in Eqs.  and .

In what follows we will assume that the target’s intensity-reflection coefficient, ${\mathcal{T}}({\bm\rho})$, is space-limited to the region illuminated by the signal beam, i.e., $|{\mathcal{T}}({\bm\rho})| = 0$ for $|{\bm\rho}| > a_L$. This condition will give the ensemble-average pseudothermal and SDPC ghost images convolution-integral relationships with ${\mathcal{T}}({\bm\rho})$ from which to determine their spatial resolutions. See [@Erkmen2008Unified; @Erkmen2010AOP] for information about ghost imaging field-of-view when the preceding restriction on ${\mathcal{T}}({\bm\rho})$ is not satisfied.

Photodetection and Image Formation
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Loss also occurs in the photodetection process, because the detectors in Fig. \[fig:setup\] will, in general, have sub-unity quantum efficiencies. Therefore, the field operator ${\hat{E}}_p({\bm\rho},t)$ driving the photocurrent, $\hat{i}_p(t)$, from CCD pixel $p$, and the field operator ${\hat{E}}_b({\bm\rho},t)$ driving the photocurrent, $\hat{i}_b(t)$, from the bucket detector satisfy [@footnote4; @Shapiro2009] $$\begin{aligned}
\label{eq:Detector}
{\hat{E}}_m({\bm\rho},t) = \sqrt{\eta}\,{\hat{E}}'_\ell({\bm\rho},t) +\sqrt{1-\eta}\,{\hat{E}}_{vac,\ell}({\bm\rho},t),\end{aligned}$$ for $(m,\ell)=(p,R)$ or $(m,\ell)=(b,T)$. Here, $\eta$ is the quantum efficiency, which is taken to be the same for both the bucket detector and the CCD camera, and ${\hat{E}}_{vac,\ell}({\bm\rho},t)$ is a vacuum-state field operator whose inclusion models the loss incurred by having $\eta < 1$, cf. Eq. (\[eq:TargetLoss\]).

We will assume ghost-image formation via continuous-time, pixel-wise correlation of the photocurrents from the CCD and the bucket detector, 