Recovery of rough surface in ducting medium from grazing angle scattered wave

A method is developed for rough surface reconstruction using fields scattered at grazing angles in a medium with a linearly varying refractive index and Neumann boundary condition. This regime represents a ducting medium, bounded by a perfectly conducting surface with a TM incident field or an acoustically hard surface. This significantly extends the iterated marching method, based upon the parabolic integral equation for forward-scattered field components [J Opt Soc Am A, 35 (2018) 504-513]. The approach, which uses a fixed frequency, is able accurately to recover multiscale surfaces, and is found to be robust with respect to measurement noise and localized perturbations