## Appendix A Mutual Coherence of an Incoherent Source
The complex cross-correlation [55] with zero time offset of these two electromagnetic fields, when accounting for the attenuation by the voltage patterns \(\mathcal{F}_{p}\) and \(\mathcal{F}_{q}\) of the two elementary antennas, as illustrated in Figure 1, is  
\[\langle\mathcal{F}_{p}(\theta_{p},\phi_{p})E_{p}(\theta,\phi,t)\,\mathcal{F}_ {q}^{*}(\theta_{q},\phi_{q})E_{q}^{*}(\theta,\phi,t)\rangle\]  
\[=\mathcal{F}_{p}(\theta_{p},\phi_{p})\mathcal{F}_{q}^{*}(\theta_{q},\phi_{q}) \langle\mathcal{E}(\theta,\phi,t-\frac{r_{p}}{c})\mathcal{E}^{*}(\theta,\phi, t-\frac{r_{q}}{c})\rangle\frac{\mathrm{e}^{2j\pi v_{o}\frac{r_{p}-r_{q}}{c}}}{r_{p}r_{q}},\]  
\[=\mathcal{F}_{p}(\theta_{p},\phi_{p})\mathcal{F}_{q}^{*}(\theta_{q},\phi_{q}) \langle\mathcal{E}(\theta,\phi,t)\mathcal{E}^{*}(\theta,\phi,t-\frac{r_{q}-r_ {p}}{c})\rangle\frac{\mathrm{e}^{2j\pi v_{o}\frac{r_{p}-r_{q}}{c}}}{r_{p}r_{q}},\]  
As soon as \(|r_{q}-r_{p}|/c\) is small compared to the reciprocal of the receiver bandwidth, it can be neglected in the complex amplitude \(\mathcal{E}^{*}\) so that the previous equation now reads  
\[\langle\mathcal{F}_{p}(\theta_{p},\phi_{p})E_{p}(\theta,\phi,t)\,\mathcal{F}_ {q}^{*}(\theta_{q},\phi_{q})E_{q}^{*}(\theta,\phi,t)\rangle\]  
\[=\mathcal{F}_{p}(\theta_{p},\phi_{p})\mathcal{F}_{q}^{*}(\theta_{q},\phi_{q}) \langle\mathcal{E}(\theta,\phi,t)\mathcal{E}^{*}(\theta,\phi,t)\rangle\frac{ \mathrm{e}^{2j\pi v_{o}\frac{r_{p}-r_{q}}{c}}}{r_{p}r_{q}},\]where the quantity \(\langle\mathcal{E}(\theta,\phi,t)\mathcal{E}^{*}(\theta,\phi,t)\rangle\equiv\langle| \mathcal{E}(\theta,\phi,t)|^{2}\rangle\) is nothing but the time-averaged intensity of the source \(\mathcal{I}(\theta,\phi)\):  
\[\langle\mathcal{F}_{p}(\theta_{p},\phi_{p})E_{p}(\theta,\phi,t) \,\mathcal{F}_{q}^{*}(\theta_{q},\phi_{q})E_{q}^{*}(\theta,\phi,t)\  
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