= Stationary phase-screen power spectrum
{title2=$S_E$}
For the <random phase screen> $E(z)=e^{i\beta W(z)}$, the <Gaussian phase-screen correlation> and <spectral measure of a stationary random field> give
$$
S_E(\nu)=\frac1{2\pi}\int_{\mathbb R}e^{-\beta^2(1-\rho(\zeta))}e^{-i\nu\zeta}\,d\zeta.
$$
If $\rho(\zeta)\to0$ and $e^{\beta^2\rho}-1$ is integrable, this is $e^{-\beta^2}\delta(\nu)$ plus the continuous density $(2\pi)^{-1}e^{-\beta^2}\int(e^{\beta^2\rho(\zeta)}-1)e^{-i\nu\zeta}d\zeta$. The total mass is one, split into coherent mass $e^{-\beta^2}$ and diffuse mass $1-e^{-\beta^2}$. Without the decay and integrability assumptions there may be additional spectral atoms or singular components.
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