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 [Chen and Spivack, J. Opt. Soc. Am. A 35, 504–513 (2018)]. The approach, which uses a fixed frequency, is able to accurately recover multiscale surfaces and is found to be robust with respect to measurement noise and localized perturbations.</jats:p
