= Random phase screen
A <random phase screen> models a thin <random medium> by multiplying a <wave> field by $e^{i\phi(x)}$, where $\phi$ is a real <random field> on the transverse plane. At the screen itself the modulus is unchanged, but later <wave propagation> converts phase variation into <interference> and <amplitude> variation.
If $\phi$ is a zero-mean <Gaussian random field>, its <phase factor> has correlation
$$
\mathbb E[e^{i(\phi(x)-\phi(y))}]=\exp\!\left(-\tfrac12\operatorname{Var}(\phi(x)-\phi(y))\right).
$$
This follows from the <characteristic function>. The approximation neglects the medium's longitudinal thickness; its <covariance> and propagation model must be specified before predicting scattering or intensity <statistics>.
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