Abstract

I will talk about a direct sampling method for imaging the periodic obstacles using only measurements from the lower or upper side of the obstacle arrays at a fixed frequency. We analyze the resolution of the lower side and upper side methods in terms of propagating modes of the Rayleigh expansion, Helmholtz–Kirchhoff equation and the distance of the measurement surface to the obstacle arrays, where the periodic structure leads to novel analysis. We give some numerical experiments to justify the competitive efficiency of our imaging functionals and the robustness against noises. The talk is based on the joint work with Lide Cai.