Application of Kirchhoff Migration from Two-Dimensional Fresnel Dataset by Converting Unavailable Data into a Constant

In this contribution, we consider an application of the Kirchhoff migration (KM) technique for fast and accurate identification of small dielectric objects from two-dimensional Fresnel experimental dataset. Generally, for successful application of the KM, a complete set of elements from the so-called multi-static response (MSR) matrix must be collected; however, in the Fresnel experimental dataset, many of the elements of an MSR matrix are not measurable. Nevertheless, the existence, location, and outline shape of small objects can be retrieved using the KM by converting unavailable data into the zero constant. However, the theoretical reason behind such conversion has not been confirmed to date. In order to explain this theoretical reason, we convert unavailable measurement data into a constant and demonstrate that the imaging function of the KM can be expressed by an infinite series of the Bessel functions of integer order of the first kind, the object’s material properties, and the converted constant. Following the theoretical result, we confirm that converting unknown data into the zero constant guarantees good results and unique determination of the objects. Finally, various numerical simulation results from Fresnel experimental dataset are presented and discussed to validate the theoretical result.