A geometric optics model for high‐frequency electromagnetic scattering from dielectric cylinders

Abstract

The cylinder is a fundamental shape for (2‐D) geophysical modeling, and cylindrical objects (e.g., pipes) are a common target for ground penetrating radar. This paper presents physical and theoretical model responses for a cylinder which provide insight into responses that can be anticipated in field data. We calculate the exact expressions for the scattered field components of an obliquely incident plane wave over an infinitely long homogeneous dielectric cylinder and express them in the time domain. We project the field on a horizontal plane over the dielectric cylinder and interpret them for a large range of permittivity contrasts. The high‐frequency approximation presented in this paper includes the processes of specular reflection and critical refraction, which satisfy Snell’s law. Assuming the velocity of the surface waves is equal to the velocity of the fastest medium, and assuming their travel path is the shortest one possible, we derive a geometric optics model which is valid over a wide range of permittivities. We show that the critically refracted response can be separated and measured from the specular reflections in the received signal. The identification and isolation of these different responses of the bistatic measurements enable a characterization of the target’s properties, such as its size, orientation, and formation. We confirm our theoretical results by comparison with measurements using a physical model.