Gaussian phase averaging ($\mathbb{E}{e}^{i\varphi }=e^{-\mathrm{Var}(\varphi )/2}$)

For a centered real Gaussian random variable $\varphi$, its characteristic function gives $\mathbb{E}{e}^{i\varphi }=\exp [-\mathrm{Var}(\varphi )/2]$. Applied to a random phase screen, this controls the coherent and diffuse wave fields.