Locally Perturbed Inaccessible Rough Surface Profile Reconstruction via Phaseless Scattered Field Data

Abstract

This work addresses an iteration scheme to observe the image of an inaccessible rough surface profile from the intensity of scattered field data. The solution of the problem is based on the integral equations written on the rough surface profile. By virtue of the surface integral equations, the phaseless scattered field is represented by a nonlinear ill-posed integral operator, which is linearized by Newton's method and regularized via Tikhonov. The surface image is reconstructed iteratively in the least-squares sense by utilizing spline-type basis functions. A detailed numerical assessment is provided, showing that the algorithm is very effective and promising.