Uncentered wave-field correlation (source code)

= Uncentered wave-field correlation
{title2=$C(\mathbf r,\mathbf r')=\mathbb E[E(\mathbf r)E(\mathbf r')^*]$}

= Wave-field correlation
{synonym}

For a complex random <wave amplitude>, this two-point <expectation> retains the <coherent field> and uses a <complex conjugate> on the second amplitude. It is not a normalized <wave-field correlation> coefficient. Subtracting $\mathbb E[E(\mathbf r)]\mathbb E[E(\mathbf r')]^*$ gives the centered <covariance function>. At coincident points the uncentered <wave-field correlation> equals the <mean wave intensity>. Under second-order <stationarity> it depends only on the separation and has a <spectral measure of a stationary random field>. A deterministic field is included by taking a degenerate ensemble.