in one detector time-constant is low, so $\Omega_B /P \gg 1$, and our assumption that the target is contained within the region illuminated by the signal beam implies that $a_L^2/A_T > 1$ if $|{\mathcal{T}}({\bm\rho})| \sim 1$ where it is nonzero. Consequently, unlike the pseudothermal case, $\mathcal{C}_Q \gg 1$ is the norm for SDPC ghost imaging in [dc]{}-coupled operation.

Signal-to-Noise Ratio {#sec:SNR}
=====================

In keeping with the analysis done in [@Erkmen2009SNR], we will be evaluating the signal-to-noise ratio (SNR) pixel-wise as the ratio of the square of the expected value to the variance for the photocurrent cross-correlation function, $$\begin{aligned}
\label{eq:SNRi}
\text{SNR} = \frac{{\langle \hat{C}({\bm\rho}_p) \rangle}^2}{{\rm Var}[\hat{C}({\bm\rho}_p)]} = \frac{{\langle \hat{C}({\bm\rho}_p) \rangle}^2}{{\langle \hat{C}^2({\bm\rho}_p) \rangle}-{\langle  \hat{C}({\bm\rho}_p) \rangle}^2}.\end{aligned}$$ The main complication in evaluating Eq.  is the second moment, $$\begin{aligned}
\label{eq:Cm2}
{\langle \hat{C}^2({\bm\rho}_p) \rangle} = \frac{1}{T_I^2}\!\int\limits_{-T_I/2}^{T_I/2}\!\!\!dt\!\!\int\limits_{-T_I/2}^{T_I/2}\!\!\!du\, {\langle \hat{i}_p(t)\hat{i}_b(t)\hat{i}_p(u)\hat{i}_b(u) \rangle}.\end{aligned}$$ After using Eq.  to write the currents in terms of the fields, Eqs.  and to normally order the fields, and Eqs.  and to propagate the fields back to the source, we are left needing to evaluate an eighth-order moment of the fields, two sixth-order moments of the fields, a fourth-order moment of the fields, a fourth-order moment of the target, three fourth-order moments of the turbulence, and 