= Rough-surface far-field intensity per illuminated length
{title2=$\frac{\langle|\psi_s|^2\rangle}{D}\sim\frac{2kq_i^2|A_i|^2\cos^2\theta_s}{\pi r}S_h(k\sin\theta_s-p_i)$}
First-order Dirichlet roughness has mean-plane trace $2iq_iA_i h(x)e^{ip_ix}$, where $p_i^2+q_i^2=k^2$ and $q_i>0$. <Stationary phase> applied to the <outgoing angular spectrum> evaluates the far-field amplitude at tangential wavenumber $k\sin\theta_s$. For a stationary surface illuminated over length $D$, the mean squared height transform divided by $D$ tends to its <power spectrum of surface height>. Thus the diffuse intensity samples the spectrum at the tangential momentum transfer. An infinite stationary surface has no finite total far-field amplitude without a window or an intensity-density convention.
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