= Wiener-Khinchin theorem
{c}
{title2=$\Gamma(\tau)=\int S(\Omega)e^{-i\Omega\tau}\,d\Omega$}
{wiki=Wiener–Khinchin_theorem}
The <Wiener-Khinchin theorem> relates the autocorrelation of a <weakly stationary process> to its power spectral density by a <Fourier transform>. The displayed convention is appropriate when the optical correlation is $\Gamma(\tau)=\langle f^*(t)f(t+\tau)\rangle$ and the analytic field contains $e^{-i\omega t}$. A <Lorentzian line shape> of half-width $\kappa$ gives exponential correlation decay $e^{-\kappa|\tau|}$, including the carrier factor $e^{-i\omega\tau}$ when the full field is correlated.
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