Focused Ground-Penetrating Radar Backprojection Through a Lossy Interface

摘要

We derive the propagation path at a lossless-lossy interface for use in backprojecting synthetic aperture radar (SAR) when used in ground- penetrating applications. To create a synthetic aperture radar (SAR) image using ground-penetrating radar (GPR) data, one must know the round-trip distance between the antenna aperture and the point to be focused on. Given a beginning point O in media II, a buried point P within media I, and the relationship between the points, the index of refraction n and the total 'luminal' distance R = n(sub1)R(sub1) + n(sub2)R(sub2) must be derived. Deriving the equations that describe the optical path length between the originating point O and the terminating point P is best done through multiple transformations. The purpose of these transformations is to express the equations in a form easily understood with minimal mathematical complexity. The price to be paid is measured in proliferation of equations. However, at the end of the process, the resulting equations are few in number, comparatively simple, and written in terms of typical media parameters (dielectric constants, relative permeabilities, etc). These equations are transcendental and require numerical solution via Newton-Raphson interaction.