Rough surface reconstruction from phaseless single frequency data at grazing angles

Abstract

We develop a method for the reconstruction of a perfectly reflecting rough surface from phaseless measurements of a field arising from single frequency scattering at grazing angles. Formulations are given for both Dirichlet and Neumann boundary conditions, and numerical experiments are presented in which close agreement is found with the exact solution. The approach is a marching method based on the parabolic integral equation, which recovers the surface progressively in range, and is iterated a small number of times to produce the final result. It is found that the approach is robust with respect to spatially localized perturbations and to measurement noise.

Inverse wave propagation problems without phase information

“…In [7] an algorithm is developed for the reconstruction of rough surfaces in two space dimensions from phaseless data arising from a single-frequency incident field. For grazing angles of incidence a paraxial approximation of the Helmholtz equation is used.…”

Imaging of Rough Surfaces by Near-field Measurement

“…In Ref. 8, the Dirichlet and Neumann boundary conditions for the electromagnetic integral equation were given. The imaging problem of separating the rough surfaces of two dielectric media is well established.…”

Recovery of rough surface in ducting medium from grazing angle scattered wave

“…Most of these use single frequency data while others have utilized multiple frequencies [11]. In particular, in [29][30][31][32][33], efficient reconstruction algorithms have been developed under the regime of grazing angle incidence using the parabolic wave equation. When the incident angle is small, and forward propagation dominates, the Helmholtz equation can be approximated by the parabolic wave equation.…”