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

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 $\mathbb{E}[E(\mathbf{r})]\mathbb{E}[E({\mathbf{r}}^{\prime }){]}^{\ast }$ 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.