significant difference between the transmissive and reflective cases, namely the $A_b/L^2$ factor that is present in our results but is absent from those in [@Erkmen2008Unified]. This factor, which will obey $A_b/L^2 \ll 1$ in a standoff-sensing scenario, is the bucket detector’s angular subtense at the target, and represents the fraction of the quasi-Lambertian reflected light that this detector collects. No such factor appeared in [@Erkmen2008Unified], because that work assumed the bucket detector collected all the light that was transmitted through the target.

The featureless background terms in our pseudothermal and SPDC ghost images affect the images’ contrast. To assess these contrasts, we will adopt the definition and approach presented in [@Erkmen2008Unified]. In particular, the image contrast $\mathcal{C}$ is the ratio of the difference between the brightest and darkest pixels in the image to the featureless background: $$\begin{aligned}
\label{eq:ContrastDef}
\mathcal{C} = \frac{\max_{\mathcal{R}}[\hat{C}({\bm\rho}_p)]-\min_{\mathcal{R}}[\hat{C}({\bm\rho}_p)]}{C_0},\end{aligned}$$ where $\mathcal{R}$ is the region within which ${\mathcal{T}}({\bm\rho})$ is nonzero. We will assume that the ghost imager completely resolves the target, so that we can use the approximation $$\begin{aligned}
\label{eq:Resolve}
\int\!d{\bm\rho}\,{\mathcal{T}}(\pm{\bm\rho})e^{-\frac{|{\bm\rho}-{\bm\rho}_p|^2}{\alpha\rho_L^2}} \approx \pi \alpha \rho_L^2 {\mathcal{T}}(\pm{\bm\rho}) .\end{aligned}$$ Defining $A_T=\int\!d{\bm\rho}\, {\mathcal{T}}({\bm\rho})$ as the target’s reflective cross-section, and taking $\max_{\mathcal{R}}[{\mathcal{T}}({\bm\rho})] = 1$, we get the following image contrast expressions for our 