  We propose reverse time migration (RTM) methods for the imaging of periodic
obstacles using only measurements from lower or upper side of the obstacle
arrays at a fixed frequency. We analyze the resolution of the lower side and
upper side RTM methods in terms of the propagating part of the Rayleigh
expansion, Helmholtz-Kirchhoff equation and the distance of the measurement
surface to the obstacle arrays. We give some numerical experiments to justify
the competitive efficiency of our imaging functionals and the robustness
against noises.
