S, T$ denotes the turbulence-induced logamplitude variance on the reference ($R$), signal ($S$), and target ($T$) paths. Each of these noise terms has an important physical interpretation, as we explain below.

The first noise term, $\Delta^2\text{Source}$, captures the fluctuations associated with decorrelation of transverse locations in the image arising from the source’s time evolution. Thus, it is inversely proportional to the number of on-target resolution cells, $\rho_L^2/A'_T$, and the number of different source patterns measured. For the pseudothermal imager, for which $\Omega_BT_0 \gg 1$ holds, this is the number of field-coherence times in the integration time, so we find $\Delta^2\text{Source}$ scaled by $T_0/T_I$. For the SPDC imager we have $\Omega_BT_0 \ll 1$, so it is the detectors’ response time that limits the measurements’ correlation behavior, hence we find $\Delta^2\text{Source}$ scaled by $4/\Omega_BT_I$ in that imager’s SNR denominator.

The $\Delta^2\text{Path}$ term is due to the optical-path interactions that degrade the measurement, i.e., the turbulent atmosphere, and the scattering off the rough target. The noise contribution from target scattering can be mitigated by aperture averaging, which, as noted above, is quantified by $\Gamma$. The effect of the turbulence is somewhat more complicated, as it contributes a scaling factor $e^{4\sigma_\ell^2}$ to all field-variation 