= Coherent attenuation by a Gaussian phase screen
{title2=$m=e^{-\beta^2/2}$}
For a unit-amplitude <random phase screen> $e^{i\beta W}$ with standard normal <marginal distribution>, the <characteristic function> gives coherent amplitude $m=\mathbb E[e^{i\beta W}]=e^{-\beta^2/2}$. The coherent power is $|m|^2=e^{-\beta^2}$, although the total power remains one. In homogeneous paraxial space the mean constant transverse field propagates without additional attenuation. Under decorrelation at large separation, the remaining power $1-e^{-\beta^2}$ is diffuse.
Back to article page
