First-order rough-surface scattered field
= First-order rough-surface scattered field
{title2=$\psi_s^{[1]}=-\mathcal E[h\partial_z\psi^{[0]}|_0]$}
Taylor expansion of the <Dirichlet boundary condition> gives the first-order boundary trace $-h\partial_z\psi^{[0]}$ at the mean plane. The <outgoing angular spectrum> then propagates it. A zero-mean surface gives zero mean for this linear rough correction, while the complete <scattered field> still contains its nonzero flat reflection.