= Ensemble-averaged wave intensity
{title2=$\mathbb E[|E|^2]=|\mathbb E[E]|^2+\mathbb E[|E-\mathbb E[E]|^2]$}
= Mean wave intensity
{synonym}
For a random complex wave amplitude $E$, its mean squared amplitude is $I=\mathbb E[|E|^2]$. Expanding $E=m+(E-m)$, with $m=\mathbb E[E]$, gives
$$
\mathbb E[|E|^2]=|m|^2+\mathbb E[|E-m|^2].
$$
The mixed terms vanish. Thus the squared <coherent field> is only one part of the mean intensity; the other is the diffuse contribution. A fixed acoustic or optical normalization converts this squared-amplitude quantity to physical <energy flux>. This ensemble mean differs from the angularly averaged radiative-transfer <mean intensity>.
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