Inverse Wave Scattering of Rough Surfaces With Emitters and Receivers in the Transition Zone

Abstract

Abstract-We deal with the problem of determining the profile of a perfectly conducting rough surface from single-frequency and multistatic data. The two fundamental polarizations are investigated, in a two-dimension scattering configuration. Emitting and receiving antennas are positioned on a probing line some wavelengths above the profile. It is shown how the boundary integral equation method can be adapted to the case where the antenna footprint is much wider that the rough part of the profile. The Newton-Kantorovich iterative inversion process is then performed on these synthetic data. Its accuracy and robustness to additive noise are studied in the context of random rough surfaces with correlation length smaller than the wavelength and slope root mean square up to 0.9.

High-order functional derivatives of the scattered field according to the permittivity-contrast function

“…lm is the second order functional derivative (20) • Third order functional derivative To find the expression of this derivative, we repeat the same calculus scheme, i.e by writing : o lm (||δχ|| 2 ) = F…”

“…Such derivatives are built by solving the forward problem, and the associated reciprocal problems obtained by switching the emitter with each receiver. This principle has been applied in different inversion schemes for applications in detection of burried objects [20], optical profilometry [21,22] and reconstruction of the geometric shape of three dimensional objects in microwave regime [23].…”