Physical surface trace and reference-plane trace
= Physical surface trace and reference-plane trace
For normal incidence on a Dirichlet rough surface, the scattered trace on the moving boundary is exactly $-e^{-ikh(x)}$. Its trace on the mean plane is instead $-1+2ikh+2k h\mathcal B h+\cdots$. The two traces are related by a normal Taylor expansion and must not be identified. Their ensemble averages can therefore have different quadratic coefficients without inconsistency.