Rough surface reconstruction from phaseless single frequency data at grazing angles. (4th October 2018)

• Record Type: Journal Article
• Authors: Chen, Yuxuan; Rath Spivack, Orsola; Spivack, Mark
• Is Part Of: Inverse problems. Volume 34:Number 12(2018:Dec.)
• Publication Date: 2018-10-04
• Subjects: inverse scattering -- iterated marching method -- rough surface reconstruction -- grazing incidence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aae1e9
• Languages: English
• ISSNs: 0266-5611

Abstract

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.