Abstract: The authors previously introduced a formalism for detecting objects through a complex dielectric interface using dyadic Green’s functions. This formalism improved upon existing approximations for the electromagnetic fields generated by and onto canonical structures such as loops and dipoles. However, targets of interest are not loops or dipoles but rather irregularly shaped structures. Using inadequate antenna models to represent complex targets can lead to signal-to-noise ratio uncertainties greater than 10 dB, often unacceptable for target detection. Restructuring the formalism has yielded relatively simple expressions for targets embedded in the same complex dielectric as the sensor, those at the dielectric interface, and those on the other side of the interface. The approach ensures that the hard part of the problem, calculations in the complex plane, need be done only once. Differences in the probability of detection are shown to be traceable to the radiation vector of a target in the same dielectric or to an equivalent target representation either at the dielectric interface or on the opposite side. In all three cases, these latter calculations are straightforward. The authors examine detection over a conducting surface with an embedded target. Results for simple and complex target geometries illustrate the power of the method.
　　In a previous investigation [1-4], the formalism for detecting complex objects embedded in complex dielectrics using the mathematical structure of the dyadic Green’s function [5] was introduced. The purpose of that study was to improve upon existing approximations for predicting the electromagnetic fields generated by and/or onto canonical structures such as loops and dipoles in conducting media. In this study, the authors further develop that mathematical formalism so as to apply it to the detection of irregularly shaped structures in two-region geometries that could be created by natural causes or human activity.
　　Two reasons motivate this effort: (1) its practical importance and (2) its value in elucidating the approximations required to handle the general case. Fig. 1 illustrates the application of image theory to the detection problem.
　　The major building block for solving the detection problem of Fig. 1 is the free-space dyadic Green’s function given by [5])
　　This section addresses two related calculations: (1) the computation of the electromagnetic field generated by a target transmitter/receiver and striking a target, and (2) the computation of the electromagnetic field generated by the target that strikes the transmitter/receiver. For brevity the plane of separation shown in Fig. 2 is called the ground plane; for example Region 1 could be air or a moist region and Region 2 could be snow (an avalanche condition). The target could be a transponder, designed to respond in such an avalanche condition.
　　The authors derive electromagnetic fields relevant to the detection of complex and irregularly shaped objects much smaller than a wavelength. The authors use a formalism based on the dyadic Green’s function (a two-region case is presented) in conjunction with components of a target’s surface and/or internal current density. The resulting mathematical structure allows one to examine the salient features of the far field generated by the source in a straightforward manner.