Finite-difference time-domain formulation of an inverse scattering scheme for remote sensing of conducting and dielectric targets: Part II - Two dimensional case

This paper introduces a technique for time-domain electromagnetic inverse scattering based upon the use of a two-dimensional, finite-difference time-domain (FD-TD) forward scattering field representation in numerical feedback loop with a nonlinear optimization routine. Causality is exploited to reconstruct the actual target surface contour in a sequential and cumulative manner as the illuminating wavefront sweeps across the target. This approach appears to require a minimum amount of scattered field information. A number of examples are reported where the only data needed is the time waveform of a scattered pulse for the transverse magnetic (TM) polarization case, observed at just a single point in the near field. These examples include the reconstruction of two-dimensional conducting and homogeneous dielectric target shapes such as triangles, rectangles, and trapezoids. A dielectric target with reentrant features, resembling the letter “J” is also reconstructed from a single point observation. The effects of measurement signal-to-noise ratio upon this inverse-scattering technique are determined via numerical experiments. These effects are discussed in two contexts: 1) probability of exact reconstruction vs. signal-to-noise ratio, and 2) sensitivity of reconstructions to noise. It is shown that, even at low signal-to-noise ratios (where the probability of exact reconstruction is also low), the imperfectly-reconstructed targets retain many of the distinguishing features of the original target. This indicates that the reconstruction process is quite robust relative to noise. Developments in nonlinear optimization appear promising for further improving the reliability and quality of target reconstruction in noise.