= Infinite-aperture spectral normalization
{title2=$F(d\nu)=\lim_{L\to\infty}\frac{2\pi}{L}\mathbb E|\widehat E_L(\nu)|^2\,d\nu$}
For the <Fourier transform> $\widehat E_L(\nu)=(2\pi)^{-1}\int_{-L/2}^{L/2}E(z)e^{-i\nu z}dz$ of a stationary random field, the periodogram measure $(2\pi/L)\mathbb E|\widehat E_L(\nu)|^2d\nu$ converges weakly to the <spectral measure of a stationary random field>. The expected squared modulus is $(4\pi^2)^{-1}\int_{-L}^L(L-|\zeta|)C(\zeta)e^{-i\nu\zeta}d\zeta$. The factor $2\pi/L$ follows from <Parseval identity>, and preserves the total power per unit length. It also avoids meaningless squares of <Dirac delta distributions> for coherent plane-wave components.
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