Numerical Method For Reconstructing A Perfectly Conducting Obstacle From Phaseless Data

The inverse scattering problems of acoustic wave and electromagnetic wave have widely applications in many fields such as radar detection,non-destructive detection and medical imaging.However,in actual measurement,only the far field(or scattered field)information can be measured,and it is difficult to accurately measure the phase information.This has led to the devel-opment of the inverse scattering problem with phaseless data.In this paper,we consider the inverse electromagnetic scattering for a perfectly conducting ob-stacle from phaseless far field data.Firstly,in order to avoid hyper-singularity,based on potential theory,the problem is transformed into a system of bound-ary integral equations composed of field equations and phaseless data equa-tions;secondly,the density function which solved by the field equations is sub-stituted into the phaseless data equations,then we linearize the parametered boundary for phaseless data equations,and calculate the Frechet derivative of far field operator;finally,we use the iteratively regularization Gauss-Newton method(IRGNM)to obtain the update of boundary,so that a new approxi-mation of the boundary can be obtained with each iteration.The novelty of this paper is that we extend a nonlinear integral equation method proposed by Johansson and Sleeman to the inverse electromagnetic obstacle problem with phaseless far field data,and we provide a example to illustrate the feasibility of this numerical method.