Phaseless inverse scattering for rough surface recovery at a single receiver

We present a reconstruction algorithm for recovering rough surface profiles from phaseless total field data measured at a single receiver as the surface undergoes controlled lateral motion. The algorithm is based on the parabolic wave equation, which offers a computationally efficient framework for forward and inverse scattering, and applies to both Dirichlet (TE polarization) and Neumann (TM polarization) boundary conditions. It operates in a marching fashion, recovering surface points sequentially along the profile. Numerical experiments demonstrate that the method yields accurate reconstructions and remains robust under measurement noise and variations in key problem parameters. The proposed approach provides a reliable and efficient tool for surface characterization in engineering applications such as non-destructive testing and remote sensing.