Ensemble-averaged wave intensity ($\mathbb{E}[|E{|}^2]=|\mathbb{E}[E]{|}^2+\mathbb{E}[|E-\mathbb{E}[E]{|}^2]$)

For a random complex wave amplitude $E$, its mean squared amplitude is $I=\mathbb{E}[|E{|}^2]$. Expanding $E=m+(E-m)$, with $m=\mathbb{E}[E]$, givesThe 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.