Power spectrum of surface height ($S_h(q)=\int C_h(\xi )e^{-iq\xi }d\xi$)

For a real zero-mean stationary height process, its power spectrum of surface height is the Fourier transform of the height covariance function. It is even and nonnegative, and ${\sigma }^2=(2\pi {)}^{-1}\int S_h(q)dq$. More general stationary processes have a spectral measure rather than a density. Weighted spectral moments control the existence of boundary derivatives and second-order mean scattering corrections.