High‐frequency limit under the Rayleigh hypothesis

The Rayleigh hypothesis (RH) is traditionally invoked to compute the scattering amplitude in rough surface scattering. This hypothesis simplifies the analytic derivation of the scattering problem and has been proven to be accurate for the determination of the Volterra series for the small perturbation method (SPM). The SPM development physically corresponds to the scattering of low‐frequency acoustical waves. In this study we focus on the high‐frequency limit under the Rayleigh hypothesis (RH). We validate the consistency of the RH with the high‐frequency limit to the order invoked in the approximation. This means that the first‐order geometrical optics (GO1) is reached even though the Rayleigh hypothesis consists of the summation of solely upward scattered fields.