propagation of these terms over 12 unique paths. To make the analysis more tractable, we use several simplifying assumptions. First, we [ac]{}-couple both of the detector outputs by inserting a narrowband notch centered at the origin in frequency space, resulting in the frequency response $$\begin{aligned}
\label{eq:DCblock}
H_B(\Omega) = e^{-2\Omega^2/\Omega^2_B}-e^{-2\Omega^2/\Omega^2_N},\end{aligned}$$ where $\Omega_N \ll \Omega_B$. We also assume that the ghost imager can resolve all structure on the target, allowing us to use the approximation in Eq. .

To evaluate the fourth-order turbulence moments, we can no longer use the square-law approximation in Eq.  that models the turbulence’s mutual-coherence function as Gaussian, because this approximation is not valid for fourth-order moments [@Wandzura1980]. To evaluate these terms we assume that the turbulence coherence length on each path is much larger than the on-target coherence length $\rho_L$. We also assume the turbulence coherence lengths are all much larger than $a_0$, implying that the turbulence functions are independent of coordinates at the source and detection planes. Although these assumptions are somewhat limiting, they still allow weak-to-medium strength turbulence for a typical situation. For instance, if the target is standing off $1\,$km, the source aperture has radius $a_0=3\,$cm, and we are at a wavelength $\lambda_0=1.5\,\mu$m, this 