transverse electric polarization: Evaluations on synthetic and experimental datasets

It is well-known that if one applies Kirchhoff migration (KM) to identify small objects when their values of magnetic permeabilities differ from those of the background (or transverse electric polarization), their location and outline shape cannot be satisfactorily retrieved because rings of large magnitudes centered at the location of objects appear in the imaging results. Fortunately, it is possible to recognize the existence and approximated location of objects in the 2D Fresnel dataset through the traditional KM, but no theoretical explanation for this phenomenon has been verified. Here we show that the imaging function of KM when tested on the Fresnel dataset can be expressed as squared zero-order and first-order Bessel functions and as an infinite series of Bessel functions of integer order greater than two. We also explain why the existence and approximate location of objects can be identified. This theoretical result is supported by numerical simulations on synthetic and experimental data.