formalized as $$\begin{aligned}
\label{eq:Corr}
\hat{C}({\bm\rho}_p) = \frac{1}{T_I}\int_{-T_I/2}^{T_I/2}\!dt\, \hat{i}_p(t) \hat{i}_b(t),\end{aligned}$$ where ${\bm\rho}_p$ is the center coordinate of the CCD’s $p$th pixel, and $T_I$ is the correlation integration time. From quantum photodetection theory [@Shapiro2009], we have that $$\begin{aligned}
\label{eq:Current}
\hat{i}_m(t) = q\int d\tau\, \hat{P}_m(\tau) h(t-\tau), \quad m=p,b\end{aligned}$$ where $$\begin{aligned}
\label{eq:Flux}
\hat{P}_m(t) = \int_{{\cal A}_m} d{\bm\rho}\, {\hat{E}}^\dagger_m({\bm\rho},t) {\hat{E}}_m({\bm\rho},t)\end{aligned}$$ is the effective (sub-unity quantum efficiency) photon flux on the active region ${\cal A}_m$ for detector $m$, and $h(t)$ is the impulse response of the detectors’ output circuit, which we have taken to be the same for both the bucket detector and the CCD camera.

To enable the performance evaluations in the sections to follow, we make the following assumptions. First, each pixel is small enough that the the average photon flux impinging on it obeys $\langle \hat{P}_p(t)\rangle  = A_p\langle {\hat{E}}^\dagger_p({\bm\rho}_p,t){\hat{E}}_p({\bm\rho}_p,t)\rangle$, where $A_p$ is the area of the ${\cal A}_p$. Second, we assume that the detector has a Gaussian impulse response, $$\begin{aligned}
h(t) = \frac{\Omega_B}{\sqrt{8\pi}}e^{-\Omega^2_B t^2/8},\end{aligned}$$ whose bandwidth, $\Omega_B$, greatly exceeds that of the incident light for the pseudothermal source ($\Omega_B T_0 \gg 1$), and is much smaller than that of the incident light for the SPDC source ($\Omega_B T_0 \ll 1$). Finally, we assume 